Modeling Gas Adsorption in Marcellus Shale With Langmuir and BET Isotherms Wei Yu, Texas A&M University; and Kamy Sepehrnoori and Tadeusz W. Patzek, University of Texas at Austin Summary Production from shale-gas reservoirs plays an important role in natural-gas supply in the United States. Horizontal drilling and multistage hydraulic fracturing are the two key enabling technolo- gies for the economic development of these shale-gas reservoirs. It is believed that gas in shale reservoirs is mainly composed of free gas within fractures and pores and adsorbed gas in organic matter (kerogen). It is generally assumed in the literature that the monolayer Langmuir isotherm describes gas-adsorption behavior in shale-gas reservoirs. However, in this work, we analyzed four experimental measurements of methane adsorption from the Mar- cellus Shale core samples that deviate from the Langmuir iso- therm, but obey the Brunauer-Emmett-Teller (BET) isotherm. To the best of our knowledge, it is the first time to find that methane adsorption in a shale-gas reservoir behaves similar to multilayer adsorption. Consequently, investigation of this specific gas- desorption effect is important for accurate evaluation of well per- formance and completion effectiveness in shale-gas reservoirs on the basis of the BET isotherm. The difference in calculating origi- nal gas in place (OGIP) on the basis of both isotherms is dis- cussed. We also performed history matching with one production well from the Marcellus Shale and evaluated the contribution of gas desorption to the well’s performance. History matching shows that gas adsorption obeying the BET isotherm contributes more to overall gas recovery than gas adsorption obeying the Langmuir isotherm, especially at early time in production. This work pro- vides better understanding of gas desorption in shale-gas reser- voirs and updates our current analytical and numerical models for simulation of shale-gas production. Introduction In recent years, the growth of shale-gas production was fueled by the improvements in horizontal drilling and multistage hydraulic- fracturing technologies. As a result, shale gas has become an increasingly important source of natural-gas supply in North America and around the world. In nature, gas shales are character- ized by extremely small grain size, extremely low permeability on the order of nanodarcies (10 6 md), small porosity, and high total organic carbon (TOC). For instance, the TOC in Marcellus Shale ranges from 2 to 20 wt%, and clay content is 10 to 45 wt% (Boyce et al. 2010). Shale can serve as both source and reservoir rock. The amount of gas in place in shale is strongly affected by the TOC, clays, and the adsorption ability of methane on the internal surface of the solid (Martin et al. 2010). In general, complex frac- ture networks that are generated connect the shale formation and the horizontal well. Shale matrix has strong gas-storage capacity but cannot transport the gas for long distance because it is very tight; a fracture network can transport the gas efficiently because of large hydraulic conductivity but has limited storage capacity (Lane et al. 1989; Carlson and Mercer 1991). Because a part of gas in shale reservoirs is adsorbed, investigation of gas adsorption can provide critical insights into evaluation of well performance, shale characterization, and optimization of fracture design in shale-gas reservoirs. Generally, natural gas in shale reservoirs is stored as free gas in both organic matter (kerogen) and larger mineral pores and nat- ural fractures, as well as adsorbed gas within organic matter (Leahy-Dios et al. 2011). The adsorbed gas has a higher density than the surrounding free gas. Clarkson and Haghshenas (2013) presented five mechanisms for methane existence in shale-gas res- ervoirs: (1) adsorption on internal surface area; (2) conventional (compressed gas) storage in natural and hydraulic (induced) frac- tures; (3) conventional storage in matrix porosity (organic and inorganic); (4) solution in formation water; and (5) absorption (so- lution) in organic matter. The organic matter is nanoporous mate- rial primarily consisting of micropores (pore length less than 2 nm) and mesopores (pore length between 2 and 50 nm) (Kang et al. 2011). The pore-size heterogeneity such as varying pore size, shape, and surface roughness greatly influences the gas- transport and -adsorption properties in shale-gas reservoirs (Fir- ouzi et al. 2014a, b). The organic matter occupies only a part of the bulk rock as connected clusters embedded in the rock or dis- persion among mineral grains (Silin and Kneafsey 2012). In the Appalachian Basin, the well performance from darker zones within Devonian shale with higher organic content is better than that from organic-poor gray zones (Schmoker 1980). Lu et al. (1995) showed that the relationship between gas-adsorption capacity and TOC is approximately linear when the TOC is high, whereas for a very low TOC, illite plays an important role in gas storage in Devonian shales. The adsorption process in shale-gas reservoirs is mainly physical adsorption, which means that the adsorption is fully reversible, allowing gas molecules to com- pletely adsorb and desorb, and the interaction force between the solid surface and the adsorbed gas molecules is controlled by the weak van der Waals force. The specific surface area, defined as surface area per gram of solid, plays an important role in control- ling the adsorption capacity. The rougher solid surface and the smaller pore sizes can contribute a larger specific surface area (Solar et al. 2010). One can calculate the specific surface area with the BET method (Brunauer et al. 1938). A rough solid sur- face with many nanometer-scale cavities can adsorb gas more strongly than an ideally polished surface (Rouquerol et al. 1999; Solar et al. 2010). A recent study conducted by the Energy Information Adminis- tration (US EIA 2014) concludes that the Marcellus Shale is one of six key tight-oil and shale-gas regions, which account for 95% of US oil-production growth and all US natural-gas production growth during 2011 to 2013. The Marcellus Shale is in the Appa- lachian Basin across six states, Pennsylvania, New York, West Virginia, Ohio, Virginia, and Maryland. The Marcellus Shale cov- ers a total area of more than 100,000 sq miles, and the depth is in the range of 4,000 to 8,500 ft with an average thickness of 50 to 200 ft (US DOE 2013). The average estimated ultimate recovery is approximately 2.325 Bcf per well, the average porosity is 8%, and TOC is 12 wt% (US EIA 2011). The Marcellus Shale has 1,500 Tcf of OGIP, with 141 Tcf of technically recoverable gas (US DOE 2013). Reservoir temperature in the Marcellus Shale is observed to be approximately 140 F, and bottomhole pressure (BHP) is up to 6,000 psi (Williams et al. 2011). The kerogen type of Marcellus Shale is primarily Type II with a mixture of Type III (Weary et al. 2000). Most publications to date have used the Langmuir isotherm to describe gas desorption in shale-gas reservoirs. In this paper, we observed that the gas desorption in some areas of the Marcellus Shale follows the BET isotherm on the basis of laboratory Copyright V C 2015 Society of Petroleum Engineers This paper (SPE 170801) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, Amsterdam, 27–29 October 2014, and revised for publication. Original manuscript received for review 3 December 2014. Revised manuscript received for review 29 October 2015. Paper peer approved 3 November 2015. 2015 SPE Journal 1
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Modeling Gas Adsorption in MarcellusShale With Langmuir and BET Isotherms
Wei Yu Texas AampM University and Kamy Sepehrnoori and Tadeusz W Patzek University of Texas at Austin
Summary
Production from shale-gas reservoirs plays an important role innatural-gas supply in the United States Horizontal drilling andmultistage hydraulic fracturing are the two key enabling technolo-gies for the economic development of these shale-gas reservoirsIt is believed that gas in shale reservoirs is mainly composed offree gas within fractures and pores and adsorbed gas in organicmatter (kerogen) It is generally assumed in the literature that themonolayer Langmuir isotherm describes gas-adsorption behaviorin shale-gas reservoirs However in this work we analyzed fourexperimental measurements of methane adsorption from the Mar-cellus Shale core samples that deviate from the Langmuir iso-therm but obey the Brunauer-Emmett-Teller (BET) isotherm Tothe best of our knowledge it is the first time to find that methaneadsorption in a shale-gas reservoir behaves similar to multilayeradsorption Consequently investigation of this specific gas-desorption effect is important for accurate evaluation of well per-formance and completion effectiveness in shale-gas reservoirs onthe basis of the BET isotherm The difference in calculating origi-nal gas in place (OGIP) on the basis of both isotherms is dis-cussed We also performed history matching with one productionwell from the Marcellus Shale and evaluated the contribution ofgas desorption to the wellrsquos performance History matching showsthat gas adsorption obeying the BET isotherm contributes more tooverall gas recovery than gas adsorption obeying the Langmuirisotherm especially at early time in production This work pro-vides better understanding of gas desorption in shale-gas reser-voirs and updates our current analytical and numerical models forsimulation of shale-gas production
Introduction
In recent years the growth of shale-gas production was fueled bythe improvements in horizontal drilling and multistage hydraulic-fracturing technologies As a result shale gas has become anincreasingly important source of natural-gas supply in NorthAmerica and around the world In nature gas shales are character-ized by extremely small grain size extremely low permeability onthe order of nanodarcies (106 md) small porosity and high totalorganic carbon (TOC) For instance the TOC in Marcellus Shaleranges from 2 to 20 wt and clay content is 10 to 45 wt (Boyceet al 2010) Shale can serve as both source and reservoir rockThe amount of gas in place in shale is strongly affected by theTOC clays and the adsorption ability of methane on the internalsurface of the solid (Martin et al 2010) In general complex frac-ture networks that are generated connect the shale formation andthe horizontal well Shale matrix has strong gas-storage capacitybut cannot transport the gas for long distance because it is verytight a fracture network can transport the gas efficiently becauseof large hydraulic conductivity but has limited storage capacity(Lane et al 1989 Carlson and Mercer 1991) Because a part ofgas in shale reservoirs is adsorbed investigation of gas adsorptioncan provide critical insights into evaluation of well performanceshale characterization and optimization of fracture design inshale-gas reservoirs
Generally natural gas in shale reservoirs is stored as free gasin both organic matter (kerogen) and larger mineral pores and nat-ural fractures as well as adsorbed gas within organic matter(Leahy-Dios et al 2011) The adsorbed gas has a higher densitythan the surrounding free gas Clarkson and Haghshenas (2013)presented five mechanisms for methane existence in shale-gas res-ervoirs (1) adsorption on internal surface area (2) conventional(compressed gas) storage in natural and hydraulic (induced) frac-tures (3) conventional storage in matrix porosity (organic andinorganic) (4) solution in formation water and (5) absorption (so-lution) in organic matter The organic matter is nanoporous mate-rial primarily consisting of micropores (pore length less than2 nm) and mesopores (pore length between 2 and 50 nm) (Kanget al 2011) The pore-size heterogeneity such as varying poresize shape and surface roughness greatly influences the gas-transport and -adsorption properties in shale-gas reservoirs (Fir-ouzi et al 2014a b) The organic matter occupies only a part ofthe bulk rock as connected clusters embedded in the rock or dis-persion among mineral grains (Silin and Kneafsey 2012) In theAppalachian Basin the well performance from darker zoneswithin Devonian shale with higher organic content is better thanthat from organic-poor gray zones (Schmoker 1980) Lu et al(1995) showed that the relationship between gas-adsorptioncapacity and TOC is approximately linear when the TOC is highwhereas for a very low TOC illite plays an important role in gasstorage in Devonian shales The adsorption process in shale-gasreservoirs is mainly physical adsorption which means that theadsorption is fully reversible allowing gas molecules to com-pletely adsorb and desorb and the interaction force between thesolid surface and the adsorbed gas molecules is controlled by theweak van der Waals force The specific surface area defined assurface area per gram of solid plays an important role in control-ling the adsorption capacity The rougher solid surface and thesmaller pore sizes can contribute a larger specific surface area(Solar et al 2010) One can calculate the specific surface areawith the BET method (Brunauer et al 1938) A rough solid sur-face with many nanometer-scale cavities can adsorb gas morestrongly than an ideally polished surface (Rouquerol et al 1999Solar et al 2010)
A recent study conducted by the Energy Information Adminis-tration (US EIA 2014) concludes that the Marcellus Shale is oneof six key tight-oil and shale-gas regions which account for 95of US oil-production growth and all US natural-gas productiongrowth during 2011 to 2013 The Marcellus Shale is in the Appa-lachian Basin across six states Pennsylvania New York WestVirginia Ohio Virginia and Maryland The Marcellus Shale cov-ers a total area of more than 100000 sq miles and the depth is inthe range of 4000 to 8500 ft with an average thickness of 50 to200 ft (US DOE 2013) The average estimated ultimate recoveryis approximately 2325 Bcf per well the average porosity is 8and TOC is 12 wt (US EIA 2011) The Marcellus Shale has1500 Tcf of OGIP with 141 Tcf of technically recoverable gas(US DOE 2013) Reservoir temperature in the Marcellus Shale isobserved to be approximately 140 F and bottomhole pressure(BHP) is up to 6000 psi (Williams et al 2011) The kerogen typeof Marcellus Shale is primarily Type II with a mixture of Type III(Weary et al 2000)
Most publications to date have used the Langmuir isotherm todescribe gas desorption in shale-gas reservoirs In this paper weobserved that the gas desorption in some areas of the MarcellusShale follows the BET isotherm on the basis of laboratory
Copyright VC 2015 Society of Petroleum Engineers
This paper (SPE 170801) was accepted for presentation at the SPE Annual TechnicalConference and Exhibition Amsterdam 27ndash29 October 2014 and revised for publicationOriginal manuscript received for review 3 December 2014 Revised manuscript received forreview 29 October 2015 Paper peer approved 3 November 2015
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 1 Total Pages 12
ID balamuralil Time 0859 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 1
measurements The Langmuir and BET isotherms were comparedwith experimental data In addition through history matchingwith one production well in the Marcellus Shale we evaluated theeffect of gas adsorption on well performance at short and longproduction times
Adsorption Model for Shale-Gas Reservoirs
Adsorption at the gassolid interface is referred to as the enrich-ment of one or more components in an interfacial layer (Singet al 1985) The organic matter in shale has a strong adsorptionpotential because of the large surface area and affinity to methaneTo simulate gas production in shale-gas reservoirs an accuratemodel of gas adsorption is very important According to the Inter-national Union of Pure and Applied Chemistry (IUPAC) standardclassification system (Sing et al 1985) there are six differenttypes of adsorption The shape of the adsorption isotherm isclosely related to the properties of adsorbate and solid adsorbentand the pore-space geometry (Silin and Kneafsey 2012) One canfind the detailed description of the six isotherm classifications inSing et al (1985)
The most commonly applied adsorption model for shale gas-reservoirs is the classic Langmuir isotherm (Type I) (Langmuir1918) which is based on the assumption that there is a dynamicequilibrium at constant temperature and pressure betweenadsorbed and nonadsorbed gas Also it is assumed that there isonly a single layer of molecules covering the solid surface TheLangmuir isotherm has two fitting parameters
veth pTHORN frac14 vLp
pthorn pL eth1THORN
where v( p) is the gas volume of adsorption at pressure p vL isLangmuir volume referred to as the maximum gas volume ofadsorption at the infinite pressure and pL is Langmuir pressurewhich is the pressure corresponding to one-half Langmuir vol-ume Instantaneous equilibrium of the sorbing surface and thestorage in the pore space is assumed to be established for theLangmuir isotherm (Freeman et al 2012) Gao et al (1994) dem-onstrated that the instantaneous equilibrium is a reasonableassumption because the ultralow permeability in shale leads tovery low gas-flow rate through the kerogen component of shale
At high reservoir pressures one can expect that natural gassorbed on the organic carbon surfaces forms multimolecularlayers In other words the Langmuir isotherm may not be a goodapproximation of the amount of gas sorbed on organic carbon-rich mudrocks Instead multilayer sorption of natural gas shouldbe expected on organic carbon surfaces and the gas-adsorptionisotherm of Type II should be a better choice Type II isothermoften occurs in a nonporous or a macroporous material (Kuilaand Prasad 2013) In 1938 Stephen Brunauer Paul HughEmmett and Edward Teller (BET) published their theory in theJournal of the American Chemical Society (ACS) (Brunaueret al 1938) The BET isotherm model is a generalization of theLangmuir model to multiple adsorbed layers The expression isshown as follows
veth pTHORN frac14 vmCp
ethpo pTHORNfrac121thorn C 1eth THORNp=po eth2THORN
where po is the saturation pressure of the gas vm is the maximumadsorption gas volume when the entire adsorbent surface is beingcovered with a complete monomolecular layer and C is a con-stant related to the net heat of adsorption which is defined as
C frac14 expE1 EL
RT
eth3THORN
where E1 is the heat of adsorption for the first layer and EL is thatfor the second and higher layers and is equal to the heat of lique-faction The assumptions in the BET theory include homogeneoussurface no lateral interaction between molecules and the upper-most layer being in equilibrium with gas phase
The standard BET isotherm assumes that the number ofadsorption layers is infinite But in the case of n adsorption layersin some finite number then a general form of the BET isothermis given
veth pTHORN frac14vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth4THORN
When nfrac14 1 Eq 4 reduces to the Langmuir isotherm Eq 1When nfrac141 Eq 4 reduces to Eq 2
Here v(p) is the specific volume of gas adsorbed at the reser-voir pressure and temperature per unit mass of bulk rock refer-enced to a standard pressure and temperature [stock-tank (ST)condition in the oil industry] The customary cubic fields are ei-ther the standard cubic feet of sorbed gas per ton of bulk rock(scfton) or the standard cubic centimeters of gas per gram ofrock The conversion factor is
1scf
ton of bulk rock
frac14 1
32
standard cm3
g of bulk rock
eth5THORN
One should note that it is very challenging to apply the BETmodel to physically explain the supercritical-methane adsorptionbecause there is no concept of a liquid if the reservoir temperatureis above the critical-methane temperature Consequently the satu-ration pressure ( po) also loses its physical meaning (Ozdemir2004) To avoid this issue the saturation pressure ( po) is treatedas pseudosaturation pressure ( ps) for the high-pressuretempera-ture methane adsorption (Clarkson et al 1997) Clarkson et al(1997) summarized various methods to estimate the pseudosatura-tion pressure at any temperature above critical temperature Inthis study the method of extrapolation of the Antoine equation isused to calculate the pseudosaturation pressure for supercritical-methane adsorption as follows (NIST 2011 Hao et al 2014)
lnps frac14 77437 13065485
194362thorn T eth6THORN
where T is temperature (K) and ps is pseudosaturation pressure(MPa)
In this study we mainly focus on fitting the experimentalmeasurements of supercritical-methane adsorption by fixing thepseudosaturation pressure and tuning three fitting parameters ofvm C and n For practical application the BET-isotherm modeleasily can be used in a reservoir simulator to model the contribu-tion of gas desorption on well performance in some shale-gas res-ervoirs Although there are some physical-adsorption models suchas the simplified local-density model the 2D equation-of-state(EOS) model (Chareonsuppanimit et al 2012 Clarkson andHaghshenas 2013) and molecular simulation (Firouzi and Wilcox2012 Firouzi et al 2014b) we did not use the mentioned modelsin this study
Fig 1 compares shapes of the Langmuir and BET isothermsGas desorption along the BET isotherm contributes more signifi-cantly at early time of production than that with the Langmuir-iso-therm curve This is because the slope of the BET-isotherm curveat high pressure is larger than that of the Langmuir-isothermcurve resulting in more adsorbed gas releasing at early produc-tion times In addition under the same pressure drop from the ini-tial reservoir pressure to the BHP the amount of releasedadsorbed gas with the BET-isotherm curve is larger than that withthe Langmuir-isotherm curve
Gas-Flow Model in Shale
An equation to describe mass balance of gas flow in shale-gas res-ervoirs by considering the gas-desorption effect is given next (Pat-zek et al 2013 Yu et al 2014a)
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frac12qgSgthorn 1 eth THORNqat
frac14
qgug
x
thorn qgug
y
thorn qgug
z
24
35 eth7THORN
where ug is Darcy velocity of gas Sg is initial gas saturation qg isthe free-gas density and qa is the adsorbed-gas mass per unit shalevolume (kilograms of adsorbed gas per cubic meter of solid)
The final governing nonlinear equation-of-transient gas flow inshale-gas reservoirs considering the gas-desorption effect isshown next and one may find more details about the derivation inour previous work (Yu et al 2014a)
x
qgk
lg
p
x
thorn
y
qgk
lg
p
y
thorn
z
qgk
lg
p
z
frac14 frac12Sg thorn 1 eth THORNKacgqg
p
t eth8THORN
where k is reservoir permeability cg is the isothermal gas-com-pressibility factor and Ka is the differential equilibrium partition-ing coefficient of gas at a given temperature (Patzek et al 2013)defined as follows
Ka frac14qa
qg
T
eth9THORN
The mass balance of adsorbed gas in one-unit bulk volume isdescribed as
qaVb 1 eth THORN frac14 qg pST TSTeth THORNqbVbv eth10THORN
where qb is bulk density of shale Vb is unit volume of bulk rockv is the specific volume of gas adsorbed per unit mass of bulkrock (scfton) which is measured at the reservoir pressure andtemperature and then transferred to standard condition and qg( pstTst) is the ST gas density
One can calculate the adsorbed-gas mass per unit shale volumeat the standard condition as
qa frac14qg pST TSTeth THORNqbv
1 eth11THORN
One can express the differential equilibrium partitioning coef-ficient of gas by
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 v
p
p
qg
eth12THORN
One can determine the isothermal gas-compressibility factor as
cg frac141
qg
qg
p
T
eth13THORN
The EOS for real gas is given by
qg frac14pM
Zeth pTHORNRT eth14THORN
where p is pressure in kPa M is the molecular weight of the gas(Mfrac14 cgMair where Mairfrac14 29 kgkmol is the molecular weight ofair) R is the ideal-gas constant with 83145 kPa m3(kmol K) T isabsolute temperature (K) and Z( p) is the gas-compressibility factor
Mahmoud (2014) developed a new correlation for calculatingthe real-gas compressibility as follows
cg frac14cpr
pc eth15THORN
cpr frac141
ppr 1
Zeth pTHORN
1404e25Tpr
ppr 5524e25Tpr
eth16THORN
ppr frac14p
pc eth17THORN
and
Tpr frac14T
Tc eth18THORN
where pc is the gas critical pressure cpr is the reduced gas compressi-bility ppr is the reduced pressure and Tpr is the reduced temperature
Substituting Eq 13 into Eq 12 yields
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNqgcg
v
p eth19THORN
Consequently for the Langmuir-isotherm equation the differen-tial equilibrium partitioning coefficient of gas can be expressed as
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
vLpL
pL thorn peth THORN2
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
v2pL
vLp2 eth20THORN
For the general form of the BET isotherm the differentialequilibrium partitioning coefficient of gas can be expressed as
300
250
200
150
100
50
00 1000 2000 3000 4000
Pressure (psi)
(a) Langmuir isotherm (b) BET isotherm
BHP
Releasedadsorbed gas
Releasedadsorbed gas
Langmuir isotherm curve BET isotherm curve
Sto
rage
Cap
acity
(sc
fton
)
300
250
200
150
100
50
0
Sto
rage
Cap
acity
(sc
fton
)
Pi BHP Pi
5000 6000 0 1000 2000 3000 4000
Pressure (psi)
5000 6000
Fig 1mdashComparison of the Langmuir and BET isotherms (a) Langmuir isotherm (b) BET isotherm
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2015 SPE Journal 3
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
A Bthorn vps
p ps peth THORN
eth21THORN
A frac14 vmCp
ps ps peth THORN n nthorn 1eth THORN p
ps
n
n nthorn 1eth THORN p
ps
n1
1thorn C 1eth THORN p
ps C
p
ps
nthorn1
eth22THORN
and
B frac14 v
ps
C 1 C nthorn 1eth THORN p
ps
n
1thorn C 1eth THORN p
ps C
p
ps
nthorn1 eth23THORN
Methane-Adsorption Measurements inMarcellus Shale
In this study measurements for methane adsorption were con-ducted by Weatherford Laboratories isotherm equipment featur-ing two independent covered oil baths metal-to-metal seals onpressure cells in place of O-ring seals pressure capabilities to10000 psi and temperatures up to 350 F The volumetric methodis used with a reference cell connecting to a sample cell Inde-pendent pressure transducers and a thermocouple or resistancetemperature detectors are used to monitor the pressure and tem-perature change within each cell Pressure and temperature dataare monitored by a computer data-acquisition system that can col-lect data at 05-second intervals Two cells are immersed in an oilbath maintained at constant temperature to minimize errorscaused by transient temperature fluctuations Free gas is containedwithin the void volume of the cells whereas the sorbed gas is con-tained in the micropores of the shale material within the samplecell There are two primary steps in measuring isotherm dataincluding a calibration step and an isotherm-measurement stepDuring calibration the empty reference- and sample-cell volumesand the void volume within the sample cell after it is filled with asorbing material are determined with helium because it does notadsorb into the sample The isotherm-measurement step involvesrepeated pressure steps with methane to determine the stabilizedequilibrium pressure and temperature conditions for each step Afull computerized interpretation is implemented to account forslight temperature and pressure variations and to improve the ac-
curacy of the measured stabilized pressure and temperature condi-tions at the end of each isotherm step which greatly increases therepeatability and consistency of the isotherm measurements Inaddition the shale samples were immediately preserved at thewellsite so that in-situ fluids are not altered by means of desicca-tion or imbibition
The Gibbs-isotherm data determined from the experimentswere corrected to the total isotherm on the basis of the followingequation (Sircar 1999 Ambrose et al 2012)
Gs frac14 Gs0
1 qf =qs
eth24THORN
where Gs0 is Gibbs-isotherm storage capacity scfton Gs is total-isotherm storage capacity scfton qf is free-gas density lbmft3and qs is sorbed-gas density lbmft3 The free-gas density dependson the Z-factors which are calculated with the NIST REFPROPprogram (NIST 2013)
For Marcellus Shale isotherm measurements of this study amass of approximately 250 g of shale samples was used and allexperiments were conducted at 130 F TOC is measured by aLECO carbon analyzer We analyzed gas-adsorption laboratorymeasurements on four samples from the lower Marcellus Shaleas shown in Fig 2 One can see that the adsorption measurementsdo not obey the Langmuir isotherm but obey the BET isothermWe used both the Langmuir and BET isotherms to fit the experi-mental measurements as shown in Fig 3 The fitting parametersof Langmuir and BET isotherms are listed in Tables 1 and 2respectively The coefficient of determination also known as R2is used to evaluate goodness of fit The measurements are betterapproximated by the BET isotherm than by the Langmuir iso-therm There are very few published high-pressure methane-adsorption data for shale Chareonsuppanimit et al (2012) pro-vided a summary of literature sources for high-pressure gas-adsorption data on shales (Nuttall et al 2005 Beaton et al 2010Weniger et al 2010) in which the highest pressure used to mea-sure gas adsorption was approximately 4000 psi However thehighest pressure used for measuring methane adsorption in thisstudy was more than 7000 psi Vermylen (2011) measured N2CH4 and CO2 adsorptions for four Barnett Shale samples with themaximum pressure of 1500 psi and found that CH4 and N2 obeythe Langmuir isotherm whereas CO2 obeys the BET isothermThis study to the best of our knowledge for the first time showsthat CH4 adsorption at high pressure in some areas of MarcellusShale behaves similar to multilayer adsorption and the BET iso-therm fits the data well
The relationship between the TOC and gas-storage capacity atthe reference pressure of 5000 psi is shown in Fig 4 illustratinga good linear relationship
Comparison of Free Gas and Adsorbed Gas
One can see from Eq 8 that (1ndash)Ka and Sg represent the contri-butions of adsorbed gas and free gas in shale The actual reservoirproperties of Marcellus Shale are used Porosity of 0142 and ini-tial gas saturation of 90 are used for calculation We calculatedthe (1ndash)Ka of four samples with Eq 20 for the Langmuir iso-therm and Eqs 21 through 23 for the BET isotherm respectivelyas shown in Fig 5 For the Langmuir isotherm Fig 5a shows thatgas desorption is comparable to free gas at low reservoir pressurewhereas gas desorption is less important at high reservoir pres-sure However for the BET isotherm Fig 5b illustrates that gasdesorption is significant at both high and low reservoir pressure
Calculation of OGIP
The traditional method for calculating the OGIP for free gas isexpressed next (Ambrose et al 2012)
vf frac14 320368 Sgi
qbBg eth25THORN
250Sample 1Sample 2Sample 3Sample 4
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0 1000 2000 3000 4000 5000 6000Pressure (psi)
7000 80000
Fig 2mdashExperimental measurements of gas adsorption from thelower Marcellus Shale
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where vf is the free-gas volume in scfton is reservoir porositySgi is the initial gas saturation qb is the bulk-rock density in gcm3 and Bg is the gas-formation volume factor (FVF) in reservoirvolumesurface volume
Ambrose et al (2012) proposed a new method to calculate thefree-gas volume by considering the volume occupied by theadsorbed gas on the surface on the basis of the Langmuir-isothermequation The porosity occupied by adsorbed gas on the basis ofthe Langmuir isotherm is
a Langmuir frac14 1318 106Mqb
qs
vLp
pthorn pL
eth26THORN
The final governing expression is shown as
vf Langmuir frac14320368
Bg
1 Sweth THORN
qb
1318 106M
qs
vLp
pthorn pL
eth27THORN
where Sw is the initial water saturation M is molecular weight ofnatural gas lbmlbm mol and qs is the adsorbed-gas density gcm3 Note that the direct measurement of the adsorbed-gas densityis difficult and it is typically assumed that the adsorbed-gas
250 160
140
120
100
Sto
rage
Cap
acity
(sc
fton
)
80
60
40
20
0
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
0 1000 2000 3000
Sample 1-Lab data
Langmuir modelBET model
Sample 3-Lab data
Langmuir model
BET model
Sample 2-Lab data
Langmuir modelBET model
Sample 4-Lab data
Langmuir modelBET model
Pressure (psi)
(a) Sample 1 (b) Sample 2
(c) Sample 3 (d) Sample 4
4000
0 1000 2000 3000 4000
Pressure (psi)
5000 6000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000 8000
Fig 3mdashComparison of fitting results with the Langmuir and BET isotherms (a) Sample 1 (b) Sample 2 (c) Sample 3 and (d) Sam-ple 4
Table 2mdashBET-isotherm parameters used for fitting the measurements
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density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores
qs frac14 01057ln peth THORN 04629 eth28THORN
where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi
One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume
vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN
where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton
In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm
The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm
a BET frac14 1318 106Mqb
qs
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth30THORN
The governing equation is obtained here
vf BET frac14320368
Bg
1 Sweth THORNqb
1318 106M
qs
8gtgtgtltgtgtgt
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
377759gtgtgt=gtgtgt
eth31THORNOne can obtain the total OGIP by summation of free-gas vol-
ume and adsorbed-gas volume
vt BET frac14 vf BET thorn va BET eth32THORN
where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton
The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales
Numerical-Simulation Methods
In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs
300
y = 25904xR 2 = 097240
Gas
-Sto
rage
Cap
acity
(sc
fton
)
180
120
60
00 002 004 006 008 01
TOC (wt fraction)
Fig 4mdashRelationship between gas-storage capacity and theTOC
1Sample 1Sample 3
Sample 2Sample 4
φSg φSg
Sample 1Sample 3
Sample 2Sample 4
01
001
0001
1
01
001
00010 1000 2000 3000 4000 5000
Pressure (psi)
(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation
(1ndashφ
) K
a
(1ndashφ
) K
a
6000 0 1000 2000 3000 4000 5000
Pressure (psi)
6000
Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation
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(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
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ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
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recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
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bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
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Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
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measurements The Langmuir and BET isotherms were comparedwith experimental data In addition through history matchingwith one production well in the Marcellus Shale we evaluated theeffect of gas adsorption on well performance at short and longproduction times
Adsorption Model for Shale-Gas Reservoirs
Adsorption at the gassolid interface is referred to as the enrich-ment of one or more components in an interfacial layer (Singet al 1985) The organic matter in shale has a strong adsorptionpotential because of the large surface area and affinity to methaneTo simulate gas production in shale-gas reservoirs an accuratemodel of gas adsorption is very important According to the Inter-national Union of Pure and Applied Chemistry (IUPAC) standardclassification system (Sing et al 1985) there are six differenttypes of adsorption The shape of the adsorption isotherm isclosely related to the properties of adsorbate and solid adsorbentand the pore-space geometry (Silin and Kneafsey 2012) One canfind the detailed description of the six isotherm classifications inSing et al (1985)
The most commonly applied adsorption model for shale gas-reservoirs is the classic Langmuir isotherm (Type I) (Langmuir1918) which is based on the assumption that there is a dynamicequilibrium at constant temperature and pressure betweenadsorbed and nonadsorbed gas Also it is assumed that there isonly a single layer of molecules covering the solid surface TheLangmuir isotherm has two fitting parameters
veth pTHORN frac14 vLp
pthorn pL eth1THORN
where v( p) is the gas volume of adsorption at pressure p vL isLangmuir volume referred to as the maximum gas volume ofadsorption at the infinite pressure and pL is Langmuir pressurewhich is the pressure corresponding to one-half Langmuir vol-ume Instantaneous equilibrium of the sorbing surface and thestorage in the pore space is assumed to be established for theLangmuir isotherm (Freeman et al 2012) Gao et al (1994) dem-onstrated that the instantaneous equilibrium is a reasonableassumption because the ultralow permeability in shale leads tovery low gas-flow rate through the kerogen component of shale
At high reservoir pressures one can expect that natural gassorbed on the organic carbon surfaces forms multimolecularlayers In other words the Langmuir isotherm may not be a goodapproximation of the amount of gas sorbed on organic carbon-rich mudrocks Instead multilayer sorption of natural gas shouldbe expected on organic carbon surfaces and the gas-adsorptionisotherm of Type II should be a better choice Type II isothermoften occurs in a nonporous or a macroporous material (Kuilaand Prasad 2013) In 1938 Stephen Brunauer Paul HughEmmett and Edward Teller (BET) published their theory in theJournal of the American Chemical Society (ACS) (Brunaueret al 1938) The BET isotherm model is a generalization of theLangmuir model to multiple adsorbed layers The expression isshown as follows
veth pTHORN frac14 vmCp
ethpo pTHORNfrac121thorn C 1eth THORNp=po eth2THORN
where po is the saturation pressure of the gas vm is the maximumadsorption gas volume when the entire adsorbent surface is beingcovered with a complete monomolecular layer and C is a con-stant related to the net heat of adsorption which is defined as
C frac14 expE1 EL
RT
eth3THORN
where E1 is the heat of adsorption for the first layer and EL is thatfor the second and higher layers and is equal to the heat of lique-faction The assumptions in the BET theory include homogeneoussurface no lateral interaction between molecules and the upper-most layer being in equilibrium with gas phase
The standard BET isotherm assumes that the number ofadsorption layers is infinite But in the case of n adsorption layersin some finite number then a general form of the BET isothermis given
veth pTHORN frac14vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth4THORN
When nfrac14 1 Eq 4 reduces to the Langmuir isotherm Eq 1When nfrac141 Eq 4 reduces to Eq 2
Here v(p) is the specific volume of gas adsorbed at the reser-voir pressure and temperature per unit mass of bulk rock refer-enced to a standard pressure and temperature [stock-tank (ST)condition in the oil industry] The customary cubic fields are ei-ther the standard cubic feet of sorbed gas per ton of bulk rock(scfton) or the standard cubic centimeters of gas per gram ofrock The conversion factor is
1scf
ton of bulk rock
frac14 1
32
standard cm3
g of bulk rock
eth5THORN
One should note that it is very challenging to apply the BETmodel to physically explain the supercritical-methane adsorptionbecause there is no concept of a liquid if the reservoir temperatureis above the critical-methane temperature Consequently the satu-ration pressure ( po) also loses its physical meaning (Ozdemir2004) To avoid this issue the saturation pressure ( po) is treatedas pseudosaturation pressure ( ps) for the high-pressuretempera-ture methane adsorption (Clarkson et al 1997) Clarkson et al(1997) summarized various methods to estimate the pseudosatura-tion pressure at any temperature above critical temperature Inthis study the method of extrapolation of the Antoine equation isused to calculate the pseudosaturation pressure for supercritical-methane adsorption as follows (NIST 2011 Hao et al 2014)
lnps frac14 77437 13065485
194362thorn T eth6THORN
where T is temperature (K) and ps is pseudosaturation pressure(MPa)
In this study we mainly focus on fitting the experimentalmeasurements of supercritical-methane adsorption by fixing thepseudosaturation pressure and tuning three fitting parameters ofvm C and n For practical application the BET-isotherm modeleasily can be used in a reservoir simulator to model the contribu-tion of gas desorption on well performance in some shale-gas res-ervoirs Although there are some physical-adsorption models suchas the simplified local-density model the 2D equation-of-state(EOS) model (Chareonsuppanimit et al 2012 Clarkson andHaghshenas 2013) and molecular simulation (Firouzi and Wilcox2012 Firouzi et al 2014b) we did not use the mentioned modelsin this study
Fig 1 compares shapes of the Langmuir and BET isothermsGas desorption along the BET isotherm contributes more signifi-cantly at early time of production than that with the Langmuir-iso-therm curve This is because the slope of the BET-isotherm curveat high pressure is larger than that of the Langmuir-isothermcurve resulting in more adsorbed gas releasing at early produc-tion times In addition under the same pressure drop from the ini-tial reservoir pressure to the BHP the amount of releasedadsorbed gas with the BET-isotherm curve is larger than that withthe Langmuir-isotherm curve
Gas-Flow Model in Shale
An equation to describe mass balance of gas flow in shale-gas res-ervoirs by considering the gas-desorption effect is given next (Pat-zek et al 2013 Yu et al 2014a)
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frac12qgSgthorn 1 eth THORNqat
frac14
qgug
x
thorn qgug
y
thorn qgug
z
24
35 eth7THORN
where ug is Darcy velocity of gas Sg is initial gas saturation qg isthe free-gas density and qa is the adsorbed-gas mass per unit shalevolume (kilograms of adsorbed gas per cubic meter of solid)
The final governing nonlinear equation-of-transient gas flow inshale-gas reservoirs considering the gas-desorption effect isshown next and one may find more details about the derivation inour previous work (Yu et al 2014a)
x
qgk
lg
p
x
thorn
y
qgk
lg
p
y
thorn
z
qgk
lg
p
z
frac14 frac12Sg thorn 1 eth THORNKacgqg
p
t eth8THORN
where k is reservoir permeability cg is the isothermal gas-com-pressibility factor and Ka is the differential equilibrium partition-ing coefficient of gas at a given temperature (Patzek et al 2013)defined as follows
Ka frac14qa
qg
T
eth9THORN
The mass balance of adsorbed gas in one-unit bulk volume isdescribed as
qaVb 1 eth THORN frac14 qg pST TSTeth THORNqbVbv eth10THORN
where qb is bulk density of shale Vb is unit volume of bulk rockv is the specific volume of gas adsorbed per unit mass of bulkrock (scfton) which is measured at the reservoir pressure andtemperature and then transferred to standard condition and qg( pstTst) is the ST gas density
One can calculate the adsorbed-gas mass per unit shale volumeat the standard condition as
qa frac14qg pST TSTeth THORNqbv
1 eth11THORN
One can express the differential equilibrium partitioning coef-ficient of gas by
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 v
p
p
qg
eth12THORN
One can determine the isothermal gas-compressibility factor as
cg frac141
qg
qg
p
T
eth13THORN
The EOS for real gas is given by
qg frac14pM
Zeth pTHORNRT eth14THORN
where p is pressure in kPa M is the molecular weight of the gas(Mfrac14 cgMair where Mairfrac14 29 kgkmol is the molecular weight ofair) R is the ideal-gas constant with 83145 kPa m3(kmol K) T isabsolute temperature (K) and Z( p) is the gas-compressibility factor
Mahmoud (2014) developed a new correlation for calculatingthe real-gas compressibility as follows
cg frac14cpr
pc eth15THORN
cpr frac141
ppr 1
Zeth pTHORN
1404e25Tpr
ppr 5524e25Tpr
eth16THORN
ppr frac14p
pc eth17THORN
and
Tpr frac14T
Tc eth18THORN
where pc is the gas critical pressure cpr is the reduced gas compressi-bility ppr is the reduced pressure and Tpr is the reduced temperature
Substituting Eq 13 into Eq 12 yields
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNqgcg
v
p eth19THORN
Consequently for the Langmuir-isotherm equation the differen-tial equilibrium partitioning coefficient of gas can be expressed as
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
vLpL
pL thorn peth THORN2
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
v2pL
vLp2 eth20THORN
For the general form of the BET isotherm the differentialequilibrium partitioning coefficient of gas can be expressed as
300
250
200
150
100
50
00 1000 2000 3000 4000
Pressure (psi)
(a) Langmuir isotherm (b) BET isotherm
BHP
Releasedadsorbed gas
Releasedadsorbed gas
Langmuir isotherm curve BET isotherm curve
Sto
rage
Cap
acity
(sc
fton
)
300
250
200
150
100
50
0
Sto
rage
Cap
acity
(sc
fton
)
Pi BHP Pi
5000 6000 0 1000 2000 3000 4000
Pressure (psi)
5000 6000
Fig 1mdashComparison of the Langmuir and BET isotherms (a) Langmuir isotherm (b) BET isotherm
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Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
A Bthorn vps
p ps peth THORN
eth21THORN
A frac14 vmCp
ps ps peth THORN n nthorn 1eth THORN p
ps
n
n nthorn 1eth THORN p
ps
n1
1thorn C 1eth THORN p
ps C
p
ps
nthorn1
eth22THORN
and
B frac14 v
ps
C 1 C nthorn 1eth THORN p
ps
n
1thorn C 1eth THORN p
ps C
p
ps
nthorn1 eth23THORN
Methane-Adsorption Measurements inMarcellus Shale
In this study measurements for methane adsorption were con-ducted by Weatherford Laboratories isotherm equipment featur-ing two independent covered oil baths metal-to-metal seals onpressure cells in place of O-ring seals pressure capabilities to10000 psi and temperatures up to 350 F The volumetric methodis used with a reference cell connecting to a sample cell Inde-pendent pressure transducers and a thermocouple or resistancetemperature detectors are used to monitor the pressure and tem-perature change within each cell Pressure and temperature dataare monitored by a computer data-acquisition system that can col-lect data at 05-second intervals Two cells are immersed in an oilbath maintained at constant temperature to minimize errorscaused by transient temperature fluctuations Free gas is containedwithin the void volume of the cells whereas the sorbed gas is con-tained in the micropores of the shale material within the samplecell There are two primary steps in measuring isotherm dataincluding a calibration step and an isotherm-measurement stepDuring calibration the empty reference- and sample-cell volumesand the void volume within the sample cell after it is filled with asorbing material are determined with helium because it does notadsorb into the sample The isotherm-measurement step involvesrepeated pressure steps with methane to determine the stabilizedequilibrium pressure and temperature conditions for each step Afull computerized interpretation is implemented to account forslight temperature and pressure variations and to improve the ac-
curacy of the measured stabilized pressure and temperature condi-tions at the end of each isotherm step which greatly increases therepeatability and consistency of the isotherm measurements Inaddition the shale samples were immediately preserved at thewellsite so that in-situ fluids are not altered by means of desicca-tion or imbibition
The Gibbs-isotherm data determined from the experimentswere corrected to the total isotherm on the basis of the followingequation (Sircar 1999 Ambrose et al 2012)
Gs frac14 Gs0
1 qf =qs
eth24THORN
where Gs0 is Gibbs-isotherm storage capacity scfton Gs is total-isotherm storage capacity scfton qf is free-gas density lbmft3and qs is sorbed-gas density lbmft3 The free-gas density dependson the Z-factors which are calculated with the NIST REFPROPprogram (NIST 2013)
For Marcellus Shale isotherm measurements of this study amass of approximately 250 g of shale samples was used and allexperiments were conducted at 130 F TOC is measured by aLECO carbon analyzer We analyzed gas-adsorption laboratorymeasurements on four samples from the lower Marcellus Shaleas shown in Fig 2 One can see that the adsorption measurementsdo not obey the Langmuir isotherm but obey the BET isothermWe used both the Langmuir and BET isotherms to fit the experi-mental measurements as shown in Fig 3 The fitting parametersof Langmuir and BET isotherms are listed in Tables 1 and 2respectively The coefficient of determination also known as R2is used to evaluate goodness of fit The measurements are betterapproximated by the BET isotherm than by the Langmuir iso-therm There are very few published high-pressure methane-adsorption data for shale Chareonsuppanimit et al (2012) pro-vided a summary of literature sources for high-pressure gas-adsorption data on shales (Nuttall et al 2005 Beaton et al 2010Weniger et al 2010) in which the highest pressure used to mea-sure gas adsorption was approximately 4000 psi However thehighest pressure used for measuring methane adsorption in thisstudy was more than 7000 psi Vermylen (2011) measured N2CH4 and CO2 adsorptions for four Barnett Shale samples with themaximum pressure of 1500 psi and found that CH4 and N2 obeythe Langmuir isotherm whereas CO2 obeys the BET isothermThis study to the best of our knowledge for the first time showsthat CH4 adsorption at high pressure in some areas of MarcellusShale behaves similar to multilayer adsorption and the BET iso-therm fits the data well
The relationship between the TOC and gas-storage capacity atthe reference pressure of 5000 psi is shown in Fig 4 illustratinga good linear relationship
Comparison of Free Gas and Adsorbed Gas
One can see from Eq 8 that (1ndash)Ka and Sg represent the contri-butions of adsorbed gas and free gas in shale The actual reservoirproperties of Marcellus Shale are used Porosity of 0142 and ini-tial gas saturation of 90 are used for calculation We calculatedthe (1ndash)Ka of four samples with Eq 20 for the Langmuir iso-therm and Eqs 21 through 23 for the BET isotherm respectivelyas shown in Fig 5 For the Langmuir isotherm Fig 5a shows thatgas desorption is comparable to free gas at low reservoir pressurewhereas gas desorption is less important at high reservoir pres-sure However for the BET isotherm Fig 5b illustrates that gasdesorption is significant at both high and low reservoir pressure
Calculation of OGIP
The traditional method for calculating the OGIP for free gas isexpressed next (Ambrose et al 2012)
vf frac14 320368 Sgi
qbBg eth25THORN
250Sample 1Sample 2Sample 3Sample 4
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0 1000 2000 3000 4000 5000 6000Pressure (psi)
7000 80000
Fig 2mdashExperimental measurements of gas adsorption from thelower Marcellus Shale
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where vf is the free-gas volume in scfton is reservoir porositySgi is the initial gas saturation qb is the bulk-rock density in gcm3 and Bg is the gas-formation volume factor (FVF) in reservoirvolumesurface volume
Ambrose et al (2012) proposed a new method to calculate thefree-gas volume by considering the volume occupied by theadsorbed gas on the surface on the basis of the Langmuir-isothermequation The porosity occupied by adsorbed gas on the basis ofthe Langmuir isotherm is
a Langmuir frac14 1318 106Mqb
qs
vLp
pthorn pL
eth26THORN
The final governing expression is shown as
vf Langmuir frac14320368
Bg
1 Sweth THORN
qb
1318 106M
qs
vLp
pthorn pL
eth27THORN
where Sw is the initial water saturation M is molecular weight ofnatural gas lbmlbm mol and qs is the adsorbed-gas density gcm3 Note that the direct measurement of the adsorbed-gas densityis difficult and it is typically assumed that the adsorbed-gas
250 160
140
120
100
Sto
rage
Cap
acity
(sc
fton
)
80
60
40
20
0
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
0 1000 2000 3000
Sample 1-Lab data
Langmuir modelBET model
Sample 3-Lab data
Langmuir model
BET model
Sample 2-Lab data
Langmuir modelBET model
Sample 4-Lab data
Langmuir modelBET model
Pressure (psi)
(a) Sample 1 (b) Sample 2
(c) Sample 3 (d) Sample 4
4000
0 1000 2000 3000 4000
Pressure (psi)
5000 6000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000 8000
Fig 3mdashComparison of fitting results with the Langmuir and BET isotherms (a) Sample 1 (b) Sample 2 (c) Sample 3 and (d) Sam-ple 4
Table 2mdashBET-isotherm parameters used for fitting the measurements
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density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores
qs frac14 01057ln peth THORN 04629 eth28THORN
where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi
One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume
vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN
where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton
In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm
The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm
a BET frac14 1318 106Mqb
qs
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth30THORN
The governing equation is obtained here
vf BET frac14320368
Bg
1 Sweth THORNqb
1318 106M
qs
8gtgtgtltgtgtgt
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
377759gtgtgt=gtgtgt
eth31THORNOne can obtain the total OGIP by summation of free-gas vol-
ume and adsorbed-gas volume
vt BET frac14 vf BET thorn va BET eth32THORN
where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton
The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales
Numerical-Simulation Methods
In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs
300
y = 25904xR 2 = 097240
Gas
-Sto
rage
Cap
acity
(sc
fton
)
180
120
60
00 002 004 006 008 01
TOC (wt fraction)
Fig 4mdashRelationship between gas-storage capacity and theTOC
1Sample 1Sample 3
Sample 2Sample 4
φSg φSg
Sample 1Sample 3
Sample 2Sample 4
01
001
0001
1
01
001
00010 1000 2000 3000 4000 5000
Pressure (psi)
(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation
(1ndashφ
) K
a
(1ndashφ
) K
a
6000 0 1000 2000 3000 4000 5000
Pressure (psi)
6000
Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation
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(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
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ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
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recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
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bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
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2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
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frac12qgSgthorn 1 eth THORNqat
frac14
qgug
x
thorn qgug
y
thorn qgug
z
24
35 eth7THORN
where ug is Darcy velocity of gas Sg is initial gas saturation qg isthe free-gas density and qa is the adsorbed-gas mass per unit shalevolume (kilograms of adsorbed gas per cubic meter of solid)
The final governing nonlinear equation-of-transient gas flow inshale-gas reservoirs considering the gas-desorption effect isshown next and one may find more details about the derivation inour previous work (Yu et al 2014a)
x
qgk
lg
p
x
thorn
y
qgk
lg
p
y
thorn
z
qgk
lg
p
z
frac14 frac12Sg thorn 1 eth THORNKacgqg
p
t eth8THORN
where k is reservoir permeability cg is the isothermal gas-com-pressibility factor and Ka is the differential equilibrium partition-ing coefficient of gas at a given temperature (Patzek et al 2013)defined as follows
Ka frac14qa
qg
T
eth9THORN
The mass balance of adsorbed gas in one-unit bulk volume isdescribed as
qaVb 1 eth THORN frac14 qg pST TSTeth THORNqbVbv eth10THORN
where qb is bulk density of shale Vb is unit volume of bulk rockv is the specific volume of gas adsorbed per unit mass of bulkrock (scfton) which is measured at the reservoir pressure andtemperature and then transferred to standard condition and qg( pstTst) is the ST gas density
One can calculate the adsorbed-gas mass per unit shale volumeat the standard condition as
qa frac14qg pST TSTeth THORNqbv
1 eth11THORN
One can express the differential equilibrium partitioning coef-ficient of gas by
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 v
p
p
qg
eth12THORN
One can determine the isothermal gas-compressibility factor as
cg frac141
qg
qg
p
T
eth13THORN
The EOS for real gas is given by
qg frac14pM
Zeth pTHORNRT eth14THORN
where p is pressure in kPa M is the molecular weight of the gas(Mfrac14 cgMair where Mairfrac14 29 kgkmol is the molecular weight ofair) R is the ideal-gas constant with 83145 kPa m3(kmol K) T isabsolute temperature (K) and Z( p) is the gas-compressibility factor
Mahmoud (2014) developed a new correlation for calculatingthe real-gas compressibility as follows
cg frac14cpr
pc eth15THORN
cpr frac141
ppr 1
Zeth pTHORN
1404e25Tpr
ppr 5524e25Tpr
eth16THORN
ppr frac14p
pc eth17THORN
and
Tpr frac14T
Tc eth18THORN
where pc is the gas critical pressure cpr is the reduced gas compressi-bility ppr is the reduced pressure and Tpr is the reduced temperature
Substituting Eq 13 into Eq 12 yields
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNqgcg
v
p eth19THORN
Consequently for the Langmuir-isotherm equation the differen-tial equilibrium partitioning coefficient of gas can be expressed as
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
vLpL
pL thorn peth THORN2
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
v2pL
vLp2 eth20THORN
For the general form of the BET isotherm the differentialequilibrium partitioning coefficient of gas can be expressed as
300
250
200
150
100
50
00 1000 2000 3000 4000
Pressure (psi)
(a) Langmuir isotherm (b) BET isotherm
BHP
Releasedadsorbed gas
Releasedadsorbed gas
Langmuir isotherm curve BET isotherm curve
Sto
rage
Cap
acity
(sc
fton
)
300
250
200
150
100
50
0
Sto
rage
Cap
acity
(sc
fton
)
Pi BHP Pi
5000 6000 0 1000 2000 3000 4000
Pressure (psi)
5000 6000
Fig 1mdashComparison of the Langmuir and BET isotherms (a) Langmuir isotherm (b) BET isotherm
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2015 SPE Journal 3
Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
A Bthorn vps
p ps peth THORN
eth21THORN
A frac14 vmCp
ps ps peth THORN n nthorn 1eth THORN p
ps
n
n nthorn 1eth THORN p
ps
n1
1thorn C 1eth THORN p
ps C
p
ps
nthorn1
eth22THORN
and
B frac14 v
ps
C 1 C nthorn 1eth THORN p
ps
n
1thorn C 1eth THORN p
ps C
p
ps
nthorn1 eth23THORN
Methane-Adsorption Measurements inMarcellus Shale
In this study measurements for methane adsorption were con-ducted by Weatherford Laboratories isotherm equipment featur-ing two independent covered oil baths metal-to-metal seals onpressure cells in place of O-ring seals pressure capabilities to10000 psi and temperatures up to 350 F The volumetric methodis used with a reference cell connecting to a sample cell Inde-pendent pressure transducers and a thermocouple or resistancetemperature detectors are used to monitor the pressure and tem-perature change within each cell Pressure and temperature dataare monitored by a computer data-acquisition system that can col-lect data at 05-second intervals Two cells are immersed in an oilbath maintained at constant temperature to minimize errorscaused by transient temperature fluctuations Free gas is containedwithin the void volume of the cells whereas the sorbed gas is con-tained in the micropores of the shale material within the samplecell There are two primary steps in measuring isotherm dataincluding a calibration step and an isotherm-measurement stepDuring calibration the empty reference- and sample-cell volumesand the void volume within the sample cell after it is filled with asorbing material are determined with helium because it does notadsorb into the sample The isotherm-measurement step involvesrepeated pressure steps with methane to determine the stabilizedequilibrium pressure and temperature conditions for each step Afull computerized interpretation is implemented to account forslight temperature and pressure variations and to improve the ac-
curacy of the measured stabilized pressure and temperature condi-tions at the end of each isotherm step which greatly increases therepeatability and consistency of the isotherm measurements Inaddition the shale samples were immediately preserved at thewellsite so that in-situ fluids are not altered by means of desicca-tion or imbibition
The Gibbs-isotherm data determined from the experimentswere corrected to the total isotherm on the basis of the followingequation (Sircar 1999 Ambrose et al 2012)
Gs frac14 Gs0
1 qf =qs
eth24THORN
where Gs0 is Gibbs-isotherm storage capacity scfton Gs is total-isotherm storage capacity scfton qf is free-gas density lbmft3and qs is sorbed-gas density lbmft3 The free-gas density dependson the Z-factors which are calculated with the NIST REFPROPprogram (NIST 2013)
For Marcellus Shale isotherm measurements of this study amass of approximately 250 g of shale samples was used and allexperiments were conducted at 130 F TOC is measured by aLECO carbon analyzer We analyzed gas-adsorption laboratorymeasurements on four samples from the lower Marcellus Shaleas shown in Fig 2 One can see that the adsorption measurementsdo not obey the Langmuir isotherm but obey the BET isothermWe used both the Langmuir and BET isotherms to fit the experi-mental measurements as shown in Fig 3 The fitting parametersof Langmuir and BET isotherms are listed in Tables 1 and 2respectively The coefficient of determination also known as R2is used to evaluate goodness of fit The measurements are betterapproximated by the BET isotherm than by the Langmuir iso-therm There are very few published high-pressure methane-adsorption data for shale Chareonsuppanimit et al (2012) pro-vided a summary of literature sources for high-pressure gas-adsorption data on shales (Nuttall et al 2005 Beaton et al 2010Weniger et al 2010) in which the highest pressure used to mea-sure gas adsorption was approximately 4000 psi However thehighest pressure used for measuring methane adsorption in thisstudy was more than 7000 psi Vermylen (2011) measured N2CH4 and CO2 adsorptions for four Barnett Shale samples with themaximum pressure of 1500 psi and found that CH4 and N2 obeythe Langmuir isotherm whereas CO2 obeys the BET isothermThis study to the best of our knowledge for the first time showsthat CH4 adsorption at high pressure in some areas of MarcellusShale behaves similar to multilayer adsorption and the BET iso-therm fits the data well
The relationship between the TOC and gas-storage capacity atthe reference pressure of 5000 psi is shown in Fig 4 illustratinga good linear relationship
Comparison of Free Gas and Adsorbed Gas
One can see from Eq 8 that (1ndash)Ka and Sg represent the contri-butions of adsorbed gas and free gas in shale The actual reservoirproperties of Marcellus Shale are used Porosity of 0142 and ini-tial gas saturation of 90 are used for calculation We calculatedthe (1ndash)Ka of four samples with Eq 20 for the Langmuir iso-therm and Eqs 21 through 23 for the BET isotherm respectivelyas shown in Fig 5 For the Langmuir isotherm Fig 5a shows thatgas desorption is comparable to free gas at low reservoir pressurewhereas gas desorption is less important at high reservoir pres-sure However for the BET isotherm Fig 5b illustrates that gasdesorption is significant at both high and low reservoir pressure
Calculation of OGIP
The traditional method for calculating the OGIP for free gas isexpressed next (Ambrose et al 2012)
vf frac14 320368 Sgi
qbBg eth25THORN
250Sample 1Sample 2Sample 3Sample 4
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0 1000 2000 3000 4000 5000 6000Pressure (psi)
7000 80000
Fig 2mdashExperimental measurements of gas adsorption from thelower Marcellus Shale
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where vf is the free-gas volume in scfton is reservoir porositySgi is the initial gas saturation qb is the bulk-rock density in gcm3 and Bg is the gas-formation volume factor (FVF) in reservoirvolumesurface volume
Ambrose et al (2012) proposed a new method to calculate thefree-gas volume by considering the volume occupied by theadsorbed gas on the surface on the basis of the Langmuir-isothermequation The porosity occupied by adsorbed gas on the basis ofthe Langmuir isotherm is
a Langmuir frac14 1318 106Mqb
qs
vLp
pthorn pL
eth26THORN
The final governing expression is shown as
vf Langmuir frac14320368
Bg
1 Sweth THORN
qb
1318 106M
qs
vLp
pthorn pL
eth27THORN
where Sw is the initial water saturation M is molecular weight ofnatural gas lbmlbm mol and qs is the adsorbed-gas density gcm3 Note that the direct measurement of the adsorbed-gas densityis difficult and it is typically assumed that the adsorbed-gas
250 160
140
120
100
Sto
rage
Cap
acity
(sc
fton
)
80
60
40
20
0
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
0 1000 2000 3000
Sample 1-Lab data
Langmuir modelBET model
Sample 3-Lab data
Langmuir model
BET model
Sample 2-Lab data
Langmuir modelBET model
Sample 4-Lab data
Langmuir modelBET model
Pressure (psi)
(a) Sample 1 (b) Sample 2
(c) Sample 3 (d) Sample 4
4000
0 1000 2000 3000 4000
Pressure (psi)
5000 6000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000 8000
Fig 3mdashComparison of fitting results with the Langmuir and BET isotherms (a) Sample 1 (b) Sample 2 (c) Sample 3 and (d) Sam-ple 4
Table 2mdashBET-isotherm parameters used for fitting the measurements
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2015 SPE Journal 5
density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores
qs frac14 01057ln peth THORN 04629 eth28THORN
where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi
One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume
vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN
where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton
In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm
The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm
a BET frac14 1318 106Mqb
qs
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth30THORN
The governing equation is obtained here
vf BET frac14320368
Bg
1 Sweth THORNqb
1318 106M
qs
8gtgtgtltgtgtgt
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
377759gtgtgt=gtgtgt
eth31THORNOne can obtain the total OGIP by summation of free-gas vol-
ume and adsorbed-gas volume
vt BET frac14 vf BET thorn va BET eth32THORN
where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton
The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales
Numerical-Simulation Methods
In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs
300
y = 25904xR 2 = 097240
Gas
-Sto
rage
Cap
acity
(sc
fton
)
180
120
60
00 002 004 006 008 01
TOC (wt fraction)
Fig 4mdashRelationship between gas-storage capacity and theTOC
1Sample 1Sample 3
Sample 2Sample 4
φSg φSg
Sample 1Sample 3
Sample 2Sample 4
01
001
0001
1
01
001
00010 1000 2000 3000 4000 5000
Pressure (psi)
(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation
(1ndashφ
) K
a
(1ndashφ
) K
a
6000 0 1000 2000 3000 4000 5000
Pressure (psi)
6000
Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation
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(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
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2015 SPE Journal 7
ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
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recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
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2015 SPE Journal 9
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
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2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
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Ka frac14qa
qg
T
frac14qg pST TSTeth THORNqb
1 eth THORNcgqg
A Bthorn vps
p ps peth THORN
eth21THORN
A frac14 vmCp
ps ps peth THORN n nthorn 1eth THORN p
ps
n
n nthorn 1eth THORN p
ps
n1
1thorn C 1eth THORN p
ps C
p
ps
nthorn1
eth22THORN
and
B frac14 v
ps
C 1 C nthorn 1eth THORN p
ps
n
1thorn C 1eth THORN p
ps C
p
ps
nthorn1 eth23THORN
Methane-Adsorption Measurements inMarcellus Shale
In this study measurements for methane adsorption were con-ducted by Weatherford Laboratories isotherm equipment featur-ing two independent covered oil baths metal-to-metal seals onpressure cells in place of O-ring seals pressure capabilities to10000 psi and temperatures up to 350 F The volumetric methodis used with a reference cell connecting to a sample cell Inde-pendent pressure transducers and a thermocouple or resistancetemperature detectors are used to monitor the pressure and tem-perature change within each cell Pressure and temperature dataare monitored by a computer data-acquisition system that can col-lect data at 05-second intervals Two cells are immersed in an oilbath maintained at constant temperature to minimize errorscaused by transient temperature fluctuations Free gas is containedwithin the void volume of the cells whereas the sorbed gas is con-tained in the micropores of the shale material within the samplecell There are two primary steps in measuring isotherm dataincluding a calibration step and an isotherm-measurement stepDuring calibration the empty reference- and sample-cell volumesand the void volume within the sample cell after it is filled with asorbing material are determined with helium because it does notadsorb into the sample The isotherm-measurement step involvesrepeated pressure steps with methane to determine the stabilizedequilibrium pressure and temperature conditions for each step Afull computerized interpretation is implemented to account forslight temperature and pressure variations and to improve the ac-
curacy of the measured stabilized pressure and temperature condi-tions at the end of each isotherm step which greatly increases therepeatability and consistency of the isotherm measurements Inaddition the shale samples were immediately preserved at thewellsite so that in-situ fluids are not altered by means of desicca-tion or imbibition
The Gibbs-isotherm data determined from the experimentswere corrected to the total isotherm on the basis of the followingequation (Sircar 1999 Ambrose et al 2012)
Gs frac14 Gs0
1 qf =qs
eth24THORN
where Gs0 is Gibbs-isotherm storage capacity scfton Gs is total-isotherm storage capacity scfton qf is free-gas density lbmft3and qs is sorbed-gas density lbmft3 The free-gas density dependson the Z-factors which are calculated with the NIST REFPROPprogram (NIST 2013)
For Marcellus Shale isotherm measurements of this study amass of approximately 250 g of shale samples was used and allexperiments were conducted at 130 F TOC is measured by aLECO carbon analyzer We analyzed gas-adsorption laboratorymeasurements on four samples from the lower Marcellus Shaleas shown in Fig 2 One can see that the adsorption measurementsdo not obey the Langmuir isotherm but obey the BET isothermWe used both the Langmuir and BET isotherms to fit the experi-mental measurements as shown in Fig 3 The fitting parametersof Langmuir and BET isotherms are listed in Tables 1 and 2respectively The coefficient of determination also known as R2is used to evaluate goodness of fit The measurements are betterapproximated by the BET isotherm than by the Langmuir iso-therm There are very few published high-pressure methane-adsorption data for shale Chareonsuppanimit et al (2012) pro-vided a summary of literature sources for high-pressure gas-adsorption data on shales (Nuttall et al 2005 Beaton et al 2010Weniger et al 2010) in which the highest pressure used to mea-sure gas adsorption was approximately 4000 psi However thehighest pressure used for measuring methane adsorption in thisstudy was more than 7000 psi Vermylen (2011) measured N2CH4 and CO2 adsorptions for four Barnett Shale samples with themaximum pressure of 1500 psi and found that CH4 and N2 obeythe Langmuir isotherm whereas CO2 obeys the BET isothermThis study to the best of our knowledge for the first time showsthat CH4 adsorption at high pressure in some areas of MarcellusShale behaves similar to multilayer adsorption and the BET iso-therm fits the data well
The relationship between the TOC and gas-storage capacity atthe reference pressure of 5000 psi is shown in Fig 4 illustratinga good linear relationship
Comparison of Free Gas and Adsorbed Gas
One can see from Eq 8 that (1ndash)Ka and Sg represent the contri-butions of adsorbed gas and free gas in shale The actual reservoirproperties of Marcellus Shale are used Porosity of 0142 and ini-tial gas saturation of 90 are used for calculation We calculatedthe (1ndash)Ka of four samples with Eq 20 for the Langmuir iso-therm and Eqs 21 through 23 for the BET isotherm respectivelyas shown in Fig 5 For the Langmuir isotherm Fig 5a shows thatgas desorption is comparable to free gas at low reservoir pressurewhereas gas desorption is less important at high reservoir pres-sure However for the BET isotherm Fig 5b illustrates that gasdesorption is significant at both high and low reservoir pressure
Calculation of OGIP
The traditional method for calculating the OGIP for free gas isexpressed next (Ambrose et al 2012)
vf frac14 320368 Sgi
qbBg eth25THORN
250Sample 1Sample 2Sample 3Sample 4
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0 1000 2000 3000 4000 5000 6000Pressure (psi)
7000 80000
Fig 2mdashExperimental measurements of gas adsorption from thelower Marcellus Shale
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where vf is the free-gas volume in scfton is reservoir porositySgi is the initial gas saturation qb is the bulk-rock density in gcm3 and Bg is the gas-formation volume factor (FVF) in reservoirvolumesurface volume
Ambrose et al (2012) proposed a new method to calculate thefree-gas volume by considering the volume occupied by theadsorbed gas on the surface on the basis of the Langmuir-isothermequation The porosity occupied by adsorbed gas on the basis ofthe Langmuir isotherm is
a Langmuir frac14 1318 106Mqb
qs
vLp
pthorn pL
eth26THORN
The final governing expression is shown as
vf Langmuir frac14320368
Bg
1 Sweth THORN
qb
1318 106M
qs
vLp
pthorn pL
eth27THORN
where Sw is the initial water saturation M is molecular weight ofnatural gas lbmlbm mol and qs is the adsorbed-gas density gcm3 Note that the direct measurement of the adsorbed-gas densityis difficult and it is typically assumed that the adsorbed-gas
250 160
140
120
100
Sto
rage
Cap
acity
(sc
fton
)
80
60
40
20
0
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
0 1000 2000 3000
Sample 1-Lab data
Langmuir modelBET model
Sample 3-Lab data
Langmuir model
BET model
Sample 2-Lab data
Langmuir modelBET model
Sample 4-Lab data
Langmuir modelBET model
Pressure (psi)
(a) Sample 1 (b) Sample 2
(c) Sample 3 (d) Sample 4
4000
0 1000 2000 3000 4000
Pressure (psi)
5000 6000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000 8000
Fig 3mdashComparison of fitting results with the Langmuir and BET isotherms (a) Sample 1 (b) Sample 2 (c) Sample 3 and (d) Sam-ple 4
Table 2mdashBET-isotherm parameters used for fitting the measurements
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density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores
qs frac14 01057ln peth THORN 04629 eth28THORN
where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi
One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume
vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN
where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton
In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm
The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm
a BET frac14 1318 106Mqb
qs
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth30THORN
The governing equation is obtained here
vf BET frac14320368
Bg
1 Sweth THORNqb
1318 106M
qs
8gtgtgtltgtgtgt
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
377759gtgtgt=gtgtgt
eth31THORNOne can obtain the total OGIP by summation of free-gas vol-
ume and adsorbed-gas volume
vt BET frac14 vf BET thorn va BET eth32THORN
where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton
The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales
Numerical-Simulation Methods
In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs
300
y = 25904xR 2 = 097240
Gas
-Sto
rage
Cap
acity
(sc
fton
)
180
120
60
00 002 004 006 008 01
TOC (wt fraction)
Fig 4mdashRelationship between gas-storage capacity and theTOC
1Sample 1Sample 3
Sample 2Sample 4
φSg φSg
Sample 1Sample 3
Sample 2Sample 4
01
001
0001
1
01
001
00010 1000 2000 3000 4000 5000
Pressure (psi)
(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation
(1ndashφ
) K
a
(1ndashφ
) K
a
6000 0 1000 2000 3000 4000 5000
Pressure (psi)
6000
Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation
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(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
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ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
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recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
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bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
where vf is the free-gas volume in scfton is reservoir porositySgi is the initial gas saturation qb is the bulk-rock density in gcm3 and Bg is the gas-formation volume factor (FVF) in reservoirvolumesurface volume
Ambrose et al (2012) proposed a new method to calculate thefree-gas volume by considering the volume occupied by theadsorbed gas on the surface on the basis of the Langmuir-isothermequation The porosity occupied by adsorbed gas on the basis ofthe Langmuir isotherm is
a Langmuir frac14 1318 106Mqb
qs
vLp
pthorn pL
eth26THORN
The final governing expression is shown as
vf Langmuir frac14320368
Bg
1 Sweth THORN
qb
1318 106M
qs
vLp
pthorn pL
eth27THORN
where Sw is the initial water saturation M is molecular weight ofnatural gas lbmlbm mol and qs is the adsorbed-gas density gcm3 Note that the direct measurement of the adsorbed-gas densityis difficult and it is typically assumed that the adsorbed-gas
250 160
140
120
100
Sto
rage
Cap
acity
(sc
fton
)
80
60
40
20
0
200
150
100
Sto
rage
Cap
acity
(sc
fton
)
50
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
120
100
80
60
Sto
rage
Cap
acity
(sc
fton
)
40
20
0
0 1000 2000 3000
Sample 1-Lab data
Langmuir modelBET model
Sample 3-Lab data
Langmuir model
BET model
Sample 2-Lab data
Langmuir modelBET model
Sample 4-Lab data
Langmuir modelBET model
Pressure (psi)
(a) Sample 1 (b) Sample 2
(c) Sample 3 (d) Sample 4
4000
0 1000 2000 3000 4000
Pressure (psi)
5000 6000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000
0 1000 2000 3000
Pressure (psi)
4000 5000 6000 7000 8000
Fig 3mdashComparison of fitting results with the Langmuir and BET isotherms (a) Sample 1 (b) Sample 2 (c) Sample 3 and (d) Sam-ple 4
Table 2mdashBET-isotherm parameters used for fitting the measurements
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 5 Total Pages 12
ID balamuralil Time 0859 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 5
density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores
qs frac14 01057ln peth THORN 04629 eth28THORN
where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi
One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume
vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN
where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton
In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm
The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm
a BET frac14 1318 106Mqb
qs
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth30THORN
The governing equation is obtained here
vf BET frac14320368
Bg
1 Sweth THORNqb
1318 106M
qs
8gtgtgtltgtgtgt
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
377759gtgtgt=gtgtgt
eth31THORNOne can obtain the total OGIP by summation of free-gas vol-
ume and adsorbed-gas volume
vt BET frac14 vf BET thorn va BET eth32THORN
where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton
The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales
Numerical-Simulation Methods
In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs
300
y = 25904xR 2 = 097240
Gas
-Sto
rage
Cap
acity
(sc
fton
)
180
120
60
00 002 004 006 008 01
TOC (wt fraction)
Fig 4mdashRelationship between gas-storage capacity and theTOC
1Sample 1Sample 3
Sample 2Sample 4
φSg φSg
Sample 1Sample 3
Sample 2Sample 4
01
001
0001
1
01
001
00010 1000 2000 3000 4000 5000
Pressure (psi)
(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation
(1ndashφ
) K
a
(1ndashφ
) K
a
6000 0 1000 2000 3000 4000 5000
Pressure (psi)
6000
Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 6 Total Pages 12
ID balamuralil Time 0900 I Path SJVol00000150132CompAPPFileSA-J150132
6 2015 SPE Journal
(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
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2015 SPE Journal 7
ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
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8 2015 SPE Journal
recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 9 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 9
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
density is equal to the liquid-phase density however in manycases in which the pore volume is dominated by micropores theadsorbed-gas density is larger than that of the liquid-phase density(Mosher et al 2013) In addition Mosher et al (2013) pointed outthat the molecular simulation can provide the unique opportunityto predict the adsorbed-gas density In this study the adsorbed-gas density of methane is calculated by the following equationwhich was proposed by Riewchotisakul and Akkutlu (2015) onthe basis of the nonequilibrium molecular dynamic simulation toaccount for the change of adsorbed phase density with pressure inorganic nanopores
qs frac14 01057ln peth THORN 04629 eth28THORN
where the adsorbed-gas density (qs) is in gcm3 and pressure (p) isin psi
One can obtain the total OGIP by summation of free-gas vol-ume and adsorbed-gas volume
vt Langmuir frac14 vf Langmuir thorn va Langmuir eth29THORN
where vf_Langmuir is the free-gas volume that is based on the Lang-muir isotherm scfton va_Langmuir is the adsorbed-gas volume thatis based on the Langmuir isotherm scfton and vt_Langmuir is thetotal-gas volume that is based on the Langmuir isotherm scfton
In this work we modified the model for calculating OGIP pro-posed by Ambrose et al (2012) by considering the BET isotherm
The porosity occupied by adsorbed gas is modified as followsfor the BET isotherm
a BET frac14 1318 106Mqb
qs
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
37775 eth30THORN
The governing equation is obtained here
vf BET frac14320368
Bg
1 Sweth THORNqb
1318 106M
qs
8gtgtgtltgtgtgt
vmC
p
po
1 p
po
1 ethnthorn 1THORN p
po
n
thorn np
po
nthorn1
1thorn ethC 1THORN p
po C
p
po
nthorn1
26664
377759gtgtgt=gtgtgt
eth31THORNOne can obtain the total OGIP by summation of free-gas vol-
ume and adsorbed-gas volume
vt BET frac14 vf BET thorn va BET eth32THORN
where vf_BET is the free-gas volume on the basis of the BET iso-therm in scfton va_BET is the adsorbed-gas volume on the basisof the BET isotherm in scfton and vt_BET is the total-gas volumeon the basis of the BET isotherm in scfton
The actual reservoir properties of Marcellus Shale are used forthe calculation of OGIP as shown in Table 3 With Eqs 26through 32 the porosities of gas adsorption free gas in placeadsorbed gas in place and the total OGIP are calculated as sum-marized in Tables 4 and 5 As shown the average total OGIP inplace is 521 scfton calculated with the BET isotherm which islarger than the 510 scfton calculated with the Langmuir isothermHence characterizing the gas-adsorption isotherm is importantfor quantifying the total OGIP and evaluating the economicpotential of gas shales
Numerical-Simulation Methods
In this work a compositional simulator is used to model multiplehydraulic fractures and gas flow in Marcellus Shale reservoirs
300
y = 25904xR 2 = 097240
Gas
-Sto
rage
Cap
acity
(sc
fton
)
180
120
60
00 002 004 006 008 01
TOC (wt fraction)
Fig 4mdashRelationship between gas-storage capacity and theTOC
1Sample 1Sample 3
Sample 2Sample 4
φSg φSg
Sample 1Sample 3
Sample 2Sample 4
01
001
0001
1
01
001
00010 1000 2000 3000 4000 5000
Pressure (psi)
(a) Langmuir isotherm used for calculation (b) BET isotherm used for calculation
(1ndashφ
) K
a
(1ndashφ
) K
a
6000 0 1000 2000 3000 4000 5000
Pressure (psi)
6000
Fig 5mdashComparison of free gas and adsorbed gas with different isotherms (a) Langmuir isotherm used for calculation (b) BET iso-therm used for calculation
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 6 Total Pages 12
ID balamuralil Time 0900 I Path SJVol00000150132CompAPPFileSA-J150132
6 2015 SPE Journal
(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 7 Total Pages 12
ID balamuralil Time 0900 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 7
ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 8 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
8 2015 SPE Journal
recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 9 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 9
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
(CMG 2012) In our simulation model local grid refinement withlogarithmic cell spacing is used to accurately model gas flowfrom shale matrix to hydraulic fractures Non-Darcy flow is con-sidered for which the non-Darcy Beta-factor used in the For-chheimer number is determined with a correlation proposed byEvans and Civan (1994) This approach was extensively used tomodel transient gas flow in hydraulically fractured shale-gas res-ervoirs (Rubin 2010 Yu and Sepehrnoori 2014a 2014b Yu et al2014b) In the simulation model the Langmuir isotherm is used tomodel gas desorption Also the adsorption data can be entered ina table form Increase in gas recovery is used to assess the contri-bution of gas desorption in this work and it is defined by
Increase in gas recovery frac14 QGas Desorption Qi
QGas Desorption
eth33THORN
where QGas Desorption is cumulative gas production with gas-desorption effect whereas Qi is cumulative gas production with-out gas-desorption effect
Basic Reservoir Model
A Marcellus Shale area of approximately 207 acres was simulatedby setting up a basic 3D reservoir model with dimensions of6000 1500 130 ft which corresponds to length width andthickness respectively as shown in Fig 6 The reservoir has twoshale layers Porosity of bottom and upper layers is approximately142 and 71 respectively The horizontal well is stimulated inthe bottom layer with 16 fracturing stages and four perforationclusters per stage with cluster spacing of 50 ft The total welllength is 3921 ft There are almost 190 days of production dataavailable for performing history matching and evaluating theeffect of gas desorption on well performance
Table 6 summarizes the detailed reservoir and fracture proper-ties of this well The reservoir is assumed to be homogeneousand the fractures are evenly spaced with stress-independent po-rosity and permeability The flowing BHP in Fig 7 is used to con-strain the simulation and cumulative gas production is thehistory-matching variable Table 7 lists reservoir permeabilityand fracture properties with a good history match without consid-ering the gas-desorption effect as shown in Fig 8
In the subsequent simulation studies we performed historymatching by considering gas desorption from the four shale sam-
Parameter Value Unit Initial reservoir pressure 5000 psiReservoir temperature 130 oFReservoir porosity 14 ndashInitial water saturation 10 ndashBg 00033 ndashM 20 lbmlbm mol ρb 263 gcm3
Table 3mdashParameters used for calculation in the Marcellus Shale
Table 5mdashOGIP calculation based on the Langmuir isotherm
6000 ft15
00 ft
Well-1
Fig 6mdashA basic 3D reservoir model for the Marcellus Shale
Parameter Value Unit Initial reservoir pressure 5100 psiReservoir temperature 130 oFReservoir permeability 800 ndReservoir porosity (upper layer) 71 ndashReservoir porosity (bottom layer) 142 ndashInitial water saturation 10 ndashTotal compressibility 3times10ndash6 psindash1
Horizontal well length 3921 ftNumber of stages 16 ndashCluster spacing 50 ftFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ftTotal number of fractures 64 ndashGas specific gravity 058 ndash
Table 6mdashReservoir and fracture parameters for the Marcellus shale
well
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 7 Total Pages 12
ID balamuralil Time 0900 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 7
ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 8 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
8 2015 SPE Journal
recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 9 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 9
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
ples and production forecasting for a 30-year period by graduallydropping the BHP at 190 days to 200 psi within 1 month and thenmaintaining 200 psi until 30 years The comparisons of gas-de-sorption effect between the Langmuir and the BET isotherms forthe four shale samples are shown in Figs 9 through 12 One cansee that gas desorption with the BET isotherm contributes moresignificantly to gas recovery than that with the Langmuir isothermat the early time of production (190 days) The increase in gas
5000
4000
3000
2000
Bot
tom
ehol
e P
ress
ure
(psi
)
1000
00 50 100 150
Time (days)
200
Fig 7mdashFlowing BHP of the Marcellus Shale well
Parameter Value Unit Reservoir permeability 800 ndFracture half-length 400 ftFracture conductivity 35 md-ftFracture height 95 ft
Table 7mdashReservoir and fracture parameters used for a good history
match
3000
2500
2000
1500
1000
500
00 50 100 150
Field data
Without desorption
Time (days)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
200
Fig 8mdashComparison between simulation data and the field dataof the Marcellus Shale well
3500 21000
18000
15000
12000
9000
6000
3000
0
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
50 100 150
Field data
Without desorptionLangmuir
BET
Field dataWithout desorptionLangmuirBET
200
Time (days)
(a) History matching (b) Production forecasting
0 5 10 15 20 25 30
Time (years)
00
Fig 9mdashComparison of well performance with the Langmuir and BET isotherms for Sample 1 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days)
(a) History matching (b) Production forecasting
Time (years)
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 10mdashComparison of well performance with the Langmuir and BET isotherms for Sample 2 (a) history matching (b) productionforecasting
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 8 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
8 2015 SPE Journal
recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 9 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 9
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
recovery after 190 days of production with the BET isotherm is176 74 9 and 63 whereas the increase in gas recovery withthe Langmuir isotherm is 3 47 29 and 11 for Samples 1through 4 respectively At 30 years of production the increase ingas recovery with the BET isotherm is 30 152 135 and 81
whereas the increase in gas recovery with the Langmuir isothermis 137 151 95 and 43 for Samples 1 through 4 respectively
Once again we performed history matching by considering theBET isotherm for the four samples as shown in Fig 13 Twomain parameters fracture half-length and fracture height weretuned to obtain a good match The other parameters were kept thesame as the history-match case without considering desorption Asshown a good match was obtained for each sample with fracturehalf-length and fracture height as shown in Table 8 In compari-son with the case without desorption the fracture half-length wasreduced for each sample although the fracture height was reducedfrom 95 to 85 ft for Sample 1 Hence one can suggest that the gas-desorption effect with the BET isotherm plays an important role inperforming history matching at early time of production
Conclusions
We analyzed the laboratory measurements of gas adsorption fromfour shale samples in the Marcellus Shale with the Langmuir andBET isotherms The effect of gas adsorption on calculation ofOGIP and well performance was investigated One can draw thefollowing conclusions from this workbull The measured gas adsorption in four samples from the lower
Marcellus Shale is described better by the BET isotherm thanby the Langmuir isotherm
bull A good linear relationship between gas-storage capacity andTOC is obtained
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000C
umul
ativ
e G
as P
rodu
ctio
n(M
MS
CF
)6000
3000
0
Fig 12mdashComparison of well performance with the Langmuir and BET isotherms for Sample 4 (a) history matching (b) productionforecasting
3000
2500
2000
1500
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1000
500
0 50 100 150
Field data
Without desorption
Langmuir
BET
Field data
Without desorption
LangmuirBET
200 0 5 10 15 20 25 30
Time (days) Time (years)
(a) History matching (b) Production forecasting
0
18000
15000
12000
9000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
6000
3000
0
Fig 11mdashComparison of well performance with the Langmuir and BET isotherms for Sample 3 (a) history matching (b) productionforecasting
3000
2500
2000
Cum
ulat
ive
Gas
Pro
duct
ion
(MM
SC
F)
1500
1000
500
0 50 100 150 200
Field dataSample 1Sample 2Sample 3Sample 4
Time (days)
0
Fig 13mdashHistory matching by considering the BET isotherm offour samples
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 9 Total Pages 12
ID balamuralil Time 0901 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 9
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
bull Gas desorption obeying the BET isotherm is comparable to thefree gas at low and high reservoir pressure
bull The average total OGIP is 521 scfton when calculated with theBET isotherm and 510 scfton calculated with the Langmuirisotherm
bull For the horizontal well investigated in this study the range ofincrease in gas recovery at 190 days of production with theBET isotherm is 63 to 176 whereas the range with the Lang-muir isotherm is 11 to 47 After 30 years of production therange of increase in gas recovery with the BET isotherm is 81to 30 whereas the range with the Langmuir isotherm is 43 to151
Nomenclature
Bg frac14 gas FVFcg frac14 isothermal gas-compressibility factor
cpr frac14 reduced gas compressibility
C frac14 constant related to the net heat of adsorptionE1 frac14 heat of adsorption for the first layer
EL frac14 heat of the second and higher layersk frac14 reservoir permeability m2
Ka frac14 differential equilibrium portioning coefficient ofgas at a given temperature
n frac14 maximum number of adsorption layersp frac14 pressure psi
pc frac14 gas critical pressure psipL frac14 Langmuir pressure psipo frac14 saturation pressure of the gas MPa
ppr frac14 reduced pressureps frac14 pseudosaturation pressure of the gas MPa
QGas Desorption frac14 cumulative gas production with gas-desorptioneffect MMscf
Qi frac14 cumulative gas production without gas-desorp-tion effect MMscf
Sg frac14 initial gas saturationT frac14 temperature K
Tpr frac14 reduced temperatureug frac14 Darcy velocity of gas ms
va_BET frac14 adsorbed gas volume that is based on the BETisotherm scfton
va_Langmuir frac14 adsorbed gas volume that is based on the Lang-muir isotherm scfton
Vb frac14 unit volume of bulk rock m3
vf_BET frac14 free-gas volume that is based on the BET iso-therm scfton
vf_Langmuir frac14 free-gas volume that is based on the Langmuirisotherm scfton
vL frac14 Langmuir volume scftonvm frac14 maximum adsorption-gas volume for a complete
unimolecular layer scftonv( p) frac14 gas volume of adsorption at pressure p scfton
vt_BET frac14 total gas volume that is based on the BET iso-therm scfton
vt_Langmuir frac14 total gas volume that is based on the Langmuirisotherm scfton
a_Langmuir frac14 porosity of adsorbed gas that is based on Lang-muir isotherm
a_BET frac14 porosity of adsorbed gas that is based on BETisotherm
qa frac14 adsorbed-gas mass per unit shale volume gm3
qb frac14 bulk density of shale gcm3
qg frac14 free-gas density gm3
qs frac14 adsorbed-gas density gcm3
Acknowledgments
We express our gratitude for financial support from the Chief Oiland Gas We also thank the contribution of Mark Kurzmack atWeatherford Laboratories for providing the detailed descriptionof isotherm measurements We also acknowledge Computer Mod-elling Group for providing the CMG software for this study
References
Ambrose R J Hartman R C Diaz-Campos M et al 2012 Shale Gas-
in-Place Calculations Part 1 New Pore-Scale Considerations SPE J 17
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
Petroleum Engineering Conference Mexico City Mexico USA
16ndash18 April SPE-153391-MS httpdxdoiorg102118153391-MS
Gao C Lee J W Spivey J P et al 1994 Modeling Multilayer Gas Res-
ervoirs Including Sorption Effects Presented at the SPE Eastern Re-
gional Conference and Exhibition Charleston West Virginia USA
8ndash10 November SPE-29173-MS httpdxdoiorg10211829173-MS
Hao S Chu W Jiang Q et al 2014 Methane Adsorption Characteris-
tics on Coal Surface Above Critical Temperature Through Dubinin-
Astakhov Model and Langmuir Model Colloids and Surfaces A Phys-icochemical Eng Aspects 444 104ndash113 httpdxdoiorg101016
jcolsurfa201312047
Kang S M Fathi E Ambrose R J et al 2011 Carbon Dioxide Storage
Capacity of Organic-rich Shales SPE J 16 842ndash855 SPE-134583-
PA httpdxdoiorg102118134583-PA
Kuila U and Prasad M 2013 Specific Surface Area and Pore-size Distri-
bution in Clays and Shales Geophysical Prospecting 61 341ndash362
httpdxdoiorg1011111365-2478
Lane H S Watson A T and Lancaster D E 1989 Identifying and
Estimating Desorption From Devonian Shale Gas Production Data
Presented at the SPE Annual Technical Conference and Exhibition
San Antonio Texas USA 8ndash11 October SPE-19794-MS http
dxdoiorg10211819794-MS
Langmuir I 1918 The Adsorption of Gases on Plane Surfaces of Glass
Mica and Platinum J Am Chem Soc 40 1361ndash1403 http
dxdoiorg101021ja02242a004
Leahy-Dios A Das M Agarwal A et al 2011 Modeling of Transport
Phenomena and Multicomponent Sorption for Shale Gas and Coalbed
Methane in an Unstructured Grid Simulator Presented at the SPE An-
nual Technical Conference and Exhibition Denver USA 30 Octoberndash2
November SPE-147352-MS httpdxdoiorg102118147352-MS
Lu X Li F and Watson A T 1995 Adsorption Measurements in De-
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 11 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
2015 SPE Journal 11
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132
12 2015 SPE Journal
Wei Yu is a research associate in the Harold Vance Depart-ment of Petroleum Engineering at Texas AampM University Hisresearch interests include reservoir modeling and simulation ofshale-gas and tight oil production carbon dioxide enhancedoil recovery (EOR) in tight oil reservoirs and nanoparticles EORYu has authored or coauthored more than 50 technicalpapers and holds one patent He holds a BS degree in appliedchemistry from University of Jinan in China an MS degree inchemical engineering from Tsinghua University in China and aPhD degree in petroleum engineering from the University ofTexas at Austin Yu is an active member of SPE
Kamy Sepehrnoori is a professor in the Department of Petro-leum and Geosystems Engineering at the University of Texas atAustin where he holds the W A (Monty) Moncrief CentennialChair in Petroleum Engineering His research interests andteaching include computational methods reservoir simula-tion parallel computing EOR modeling naturally fracturedreservoirs and unconventional resources Sepehrnoori is the
director of the Reservoir Simulation Joint Industry Project in theCenter of Petroleum and Geosystems Engineering He holds aPhD degree from the University of Texas at Austin
Tadeusz W Patzek is a professor in the Department of Chemi-cal and Petroleum Engineering at King Abdullah University ofScience and Technology where he is the director of theUpstream Petroleum Engineering Research Center Beforethat Patzek was professor and chair of the Department of Pe-troleum and Geosystems Engineering at the University of Texasat Austin His research involves mathematical (analytic andnumerical) modeling of Earth systems with emphasis on multi-phase-fluid-flow physics and rock mechanics Patzek alsoworks on smart process-based control of very large water-floods in unconventional low-permeability formations and onthe productivity and mechanics of hydrocarbon-bearingshales He holds MS and PhD degrees in chemical engineeringfrom the Silesian Technical University in Poland
J170801 DOI 102118170801-PA Date 19-December-15 Stage Page 12 Total Pages 12
ID balamuralil Time 0902 I Path SJVol00000150132CompAPPFileSA-J150132