7/27/2019 Reservoir Evaluation of Horizontal Wells http://slidepdf.com/reader/full/reservoir-evaluation-of-horizontal-wells 1/16 S SPE 22389 Reservoir Evaluation of Horizontal Bakken Well Performance on the Southwestern Flank of the Williston Basin M.R. Reisz, Union Texas Petroleum SPE Member Copyright 1992, Society of Petroleum Engineers, Inc. This paper was prepared for presentation at the SPE International Meeting on Petroleum Engineering held in Beijing, China, 4 7 March 1992. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author s . Contents of the paper, as p re sen ted , have n ot b ee n reviewed by the Society of Petroleum Engineers a nd a re su bj e ct to correction by the author s . T h e m ate,ri al , as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers pressnted at SPE meetings aresubject to publication review by Editorial Committees ofthe Society of PetroleumEngineers. Permissionto copy s restricted to an abstractofnotmorethan300words.Illustrations maynotbe copied. Theabstmct sh Uld contain conspicuousacknowledgment o f whe re a nd by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL. STR CT This paper presents the results of a reservoi r performance study for hori zonta 1 and vertical Bakken wells in the Fairway of the Williston Basin. A combination of forecasting methods were utilized including decline curve analysis, material balance, analytical solutions, and empirical correlations. The results indicate that recoverable reserves from hori zonta1 well s the Fairway are 2.5 to 3.0 times a vertical well for 1.5 to 2.0 times the cost .. Simple theoretical calculations combined with field data are useful in making initial estimates of original oil in place, recoverable reserves, and drainage area. INTRODUCTION The Bakken formation, located in northwestern North Dakota and northeastern Montana (Figure 1), is the source of a large portion of the oil generated and produced in the Williston Basin. The Mississippian Devonian age Bakken shale is a n at ur al ly fractured formation that is both source and reservoir rock. The Bakken consists of three members. References and illustrations at end of paper. 9 The upper and lower members are black shales, and the middle member is a dolomitic shaley si1tstone. Located above the Bakken is the Lodgepole (dense lime), and below is the Three Forks sand. The overpressured Bakken, found at approximately 10,000 [3048 m] with a virgin reservoir pressure corresponding to a 0.6 to 0.7 psi ft gradient [13.6 - 15.8 kPa/m], has g n r t ~ over 100 billion barrels [15.9 E 09 m] of oil based on industry estimates. The key to Bakk,en producti on, in the mature portion of the Williston Basin, is having a permeable interval in which to put the oil after it has been generated. Both the Lodgepole and Three Forks have potential oil storage capacity. The Antelope field located on the Nesson Anticline in northeastern McKenzie County, is a good example of increasing the available storage capacity with the presence of a permeable sand below the Bakken. Figure 2 shows the location of the study area in Billings and McKenzie counties along the Billings Nose Trend. This area is referred to as the Fainilay . In the Fairway only the upper Bakken is considered net pay, and future discussi on will refer to the upper Bakken as Bakken.
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7/27/2019 Reservoir Evaluation of Horizontal Wells
Reservoir Evaluation of Horizontal Bakken Well Performance on
the Southwestern Flank of the Williston Basin
M.R. Reisz, Union Texas PetroleumSPE Member
Copyright 1992, Society of Petroleum Engineers, Inc.
This paper was prepared for presentation at the SPE International Meeting on Petroleum Engineering held in Beijing, China, 4 7March 1992.
This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author s . Contents of the paper,as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author s . The mate,rial, as presented, does not necessarily reflect
any position of the Society of Petroleum Engineers, its officers, or members. Papers pressnted at SPE meetings are subject to publication review by Editorial Committees of the Societyof Petroleum Engineers. Permissionto copy srestricted to an abstract of notmorethan300 words. Illustrations maynotbe copied. Theabstmct sh Uld contain conspicuousacknowledgmentof where and by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL.
STR CT
This paper presents the results of areservoi r performance study for hori zonta1and vertical Bakken wells in the Fairway ofthe Williston Basin. A combination offorecasting methods were utilized includingdecline curve analysis, material balance,analytical solutions, and empiricalcorrelations.
The results indicate that recoverablereserves from hori zonta1 well s the Fairway are 2.5 to 3.0 times a verticalwell for 1.5 to 2.0 times the cost .. Simpletheoretical calculations combined with fielddata are useful in making initial estimatesof original oil in place, recoverablereserves, and drainage area.
INTRODUCTION
The Bakken formation, located in northwesternNorth Dakota and northeastern Montana
(Figure 1), is the source of a large portionof the oil generated and produced in theWilliston Basin. The Mississippian Devonianage Bakken shale is a natural ly fracturedformation that is both source and reservoirrock. The Bakken consists of three members.
References and illustrations at end of paper.
9
The upper and lower members are black shales,and the middle member is a dolomitic shaleysi1tstone. Located above the Bakken is theLodgepole (dense lime), and below is theThree Forks sand. The overpressured Bakken,found at approximately 10,000 [3048 m] witha virgin reservoir pressure corresponding toa 0.6 to 0.7 psi ft gradient [13.6 - 15.8kPa/m], has g n r t ~ over 100 billionbarrels [15.9 E 09 m] of oil based on
industry estimates.The key to Bakk,en production, in the matureportion of the Williston Basin, is having apermeable interval in which to put the oilafter it has been generated. Both theLodgepole and Three Forks have potential oilstorage capacity. The Antelope field locatedon the Nesson Anticline in northeasternMcKenzie County, is a good example ofincreasing the available storage capacitywith the presence of a permeable sand belowthe Bakken.
Figure 2 shows the location of the study areain Billings and McKenzie counties along theBillings Nose Trend. This area is referredto as the Fainilay . In the Fairway onlythe upper Bakken is considered net pay, andfuture discussion will refer to the upperBakken as Bakken.
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2 RESERVOIR EV LU TION OF HORIZONT L B KKEN WELL PERFORM NCE SPE 22389
ORIGIN L OIL IN PL CE
For singl e phase flow another form of thematerial balance equation is
Calculation of the original Bakken oil inplace is a non-unique answer, due to thenumber of unknowns in a fractured reservoir.
In a conventional homogenous reservoir,original oil in place can be determinedvolumetrically from the relationship 1,2
· 1
· 2
· 3
N= NpBo / Bo - Boi
7758A l -Sw
Bo
In the Bakken, there is uncertainty in botharea (A) and thickness h . Therefore,another approach is needed to arrive atsatisfactory answers. The obvious method isa form of the material balance equation,which assumes that reservoir voidage causedby production of reservoir fluids is equal to
expansion of reservoir fluids due to a dropin pressure. By definition original oil inplace (N) can be represented in simplest formby the equation 1,3
U OILQt=Qi [ l - OOIP RF ]
This equation 4 is helpful in reservoirs withsingle phase flow where little is known aboutthe reservoir properties. By utilizing therelationship in equation 3 and solving forOOIP, one gets
OBJECTIVES
Several key points are supported byperformance data: an average initial declineof 40-45 , a final decl ine' of 25-35 , abreakeven point of approximately 150 M O
[23.8 E+03 m] at NPV(15) = 0, recoverablereserves 2.5-3.0 times a vertical well, and20-25 of recoverable reserves produced infirst year.
Since 1ate 1987 the Bakken pl ay has beendomi nated by' hori zonta1 dri ll-jng. There areapproximately 140 horizontal wells that haveproduced oil from the Bakken formation, andan equal number of vertical wells.
The real challenge, in an area of horizontaldevelopment, is to make an early and accurateeva1uati on of performance characterist ics,recoverable reserves, and drainage area.Management needs th i s data to make adetermi nat ion of the economi c vi abil ity forhorizontal development in a play such as theBakken. The factors which control Bakkenproduction were studied, and key reservoirparameters were identified for early analysisof recoverable reserves. The range ofultimate recoveries for Bakken drainholesindicate that no single factor can accurately
predict future performance. Results fromdecl ine curve analysis were compared withanalytical solutions and material balance togain a higher confidence level in the rangeof estimated values.
The main goals of this work included:
• 4. Estimation of original oil in place,recoverab1e reserves, and drai nage areas.
2. Early evaluation of plays through theidentification of key parametersaffecting well performance.
A total of 21 wells from 7 fields in the Fairway were studied in deta.il. This group
of wells are referred to as Group A . Theselection criteria for the study groupincluded: a minimum of 1 year productionhistory, and data availablle on azimuth,length of drainhole, path of drainhole, andnet pay.
The following sections discuss initialestimates and results obtained in this study.
OOIP= U OIL l -Q t /Q i RF
This equation is valid for L/2Xe penetrationratio > 0.5 and Qt/Qi ratio> 0.5 earlytime data . One can now calculate OOIP withan equation that utilizes rate-timerelationships, and compare the results with
other methods. One can also set equation 4equal to equation 1 and solve for drainagearea (A). This equation is represented by
Area = UM OIL (BO) I-Qt/Qi (RF) 0 h (I-Sw) (7758)
· 5
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The results obtained from these equations arein the range 2.0 to 2.7 MM O [318-429 E+03m] per square mile [2.6 km
Table 1provides OOIP and other pertinent informationon Bakken drainho1es selected from different
fields throughout the Fairway . Productiondata has been updated through February 1991.
The magnitude of fracture volume as a percentof total oi l in place is an important number.An examination of storage capacity infractures indicates t ha t l ess than 10 of thetotal oil in place may be stored in thefractures of the upper Bakken member. Thisnumber is consistent with empiricalcorrelations from Nelson 5 .
In summary, a number of different approaches
were used to obtain estimates of OOIP,including volumetric, material balance 3 6 andJoshi s OOIP equation 4. The range of 2.0 to2.7 MM O [318-429 E+03 m] per square mile[2.6 km
2] is a reasonable approximation.
RECOVERABLE RESERVES
Vertical Wells
Good agreement has been obtained in theestimation of recoverable oil from verticalBakken wells using both decline curveana1ys is and log of pressure versus
cumulative production plots. Vertical Bakkenreserves average 108 M O per well [17.2 E+03m] from a data se t of 119 wells in the Fairway .
The decline characteristics of the verticalwells were very predictable. The vastmajority of vertical Bakken wells had declinerates between 15-17% with a range of 10-20%.Wells with a 10-12% decline and goodproductivity were connected to an effectivefracture system and a large drainage area.
Horizontal Wells
Horizontal drainho1es exhibit a number ofdecline characteristics resulting from avariety of factors. The initial decline isassociated with the effectiveness of thefracture system and size of the area beingdrained. Figures 3, 4, and 5 show individualperformance data from Table 1. These threewells have estimated recoverable reserves in
11
excess of 400 per well [63.6 E+03 m] ,
and should give insight concerning horizontalBakken performance characteristics.
Figure 3 shows Meridian #33-11H in theElkhorn Ranch area. This well has ac ~ m u 1 a t i v e production of 280 M O [44.5 E+03m] through February of 1991 and estimatedrecoverable reserves of 442 M O [70.3 E+03m The initial stabilized rate was 300BOPO [47.7 m/d ] followed by a 55 decline.The current dec line rate is 25%. The well inFigure 4 has excellent production for thefirst si x months with ini}ia1 production inexcess of 600 BOPO [95.4 m/d]. The #1-7 hasan overall decll ine rate of 56 with a 25
decline for the last si x months. The wellhas a cumulative of 131 M O [20.8 E+03 m]
and estimated recoverable reserves of 405M O
[64.4 E+03 m] • Figure 5 shows a consistent31 decline, a cumulative of 160 M O [25.4E+03 mJ and an estimated 425 M O [67.6E+03 m] of reserves from the #14-27H.Dec1ine performance is a funct ion of theeffective areal extent of the fracture systemand the permeability of the fracturesintersected by the we11bore.
Table 1 shows calculated drainage areasrangi ng from 469 acres [1898 E+03 m ] for#14-27H to 664 acres [2687 E+03m2
] for#33-11H. Three wells listed in Table 1 from
the Bicentennial area are estimated to haverecoveries in the 150-200 M O [23.8-31.8 E+03m] range with calculated drainage areas of210-230 acres [fl50-931 E+03 m] •
Figure 6 is a plot of rate versus time forthe entire Rough Rider Field. Normal izingand grouping of production data can yieldpredictive characteristics early in the lifeof wells. The Rider Field has averaged286 BOPO [45.5 m/d ] from 10 wells in thefirst month, and has a decline rate of 25%.
Figure 7 is a normalized plot of the entire
Group A wells, and conta ins performancetrends representative of a Bakken welllocated in the Fairway . Figure 7illustrates an initial decline of 40-45% from21 wells in the first two years, followed bya 25-35% decline. An overall decline rate of30-35% can be anticipated. Figures 8 and 9show the distribution of first monthproduction rate and recoverable reserves.
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4 RESERVOIR EVJILUATION OF HORIZONTAL BAKKEN WELL PERFORMANCE SPE 2238
Approximately 70 of Group A wells have astabili zed ihitial rate of 200 BOPD [31.8m/d ] or greater and 48 have recoverablereserves greater than 200 O [31.8 E+03 m
Group A reserves range from 35 O to 442 O [5.6-70.3 E+q3 m] with an average of 223 O [35.5 E+03 m] .
Key Parameters
The range of ultimate recoveries for Bakkendrainholes dictates that a list of keyparameters be identified for earlyevaluation. Unfortunately for horizontaldrainhole analysis, there is no single factorthat can accurately predict futureperformance. Tables 2A-2C are key criteriacharts. Each table consists of a number of
parameters that should be considered in theearly evaluation of ultimate recoveries.Zonal penetration 7 within the pay, drainholepath, ori entat ion, product ivi ty and afracture index are al l key parameters. Theseparameters were reviewed, ranked, and a valueassigned to arrive at a composite successfactor. The ranking scale A through E)utilized in this study is shown in Table 2A.
Table 2A shows the same wells listed inTable 1. These wells have an averagerecovery of 261 O [41.5 E+03 m] • Table2B and Table 2C provide examples of other
combi nat ions of well s ba:sed upon theselection criteria chosen in each table.
Meridian 14-27H in the Rough Rider area bothave calculated drainage areas Table 1) ithe 400-500 acre [1619-2023 E+03 m] rangeBoth are expected to have recoveries iexcess of 400 O [63.6 E+03 m Severaother wells in Table 1 have calculate r i n ~ e areas in the 200-300 acre [809-121E+03 m] range. At this time, it is noknown whether these values are representativdrainage areas or are influenced by the Qt/Qratio in the drainage area formulaAdditional work in this area is planned.
Joshi s paper on Methods Calculate AreOra ined by Hori zonta1 Well s 8 was verhelpful in calcul ating the drainage area oBakken wells. For optimum recoveries fromhorizontal drainholes, industry must have
good understanding of drainage areas and thproper spacing of wells. The calculatedrainage areas in Table 1 were obtained usinequation 5.
The physical 3D model for a horizontadrainhole and its drainage area is defined bFigure 10 9 . The drainhole length (L) is ithe x direction. This is the lowpermeability direction of the reservoir, anis perpendicular to the dominant naturafractures. The sides of the drainagrectangle are 2Xe and 2Ye. The thickness othe reservoir (h) is in the z direction
The Xw and Yw values represent the locatioof drainhole along the x and y axes.
The effective permeability in the horizontaplane of an anisotropic reservoir is equal tothe square root of Kx times Ky. Threctangular drainage area of a vertical welcan be represented by the equations 8
Tables 2A-2C support and identify a broadrange of ult imate recoveri es for a Bakkendrainhole. This approach allows foridentification of key parameters, and anearly analysis of successful wells. It alsoprovi des a method to quant i fy the factorsthat affect horizontal performance, and toevaluate how critical a particular parameteris in a given play. Recoverable reserves inTables 2A-2C support an ultimate recovery of2.5 to 3 times a vertical well.
DRAINAGE AREA
Much work remains in determination ofdrainage areas for horizontal drainholes.Different reservoir conditions and geometrieswill have an effect on actual drainage areas,and must be considered in the evaluation.The Slawson 1-7 in the Ash Coulee area and
12
2 Xe ) 2 Ye) = Area 43560)
and
e / 2Xe = ..jXy
in an anisotropic reservoir 8
can be rewritten as
2Ye = 2Xe..jXy
· 6
· 7
Equation
· 8
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Solving equations 6 and 7 simultaneously, oneobtains the drainage lengths for a vert ica lwell in an anisotropic reservoir, assumingthat drainage area and permeabil i ty values
are known.
One can calculate 2Xe drainage length for ahorizontal drainhole based upon the followingassumption; 2Xe is equal to the drainholelength (L) in the x direction plus drainageradius of the vertical well at each end ofthe horizontal drainhole 8 Thisrelationship can be stated as
9)
Figure 9 represents an idealized view of
drainage volume for both vertical andhori zonta1 well s. Dra inage 1ength for ahorizontal drainhole along the highpermeability direction Ye Figure 10) isassumed to be the same as the vertical well.
Per Joshi 9 , the two following relationshipsgive a comparison of horizontal drainage area(Ah) to vertical drainage area (Av).
See Appendix A for an example problemutilizing well and reservoir parameters fromthe first horizontal drainhole in the Bakkenformation, Meridian #33-11H. (Note:Production data and calculations have notbeen updated. This example representsinitial results.) A summary of the wellparameters both known and assumed arecontained in Table 3. Reservoir parametersare summarized in Table 4. In Appendix Aseveral different methods, including Joshi smethod 8 , will be presented and results
compared.In summary, horizontal drainage area (Ah) istwo to three time Av vertical drainagearea). This means that a horizontal Bakkendrainhole should achieve a drainage areabetween 320 - 480 acres [1295-1942 E+03 m]
where a vertical Bakken well drains 160 acres[647 E+03 m] For a ver tical Bakken wellthat drains 320 acres [1295 E+03 m] the
horizontal well could drain 640 + acres [2590E+03 m Based upon an average verticalwell recoveringr 108 O [17.2 E+03 m] andthe increased drainage area from horizontal
wells, a horizontal drainhole should recover300 O [47.7 E+03 m ] for a dra inho1e 1engthof 2000 feet [510 mJ. This is consistentwith other work in the report and offers ahigh level of confidence in the ultimaterecovery expected from a hori zonta1 Bakkendrainhole.
PRODUCTIVITY PROBLEMS
A revi ew of performance data 10,11,12 and keyparameters in the planni ng and drill i ng ofBakken horizontal drainholes reveals fourmajor reasons fl:>r 1ess than ideal results:
1. Formation damageThe inability to effectively removeformat ion damage wi become worseas the reservoir pressure decreases.
2. OverdrillingCurrent well spacing in the Fairway appears too dense in someareas for horizontal drainholes.
OrientationIdeally the drainhole is paral le l tothe 10 .' permeabil i ty direct ion ofthe resl rvoi r.
Porpo is iProblems at the well site can preventzonal penetration in the desiredhorizontal segment of the drainhole.
For the majority of the prospective Bakkenacreage in the Williston Basin, i t may not beenough to encounter fractures. Initially theoverpressuring of the Bakken enhances theeffect iveness I:>f the fracture network.However, as the pressure in the reservoi r fractures) decreases, the effect iveness ofthe fractures may also decrease. Therefore,i t is desirable to prop the fractures around
the wellbore open for optimum long-termproductivity.
Format ion damagl is a major concern in theBakken. The invaded zone around the well boremay reduce well productivity. Thus, a keybenefit in the drilling of horizontaldrainholes may be lost or reduced. Thiscond i t ion wi be more prevalent whenexcessive mud weights are used to control
13
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6 RESERVOIR EVJlILUATION OF HORIZONTAL BAKKEN WELL PERFORMANCE SPE 2238
problems of hole stability or when a portionof r e s ~ r v o i r is partially depleted.Undoubtedly, fracture collapse and nearwell bore formation damage have occurred andprevented some of the Bakken horizontaldrainholes from achieving their productivepotential
ROCK AND FLUID PROPERTIES
Arange of rock and fluid property values forthe Bakken have been identified to assist inthis study and future analytical studies.
Although there are large amounts of dataavailable concerning rock and fluidproperties in the Bakken, there does not seemto be a consensus about the critical
parameters. Core data, DST's, reservoirfluid studies, pressure build-ups, etc havebeen obtained by numerous operators, butnever incorporated into a c:ommon databaseavailable to the general industry. In 1990,a group of companies began a cooperativeeffort to gather Bakken data.
Tables 5 and 6 13 display a l ange of valuesfor different parameters that were utilizedin this study. Core analysis on Union TexasPetroleum s Federal 12-1 located in Sec. 12,T144N-R102W, indicates an average porosity of3 Permeabilities are in the 0.02 - 0.05 md.
range in the Bakken and 0.25 md. in theLodgepole. The maximum permeability of 0.59md. was recorded from a fractured sample.This well has an EUR of 101 M O [16 E+03 m]
and is representati ve of a typi cal Bakkenwell.
RECOVERY FACTORS
Documented numbers are not available forrecovery factors in horizontal Bakken wells.Joshi indicates a 16 recovery factor is agood approximation and is consistent with the15 to 20 range listed in Table 5. Thesenumbers were obtained from commi ss ion heari ngexhibits. Joshi has indicated that increasedrecovery factors from drainholes may be2 - 5 higher than for vertic:al wells 8 9
FUTURE WOR
Our understanding of fractured reservoirwill increase dramatically with continuedapplication of horizontal drainholtechnology. Additional study orel ationships and plotting parameters wilimprove early answers when limited data iavailable.
Two major concerns in the Bakken shale arthe 1ocation and productivi ty of unproppenatural fractures It is necessary to havalternatives for wells that do not perform aplanned. Future work may include:
1. Additional refinements in bothcompletion and stimulation techniques
A wellbore mini frac .2. Better definition of fracture areas.3. Solutions to hole stability4. Improved analytical models.5. Improved methods for early analysis.
CONCLUSIONS
Drainage area and recoverable reservefor a horizontal well are 2.5 to 3.0times that of a vertical well.
2. Original oil in place in the Fairway
ranges from 2.0 MM O to 2.7 MM O429 E+03 m] per square mile [2.6 km].
3. Recoverable reserves of 200-250 M O
[32-40 E+03 m] with better wellrecovering 300-500 M O [48-79 E+03 m
4. Fracture network effect i veness determi neproductivi ty and dec1ine characteri st ics
5. Average initial decline is 40-45% withfinal decline of 25-35%.
6. Bakken drainholes, usually recover 20-25%of their reserves in the first year.
7. Formation damage ,can have significanimpact on productivity.
8. Effective H (thickness) of the reservoiis larger than the actual thickness (hof the upper Bakken shale.
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The author wishes to thank the management ofUnion Texas Petroleum for their support inthe publication of this study. The valuableinput and insights from D.T. Boyd and V.K.Bangia are greatly appreciated. C.D. Croweand S. Housley did a great job in preparation
of manuscript and tables.
e externalf = fractureh = horizonta'i
n = net drainhole lengthp = produced oilv = verticalW= wellbore
1. Frick, T.C., Petroleum ProductionHandbook P = 37-10 thru 37-12, MilletThe Printer, Inc. , Dallas, Tx., 1962.
2. Agulleria, R., The Uncertainty ofEvaluating Original Oil-In-Place inNaturally Fractured Reservoirs , SPWLA19th Annual Logging Symposium June 1316 1978.
3. ORYX North Dakota Industrial CommissionHearing, Case No. 5030 Exhibit 6.
4. Joshi, S.D., Production ForecastingMethods for Horizontal Wells , SPE 17580SPE International Mtg. Tianjin, ChinaNov. 1-4, 1988.
5. Nelson, R.ll., Geologic Analysis ofNatura y Fractured Reservoi rs, Chapt. 1P = 72-102 t Gulf Publishing CompanyHouston Tx., 1985.
6. King G.R., Material Balance Techniquesfor Coal Seam and Devon ian Shale GasReservoirs , SPE 20730 Annual Mtg. inNew Orleans, La., Sept. 23-26, 1990.
7. Williams Petroleum Consulting andMinerals Diversified Services, Inc., Williston Basin Bakken FormationStudies, Part I and II , Industry Reportin 1990.
8. Joshi, S.D., Methods Calculate AreaOra ined By Hori zonta1 Well s , Oi 1 and GasJournal (Sept. 17 1990), P = 77-82.
9. Joshi, S.D., Reservoir Aspects ofHorizontal Wells , SPE Short Course at
the
initial reservoir pressure, psia[kPa]bubble point pressure, psiainitial production rate, BOPD mid
= production rate at time t),BOPD[m3/d ]
= drainage radius, ft. [m]= drainage diameter, ft. [m]= recovery factor, = initial oil saturat ion, = water saturation, = viscosity, cpo [Pa s] half the side of a drainage area
which is parallel to the horizontalwell, ft. [m]
= fracture half length, ft. [m]= distance from drainage boundary to
the center of the drainhole, ft. [m]= drainage length of rectangle
(diameter), ft. [m]
= half the side of the drainage areawhich is perpendicular to thehorizontal well, ft. [m]
distance from the x axis drainageboundary to the dra inho1e, ft. [m]
= side of drainage rectangle inhorizontal plane, ft. [m]
porosity,
a
A
b
Bo
coeEUR
h
PbQiQt
= half the major axis of drainageellipse, ft. [m]
= drainage area, acres [m2]
= half the minor axis of the drainageel l ipse, t [m]
8 RESERVOIR EVtlLUATION OF HORIZONTAL BAKKEN WELL PERFORMANCE SPE 2238
Annual Mtg. in New Orleans, P = 46, Sept.20; 1990:
10. Mukherjee, H., A Parametric Comparisonof Hori zonta1 and 'Vert ical Well
Performance , SPE 18303, Annual Mtg. inHouston, Tx., Oct. 2-5, 1988.11. Karcher, B J Some Practical Formulas
To Predict Horizontal Well Behavior , SPE15430, Annual Mtg. in New Orleans, La.,Oct. 5-8, 1986.
12. Joshi, S.D., Augmentation of WellProductivity With Sl ant and Hori zonta1Wells , Journal of Petroleum Technology(June 1988), P = 729-739.
13. Williams, LT Pressure TransientAnalysis of Horizontal Wells in aNaturally Fractured Reservoir , SPE20612, Annual Mtg. in New Orleans, Sept.
23-26, 1990.
APPENDIX A
EXAMPLE PROBLEM: Drainage Area of theMeridian 33-11H locatedin Sec. 11-143N-102W(Elkhorn Area)
ver tical well (320 acre [1295 E+03 mdrainage case) is 2Xe = 3474 [1059 m] and Y= 4012 [1223 m].
For a horizontal drainhole Xe
can bcalculated from equation 9
. . . . .A-
2Xe = 2082' + 2 (2106 ) = 6294 ft
The rectangular anisotropic drainage lengthfor 33-11H is calculated as 2Xe = 6294[1918 m] and 2Ye = 4012 [1223 m]. Th
r i n ~ e area is equal to 580 acres [234E+03 m] This number is consistent with thdrainage area of 646 acres [2614 E+03 m
which was calculated from equation(material balance).
METHOD 2:
The drainage area of a conventional well ian isotropic reservoir can be obtained by thequation
METHOD 1:
Solving equations A-I and A-2 simultaneously,we obtain
The calculation of the drainage area for ahorizontal drainhole in an anisotropicreservoir such as the Bakken, can be
obtained. Beginning with equations 6 and 7and solving for a 320 acre [1295 E+03 m ]
vertical drainage case (assumed)
. . . . . (A-5
. . . . . (A-6
Area = 4Xe ~
Area = EUR (Bo) (5.615)(RF) h (l-Sw)
From equation 6, the Area would be equal t Xe times 2Ye for a rectangular drainagarea. From equation 8 2Ye can be written iterms of 2Xe for an anisotropic reservoirTherefore, the area of a rectangul aanisotropic drainage area can also brepresented by the equation
. . . . . (A-I)
. . . . . (A-2)
Ye /2Xe = jXy Kx
Ye / 2Xe = 1.155
(2Xe) (2Ye) = 320 x 43560
(1/2Xe) (2Xe) (2Ye) (2Ye)= 320 x 43560 x 1.155
4Ye = 16.1 x 10
2Ye = 4012
Substituting equation A-6 into equation A-
and solving, drainage length (2Xe) i. . . . . (A-3) obtained for a well in an anisotropireservoir where the drainage area is noknown.
Substituting 4012 [1223 m] into equationA-2, 2Xe = 3474 [1059 m]. The rectangularanisotropic drainage lengths for this
4Xe2 = UR Eo 5 .615
RF He f f 0 l -SW
A-7
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Substituting 4784 [1458 m] into equationA-2, Ye = 5526 [1684 m]. The drainage areais equal to 607 acres [2456 E+03 m2]. Thisnumber is consistent with the drainage areaof 646 acres [2614 E+03 m2], which wascalculated from equation 5.
M THO
The average of the area of an ellipse and thearea of a rectangle plus a circle will alsogive a consistent answer 669 acres [2707E+03 m2] .
The area of a rectangle plus a circle isequal to
2Xe) 2Ye) + pie r2ev) / 43560
= 6294 ) 4012 ) + pie 2106)2 / 43560= 859 acres
The average of 478 acres [1934 E+03m2] ellipse and 859 acres [3476 E+03m2] rectangle pl us ci rcl e) is equal to 669acres [2707 E+03 m2].
Area of El lips e = pie a) b)43560
a = Ln / 2 re v
1/2 of major axis1041 + 2106 = 3147
A-8)
A-9)
1/2 of minor axis A-I0)
b = 2106
Area of Ellipse = pie 3147 ) 2106 ) / 43560= 478 acres
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7/27/2019 Reservoir Evaluation of Horizontal Wells