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1-1. IntroductionReservoir stimulation and artificial lift are the twomain activities of the production engineer in the

petroleum and related industries. The main purposeof stimulation is to enhance the property value by

the faster delivery of the petroleum fluid and/or toincrease ultimate economic recovery.Matrix stimulation and hydraulic fracturing areintended to remedy, or even improve, the naturalconnection of the wellbore with the reservoir, whichcould delay the need for artificial lift. This chapter outlines stimulation techniques as tools to help manageand optimize reservoir development.

nderstanding stimulation requires understandingthe fundamental issues of petroleum production andthe position and applicability of the process.1-1.1. Petroleum production

!etroleum reservoirs are found in geologic formationscontaining porous roc". !orosity φ is the fractionof the roc" volume describing the maximum

possible fluid volume that can be stored.!etroleum, often referred to in the vernacular as oil or gas depending on the in#situ conditions of

pressure and temperature, is a mixture of hydrocarbonsranging from the simplest, methane, to longchainhydrocarbons or complex aromatics of considerablemolecular weights. $rude oils are frequentlyreferred to as paraffinic or asphaltenic, depending onthe dominant presence of compounds within those

hydrocarbon families.The phase behavior of petroleum hydrocarbons isusually greatly simplified, separating compounds inthe gaseous phase from those in the liquid phase intotwo pseudocompounds %oil and gas&. The bubblepoint

pressure pb of the mixture becomes important.'f the reservoir pressure is greater than this value,the fluid is referred to as undersaturated. 'f the reservoir

pressure is below pb, free gas will form, and thereservoir is "nown as saturated or two phase. (asreservoirs exist below the dewpoint pressure.!etroleum reservoirs also always contain water.

The water appears in two forms) within the hydrocarbonzone, comprising the interstitial or connatewater saturation S wc, and in underlying water zones,which have different magnitudes in different reservoirs.The connate water saturation is always present

because of surface tension and other adhesionaffinities between water and roc" and cannot bereduced.The underlying water, segregated from hydrocarbons


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by gravity, forms a gas#water or oil#water contact that is not sharp and may traverse severalfeet of formation because of capillary pressureeffects. The water may intrude into the hydrocarbonzone as a result of perturbations made during petroleum

production.The ideas of porosity and connate water saturationare coupled with the areal extent of a reservoir

A and the reservoir net thic"ness h to provide thehydrocarbon volume, referred to as initial#oil#inplaceor initial#gas#in#place)V HC * Ahφ%+ S wc&. %+#+&-ecause oil and gas production rates in the petroleumindustry are accounted in standard#conditionvolumes %e.g., standard pressure p sc * + . psi or + atm 0+ ∼ +12 !a3 and standard temperature T sc *4156 0+2.45$3&, the right#hand side of 7q. +#+ isdivided by the formation volume factor for oil Boor for gas B g .8ells drilled to access petroleum formationscause a pressure gradient between the reservoir

pressure and that at the bottom of the well. 9uring production or in:ection the pressure gradient forcesfluids to flow through the porous medium. $entralto this flow is the permeability k , a concept firstintroduced by 9arcy %+;24& that led to the well"nown9arcy&where pwf and r w are the bottomhole flowing pressureand wellbore radius, respectively.7quation +#> is also well "nown and forms the

basis to quantify the production %or in:ection& of fluidsthrough vertical wells from porous media. 't is

perhaps the most important relationship in petroleumengineering.The permeability k used in 7q. +#> is absolute,implying only one fluid inhabiting and the same fluid

flowing through the porous medium. This is, of course, never true for oil or gas flow. 'n the presenceof another fluid, such as connate water, an effective

permeability is in force, which is usually symbolized by a subscript %e.g., k o& and always implied. Theeffective permeability in a reservoir is smaller thanthe absolute permeability, which may be measuredin a laboratory on cores extracted from the reservoir.'f more than one fluid flows, relative permeabilities


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that are functions of the fluid saturations are ineffect)%+# &where k ro, k rw and k rg are the relative permeabilitiesand k o, k w and k g are the effective permeabilities of oil, water and gas, respectively.7quation +#>, in con:unction with appropriate differentialequations and initial and boundary conditions,is used to construct models describing petroleum

production for different radial geometries.These include steady state, where the outer reservoir

pressure pe is constant at the reservoir radius r e? pseudosteady state, where no flow is allowed at theouter boundary %q * 1 at r e&? and infinite acting,where no boundary effects are felt. 8ell#"nownexpressions for these production modes are presentedin the next section.Regardless of the mode of reservoir flow, the nearwellzone may be sub:ected to an additional pressuredifference caused by a variety of reasons, whichalters the radial %and horizontal& flow converginginto the well.The s"in effect s, which is analogous to the filmcoefficient in heat transmission, was introduced by@an 7verdingen and Aurst %+B B& to account for these phenomena. 6undamentally a dimensionlessnumber, it describes a zone of infinitesimal extentthat causes a steady#state pressure difference, convenientlydefined as%+#2&

Cdding 7qs. +#> and +#2 results in%+#4&where the pwf in 7q. +#4 is different from that in 7q.+#>. C positive s"in effect requires a lower pwf ,whereas a negative s"in effect allows a higher valuefor a constant rate q. 6or production or in:ection, alarge positive s"in effect is detrimental? a negatives"in effect is beneficial.Two extensions of 7q. +#4 are the concepts of effective wellbore radius and the important productivity%or in:ectivity& index.8ith simple rearrangement and employing a basic

property of logarithms, 7q. +#4 yields%+# &Theexpression r we –s is the effective wellbore radius,denoted as r wD. C positive s"in effect causes theeffective wellbore radius to be smaller than the actual,whereas a negative s"in effect has the oppositeresult.C second rearrangement yields


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%+#;&The left#hand side of 7q. +#; is the well productivity%or in:ectivity for pwf E p& index.The entire edifice of petroleum production engineeringcan be understood with this relationship.6irst, a higher kh product, which is characteristicof particular reservoirs, has a profound impact. Thecurrent state of worldwide petroleum production andthe relative contributions from various petroleumproducing

provinces and countries relate intimatelywith the kh products of the reservoirs under exploitation.They can range by several orders of magnitude.There is virtually nothing that a petroleum engineer can do to substantially alter this situation. Mature

petroleum provinces imply that following theexploitation of far more prolific zones is theexploitation of increasingly lac"luster zones withsmall "h values, which characterize more recentlydiscovered formations.C second element of mature fields is reservoir

pressure depletion, the effect of which can be seenreadily from 7q. +#;. Clthough the right#hand sideof the equation may be constant, even with a high"h, the production rate q will diminish if p pwf isreduced. 6or a constant pwf, reduction in the reservoir

pressure p has this effect.The role of the petroleum production engineer,who must deal with the unalterable "h and pressureof a given reservoir, is to maximize the productivityindex by reducing the s"in effect and/or the required

bottomhole flowing pressure to lift the fluids to thetop. Maximizing the productivity index by reducingthe s"in effect is central to the purpose of this volumeand constitutes the notion of stimulation? reducingthe bottomhole flowing pressure leads to artificiallift %both gas and pump assisted&. 6inally, the bottomholeflowing pressure may have an allowablelower limit to prevent or retard undesirable phenomenasuch as sand production and gas or water coning.+#+.=. nitsThe traditional petroleum engineering oilfield unitsare not consistent, and thus, most equations that are

cast in these units require conversion constants. 6or example, +/%=F& in 7q. +#> is appropriate if G' unitsare used, but must be replaced by the familiar valueof + +.= if q is in GT-/9 %which must be multipliedalso by the formation volume factor - in R-/GT-&?H is in cp? h, r and rw are in ft? and p and pwf are in

psi. Table +#+ contains unit conversion factors for thetypical production engineering variables.6or unit conversions there are two possibilities.


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7ither all variables are converted and then two versionsof the equation exist %one in oilfield and a secondin G' units&, or one equation is provided and theresult is converted. 'n this volume the second optionis adopted. (enerally, the equations are in the traditionaloilfield units predominant in the literature.+#=. 'nflow performanceThe well production or in:ection rate is related to the

bottomhole flowing pressure by the inflow performancerelationship %'!R&. C standard in petroleum

production, '!R is plotted always as shown in 6ig. +#+.9epending on the boundary effects of the welldrainage, '!R values for steady#state, pseudosteadystateand transient conditions can be developed readily.'n the following sections, the relationships for the three main flow mechanisms are presented firstfor vertical and then for horizontal wells. The expressions, almost all of which are in wide use,arein oilfield units. C complete outline of their developmentis in 7conomides et al . %+BB &.1-2.1. IPR for steady state7quation +#4 can be converted readily to a steadystateexpression by simply substituting p with pe andr with r e. Thus, in oilfield units and with simplerearrangements, the '!R for oil is%+#B&C plot of pwf versus q forms a straight line, the verticalintercept is pe, and the flow rate at the horizontalintercept %i.e., at pwf * 1& is "nown as the absoluteopen#flow potential. The slope is, of course, constantthroughout the production history of the well, assumingsingle#phase flow, and its value is exactly equalto the reciprocal of the productivity index.6or gas, the analogous expression is approximately%+#+1&where Z

—

is the average gas deviation factor %fromideality&,T is the absolute temperature in 5R, and µ – is the average viscosity.7quation +#+1 has a more appropriate form usingthe Cl#Aussainy and Ramey %+B44& real#gas pseudopressure

function, which eliminates the need to averageµ and Z )%+#++&6or two#phase flow, production engineers haveused several approximations, one of which is the@ogel %+B4;& correlation, which generally can bewritten as%+#+=&%+#+>&


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where qo is the oil production rate, qo,max is the maximum possible oil rate with two#phase flow, and AO ! is the absolute open#flow potential of single#phase oilflow.The usefulness of the @ogel approximation is thatit can be used to predict the oil production rate whenfree gas flows %or is present& although only oil propertiesare employed. 6or steady state, 7qs. +#+= and+#+> can be combined with 7q. +#B)%+#+ &The subscript o is added here to emphasize the

point that oil properties are used. The subscript isfrequently omitted, although it is implied. Clthoughneither 7q. +#++ %for gas& nor 7q. +#+ %for twophaseflow& provides a straight#line '!R, all steadystate'!Rs provide a stationary picture of well deliverability.Cn interesting group of '!R curves for oilis derived from a parametric study for different s"ineffects, as shown in 6ig. +#=.I 7xample of steady#state '!R) s"in effect variationGuppose that k * 2 md, h * 2 ft, pe * 2111 psi,

B * +.+ R-/GT-, µ * 1. cp, r e * +211 ft andr w * 1.>=; ft. 9evelop a family of '!R curvesfor an undersaturated oil reservoir for s"ineffects from 2 to =1.Solution

sing 7q. +#B and substituting for the givenvariables)6igure +#= is a plot of the family of '!R curves. 6or a reasonable pwf * =111, the flowrates at s * =1, 1 and 2 are approximately >42,+=>1 and >111 GT-/9, respectively, showing theextraordinary impact of a negative s"in effect.1-2.2. IPR for pseudosteady stateCt first glance, the expression for pseudosteady#stateflow for oil,%+#+2&appears to have little difference from the expressionfor steady state %7q. +#B&. Aowever, the difference issignificant. 7quation +#+2 is given in terms of theaverage reservoir pressure p – , which is not constant

but, instead, integrally connected with reservoir depletion.Material#balance calculations such as the onesintroduced by Aavlena and Jdeh %+B4>& are requiredto relate the average reservoir pressure with time andthe underground withdrawal of fluids.'nterestingly, the productivity index for a givens"in effect is constant although the production ratedeclines because p – declines. To stem the decline, the


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production engineer can ad:ust the pwf , and thus, artificiallift becomes an important present and futureconsideration in well management. Guccessive '!R curves for a well producing at pseudosteady state atdifferent times in the life of the well and the resultingdifferent values of p – are shown in 6ig. +#>.The analogous pseudosteady#state expressions for gas and two#phase production are%+#+4&%+#+ &I 7xample of pseudosteady#state '!R) effect of average reservoir pressureThis example repeats the preceding K7xampleof steady#state '!R) s"in effect variationK %page+# & for s * 1 but allows p to vary from 2111 to>111 in increments of 211 psi.Solution

sing 7q. +#+2 and substituting for the givenvariables %including s * 1&)q * 1. 2% p

pwf &.'n the 6ig. +#> family of '!R curves for differentvalues of p – , the curves are parallel, reflectingthe constant productivity index. %This type of construction assumes that oil remains undersaturatedthroughout? i.e., above the bubblepoint

pressure.&1-2.3. IPR for transient (or infiniteacting)flowThe convection#diffusion partial differential equation,describing radial flow in a porous medium, is%+#+;&wherec t is the total system compressibility, p is pressure,t is time, and r is radial distance. This equation,in wide use in many other engineering fields, providesa well#"nown solution for an infinite#actingreservoir producing at constant rate at the well.

sing dimensionless variables %for oil, in oilfieldunits& for pressure and time, respectively)%+#+B&%+#=1&6or r * r w %i.e., at the well& a useful approximateform of the solution in dimensionless form is simply%+#=+&7quation +#=+ provided the basis of both the forecastof transient well performance and the Aorner %+B2+& analysis, which is one of the mainstays of

pressure transient analysis presented in $hapter =.Clthough 7q. +#=+ describes the pressure transientsunder constant rate, an exact analog for constant pressure


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%+#=4&The large half#axis a of the horizontal drainageellipse formed around a horizontal well within anequivalent radius r eH is%+#= &where r eH is the equivalent radius in a presumed circular shape of a given drainage area. 7quation +#=transforms it into an elliptical shape.7quation +#=2 can be used readily to develop ahorizontal well '!R and a horizontal well productivityindex.C comparison between horizontal %7q. +#=2& andvertical %7q. +#B& productivity indexes in the sameformation is an essential step to evaluate the attractivenessor lac" thereof of a horizontal well of agiven length over a vertical well. Guch comparisongenerally suggests that in thic" reservoirs %e.g., h E+11 ft& the index of anisotropy becomes important.The smaller its value %i.e., the larger the vertical permeability&,the more attractive a horizontal well isrelative to a vertical well. 6or thinner formations%e.g.,h O 21 ft&, the requirements for good vertical

permeability relax.C s"in effect can also be added to the horizontalwell deliverability of 7q. +#=2, inside the large

parentheses in the denominator and multiplied by thescaled aspect ratio & a'# h(%.6or gas and two#phase flow, 7q. +#=2 can bead:usted readily by the transformations %comparedwith 7q. +#B& shown in 7qs. +#++ and +#+ .

6or pseudosteady state, a generalized horizontalwell production model, accounting for any positioningof a well laterally and vertically within adrainage, was presented by 7conomides et al$%+BB4&. The basic model in 6ig. +#2 has reservoir dimensions xe, ) e and h, horizontal well length %andan angle ϕ between the well pro:ection on the horizontal

plane and xe.The solution is general. 6irst, the pseudosteadystate

productivity index * is used)%+#=;&where the reservoir permeability k is assumed to beisotropic throughout %it is ad:usted later& and xe is thewell drainage dimension. The constant allows theuse of oilfield units? the productivity index is inGT-/9/psi. The summation of the s"in effects Σ saccounts for all damage and mechanical s"in effects.6inally, the dimensionless pressure is 7quation +#=B decomposes a three#dimensional%>9& problem into one two#dimensional term andone one#dimensional term. The first term on the


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right#hand side accounts for horizontal positioningeffects, with C H as a shape factor. The second termaccounts for both the reservoir thic"ness %causing adistortion of the flow lines& and the additional effectsfrom vertical eccentricity in the case that the well isnot positioned at the vertical middle of the reservoir.The vertical effects s"in effect s x is %after Puchu" et al$, +B;;&%+#>1&where se is the vertical eccentricity s"in)%+#>+&where + w is the elevation from the bottom of thereservoir. 6or a well at the vertical middle, se * 1.I 7xample calculation of s x for two thic"nessesCssume that %* =111 ft and r w * 1.>=; ft.$alculate s x for h * 21 ft and h * =11 ft.Solution

sing 7q. +#>1 for h * 21 ft)6or h * =11 ft, s x * .4. This calculation suggeststhat for thic"er reservoirs the distortion of the flowlines has relatively more severe detrimentaleffects.6igure +#4 provides values for s x for a rangeof reservoir thic"nesses and a centered well%r w * 1. ft&.6or the case of a vertically eccentered well,6ig. +# provides values for se for various levelsof eccentricity. The values in 6ig. +# are thesame for symmetrical eccentricity? i.e., se is thesame for + w (h * 1.+ and 1.B. Ct + w (h * 1.2,

se * 1, as expected.To account for the position of the well in thehorizontal plane, a series of shape factors is presentedin Table +#=. Clthough the solution presented

by 7conomides et al$ %+BB4& is generaland a computer program is available, the libraryof shape factors in Table +#= is useful for quic" approximations %in the style of the classic 9ietz0+B423 factors for vertical wells&. Multiple horizontalwell configurations are also included.I 7xample calculation of horizontal well productivityindex) comparison with a vertical well

Cssume that %* =111 ft, xe * ) e * = 11 ft,h * =11 ft, r w * 1.>=; ft, B * + R-/GT- andµ * + cp. The well is in the vertical middle %i.e.,

se * 1&. !ermeability k * +1 md. 6or this example,the productivity index is calculated for anisotropic reservoir. Aowever, the permeability of most reservoirs is not isotropic between the verticaland horizontal planes, resulting in a considerable reduction in the productivity index, asshown in the next section.


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Solution6rom the K7xample calculation of s x for twothic"nessesK ( page +#; ), s x * .4, and from Table+#= for xe * ) e and %(xe * =111/= 11 ≈ 1. 2,C H * +. B.

sing 7q. +#=B)and using 7q. +#=;)The productivity index of a vertical well in thesame formation, under pseudosteady#state conditionsand assuming that the well is in the center of the square reservoir, isThe drainage area is = 11 ∼ = 11 ft, resultingin r e * +2=1 ft. Thus,The productivity index ratio between a horizontaland a vertical well in this permeabilityisotropicformation is ++. /+.; * 4. .1-2.!. Permea"ility anisotropy6rom dealing with vertical wells, petroleum engineerslearned to generally ignore the concept of permeabilityanisotropy and refer to reservoirs as having

permeabilities equal to 1.+, >, +11 md, etc., as if permeabilitywere a scalar quantity.Clthough it has been "nown for a long time that

permeability has different values in different directions%i.e., it is a vector& and although the impact of such anisotropy is recognized in waterflooding andeven in the spacing of wells, for production from asingle vertical well it is of little concern. Mus"at%+B> &, in one of his many early contributions, suggestedthat the permeability affecting vertical well

production is%+#>=&where k

–

is the average permeability, which for a verticalwell is equal to the average horizontal permeabilityk

–

H , and k x and k ) are the permeabilities in the x and ) directions, respectively.Clthough the KaverageK permeability in 7q. +#>=could equal +1 md, this value could result because

the permeabilities in the x direction and ) directionare both equal to +1 md or because k x * +11 md andk ) * + md. Aorizontal#to#horizontal permeabilityanisotropy of such magnitude is rare. Aowever, permeabilityanisotropies in the horizontal plane of >)+and higher are common %8arpins"i, +BB+&. Qogically,a horizontal well drilled normal to the maximumrather than the minimum permeability should

be a better producer.


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Guppose all permeabilities are "nown. Then thehorizontal well length, wellbore radius and reservoir dimensions can be ad:usted. These ad:usted variables,

presented by -esson %+BB1&, can be usedinstead of the true variables in predicting well performancewith the model in Gection +#=. )Qength) %+#>>&8ellbore radius) %+#> &where%+#>2&%+#>4&%+#> &%+#>;&%+#>B&%+# 1&I 7xample of horizontal well productivity index inan anisotropic reservoir Repeat the calculations in K7xample calculationof horizontal well productivity index) comparisonwith a vertical wellK %page +#;& but withk x * =1 md, k ) * 2 md %the average horizontal

permeability is still +1 md& and k + * + md.Cssume that the well is parallel to the xe boundary?i.e., the angle ϕ* 1.Solution6rom 7qs. +#>2 and +#>4, α * >.+4 and β *1. 1 , respectively. The horizontal well lengthis then ad:usted using 7q. +#>> and becomesB4 ft. The wellbore radius is ad:usted using7q. +#> and becomes 1.2++ ft. The reservoir dimensions xe, ) e and h are ad:usted using 7qs.+#> through +#>B and become +>1 , =41; and

>= ft, respectively.The vertical effect s"in effect from 7q. +#>1 is

.;2. The ad:usted reservoir dimensions become= xe * ) e. The ad:usted penetration ratio %(xeremains the same %1. 2&. Thus, from Table +#=the shape factor is =.2>.

sing 7q. +#=B for dimensionless pressure andsubstituting with the ad:usted variables)and using 7q. +#=;, the productivity index

becomesrepresenting a 42 reduction from the valueof ++. GT-/9/psi calculated in the precedingK7xample calculation of horizontal well productivityindex) comparison with a vertical wellK for the isotropic case.

1-3. #lterations in t$e nearwell"oreone

The s"in effect s is intended to describe alterations


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in the near#wellbore zone. Jne of the most common problems is damage to the permeability that can becaused by practically any petroleum engineeringactivity, from drilling to well completions to stimulationitself. Cs mentioned in Gection +#+.+, the s"ineffect is a dimensionless number that can beobtained from a well test, as explained in detailin $hapter =.The nature of radial flow is that the pressure differencein the reservoir increases with the logarithmof distance? i.e., the same pressure is consumed withinthe first foot as within the next ten, hundred, etc.'f the permeability of the near#wellbore zone isreduced significantly it is entirely conceivable thatthe largest portion of the total pressure gradient may

be consumed within the very near wellbore zone.Gimilarly, recovering or even improving this permeabilitymay lead to a considerable improvement inthe well production or in:ection. This is the role of matrix stimulation.1-3.1. %&in analysis6igure +#; describes the areas of interest in a wellwith an altered zone near the wellbore. 8hereas k is the KundisturbedK reservoir permeability, k s is the

permeability of this altered zone.The @an 7verdingen and Aurst %+B B& s"in effecthas been defined as causing a steady#state pressuredifference %7q. +#2&. G"in effect is mathematicallydimensionless. Aowever, as shown in 6ig. +#;, itreflects the permeability k s at a distance r s. C relationshipamong the s"in effect, reduced permeabilityand altered zone radius may be extracted. Cssumingthat p s is the pressure at the outer boundary of thealtered zone, from 7q. +#B the undamaged relation is%+# +&and if damaged,%+# =&using the respective values of undamaged ideal anddamaged real bottomhole flowing pressure.7quations +# + and +# = may be combined with thedefinition of s"in effect and the obvious relationship%+# >&to obtain%+# &7quations +# and +#2 can then be combined)%+# 2&which is the sought relationship. This is the well"nownAaw"ins %+B24& formula.7quation +# 2 leads to one of the best "nown conceptsin production engineering. 'f k s O k , the well isdamaged and s E 1? conversely, if k s E k , then s O 1


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and the well is stimulated. 6or s * 1, the near#wellbore permeability is equal to the original reservoir permeability.$ertain well logs may enable calculation of thedamaged radius, whereas pressure transient analysismay provide the s"in effect and reservoir permeability.7quation +# 2 may then provide the value of thealtered permeability k s.6ric" and 7conomides %+BB>& postulated thatin the absence of production log measurements, anelliptical cone is a more plausible shape of damagedistribution along a horizontal well. C s"in effectexpression, analogous to the Aaw"ins formula, wasdeveloped)%+# 4&where & a'# is the index of anisotropy and a sH,max isthe horizontal axis of the maximum ellipse, normalto the well tra:ectory. The maximum penetration of damage is near the vertical section of the well. Theshape of the elliptical cross section depends greatlyon the index of anisotropy.The s"in effect seq is added to the second logarithmicterm in the denominator of the horizontal well

production expression %7q. +#=2& and must be multiplied by & a'# h (%. Jne obvious, although not necessarilydesirable, way to offset the effects of damageis to drill a longer horizontal well.1-3.2. 'omponents of t$e s&in effectMatrix stimulation has proved to be effective inreducing the s"in effect caused by most forms of damage. Aowever, the total s"in effect is a compositeof a number of factors, most of which usuallycannot be altered by conventional matrix treatments.The total s"in effect may be written as%+# &The last term in the right#hand side of 7q. +#represents an array of pseudos"in factors, such as

phase#dependent and rate#dependent effects thatcould be altered by hydraulic fracturing treatments.The other three terms are the common s"in factors.The first is the s"in effect caused by partial completionand slant. 't has been well documented by$inco#Qey et al$ %+B 2a&. The second term representsthe s"in effect resulting from perforations, asdescribed by Aarris %+B44& and expounded upon byPara"as and Tariq %+B;;&. The third term refers tothe damage s"in effect.Jbviously, it is of extreme importance to quantifythe components of the s"in effect to evaluate theeffectiveness of stimulation treatments. 'n fact, the

pseudos"in effects can overwhelm the s"in effect


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caused by damage. 't is not inconceivable to obtains"in effects after matrix stimulation that are extremelylarge. This may be attributed to the usually irreducibleconfiguration s"in factors.1-3.3. %&in effect caused "y partialcompletion and slant6igure +#B is relevant to $inco#Qey et al$ presents the pseudos"in factorscaused by partial penetration and slant. To usethem, it is necessary to evaluate several dimensionlessgroups)$ompletion thic"ness hw" * hw /r w %+# ;&7levation + w" * + w /r w %+# B&Reservoir thic"ness h " * h /r w %+#21&!enetration ratio hw" - h w /h. %+#2+&The terms h " , hw" , + w" /h " and hw" cosθ/h " must

be "nown to evaluate the s"in effect.

Cs an example, assume h "

* +11, + w"

/h "

* 1.2%midpoint of the reservoir& and hw" cosθ/h " * 1.=2%θ * 415, hw /h * 1.2&. 6or this case, sc θ * 2.4 %fromTable +#>&. 'f the penetration ratio is reduced to 1.+,the s"in effect increases to +2.2.'t is apparent that this s"in effect alone coulddwarf the s"in effect caused by damage. The s"ineffect resulting from the partial penetration lengthhw" may be unavoidable because it typically resultsfrom other operational considerations %such as the

prevention of gas coning&.6rom Table +#> and for full penetration it can be

seen readily that a deviated well, without damage,should have a negative s"in effect. Thus, a smalls"in effect or even one equal to zero obtained from a well test in a highly deviated well maymean considerabledamage. Removal of this damage withappropriate stimulation could increase the deviatedwell production %or in:ection& considerably.1-3.4. Perforation s&in effectPara"as and Tariq %+B;;& developed a procedure tocalculate the s"in effect caused by perforations. Thiss"in effect is a composite involving the plane#floweffect s H , vertical converging effect sV and wellbore

effect swb)%+#2=&The pseudos"in factor s H is given by%+#2>&where r w %θ& is the effective wellbore radius and is afunction of the perforation phasing angle θ)%+#2 &where l p is the length of the perforation and αθ is a


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phase#dependent variable and can be obtained fromTable +# .The vertical pseudos"in factor sV can be calculatedafter certain dimensionless variables are determined)%+#22&where h is the distance between perforations and isexactly inversely proportional to the shot density?%+#24&where r perf is the perforation radius? and%+#2 &The vertical pseudos"in effect is then%+#2;&where a and b are%+#2B&%+#41&The values of the constants a +, a =, b+ and b= aregiven in Table +#2 as functions of the phasing angle θ.6inally, the wellbore s"in effect swb can be approximated

by%+#4+&The constants c+ and c= can be obtained fromTable +#4.Cs an example, assume r w * 1. 14 ft, l p * 1.44 ft,h * 1.>>> ft %> shots per foot 0spf3&,k H /k . * >, r perf *1.1=1; ft 01.=2 in.3 and θ * B15.6rom 7q. +#2 and Table +# , r w %θ& * 1. B ft,and thus from 7q. +#2>, s H * 1.42. 6rom 7qs. +#22,+#24 and +#2 , the dimensionless variables h " , r p"and r w" are equal to 1.;4, 1.12 and 1.>;, respectively.6rom 7q. +#2B and Table +#2, a * =.2;, andfrom 7q. +#41 and Table +#2, b * +. >. Then, from 7q. +#2;, sV * +.B, and from 7q. +#4+ andTable +#4,

swb * 1.1=.The total perforation s"in effect obtained with7q. +#2= is equal to +.> for this example.I $ombination of damage and perforation s"ineffectPara"as and Tariq %+B;;& showed that the damageand perforation s"in effect can be approximated by%+#4=&where the perforations terminate inside the damagezone %l p O l / &,r s is the damage zone radius,and % s / &o is the equivalent openhole s"in effect %7q. +# 2&. 'f, for example, l p * +.= ft %r s * +.414ft& and the permeability reduction ratio k /k s * 2,from 7q. +#4= and the perforation s"in effect calculatedin the previous section, % s/ & p * +=.Para"as and Tariq %+B;;& also showed thatthe damage s"in effect for perforations terminatingoutside the damaged zone can be approximated

by


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%+#4>&where s p is the perforation s"in effect evaluatedat the modified perforation length l p and modifiedradius r w )%+#4 &%+#42&The quantities l p and r w are used instead of l pand r w, respectively, to calculate s p as presentedin Gection +#>. .Cssume that in the previous example l / * 1. ft,which ma"es the modified length l p and modifiedradius r w equal to 1.> and 1. =4 ft, respectively.6rom 7q. +#4>, % s / & p * +, which is amar"ed decrease from the value calculated for the length of the damage larger than the lengthof the perforations.1-3.!. Hydraulic fracturing in productionengineering'f removal of the s"in effect by matrix stimulationand good completion practices does not lead to aneconomically attractive well, the potential benefitfrom hydraulic fracturing is illustrated by revisitingK7xample of steady#state '!R) s"in effect variationK%page +# &. 8ith permeability equal to 2 md, thereduction in the s"in effect from +1 to 1 %e.g., pwf *=111 psi& results in production rates of 241 and +=>1GT-/9, respectively, and this difference of 4 1GT-/9 is clearly an attractive target for matrix stimulation.Aowever, at a permeability of 1.12 md, allrates would be divided by +11, resulting in an incremental

production of only 4. GT-/9.'nterestingly, for k * 1.12 md, reducing the s"ineffect to 2 leads to a poststimulation production rateequal to >1 GT-/9 and an incremental productionrate %over the s * +1 case and k * 1.12 md& of about=2 GT-/9. Guch an equivalent s"in effect can be theresult of hydraulic fracturing.C great portion of this volume is devoted to thistype of stimulation, its fundamental bac"ground andthe manner with which it is applied in petroleumengineering. Aere, hydraulic fractures are presentedas well production or in:ection enhancers.!rats %+B4+&, in a widely cited publication, presentedhydraulic fractures as causing an effectivewellbore radius and, thus, an equivalent s"in effectonce the well enters %pseudo&radial flow. 'n other words, the reservoir flows into a fractured well asif the latter has an enlarged wellbore. 6igure +#+1is !rats< development graphed as the dimensionlesseffective wellbore radius r w" versus the relative


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capacity parameter a .The dimensionless relative capacity parameter has

been defined as%+#44&where k is the reservoir permeability, x f is the fracturehalf#length, k f is the fracture permeability, andw is the fracture width.The dimensionless effective wellbore radius issimply%+#4 &Thus, if x f and k f w are "nown %as shown later inthis volume, this is the essence of hydraulic fracturing&,then 6ig. +#+1 enables calculation of the equivalents"in effect s f that the well will appear to havewhile it flows under pseudoradial conditions. $inco s Qey and Gamaniego#@. %+B;+b& laterintroduced adirect correlation for s f %6ig. +#++&.(raphed on the x#axis of 6ig. +#++ is the dimensionlessfracture conductivity C f" , which is simply%+#4;&and is related to !rats< relative capacity by%+#4B&The following example illustrates the impact of ahydraulic fracture on well production.I 7xample calculation of production froma hydraulically fractured well

sing the variables in K7xample of steady#state'!R) s"in effect variationK %page +# & but with k *1.2 md, demonstrate the production improvementfrom a hydraulic fracture at C f" * 2 and x f * 211

ft. Clso, compare this result with the pretreatment production if s * +1 and after a matrix stimulation,assuming that all s"in effect is eliminated % s * 1&.

se pwf * =111 psi.SolutionThe '!R for this well is simply

sing 6ig. +#++ %6ig. +#+1 can also be used& andC f" * 2)which for x f * 211 ft and r w * 1.>=; ft gives

s f * 4. .The production rates at pretreatment % s * +1&,after matrix stimulation % s * 1& and after fracturing

% s * 4. & are 24, +=> and 2+; GT-/9, respectively.I (eneral requirements for hydraulic fractures8hat general requirements should be expectedfrom the design of hydraulic fracturesS Cs discussedin later chapters of this volume, the executionof a hydraulic fracture should provide a fracturelength and propped width, and selection of the

proppant and fracturing fluid is crucial for fracture permeability. -ecause of physical constraints the


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resulting values may not be exactly the desiredideal values, but certain general guidelines should

permeate the design.The dimensionless fracture conductivity C f"is a measure of the relative ease with which thereservoir %or in:ected& fluid flows among the well,fracture and reservoir. Jbviously, in a low#permeabilityreservoir even a fracture of narrow widthand relatively low permeability results de facto ina high#conductivity fracture. The limiting value isan infinite#conductivity fracture, which mathematically implies that once fluid enters thefracture it isinstantaneously transported into the well. Thus, inlow#permeability reservoirs, the length of the fractureis critical and the design must consider thisrequirement. The longer the fracture, sub:ect to theeconomic constraints of its execution, the moredesirable it is.$onversely, for high#permeability reservoirs, asshown by 7q. +#4;, to increase C f" requires increasingthe k f w product. Thus, maximizing conductivitymust be the ma:or result from the design. Crrestingthe length growth and inflating the fracture aremeans to accomplish this purpose. C processinvolving tip screenout %TGJ& has been developed,exactly to effect such a fracture geometry.I Jptimal fracture conductivity8ith advent of the TGJ technique especially inhigh#permeability, soft formations %called frac and

pac"&, it is possible to create short fractures with

unusually wide propped widths. 'n this context astrictly technical optimization problem can be formulated)how to select the length and width if the

propped fracture volume is given. The followingexample from @al" and 7conomides %+BB2&addresses this problem, using the method derived

by !rats %+B4+&.I 7xample of optimal fracture conductivity$onsider the following reservoir and well data)k * 1. md, h * 42 ft, r e/r w * +111, µ * + cp, pe *2111 psi and pwf * >111 psi. 9etermine the optimalfracture half#length x f , optimal propped widthw and optimal steady#state production rate if thevolume of the propped fracture is V f * >211 ft >.

se a value of +1,111 md for the fracture permeabilityk f , ta"ing into account possible damage tothe proppant, and assume that the created fractureheight equals the formation thic"ness. se the$inco#Qey and Gamaniego#@. %+B;+b& graph %6ig.+#++&, which assumes pseudoradial flow.Solution


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The same propped volume can be established bycreating a narrow, elongated fracture or a wide butshort one. 'n all cases the production rate can beobtained from 7q. +#B, which with the incorporationof s f ta"es the formJbviously, the aim is to minimize the denominator.This optimization problem was solved by !rats%+B4+& for steady#state flow. Ae found the maximum

production rate occurs at a * +.=2 %C f" *+.=4 from 7q. +#4B&. 6or this value of a , r w / x f *1.== from 6ig. +#+1 and 7q. +#44 gives

sing V f * =whx f with this x f /w ratio,and x f * >1 ft? hence, w * x f /=111 * 1.1> ft *1. in. 6rom r w * 1.== x f and r w * 1.>> ft, 7q.+# gives r w /r w * e s * B1, and s * %ln B1& *

4.+.6or pe * 2111 psi and pwf * >111 psi, the optimized

production rate is't is necessary to chec" if the resulting halflengthis less than r e %otherwise x f must be selectedto be equal to r e&. Gimilarly, the resulting optimalwidth must be realistic? e.g., it is greater than >times the proppant diameter %otherwise a thresholdvalue must be selected as the optimal width&. 'nthis example both conditions are satisfied.This example provides an insight into the realmeaning of dimensionless fracture conductivity.The reservoir and the fracture can be considered asystem wor"ing in series. The reservoir can deliver more hydrocarbons if the fracture is longer, but

with a narrow fracture, the resistance to flow may be significant inside the fracture itself. The optimaldimensionless fracture conductivity C f",opt * +.=4in this example corresponds to the best compromise

between the requirements of the two subsystems.

1-4. u"ing performance and*+#, analysis

The inflow performance relationships described inGection +#= provide a picture of the pressure andrates that a reservoir with certain characteristics %permeability,thic"ness, etc.&, operating under certain conditions %pressure, mode of flow&, can deliver into

the bottomhole of a well. The fluid must traverse a path from the bottom of the well to the top and theninto surface equipment such as a separator. 6igure+#+= describes such a path, which consists of severalsegments, :oints and valves, all of which cause a

pressure drop. UJ9CQ analysis considers the reservoir/wellbore system and uses calculations of the

pressure loss across each segment to predict the productionrate and identify any restrictions that may


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reduce the hydrocarbon flow rate.Ct its simplest manifestation, for a given wellhead

pressure, tubing performance allows calculation of the required bottomhole flowing pressure to lift arange of flow rates to the top. The total pressure dropin the well consists of the hydrostatic and friction

pressure drops.Geveral correlations for tubing performance are inuse in the petroleum industry %-eggs and -rill, +B >?Aagedorn and -rown, +B42&. -rown %+B &, in awidely used wor", outlined the procedure for pressuredrop calculations in production strings as shownin 6ig. +#+> for two wellhead flowing pressures. Csthe flow rate increases %on the right side of thecurves& the required bottomhole flowing pressureincreases, reflecting higher friction pressures at thehigher rates. Jn the left side of the curves, the peculiar shape is due to liquid holdup? lower rates do nothave sufficient momentum to purge liquid accumulationin the well, resulting in an unavoidable increasein the hydrostatic pressure.The correlations to calculate the required pressuredrops ta"e full account of the phase behavior of the,almost always, two#phase oil and gas mixture. Cnincrease in the wellhead pressure ordinarily resultsin a disproportionate increase in the bottomhole pressure

because the higher pressure level in the tubingcauses a more liquid#li"e fluid and a larger hydrostatic

pressure component %density is higher&.$ombining the tubing performance curve, often

"nown in vertical wells as the vertical lift performance%@Q!&, with an '!R provides the well deliverabilityat the determined bottomhole flowing pressure%6ig. +#+ &.UJ9CQ analysis is one of the most powerful toolsin production engineering. 't can be used as an aid in

both the design and optimization of well hydraulicsand '!R modification. 6igure +#+2 shows one of themost common uses of UJ9CQ analysis. The well'!R is plotted with three @Q! curves %e.g., each correspondingto a different wellhead pressureVand

perhaps a different artificial lift mechanismVin thecase of an oil well or a different tubing diameter in

a gas well&. The three different production rates over time can be balanced against the incremental economicsof the various well completion options.6igure +#+4 demonstrates a single @Q! but threedifferent '!Rs %e.g., each corresponding to a differenthydraulic fracture design&. Cgain, the incremental

benefits over time must be balanced against theincremental costs of the various fracture designs.The use of UJ9CQ analysis as an engineering


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investigative tool is shown in 6ig. +#+ . Guppose thatseveral perforations are suspected of being closed. Ccalculation allowing several different scenarios of the number of open perforations and comparisonwith the actual flow rate can provide a convincinganswer to the problem.

1-!. +ecision process for wellstimulationTo be done properly, the engineering exercise of thedecision process for well stimulation requires considerable"nowledge of many diverse processes. 6ewactivities in the petroleum or related industries usesuch a wide spectrum of sciences and technologiesas well stimulation, both matrix and fracturing. Thisvolume is intended to present these technologies andtheir interconnections.Cs with many engineering processes, stimulation

must culminate in the design, selection of the specifictreatment and, of course, selection of candidatewells. To choose among the various options, of which one is to do nothing, a means for an economiccomparison of the incremental benefits weightedagainst the costs is necessary. 1-!.1. %timulation economics-ecause the whole purpose of stimulation is toincrease the value of the producing property throughan accelerated production rate or increased recovery,economics should be the driver in deciding whether to conduct the stimulation, what type of stimulationto do and which various aspects of the treatment toinclude.Geveral economic indicators can be used to showthe value of stimulation. -ecause of the wide varietyof operating conditions, companies may not have asingle indicator for the KanswerK in all stimulationinvestments. Clthough the common ground in economicsis profit, in many petroleum activities liquidity,ris" and corporate goals may ma"e it necessaryto choose investments that differ from the ultimatemaximum value of a pro:ect.The oldest indicator used in oil production is payouttime, which is the amount of time necessary to

recoup the money invested. 'f the actual time is lessthan the required time, the investment is consideredattractive)%+# 1&where ∆W' is the incremental revenue %minus theincremental expenses and taxes that are due to operations&,' is the time period increments %e.g., years& inwhich it is received, and cost consists of the totalexpenses associated with the stimulation. This indicator


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does not provide for the time value of moneyor the net value %profit& for the operator? rather, itis a measure of liquidity or how fast the investmentwill be recovered.The indicator can be ad:usted to show the timevalue of money %discounted payout&, the hurdle ratenecessary for the company to invest or both factors.The hurdle rate is the annualized percentage of return that must be achieved to ma"e the pro:ect asgood an investment as the average company investment.The discounted payout is%+# +&The interest %hurdle& rate#is the indicator that suggestswhen the investment will be returned withoutlowering the corporate investment returns andaccounting for inflation %time value of money&.8hen the full stream of cash flows for the pro:ectedrelative life of the pro:ect is used, an indicator called net present value %U!@& is defined as%+# =&

U!@ gives a dollar value added to the property at present time. 'f it is positive, the investment is attractive?if it is negative, it means an undesirable investment.

U!@ is the most widely used indicator showinga dollar amount of net return.To get an indicator on relative profitability againstmore global investments such as stoc"s, bonds andcorporate profits, the rate of return %RJR& is used.RJR is simply varying #to get an U!@ equaltozero. That value of #is the RJR. The limitation in

using the RJR indicator is that it does not provide amechanism of how the cash comes in %cash flow versustime&.'n 6ig. +#+; there are two investment possibilities.C has the highest U!@ for small interest rates butfalls off quic"ly with increasing rates, whereas - hasa smaller U!@ with low rates but remains flatter asrates rise. This means that C ma"es more money, butas interest rates rise its return is hurt more than thatfor -. - pays the money bac" with a better RJR,even if it has a smaller U!@ at low interest rates.Cnother indicator of investment profitability is the

benefits to cost ratio %-$R&)%+# >&which shows the relationship of relative return for agiven investment %cost& size. -$R is a good indicator if there are more investment opportunities thanmoney to invest.1-!.2. P$ysical limits to stimulationtreatments


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!hysical limits are dominant aspects for stimulationtreatment decisions as often as economic indicators.6or the well, these include the following)I Maximum allowable treating pressure limits in:ectionrates and the type of treating fluids.I Tubular size limits rates and pipe erosion.I 8ell location size limits the equipment and materialsthat can be used.I Tubular integrity prevents or limits the type of treatments that can be employed without compromise.I $ompletion tools and their location limit wherethe treatment is placed and the magnitude of therates and volumes.I Xonal isolation is whether the zone can be isolatedfrom other intervals through perforating and/or

pipe integrity limitations.Typical reservoir constraints areI production failures) water or gas coning or influx,formation sandingI physical location of the zones and their thic"nesses)

pay zone qualities limit or dictate treatments.

1- . Reser/oir engineeringconsiderations for optimalproduction en$ancementstrategies 0$ost#effective production improvement has been theindustry focus for the past several years. 6racturing,stimulating, reperforating and recompleting existing

wells are all widely used methods with provenresults in increasing the U!@ of old fields. Uowreentry drilling is generating high interest for the

potential it offers to improve recovery from damagedor depleted zones or to tap into new zones at a generallylow cost. Cpplied to mature reservoirs, allthese strategies have the advantage of starting witha fair to good reservoir description as well as awor"ing tra:ectory to the target formation. 7venwhen a new well is drilled, the decision whether todrill a vertical, slanted or horizontal well and how tocomplete the productive interval can profoundly

effect the well


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nearby reservoir limits and reservoir flow characteristics.Creas drained by an isolated well in an effectivelyinfinite reservoir are diagrammed in 6igs.+#+Ba and +#+Bb. C vertical well creates a circular cylinder pressure sin" whereas a hydraulically fracturedwell creates a pressure sin" in the shape of afinite slab with dimensions defined by the formationthic"ness and the total fracture length. 8ith adequatevertical permeability the horizontal well drainagearea is similar to that of a vertical fracture, with thetotal fracture length equal to that of the horizontalwell. The extent of the effective drainage area isapproximately defined by the locus of points equidistantfrom the surface of the pressure sin" associatedwith the well. This forms a circle for a vertical well?an approximate ellipse is formed for hydraulicallyfractured and horizontal wells.8ells drilled in a square pattern impose a squaredrainage area. 6or vertical wells, this is similar to thecircular effective drainage shape %6ig. +#+Bc&, but for horizontal wells, the equivalent drainage efficiencycorresponds to an elongated area. Cs a rule of thumb, the length of the horizontal well drainagearea can be as long as the length of the horizontalwell plus one diameter of the comparable verticalwell drainage area. 6or the case in 6ig. +#+Bd, onehalf as many horizontal wells of the length showncould be used to drain the same pattern, as shown in6ig. +#=1a. 8ith longer horizontal wells, even fewer are required.

6igure +#=1b shows another consideration. 'f thevertical well pattern does not ta"e the direction of maximum horizontal stress σΗ,max into account,hydraulically fracturing the wells may result inunplanned drainage geometries.1- .2. ell drainage /olumec$aracteri ations and productionoptimi ation strategies6igures +#+B and +#=1 assume that the reservoir ishomogeneous and isotropic over vast areas. 'n reality,typical reservoir geology is much more complex.6ormation flow characteristics may favor one well

geometry over others. The chart in 6ig. +#=+ summarizes production optimization strategies for a seriesof +1 common well drainage volume characterizations.The chart addresses five potential well paths)conventional vertical, hydraulically fractured vertical,slanted, horizontal and hydraulically fracturedhorizontal. 6or any one of the drainage volume characterizations,well path options are shown in bloc" diagrams.


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Qaminated reservoirs %chart row on 6ig. +#=+&are a good starting point to understanding the informationin the chart. The chart distinguishes layeredfrom laminated by defining a reservoir as layered if the recognized sands are thic" enough to be targeted

by a horizontal well. 'f not, the reservoir is classedas laminated. 'n general, laminated reservoirs have

poor vertical permeability. C horizontal well is notan option in this case because the productivity would

be severely penalized by the low vertical permeability,and in a thic" formation, a horizontal well maynot even produce the entire formation thic"ness. Cvertical wellVbarefoot, perforated and gravel

pac"ed, or gravel pac"edVcan provide excellent productivity in formations with moderate mobility. Cslanted well can produce a marginal increase in productivityover a vertical well.'n very high mobility laminated reservoirs %such asturbidites&, a frac and pac" may provide sand controland the means to bypass near#wellbore damage.Aowever, in a low#mobility reservoir, hydraulicallyfracturing the well is preferred over any other option

because it provides an effective planar sin", greatlyincreasing the well productivity. 6or thin and laminatedreservoirs, hydraulic fractures in a horizontalwell may be the optimal choice because the longer well provides greater reach that increases the drainagevolume of the well and the hydraulic fracturesenable horizontal flow to the well through the entireformation thic"ness. Aydraulic fractures in a horizontal

well can be planned either as longitudinal, bydrilling the well in the direction of maximum horizontalstress, or as transverse, by drilling the well inthe direction of minimum stress.Aorizontal wells offer particular advantages in naturallyfractured reservoirs %chart row 2 on 6ig. +#=+&when they are drilled normal to the fracture planes.Qocating natural fractures and determining their orientationis crucial to developing the best well designin these formations. Aydraulic fracturing places

proppant in a series of natural fractures, which typicallyresults in a propped fracture that is parallel to

the natural fractures. C horizontal well normal tonatural fractures usually provides better productivitythan hydraulic fracturing.Clthough natural fractures usually are subvertical%nearly vertical&, shallower reservoirs and overpressuredzones may have subhorizontal %nearly horizontal&fractures open to flow. @ertical and slanted wellsare a reasonable choice in these cases. 'n:ection of

proppant into horizontal fractures in overpressured


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zones "eeps them open after production lowers the pore pressure. Jtherwise, the weight of the overburdentends to close horizontal natural fractures.Qi"ewise, high#pressure in:ection can reopen naturalfractures in depleted zones or natural fractures thatwere plugged during drilling.Moving up the chart to the layered reservoirs inrow > offers an opportunity to address the importanceof conformance control. The conventional verticalwell commingles production from multiple layers.!roductivity and storage capacity contrasts canresult in the differential depletion of layers that arenot in hydraulic communication vertically other thanat the well. 'n this case, when the production rate isreduced or the well is shut in, crossflow occurs in thewellbore as the higher pressure layers recharge thedepleted zones. Cnother ris" of commingled productionis that downdip water or updip gas will advanceto the well, resulting in early brea"through of unwanted fluids in the most productive layer or layers.'n this case the oil in the lower productivity layersis bypassed. Reentry drilling offers a modernsolution by targeting the bypassed oil with a horizontalwell.Gtrategies for conformance control begin with perforatingwith a higher shot density in the lower productivitylayers. Aydraulic fracturing in layeredreservoirs can be useful for conformance control,especially if the treatment is phased to target contrastingzones separately. nphased, ill#designed

hydraulic fracture treatments can be detrimentalto production by opening up the high#productivityzones and aggravating the productivity imbalance.C single horizontal well is not an option for a layeredreservoir because it produces from only onelayer, but stac"ed reentry laterals are a highly effectivestrategy. 'n the latter design, the length of thelateral can be roughly inversely proportional to thelayer


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and pac" treatments designed for sand control.-ecause the deviated tra:ectory may be detrimentalto the fracture treatment design, some operatorsdirect the tra:ectory downward to nearly vertical

before passing through the productive formationif hole stability problems do not preclude thisapproach.Ct the top row of the chart in 6ig. +#=+ are thic",homogeneous formations. Cny of the well pathoptions may be applied for these reservoirs. Mobilityextremes may favor hydraulic fracturing, whereasmoderate mobility allows using less expensive, conventionalvertical well completions. C slanted wellmay be more cost effective than hydraulic fracturingor a horizontal well, provided that the ratio of verticalto horizontal permeability is not too small.Aydraulic fractures along a horizontal well can compensatefor a productivity reduction caused by lowvertical permeability in a thic" reservoir.Thic" reservoirs with overlying gas or underlyingwater pose special production problems for whichchart row = on 6ig. +#=+ illustrates some important

points. 'n vertical wells, a strategy to delay bottomwater brea"through is to perforate near the top of the productive interval. Aowever, the pressure gradientresulting from radial flow toward the well is sufficientto draw the water upward in the shape of acone. Jnce the water reaches the deepest perforations,water may be preferentially produced becausethe water mobility may be greater than oil mobility

for low#gravity crudes %owing to the higher oil viscosity&and/or there may be considerable energy tosupport water production because of a strong bottomwater drive. Jnce water brea"through occurs,there may be little further rise of the cone, andadditionaloil production will be at an increasing water cutand marginal. Jne strategy to produce additional oil isto plug bac" the well above the top of the cone andreperforate. Cnother is to try to in:ect gel radially

below the perforations. Ct times, water brea"throughis delayed or avoided with gel in:ection, and the shapeof the cone is widened in any case so that a greater

volume of oil is displaced toward the perforations.C horizontal well drilled near the top of the oilzone above bottomwater produces a pressure gradientnormal to the well, and the bottomwater will risein the shape of a crest instead of a cone. The crestshapedwater advance displaces oil in its path, leadingto greater oil recovery than with a vertical well

by virtue of the flow geometry. 7hlig#7conomideset al . %+BB4& discussed strategies for production


29/32

enhancement under a strong bottomwater drive.!revious wor" cited from the literature has analyticalestimates for brea"through time and indicates thatrecovery efficiency is independent of the productionrate under a strong bottomwater drive. 7hlig#7conomides et al$ showed that the relationship

between recovery and the spacing of parallel horizontalwells is%+# &that recovery efficiency is a simple function of thehalf#spacing between wells)%+# 2&and that the optimal half#spacing between wells is%+# 4&'n these three equations, r . is the fraction of thewell drainage volume occupied by the crest at thetime of water brea"through. 6or the optimal wellspacing from 7q. +# 4 and a well standoff from theoil#water contact + w approximately equal to thethic"ness of the oil column h, the maximum waterfreeoil recovery %assuming piston#li"e displacement&is π/4 * 1.2=>4. 'n this case, the optimal interwellspacing is most li"ely too close for conventional welldrilling but may be economical if the laterals can bedrilled from a common main trun".'nterestingly, the same conditions that penalize ahorizontal well in a reservoir without overlying gasor underlying water %thic" zone, low vertical permeability&favor the horizontal well if overlying gas or underlying water is present. This also illustratesdesigning the well spacing to be close enough tocause interwell interference. The interwell or interlateralinterference is beneficial in this case becauseit both accelerates production and enhances recovery.Cnother case that may favor close parallel lateralspacing is in chart row 4 on 6ig. +#=+. Clthough orientinga horizontal well normal to natural fractures

boosts well productivity, this approach may ris" early water brea"through, especially in reservoirsunder waterflood. 'n:ecting water opposite of a ban" of parallel laterals drilled at sufficiently close spacingmay allow them to withdraw oil from the matrixroc" before the in:ected water front advances to the

production wells. 8ater may be in:ected above fracturing pressure to boost in:ectivity. 8hen horizontalor multilateral wells are not economically :ustified,the li"ely short#circuiting of water between verticalwell in:ector/producer pairs may be plugged by gel,thereby forcing the displacement process into thematrix roc".The remaining rows through +1 on the chart are


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reminiscent of >9 reservoir geometries. Clthoughconventional vertical wells do not address a >9reservoir geometry, hydraulically fractured and horizontalwells do, and "nowledge of structural andstratigraphic reservoir heterogeneities can greatlyimprove the design of these wells.Gtructural compartmentalization %chart row on6ig. +#=+& results from faults that may not be visiblein seismic data interpretations. 7ven if faults areclearly indicated in the seismic data, only dynamicdata derived from formation or well tests or longer term production history matching can establishwhether the faults are sealing or conductive.Gtratigraphic compartmentalization %chart row ;& isa result of depositional processes. 6acies with considerablecontrasts in flow characteristics may serveas buffers or flow conduits that act as first#order controlson well productivity and ultimate hydrocarbonrecovery. -oth structural and stratigraphic heterogeneitiesmay be complicated by diagenetic processesoccurring at a later time.Aorizontal wells can target one or more reservoir compartments, and multibranch wells enable shut#off of a branch that produces unwanted gas or water. 'n tight reservoirs with considerable faulting,the faultsmay be associated with natural fractures that can betargeted with horizontal wells, or they may providereliable information on the maximum stress directionthat is essential for planning hydraulic fractures invertical or horizontal wells.

Gtratigraphic limits %chart row ; on 6ig. +#=+& mayaccount for additional reservoir compartmentalization,

both vertically and areally. 'n some cases thereservoir sands may be too thin to be individuallyidentified in a seismic data cross section, but theymay have sufficient areal extent to be visible in seismicattribute maps for a structural horizon. 'n thatcase, horizontal wells may be an ideal strategy for

producing thin formations and for reaching multiplesands.$hart row B on 6ig. +#=+ refers to elongated compartmentalization.Clthough these diagrams depict

fluvial reservoir geology, elongated reservoirs canalso occur in heavily faulted formations. 'n either case, the apparent drilling strategies depend on theob:ective for the well. 6or example, the well directioncan be planned to stay in an elongated reservoir

body or to intersect as many reservoir bodies as possible.The latter case implies drilling in the directionnormal to the elongation, which for a fluvial reservoir means drilling normal to the downslope direction


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at the time of deposition. Cnother approach may be a multibranch well designed to target channelsidentified with borehole seismic measurements in thehorizontal trun" well.Aydraulic fracturing offers different challengesand possibilities. 6irst, unli"e a well tra:ectory plan,the direction of the hydraulic fracture is not a designchoice. Rather, the fracture propagates normal to thedirection of minimum stress. C hydraulic fracturemay propagate into isolated sand bodies not contacted

by the drilled well tra:ectory, but in other cases the fracture propagation may be inhibited byfacies changes or structural discontinuities, and ascreenout may occur. 'n general, drilling solutionsmay be more flexible in elongated reservoir systems.The last chart row on 6ig. +#=+ is for the specialgeometry of the attic compartment. 'n this case,steeply dipping beds may be in contact with an updipgas cap, downdip aquifer or both. Jne strategy is todrill a horizontal well that passes through several of the beds and stays sufficiently below the updip gasand above the downdip water. Clthough this seemsto be an efficient approach, it suffers from a significantdisadvantage in that flow is commingled amongthe layers, and when gas or water brea"through occursit interferes with production from other layers. The

better strategy may be to drill multiple horizontalwells, each on stri"e and staying in a specific bed.The advantage to this strategy is that each of the wellsis optimal in its standoff from the gas#oil or oil#water

contact, thus delaying multiphase production as longas possible, and in its productive length within the formation,thus maximizing productivity.

1- . %timulation e ecutionC good understanding of :ob execution is necessaryfor ma"ing decisions on the applicability and ris" of various treatments. Cs with any well wor", basicsafety procedures must be developed and followedto prevent catastrophic failure of the treatment,which could result in damage to or loss of the well,

personnel and equipment. Gpecific standards andoperating procedures have been developed for stimulationtreatments, which if followed can lead to asafe, smooth and predictable operation. $hapters ++and +B fully detail execution concerns.1- .1. 5atri stimulationMatrix stimulation, mainly acidizing, is the originaland simplest stimulation treatment. More than

1,111 acid treatments are pumped each year in oiland gas wells. These treatments %6ig. +#==& typically


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involve small crews and minimal equipment. Theequipment usually consists of one low#horsepower,single#action reciprocating pump, a supply centrifugaland storage tan"s for the acid and flush fluids.-lending equipment is used when solids are addedto the treatment.The most common process is for the fluids to be

preblended at the service company facility and thentransported to the location. This allows blendingsmall volumes accurately, controlling environmentalhazards. The fluids are then pumped with little effortor quality ris".1- .2. Hydraulic fracturing

nli"e matrix stimulation, fracturing can be one of the more complex procedures performed on a well%6ig. +#=>&. This is due in part to the high rates and pressures, large volume of materialsin:ected, continuous

blending of materials and large amount of un"nown variables for sound engineering design.The fracturing pressure is generated by singleactionreciprocating pumping units that have

between 11 and =111 hydraulic horsepower %6ig.+#= &. These units are powered by diesel, turbine or electric engines. The pumps are purpose#built andhave not only horsepower limits but :ob specificationlimits. These limits are normally "nown %e.g., smaller

plungers provide a higher wor"ing pressure andlower rates&. -ecause of the erosive nature of thematerials %i.e., proppant& high pump efficiency must

be maintained or pump failure may occur. The limitsare typically met when using high fluid velocitiesand high proppant concentrations % +; ppg&. Theremay be numerous pumps on a :ob, depending on thedesign.Mixing equipment blends the fracturing fluid system,adds the proppant and supplies this mixture tothe high#pressure pumps. The slurry can be continuouslymixed by the equipment %6ig. +#=2& or batchmixed in the fluid storage tan"s. The batch#mixedfluid is then blended with proppant in a continuousstream and fed to the pumps.

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