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Society of Petroleum Engineers

SPE 26169

Inflow Performance and Production Forecasting of Horizontal WellsWith Multiple Hydraulic Fractures in Low-Permeability Gas ReservoirsGenliang Guo and A.D. Evans, U. of Oklahoma

SPE Members

Copyright 1993, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the SPE Gas Technology Symposium held in Calgary, Alberta, Canada, 28-30 June 1993.

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 material, as presented, does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Societyof Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A. Telex, 163245 SPEUT.

ABSTRACT

The applications of horizontal welltechnology coupled with hydraulic fracturingin the development of low permeability gasreservoirs are investigated.

Analytical single phase and multiphasepseudo-steady state inflow performanceequations for a horizontal wellboreintersect ing mul t iple hydraul ic fractures arepresented. The effects of permeabilityanisotropy, wellbore location eccentricity,and fracture characteristics are considered~

The phenomena of non-Darcy flow is alsoaccounted for in the inflow equationassociated with the flow of gas phase. Thesesolutions provide a basis for theproductivity evaluation and productionforecasting of horizontal wells with multiplehydraulic fractures.

A new analytical method for predicting thefuture production performance of gasreservoirs is derived. The method is based onmaterial balance analyses in which explicitpressure expressions as functions ofcumulative production data and gas propertiesare derived for various types of gasreservoirs. Detailed production forecastingprocedures are developed by using the derivedpressure functions and appropriate inflowperformance equations. The new productionforecasting method has been furtherimplemented on a computer. As a result, thefuture production performance of a gas

References and Illustrations at end of paper.

303

reservoir can be easily predicted for anygiven scheme of horizontal drilling coupledwith hydraulic fracturing, and combinationsof reservoir rock and fluid properties.

With an economic evaluation, the new methodmay be used in the initial screening ofhorizontal drilling and hydraulic fracturingprospects in low permeability gas reservoirs.It may also be used in daily productionoperations and reservoir management. Ahypothetical case study is presented whichdemonstrates the applicability of the newinflow performance equations and productionforecasting method in the recoveryoptimization of a low permeability gasreservoir by combining horizontal drillingand hydraulic fracturing technology.

INTRODUCTION

As an environmentally sound alternative tocrude oil, natural gas is becoming anincreasingly significant energy resource.Many low permeability gas reservoirs arehistorically considered to be non-commercialdue to low production rates. Most verticalwells drilled in tight gas reservoirs arestimulated using hydraulic fracturing and/oracidizing treatments to attain economicalflow rates.

Recently, studies show that horizontal welltechnology may provide another viableapproach for tapping low permeability gasreservoirs[I-4J. The combination of horizontalwell drilling and hydraulic fracturing

2 INFLOW PERFORMANCE AND PRODUCTION FORECASTING OF HORIZONTAL WELLSWITH MULTIPLE HYDRAULIC FRACTURES IN LOW PERMEABILITY GAS RESERVOIRS

SPE 26169

The single phase inflow equation for a nonfully penetrating well intersecting naturalfractures, as shown in Figure 2, is given as:

If the horizontal wellbore is completelyperforated, equation (1) and equation (2) canbe used directly to model the inflow

(7 )

(8 )

(6)

(3 )

• • • • • • • • • • •• (4)

. • • • • • • • • • •• (2 )

. . . . • • • • • • •• (5)

A'=0.738

S = -lft(.!::L)"\'4r..

Sr:A = 1n~ 30.8828CM

( = 2~h~L~

"[1.5(1 + p) - v'JJ1r..L

c. = _1_1 1 + (

I'" - ---.L.... - 1 + (

.rTIb - IN- 2)L Iwhere r' - l..!1 N..- "

COB~ "LB1n'. ).!arccosh 2aN

3 Si~ "L~:;IUI)

In equations (1) and (2), C1 and Cz arecalculated by the following equationsassuming an open hole completion:

To induce multiple hydraulic fracturesalong a horizontal wellbore, the horizontalsection of the well must be cased. The basictheory of rock mechanics shows that theinduced multiple hydraulic fractures shouldbe parallel to each other, and can beorthogonal to the horizontal wellboredepending on its inclination with the in-situprincipal stress directions. The geometricconfiguration of a horizontal well withmultiple hydraulic fractures is, therefore,very similar to that of a horizontal wellintersecting natural fractures as shown inFigure 1 and Figure 2.

INFLOW PERFORMANCE EQUATIONS POR A HORIZONTALWELL WITH HULTIPLE HYDRAULIC PRACTURES

Various steady state and pseudo steadystate inflow performance equations forhorizontal wells in non-fractured reservoirshave been reported in the literature[7-15]. Theeffects of natural and induced fractures onhorizontal well productivity have beennumerically or analytically investigated byvarious authors I5 ,9,lO]. More recently,analytical inflow performance equations fora horizontal well intersecting discretenatural fractures have also beenpresented[16] .

Single Phase Inflow Performance Equations:

Comprehensive pseudo-steady state inflowperformance equations for a horizontalwellbore intersecting a number of uniformlyspaced, parallel natural fractures have beenpresented in the literature(16). The singleliquid phase inflow equation for a fullypenetrating horizontal well intersectingnatural fractures, as shown in Figure 1, isgiven as:

q- 2"kbh~-1'wt!) {~h1'( u:bX-!!-)]yCAlr: (1 + ~) z

In this study, analytical inflowperformance equations for a horizontal wellwith multiple hydraulic fractures arederived. A new semi-analytical productionforecasting method for predicting productionperformance of depletion type and naturalwater drive gas reservoirs are developedbased on material balance analyses. Theapplicability of the derived inflowperformance equations and productionforecasting methods in exploiting lowpermeability gas reservoirs using acombination of horizontal well technology andhydraulic fracturing are demonstrated by acase study.

appears even more attractive[5,6]. However, thesuccess of producing low permeability gasreservoirs by coupling horizontal welltechnology and hydraulic fracturing relies oncareful reservoir and production performanceanalyses, which require the use ofappropriate inflow performance equations andan adequate production forecasting method foranalyzing the performance of horizontal wellswith multiple hydraulic fractures.

304

SPE 26169 GENLIANG GUO AND RONALD D. EVANS 3

Equation (9) and Equation (10) may beconsidered as the general single liquid phaseinflow performance equations for horizontalwells with multiple hydraulic fractures.

(14)

(13 )

fractures arethe inflow

be furtherCI = 90° into

If the hydraulically inducedorthogonal to the wellbore,performance equations cansimplified by substitutingequations (11) and (12) as:

performance characteristics of horizontalwells with multiple hydraulic fractures. Inmost cases, however, hydraulic fractures areinduced primarily due to very low rock matrixpermeability, and subsequent negligibledirect flow from the rock matrix to thewellbore. The horizontal well is thereforeonly perforated at the fracture intervals,and the production is primarily via thehydraulic fractures. The two coefficients,C1

and C2 ' . become C1 = 0 and C2 = 1. 0 .Substituting them into equation (1) and~quation (2), one obtains the inflowperformance equations for a horizontal wellwith multiple hydraulic fractures when thewellbore are cased and selectively perforatedat the fractures. Hence, the inflow equationfor a fully penetrating horizontal well withmultiple hydraulic fractures is given as:

The inflow equation for a non fullypenetrating horizontal well with multiplehydraulic fractures is given as:

(15)

Multiphase Inflow Performance Equations:

Once the single phase inflow performanceequations are obtained, the multiphase inflowequations can be derived by introducing thereservoir properties, such as relativepermeability and capillary pressure, into thecorresponding single phase equations. Usingequation (9), the multiphase inflowperformance equations for a fully penetratinghorizontal well with multiple hydraulicfractures can be obtained as follows:

I

N

cos wbs1nzll

.!.a.rccosh ~~) + .J!!!lnLE..) +3 -' WL,s1nl1) L'\ h~

ail. 205

(10)

It is generally assumed that hydraulicallyinduced fractures will fully penetrate thewhole reservoir thickness. Substitutingh = h r into equation (9) and equation (10 )"one obtains equation (11) and equation (12)respectively.

(11 )

+ lL

coaJ.. tcL;;t;( k.b In(4hLf ll1nll))-arccosu - - +--3 S1~ ffL~:;M) 2kf c ye.ur:

........... , (12 )

I cos~wbs1n'lI ).!.a.rccosb ~3 si-' ffL,s1nl1),lit 205

(16)

305


SPE 26169

• k..,.k,[(m(p;J - m(P.....)I >C

q, 1422T

IN

cos nbs1n·..!arccosh ~ 21m ) + l!hn(..!L) +3 Sin( nL~;IllI ) L·' hr

Similarly, one can show that the gas inflowperformance equation with the non-Darcy floweffects for a non-fully penetratinghorizontal well intersecting hydraulicfractures can be obtained as:

· . . . . . . . . • •. (17)

(22)

(23)

The equation for gas flow can also beexpressed in terms of pressure squared as:

and· . . . . • . • . . .. (18)

(27 )

(25 )

(26)

. • • • • • • • • • •. (24)

PRODUCTION PORECASTING OP HORIZONTAL WELLSWJ:TR KULTIPLERYDRAOLIC PRACTURES IN LOW

PERMEABILITY GAS RESERVOIRS

(19)

(20)

Similarly, the multiphase inflowperformance equations for a non-fullypenetrating horizontal wells with multiplehydraulic fractures can be obtained byintroducing relative permeability andcapillary pressure terms into equation (10).

Depletion Gas Reservoirs

Material Balance Analysis:

For a confined and depletion type gasreservoir, the law of conservation of massindicates that the pressure drop should beproportional to the amount of gas withdrawnfrom the reservoir. Therefore, the averagereservoir pressure at a given time isproportional to the corresponding cumulativegas production.

Assuming water influx into a gas reservoirfrom an adjoining aquifer is insignificant,the reservoir volume occupied by hydrocarbonswill not decrease, except for a slightreduction due to connate water expansion andpore volume compaction as reservoir pressuredeclines during production. These types ofreservoirs are termed depletion gasreservoirs. The material balance equation ofsuch an isothermal gas reservoir is givenas l17 ] :

• • . . • • • • • • •. (28)5!G .1 -[1 _(c,..s,.. + CdAP]~1 - S"" BJ.l .!ar"""M[CO.~~I] .J/;!,.J.l!.) .:q;;.~[,.J~). 2Da~]I] .~.L~:'") L"\b, ll;;;;J<;c \ ye..:

· . . . . . . . . . .. (21)

Assume the fracture length is smallcompared to the dimensions of its subdrain"age block so that pseudo-radial flowexists within the sub block. The effect ofnon-Darcy flow can then be incorporated byintroducing approximate non-Darcycoefficients into equations (17) for fullypenetrating horizontal wells with multiplehydraulic fractures as l17 ,18J:

Effect of Non-Darcy Flow on Gas InflowEquations:

In the above discussions, it is assumedthat the effect of non-Darcy flow isnegligible. However, in the vicinity of andwithin a horizontal wellbore intersectingnatural fractures, flow velocity may be highenough that non-Darcy flow effects may becomesignificant and can not be neglected. This isparticularly true for gas production.

306


In equation (28) E is the gas expansionfactor, G is the original gas in place, Gpis the cumulative gas production and4P = P j - "P, where P j is the initialreservoir pressure and P is the averagereservoir pressure. The second term in thebracket accounts for the hydrocarbon porevolume reduction due to connate waterexpansion and pore compressibility.

Generally, the gas expansion factor isapproximately a linear function of reservoirpressure, and can be obtained from standardPVT analysis and hence can be approximatedas:

Therefore, equation (34) will be the generalpressure solutions for a depletion gasreservoir and can be used in future gasproduction forecasting.

Water Drive Gas Reservoirs

If the reduction in reservoir pressureleads to a significant expansion of theadjacent aquifer water and consequent influxinto the reservoir, the material balanceequation of such a water drive gas reservoiris [17J :

. . . . . . . . . . .. (37)

· . . . . . . . . . .. (29 )

where Be is the slope of experimental E vs.Pdata. Substituting equation (29) intoequation (28), one can obtain the followingpressure equation in quadratic form:

where We is the cumulative water influxresulting from the pressure drop. It isassumed that there is no difference betweensurface and reservoir volumes of water, andthe effects of connate water expansion andpore volume compaction are negligible.

Explicit pressure solutions as functions ofproduction data and gas properties areobtained by solving equation (30) as follows:

The modelling of water influx is not aneasy task and involves great uncertaintiessince the information on the aquifer isusually minimal. This is especially true inthe early stage of production planning. Forsimplicity, it is assumed that the aquifer isrelatively small so that a pressure drop inthe reservoir is instantaneously transmittedthroughout the entire reservoir-aquifersystem. The aquifer model is then givenas[17J:

where A = a ( c"s" - Cf )

'\ 1 - S""

B = a + E ( c"s., - Cf )• i 1 - S""

(30)

(31 )

• • • • • • • • • • •• (32)

. . . . . . . . . . .. (33)

w• .. cwl1P . . . . . . . . . . .. (38)

In many cases, connate water expansion andpore compressibility are negligible due tothe high compressibility of natural gas. Asa result, the material balance equationbecomes:

In equation (38), C is the total aquifercompressibility (cw + c f ) W is the totalvolume of water, and 4P is the pressure dropat the original reservoir-aquifer boundary. 4Pmay be approximated by (Pj - "P) • Substitutingequations (29) and (38) into equation (37),one obtains:

(39 )

(40)where A = a.cw

(34)

(for A" 0, B 'I< 0)1Pi + _-....:B=-=i::""YL;B=...'__- ....:4::;:A:..:.C

11.. 2A

P j - E.B

(35) (41)

· . . . . . . . . . .. (36)

•••••••••• " (42)

(for A = 0, B 'I< 0)

(43)

Solutions of equation (39) can be obtainedas:

11· P j - (=:X~)

It can be shown that equation (36) can alsobe directly deduced from equation (34).

Substituting equation (29) into equation (35)and after some algebraic manipulations oneobtains:

307


SPE 26169

One can show that the second solution inequation (43) will reduce to equation (36)when the volume of the aquifer is negligible(W=O.O).

When the volume of the aquifer is large,more sophisticated unsteady state aquifermodels are needed to replace equation (38).It is believed that similar pressuresolutions can be obtained by using the sameapproach.

(54)

(55)

Production Forecasting:

With derived inflow performance equationsand the pressure expres~ions as functions ofproduction data and reservoir fluidproperties, future gas production forecastingprocedures can be developed by partitioningthe gas reservoir depletion process intosuccessive time steps, during each of whichthe reservoir can be considered as in pseudosteady state. In the i-th time step, theproduction calculations for a depletion gasreservoir can be carried out by the followingequations:

The production forecasting of a depletiongas reservoir can be easily performed byimplementing the above procedures on acomputer.

The procedures for the productionforecasting of a water drive gas reservoirare similar to those given by equations (44)through (55) except that equations (46)through (48) should be replaced by thecorresponding equations for a water drive gasreservoir [equations (40) through (42)].

EXAMPLE APPLICATION

Depicted in Figure 4 through Figure 8 arefive proposed horizontal well drillingscenarios from drilling one well to drillingfive wells. It is assumed that the minimumprincipal in-situ stress is in the directionof NE-SW, parallel to the proposed horizontalwell orientation. As a result, any inducedfractures will be orthogonal to thehorizontal wellbore.

Shown in Figure 3 is the net pay isopachmap of a hypothetical low permeability gasreservoir. It has an area of 736 acres,original gas in place of 9.24 tcf. Additionalreservoir and well data as well as economicevaluation parameters are given in Table 1.It is proposed that horizontal drilling andhydraulic fracturing techniques be used toproduce the reservoir due to low rock matrixpermeability.

The combination of horizontal well drillingand hydraulic fracturing technologiesprovides a mechanism for more efficientrecovery of natural gas from low permeabilityreservoirs. However, the success of thesetechnologies require quantitative engineeringanalyses. The purpose of this case study isto show the applicability of the derivedinflow performance equations and productionforecasting method in the initial screeningof horizontal well drilling and hydraulicfracturing schemes in exploiting a gasreservoir.

(45)

(48)

(44)

(for A"O)

A = 0, B * 0)

. . • • . . . . • •• (52)

· • . • • . . . . • •• (51)

· • • • • • • • • • •• (50)

· . . . . . . . . . .. (47)

• • • • • • • • • • •• (53)

· . . . . . . . . . .. (46)

· . . . . . . . . . .. (49 )

(S.,) 1 '" _--;-S..:::,.J::J..1_+_C~,,(,-,P1=-:- ,-(P_)_ju.U__

1 _(C,,(Sw)1-1- Cr\p _1 - S"" } 1

(Z)1 '" 35.37 (CP) 1+ Pwf)

II 2 (E) jT

( )j _ ( C,,(S,,) j-l - Cr )

B - a. + Ej 1 _ S

""

(RF)j =~G

308


Effect of Hydraulic Fractures on HorizontalWell Productivity

For the single well case shown in Figure 4,let's assume that hydraulic fractures of 400ft are induced along the horizontal wellbore.The effect of fractures on the horizontalwell productivity is shown in Figure 9, inwhich gas production rate is plotted as afunction of producing time and number offractures induced. One can see that at leastthree fractures must be created in order toobtain the same initial production capacityfor a cased horizontal well compared to thatof the non-stimulated open hole horizontalwell. The production rate can be increasedfour times as much if seven fractures arecreated.

Effect of Additional Drilling on ReservoirProductivity

Shown in Figure 10 is the total gasproduction rate of the reservoir as afunction of producing time and number ofhorizontal wells drilled, in which nofractures are induced. Consistent with commonbelief, the total reservoir productioncapacity can be dramatically increased ifmore wells are drilled. The total gasproduction rate of the reservoir is increasedfrom 200 MSCF/D for a single well to 4300MSCF/D for five wells.

Optimization of Horizontal Well Drilling andHydraulic Fracturing

The fact that more drilling and additionalfracturing also means increased investmentindicates that there must be an optimalnumber of wells coupled with an optimalnumber of fractures which should be drilledor induced to maximize the profits and/orhydrocarbon recovery. In the followingdiscussions, an economic evaluation isperformed using gas production rate profilesgenerated by the derived productionforecasting method in this study fordifferent combinations of wells andfractures.

Shown in figure 11 is the discounted netpresent value (NPV) profile for open holehorizontal wells with no hydraulic fractures,in which the NPV of the reservoir is plottedas a function of producing time and number ofwells drilled. It can be observed that thetwo well system depicted in Figure 5 resultsin the maximum profit after 20 years'production.

When hydraulic fractures are created alonghorizontal wellbores, it is assumed that thehorizontal wells are cased and the production

309

is solely from fractures. Figure 12 shows theNPV profile when three hydraulic fracturesare created along each horizontal well. Onecan see that the optimal scenario in thiscase is to drill three wells. However, as canbe seen from Figure 13 through Figure 16, theoptimal drilling scenario is to drill twowells if more than three fractures arecreated along each well. The optimal drillingscenarios identified from Figure 11 throughFigure 16 are further compared in Figure 17,in which Wx-Fy corresponding to the case ofdrilling x wells and creating y fracturesalong each well. It is evident that theoptimum scheme for producing this reservoiris to drill two wells and create sevenfractures on each well. Furthermore, thiseconomically optimal scheme also maximizesthe gas recovery, as can be seen from Figure18 in which gas recovery factor is plotted asfunctions of producing time for the scenariosconsidered in Figure 17. This conclusion isonly true for the assumed well length,fracture length and reservoir and well data.Different conclusion may be obtained ifdifferent sets of data are used in theanalysis.

CONCLUSIONS

Analytical single phase and multiphasepseudo-steady state inflow performanceequations for horizontal wells intersectinghydraulic fractures are derived. Thephenomena of non-Darcy flow is considered inthe gas inflow equations. These derivedinflow equations provide engineers withrelatively simple tools for evaluating theproductivity of horizontal wells intersectinghydraulic fractures.

An analytical production forecasting methodfor predicting future gas productionperformance of a low permeability gasreservoir is derived based on a materialbalance analysis. The methodology can be usedfor initial screening of horizontal drillingand hydraulic fracturing schemes forexploiting a low permeability gas reservoir.

A case study indicates that the combinationof horizontal well and hydraulic fracturingtechnology provides an attractive approachfor exploiting low permeability gasreservoirs. It appears that the best strategyis to drill fewer horizontal wells and createmore fractures. However, productionforecasting and economic evaluation must beperformed in order to identify the optimalschemes for horizontal well drilling andhydraulic fracturing.


SPE 26169

NOMENCLATURE

a = reservoir width, ft.a'= half the major axis of a drainage

ellipse, ft.A = drainage area, ft 2 •

A'= constant.b = reservoir length, parallel to

horizontal well, ft.B = formation volume factor, RB/STB.c = fracture aperture, ft.C!' C2 = weighing functions, dimensionless.CAl = shape factor corresponding to the

location of a horizontal well in avertical plane, dimensionless.

CA2 = shape factor corresponding to thelocation of a horizontal well in theplane of the vertical fracture,dimensionless.

C~ = horizontal well shape factor,dimensionless.

CAF = vertical fracture shape factor,dimensionless.

e = vertical distance between the axis ofa horizontal well and the middle of areservoir thickness, ft.

h = reservoir thickness, ft.h f = fracture height, ft.J = productivity index, bbl/day/psi.k = rock matrix permeability, md.k f = fracture permeability, md.k h = horizontal permeability in matrix, md.k v = vertical permeability in matrix, md.k rom = relative permeability of oil in rock

matrix, dimensionless.k rof = relative permeability of oil in

natural fractures, dimensionless.kr~ = relative permeability of gas in rock

matrix, dimensionless.k rgf = relative permeability of gas in

natural fractures, dimensionless.k,~ = relative permeability of water in

rock matrix, dimensionless.k~f = relative permeability of water in

natural fractures, dimensionless.L = horizontal well length, ft.Lf = fracture length, ft.m(P) = real gas pseudo pressure, (STB

psi)/(RB cp).n normal vector, ft.N = number of fractures intersected by a

horizontal well.Nm = movable hydrocarbon reserve, STB.Np = cumulative oil production, STB.P = average pressure, psi.Pc = capillary pressure, psi.Pf = pressure in a fracture, psi.Pe = pressure at reservoir boundary, psi.Pwf = bottom hole flowing pressure, psi.Ck = flow rate directly from matrix to

horizontal wellbore, STB/day.qf = flow rate from matrix to fractures,

then from fractures to horizontal

310

wellbore, STB/day.q = total flow rate, STB/day.r w = wellbore radius, ft.Rs = solution gas oil ratio, scf/STB.S = skin factor, dimensionless.S~ = shape dependent pseudo-skin factor,

dimensionless.SgC = critical gas saturation;

dimensionless.t = time, day.Zg = gas factor, dimensionless.

Greek:

a = angle between a horizontal well axisand natural fractures, degree.

P = permeability anisotropic ratio,dimensionless.

Pl = non-Darcy flow coefficient in rockmatrix, 11ft.

P2 = non-Darcy flow coefficient infractures, 11ft.

~ = porosity, dimensionless.y = 1.781, exponential of Euler's

constant, dimensionless.~ = reservoir fluid viscosity, cpoA = proportional constant, dimensionless.

Subscripts:

0 = oilw = water or wellg = gasm = matrixf = fracturei = initialb = bubble point

ACKNOWLEDGBKENTS

The authors wish to thank the OklahomaCenter for the Advancement of Science andTechnology (OCAST) for their financialsupport for this research.

REFERENCES

1. de Montigny, o. and Combe, J.:"HoleBenefits, Reservoir Types Key to Profit",OGJ, April 11, 1989.

2. Giger, F .M. : "Low-Permeability ReservoirsDevelopment Using Horizontal Wells",SPE/DOE Paper 16406, presented at theSPE/DOE Low Permeability ReservoirsSymposium held in Denver, Colorado, May18-19, 1987.

3. Joshi, S.D.:"A Review of Horizontal Welland Drainhole Technology", SPE Paper16868, presented at the 62nd AnnualTechnical Conference held in Dallas, TX,September 27-30, 1987.

4. Sung, W. and Ertekin, T.:"Performance


comparison of Vertical and HorizontalHydraulic Fractures and HorizontalBoreholes in Low Permeability Reservoirs:A Numerical Study", SPE/DOE Paper 16407,presented at the SPE/DOE Low PermeabilityReservoirs symposium held in Denver,Colorado, May 18-19, 1987.

5. Mukherjee, H. and Economides, M.J.:"AParametric Comparison of Horizontal andVertical Well Performance", SPE paper18303, presented at the 63rd AnnualTechnical Conference, Houston, TX, October2-5, 1988.

6. Conlin, J.M., Hale, J.L., Sabathier, J.C.,Faure, F. and Mas, D.:"Multiple-FractureHorizontal Wells: Performance andNumerical Simulation", SPE Paper 20960,presented at Europec 90, The Hague,Netherlands, 22-24 October 1990.

7. Merkulov, V.P.: "Le debit des puits devieset horizontaux", Neft. Khoz (1958) 6, 5156 (original paper in Russian) .

8. Giger, F.M., Reiss, L.H., Jourdan, A.P.:"The Reservoir Engineering Aspects ofHorizontal Drilling", SPE paper 13024,presented at the 1984 Annual TechnicalConference, Houston, Texas, September 1619, 1984.

9. Giger, F.M.:"Horizontal Wells ProductionTechniques in Heterogeneous Reservoirs",SPE paper 13710, presented at the SPEMiddle East Oil Technical Conference,Bahrain, March 11-14, 1985.

10. Karcher, B.J., Giger, F.M., and Combe,J.:"Some Practical Formulas To PredictHorizontal Well Behavior", SPE paper15430, presented at the 61st AnnualTechnical Conference, New Orleans, LA,october 5-8, 1986.

11. Joshi, S.D.:"Augmentation of WellProductivity Using Slant and HorizontalWells", SPE paper 15375, presented at the61st Annual Technical Conference, NewOrleans, LA, October 5-8, 1986.

12. Babu, D.K. and Odeh, A.S.:"Productivityof a Horizontal Well", SPE paper 18298,presented at the 63rd Annual TechnicalConference, Houston, Texas, October 2-5,1988.

13. Kuchuk, F.J., and Goode, P.A.:"PressureTransient Analysis and Inflow Performancefor Horizontal Wells", SPE paper 18300,presented at the 63rd Annual TechnicalConference, Houston, TX., October 2-5,1988.

14. Mutalik, S.P., Godbole, S.P. and Joshi,S.D.:"Effect of Drainage Area Shapes onthe Productivity of Horizontal Wells", SPEpaper 18301, presented at the 63rd AnnualTechnical Conference, Houston, Texas,October 2-5, 1988.

15. Goode, P.A. and Wilkinson, D.J.:"InflowPerformance of Partially Open HorizontalWells", JPT. August, 1991.

16. GUo, G. and Evans, R.D.:"InflowPerformance of a Horizontal WellIntersecting Natural Fractures", SPE Paper25501, presented at the SPE 1993Production Operations Symposium, OKC, OK,March 21-23, 1993.

17. Dake, L.P.:"Fundamentals of ReservoirEnqineering",Elsevier ScientificPublishing Company, 1978.

18. Celier, G.C.M.R., Jouault, P. and deMontigny, O.A.M.C.: "Zuidwal: A Gas FieldDevelopment With Horizontal Wells", SPEpaper 19826, presented at the 64th AnnualTechnical Conference, San Antonio, TX.,October 8-11, 1989.

311


Table 1. Reservoir, Well And Economic Data

SPE 26169

Reservoir Porosity ell 0.20

Fracture Length Lf 400 ft

Fracture Aperture c 0.25 inches

Fracture Permeability k f 4.0xlO4 md

Horizontal Well Length L 2000 ft

Horizontal Wellbore Radius x" 6 inches

Connate Water Saturation S"c 0.20

Rock Compressibility Cf 8.6xlO-6 psia-1

Water Compressibility C" 3.0xlO-ti psia-1

Horizontal Permeability k h0.10 md

Vertical Permeability k v 0.01 md

Critical Gas Saturation SgC 0.05

Original Gas in Place G 9.24 tcf

Original Reservoir Pressure Pj 3300 psi

Original Gas Expansion Factor Ej 185.24 scf/rcf,

Reservoir Temperature T 200°F

Specific Gravity Yg 0.85

Drilling and Completion Costs $1.5 million/well

Hydraulic Fracturing Costs $20000/fracture

312


h

LI4

a

Figure 1. A Fully Penetrating Horizontal WellIntersecting Natural Fractures

Plan

~~

LfN L f N-1 La L 11

+9 t\

~'\7V

CN C N-1 C2 C 1

" - -- -b

Elevatlon

a

~~ ....h '\ / L

" - -- -b

Figure 2. A Non-Fully Penetrating HorizontalWell Intersecting Natural Fractures

313


SPE 26169

Figure 4. One Well System

o

Figure 3. Net Pay Isopach Map OfThe Grynberg Reservoir

o-+rrTTT'l'TTT'IT'ITTTT'l"TT'T1nTT"IT'ITTTT'l'TTT'IT'ITTTT'lTTT'lrTT'l

~

W~z-0-g~.,.

zLtgtIl N

0

0 2000 4000 6000 8000 10000SW-NE (IN FEET)

o 2000 4000 6000 8000 10000SW-NE (IN FEET)

Figure 5. Two Well System Figure 6. Three Well System

314


o +n"TTT""""I'TT"lTlTI'TT"l"TTT"""""TTTTTT'lI'TT"lTTT"I'TT"l"TTTTTT'l

~

m~~;: ....Z

~~

o 2000 4000 15000 6000 100005W-NE (IN FEET)

§II]

W~~8;:!;i!zL1§(liN

0

0 2000 4000 6000 8000 10000SW-NE (IN FEET)

~

~

~

~~~~

~§

Figure 7. Four Well System

No. of Fraet_Induoe"7 F"racture Length - 400 ft

Wellbore Length - 2000 l't

Figure 8. Five Well System

No. of W.'1aDrilledi5

Wellbore Length - 2000 ft

o 2000 4000 5000Producing Tim. (Dclys)

8000 o 2000 4000 8000Producing TIme (Days)

8000

Figure 9. Gas Production Rate as aFunction of Producing Time and

Number of Fractures Induced

315

Figure 10. Total Gas ProductionRate as a Function of Producing

Time and Number of Wells Drilled


SPE 26169

80002000 4000 6000Producing TIme (Days)

Well Length - 2000 ftFracture Length - 400 ftNo. of Fract...re. InduCBd Per Well - :5

.....

T:go

IJ~ .....

I

jI1"1'I

"'"I"08000

WAil Length - 2000 ftNo Fl"Octure. Induced

No of W.II. Drtll<td

--~======~=---....-====""""".- !

2000 4000 6000Producing Time (Days)

.....

~

10.II;1j""leo:>II1"1'

0

I"0

Figure 11. Discounted Net Present Value Profilefor Open Hole Horizontal Wells With No Fractures

Figure 12. Discounted Net Present Value Profilefor Cased Horizontal Wells With Three Fractures

CD

T.....:g

10J~

j..,.II ...II~

I"0

No of Well. DrfllocI

Well Length - 2000 ftFl"Qct...... ~ngth - 400 ftNo. of Fl"Octure. Induced Per Well- 4


8000

~

T....:g

.I.50J~

j'?II~II

....I"

0

No. of .....11. Drtll<td

Well Length - 2000 ftFrO¢ture Length - 400 ftNo. of Fracture. Induced Per Well - 5


8000

Figure 13. Discounted Net Present Value Profilefor Cased Horizontal Wells With Four Fractures

Figure 14. Discounted Net Present Value Profilefor Cased Horizontal Wells With Five Fractures

316



Well IAngth - 2000 ftFracture Length - 400 ftNo. of Fracture.. Induced Per Well - 7

2

1.nt.I.!o.I'!:

J'?~

I~jl

~I


No of W"'. Drilled

:::::;;~~~~~~~~~~~~!

Well Le"9th - 2000 1tFracture Length - <400 ftNo. of Fractures Induced Per Well - e

2

1.nt.I.!o.I'!:

J'?~

I~jl

.n'I

0

Figure 15. Discounted Net Present Value Profilefor Cased Horizontal Wells With Six Fractures

Figure 16. Discounted Net Present Value Profilefor Cased Horizontal Wells With Seven Fractures


0q

~<:>...-Eafa~c:i

~~~

lk:c:i..c

C)

~d

~ 080002000 4000 6000Producing Time (Days)

.....-:::::::::::::==:::======= W2-F7W2-F8WZ-1'lII=_-------- W2-F4

_ _ --------- W2-FOW:il-r:il

~

leDt.I .....!.I'!:<:>

J....~I

leDjl

CN

'I0

Figure 17. Comparison of the Optimal DrillingScenarios for Different Number of Fractures Induced

Figure 18. Gas Recovery Profile

317

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