reservoir evaluation of horizontal wells

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S

SPE 22389

Reservoir Evaluation of Horizontal Bakken Well Performance on

the Southwestern Flank of the Williston Basin

M.R. Reisz, Union Texas PetroleumSPE Member

Copyright 1992, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the SPE International Meeting on Petroleum Engineering held in Beijing, China, 4 7March 1992.

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author s . Contents of the paper,as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author s . The mate,rial, as presented, does not necessarily reflect

any position of the Society of Petroleum Engineers, its officers, or members. Papers pressnted at SPE meetings are subject to publication review by Editorial Committees of the Societyof Petroleum Engineers. Permissionto copy srestricted to an abstract of notmorethan300 words. Illustrations maynotbe copied. Theabstmct sh Uld contain conspicuousacknowledgmentof where and by whom the paper is presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836 U.S.A. Telex, 730989 SPEDAL.

STR CT

This paper presents the results of areservoi r performance study for hori zonta1and vertical Bakken wells in the Fairway ofthe Williston Basin. A combination offorecasting methods were utilized includingdecline curve analysis, material balance,analytical solutions, and empiricalcorrelations.

The results indicate that recoverablereserves from hori zonta1 well s the Fairway are 2.5 to 3.0 times a verticalwell for 1.5 to 2.0 times the cost .. Simpletheoretical calculations combined with fielddata are useful in making initial estimatesof original oil in place, recoverablereserves, and drainage area.

INTRODUCTION

The Bakken formation, located in northwesternNorth Dakota and northeastern Montana

(Figure 1), is the source of a large portionof the oil generated and produced in theWilliston Basin. The Mississippian Devonianage Bakken shale is a natural ly fracturedformation that is both source and reservoirrock. The Bakken consists of three members.

References and illustrations at end of paper.

9

The upper and lower members are black shales,and the middle member is a dolomitic shaleysi1tstone. Located above the Bakken is theLodgepole (dense lime), and below is theThree Forks sand. The overpressured Bakken,found at approximately 10,000 [3048 m] witha virgin reservoir pressure corresponding toa 0.6 to 0.7 psi ft gradient [13.6 - 15.8kPa/m], has g n r t ~ over 100 billionbarrels [15.9 E 09 m] of oil based on

industry estimates.The key to Bakk,en production, in the matureportion of the Williston Basin, is having apermeable interval in which to put the oilafter it has been generated. Both theLodgepole and Three Forks have potential oilstorage capacity. The Antelope field locatedon the Nesson Anticline in northeasternMcKenzie County, is a good example ofincreasing the available storage capacitywith the presence of a permeable sand belowthe Bakken.

Figure 2 shows the location of the study areain Billings and McKenzie counties along theBillings Nose Trend. This area is referredto as the Fainilay . In the Fairway onlythe upper Bakken is considered net pay, andfuture discussion will refer to the upperBakken as Bakken.



2 RESERVOIR EV LU TION OF HORIZONT L B KKEN WELL PERFORM NCE SPE 22389

ORIGIN L OIL IN PL CE

For singl e phase flow another form of thematerial balance equation is

Calculation of the original Bakken oil inplace is a non-unique answer, due to thenumber of unknowns in a fractured reservoir.

In a conventional homogenous reservoir,original oil in place can be determinedvolumetrically from the relationship 1,2

· 1

· 2

· 3

N= NpBo / Bo - Boi

7758A l -Sw

Bo

In the Bakken, there is uncertainty in botharea (A) and thickness h . Therefore,another approach is needed to arrive atsatisfactory answers. The obvious method isa form of the material balance equation,which assumes that reservoir voidage causedby production of reservoir fluids is equal to

expansion of reservoir fluids due to a dropin pressure. By definition original oil inplace (N) can be represented in simplest formby the equation 1,3

U OILQt=Qi [ l - OOIP RF ]

This equation 4 is helpful in reservoirs withsingle phase flow where little is known aboutthe reservoir properties. By utilizing therelationship in equation 3 and solving forOOIP, one gets

OBJECTIVES

Several key points are supported byperformance data: an average initial declineof 40-45 , a final decl ine' of 25-35 , abreakeven point of approximately 150 M O

[23.8 E+03 m] at NPV(15) = 0, recoverablereserves 2.5-3.0 times a vertical well, and20-25 of recoverable reserves produced infirst year.

Since 1ate 1987 the Bakken pl ay has beendomi nated by' hori zonta1 dri ll-jng. There areapproximately 140 horizontal wells that haveproduced oil from the Bakken formation, andan equal number of vertical wells.

The real challenge, in an area of horizontaldevelopment, is to make an early and accurateeva1uati on of performance characterist ics,recoverable reserves, and drainage area.Management needs th i s data to make adetermi nat ion of the economi c vi abil ity forhorizontal development in a play such as theBakken. The factors which control Bakkenproduction were studied, and key reservoirparameters were identified for early analysisof recoverable reserves. The range ofultimate recoveries for Bakken drainholesindicate that no single factor can accurately

predict future performance. Results fromdecl ine curve analysis were compared withanalytical solutions and material balance togain a higher confidence level in the rangeof estimated values.

The main goals of this work included:

• 4. Estimation of original oil in place,recoverab1e reserves, and drai nage areas.

2. Early evaluation of plays through theidentification of key parametersaffecting well performance.

A total of 21 wells from 7 fields in the Fairway were studied in deta.il. This group

of wells are referred to as Group A . Theselection criteria for the study groupincluded: a minimum of 1 year productionhistory, and data availablle on azimuth,length of drainhole, path of drainhole, andnet pay.

The following sections discuss initialestimates and results obtained in this study.

OOIP= U OIL l -Q t /Q i RF

This equation is valid for L/2Xe penetrationratio > 0.5 and Qt/Qi ratio> 0.5 earlytime data . One can now calculate OOIP withan equation that utilizes rate-timerelationships, and compare the results with

other methods. One can also set equation 4equal to equation 1 and solve for drainagearea (A). This equation is represented by

Area = UM OIL (BO) I-Qt/Qi (RF) 0 h (I-Sw) (7758)

· 5



SPE 22389 M R. REISZ 3

The results obtained from these equations arein the range 2.0 to 2.7 MM O [318-429 E+03m] per square mile [2.6 km

Table 1provides OOIP and other pertinent informationon Bakken drainho1es selected from different

fields throughout the Fairway . Productiondata has been updated through February 1991.

The magnitude of fracture volume as a percentof total oi l in place is an important number.An examination of storage capacity infractures indicates t ha t l ess than 10 of thetotal oil in place may be stored in thefractures of the upper Bakken member. Thisnumber is consistent with empiricalcorrelations from Nelson 5 .

In summary, a number of different approaches

were used to obtain estimates of OOIP,including volumetric, material balance 3 6 andJoshi s OOIP equation 4. The range of 2.0 to2.7 MM O [318-429 E+03 m] per square mile[2.6 km

2] is a reasonable approximation.

RECOVERABLE RESERVES

Vertical Wells

Good agreement has been obtained in theestimation of recoverable oil from verticalBakken wells using both decline curveana1ys is and log of pressure versus

cumulative production plots. Vertical Bakkenreserves average 108 M O per well [17.2 E+03m] from a data se t of 119 wells in the Fairway .

The decline characteristics of the verticalwells were very predictable. The vastmajority of vertical Bakken wells had declinerates between 15-17% with a range of 10-20%.Wells with a 10-12% decline and goodproductivity were connected to an effectivefracture system and a large drainage area.

Horizontal Wells

Horizontal drainho1es exhibit a number ofdecline characteristics resulting from avariety of factors. The initial decline isassociated with the effectiveness of thefracture system and size of the area beingdrained. Figures 3, 4, and 5 show individualperformance data from Table 1. These threewells have estimated recoverable reserves in

11

excess of 400 per well [63.6 E+03 m] ,

and should give insight concerning horizontalBakken performance characteristics.

Figure 3 shows Meridian #33-11H in theElkhorn Ranch area. This well has ac ~ m u 1 a t i v e production of 280 M O [44.5 E+03m] through February of 1991 and estimatedrecoverable reserves of 442 M O [70.3 E+03m The initial stabilized rate was 300BOPO [47.7 m/d ] followed by a 55 decline.The current dec line rate is 25%. The well inFigure 4 has excellent production for thefirst si x months with ini}ia1 production inexcess of 600 BOPO [95.4 m/d]. The #1-7 hasan overall decll ine rate of 56 with a 25

decline for the last si x months. The wellhas a cumulative of 131 M O [20.8 E+03 m]

and estimated recoverable reserves of 405M O

[64.4 E+03 m] • Figure 5 shows a consistent31 decline, a cumulative of 160 M O [25.4E+03 mJ and an estimated 425 M O [67.6E+03 m] of reserves from the #14-27H.Dec1ine performance is a funct ion of theeffective areal extent of the fracture systemand the permeability of the fracturesintersected by the we11bore.

Table 1 shows calculated drainage areasrangi ng from 469 acres [1898 E+03 m ] for#14-27H to 664 acres [2687 E+03m2

] for#33-11H. Three wells listed in Table 1 from

the Bicentennial area are estimated to haverecoveries in the 150-200 M O [23.8-31.8 E+03m] range with calculated drainage areas of210-230 acres [fl50-931 E+03 m] •

Figure 6 is a plot of rate versus time forthe entire Rough Rider Field. Normal izingand grouping of production data can yieldpredictive characteristics early in the lifeof wells. The Rider Field has averaged286 BOPO [45.5 m/d ] from 10 wells in thefirst month, and has a decline rate of 25%.

Figure 7 is a normalized plot of the entire

Group A wells, and conta ins performancetrends representative of a Bakken welllocated in the Fairway . Figure 7illustrates an initial decline of 40-45% from21 wells in the first two years, followed bya 25-35% decline. An overall decline rate of30-35% can be anticipated. Figures 8 and 9show the distribution of first monthproduction rate and recoverable reserves.



4 RESERVOIR EVJILUATION OF HORIZONTAL BAKKEN WELL PERFORMANCE SPE 2238

Approximately 70 of Group A wells have astabili zed ihitial rate of 200 BOPD [31.8m/d ] or greater and 48 have recoverablereserves greater than 200 O [31.8 E+03 m

Group A reserves range from 35 O to 442 O [5.6-70.3 E+q3 m] with an average of 223 O [35.5 E+03 m] .

Key Parameters

The range of ultimate recoveries for Bakkendrainholes dictates that a list of keyparameters be identified for earlyevaluation. Unfortunately for horizontaldrainhole analysis, there is no single factorthat can accurately predict futureperformance. Tables 2A-2C are key criteriacharts. Each table consists of a number of

parameters that should be considered in theearly evaluation of ultimate recoveries.Zonal penetration 7 within the pay, drainholepath, ori entat ion, product ivi ty and afracture index are al l key parameters. Theseparameters were reviewed, ranked, and a valueassigned to arrive at a composite successfactor. The ranking scale A through E)utilized in this study is shown in Table 2A.

Table 2A shows the same wells listed inTable 1. These wells have an averagerecovery of 261 O [41.5 E+03 m] • Table2B and Table 2C provide examples of other

combi nat ions of well s ba:sed upon theselection criteria chosen in each table.

Meridian 14-27H in the Rough Rider area bothave calculated drainage areas Table 1) ithe 400-500 acre [1619-2023 E+03 m] rangeBoth are expected to have recoveries iexcess of 400 O [63.6 E+03 m Severaother wells in Table 1 have calculate r i n ~ e areas in the 200-300 acre [809-121E+03 m] range. At this time, it is noknown whether these values are representativdrainage areas or are influenced by the Qt/Qratio in the drainage area formulaAdditional work in this area is planned.

Joshi s paper on Methods Calculate AreOra ined by Hori zonta1 Well s 8 was verhelpful in calcul ating the drainage area oBakken wells. For optimum recoveries fromhorizontal drainholes, industry must have

good understanding of drainage areas and thproper spacing of wells. The calculatedrainage areas in Table 1 were obtained usinequation 5.

The physical 3D model for a horizontadrainhole and its drainage area is defined bFigure 10 9 . The drainhole length (L) is ithe x direction. This is the lowpermeability direction of the reservoir, anis perpendicular to the dominant naturafractures. The sides of the drainagrectangle are 2Xe and 2Ye. The thickness othe reservoir (h) is in the z direction

The Xw and Yw values represent the locatioof drainhole along the x and y axes.

The effective permeability in the horizontaplane of an anisotropic reservoir is equal tothe square root of Kx times Ky. Threctangular drainage area of a vertical welcan be represented by the equations 8

Tables 2A-2C support and identify a broadrange of ult imate recoveri es for a Bakkendrainhole. This approach allows foridentification of key parameters, and anearly analysis of successful wells. It alsoprovi des a method to quant i fy the factorsthat affect horizontal performance, and toevaluate how critical a particular parameteris in a given play. Recoverable reserves inTables 2A-2C support an ultimate recovery of2.5 to 3 times a vertical well.

DRAINAGE AREA

Much work remains in determination ofdrainage areas for horizontal drainholes.Different reservoir conditions and geometrieswill have an effect on actual drainage areas,and must be considered in the evaluation.The Slawson 1-7 in the Ash Coulee area and

12

2 Xe ) 2 Ye) = Area 43560)

and

e / 2Xe = ..jXy

in an anisotropic reservoir 8

can be rewritten as

2Ye = 2Xe..jXy

· 6

· 7

Equation

· 8



SPE 22389 M.R. REISZ 5

3.

Ah LzlOOO ft = 2 A v10)

Ah Lz2 ft = 3 Av11

4.

Solving equations 6 and 7 simultaneously, oneobtains the drainage lengths for a vert ica lwell in an anisotropic reservoir, assumingthat drainage area and permeabil i ty values

are known.

One can calculate 2Xe drainage length for ahorizontal drainhole based upon the followingassumption; 2Xe is equal to the drainholelength (L) in the x direction plus drainageradius of the vertical well at each end ofthe horizontal drainhole 8 Thisrelationship can be stated as

9)

Figure 9 represents an idealized view of

drainage volume for both vertical andhori zonta1 well s. Dra inage 1ength for ahorizontal drainhole along the highpermeability direction Ye Figure 10) isassumed to be the same as the vertical well.

Per Joshi 9 , the two following relationshipsgive a comparison of horizontal drainage area(Ah) to vertical drainage area (Av).

See Appendix A for an example problemutilizing well and reservoir parameters fromthe first horizontal drainhole in the Bakkenformation, Meridian #33-11H. (Note:Production data and calculations have notbeen updated. This example representsinitial results.) A summary of the wellparameters both known and assumed arecontained in Table 3. Reservoir parametersare summarized in Table 4. In Appendix Aseveral different methods, including Joshi smethod 8 , will be presented and results

compared.In summary, horizontal drainage area (Ah) istwo to three time Av vertical drainagearea). This means that a horizontal Bakkendrainhole should achieve a drainage areabetween 320 - 480 acres [1295-1942 E+03 m]

where a vertical Bakken well drains 160 acres[647 E+03 m] For a ver tical Bakken wellthat drains 320 acres [1295 E+03 m] the

horizontal well could drain 640 + acres [2590E+03 m Based upon an average verticalwell recoveringr 108 O [17.2 E+03 m] andthe increased drainage area from horizontal

wells, a horizontal drainhole should recover300 O [47.7 E+03 m ] for a dra inho1e 1engthof 2000 feet [510 mJ. This is consistentwith other work in the report and offers ahigh level of confidence in the ultimaterecovery expected from a hori zonta1 Bakkendrainhole.

PRODUCTIVITY PROBLEMS

A revi ew of performance data 10,11,12 and keyparameters in the planni ng and drill i ng ofBakken horizontal drainholes reveals fourmajor reasons fl:>r 1ess than ideal results:

1. Formation damageThe inability to effectively removeformat ion damage wi become worseas the reservoir pressure decreases.

2. OverdrillingCurrent well spacing in the Fairway appears too dense in someareas for horizontal drainholes.

OrientationIdeally the drainhole is paral le l tothe 10 .' permeabil i ty direct ion ofthe resl rvoi r.

Porpo is iProblems at the well site can preventzonal penetration in the desiredhorizontal segment of the drainhole.

For the majority of the prospective Bakkenacreage in the Williston Basin, i t may not beenough to encounter fractures. Initially theoverpressuring of the Bakken enhances theeffect iveness I:>f the fracture network.However, as the pressure in the reservoi r fractures) decreases, the effect iveness ofthe fractures may also decrease. Therefore,i t is desirable to prop the fractures around

the wellbore open for optimum long-termproductivity.

Format ion damagl is a major concern in theBakken. The invaded zone around the well boremay reduce well productivity. Thus, a keybenefit in the drilling of horizontaldrainholes may be lost or reduced. Thiscond i t ion wi be more prevalent whenexcessive mud weights are used to control

13



6 RESERVOIR EVJlILUATION OF HORIZONTAL BAKKEN WELL PERFORMANCE SPE 2238

problems of hole stability or when a portionof r e s ~ r v o i r is partially depleted.Undoubtedly, fracture collapse and nearwell bore formation damage have occurred andprevented some of the Bakken horizontaldrainholes from achieving their productivepotential

ROCK AND FLUID PROPERTIES

Arange of rock and fluid property values forthe Bakken have been identified to assist inthis study and future analytical studies.

Although there are large amounts of dataavailable concerning rock and fluidproperties in the Bakken, there does not seemto be a consensus about the critical

parameters. Core data, DST's, reservoirfluid studies, pressure build-ups, etc havebeen obtained by numerous operators, butnever incorporated into a c:ommon databaseavailable to the general industry. In 1990,a group of companies began a cooperativeeffort to gather Bakken data.

Tables 5 and 6 13 display a l ange of valuesfor different parameters that were utilizedin this study. Core analysis on Union TexasPetroleum s Federal 12-1 located in Sec. 12,T144N-R102W, indicates an average porosity of3 Permeabilities are in the 0.02 - 0.05 md.

range in the Bakken and 0.25 md. in theLodgepole. The maximum permeability of 0.59md. was recorded from a fractured sample.This well has an EUR of 101 M O [16 E+03 m]

and is representati ve of a typi cal Bakkenwell.

RECOVERY FACTORS

Documented numbers are not available forrecovery factors in horizontal Bakken wells.Joshi indicates a 16 recovery factor is agood approximation and is consistent with the15 to 20 range listed in Table 5. Thesenumbers were obtained from commi ss ion heari ngexhibits. Joshi has indicated that increasedrecovery factors from drainholes may be2 - 5 higher than for vertic:al wells 8 9

FUTURE WOR

Our understanding of fractured reservoirwill increase dramatically with continuedapplication of horizontal drainholtechnology. Additional study orel ationships and plotting parameters wilimprove early answers when limited data iavailable.

Two major concerns in the Bakken shale arthe 1ocation and productivi ty of unproppenatural fractures It is necessary to havalternatives for wells that do not perform aplanned. Future work may include:

1. Additional refinements in bothcompletion and stimulation techniques

A wellbore mini frac .2. Better definition of fracture areas.3. Solutions to hole stability4. Improved analytical models.5. Improved methods for early analysis.

CONCLUSIONS

Drainage area and recoverable reservefor a horizontal well are 2.5 to 3.0times that of a vertical well.

2. Original oil in place in the Fairway

ranges from 2.0 MM O to 2.7 MM O429 E+03 m] per square mile [2.6 km].

3. Recoverable reserves of 200-250 M O

[32-40 E+03 m] with better wellrecovering 300-500 M O [48-79 E+03 m

4. Fracture network effect i veness determi neproductivi ty and dec1ine characteri st ics

5. Average initial decline is 40-45% withfinal decline of 25-35%.

6. Bakken drainholes, usually recover 20-25%of their reserves in the first year.

7. Formation damage ,can have significanimpact on productivity.

8. Effective H (thickness) of the reservoiis larger than the actual thickness (hof the upper Bakken shale.



SPE 22389 M.R. REISZ 7

NOMENCLATURE Subscripts

ACKNOWLEDGMENTS

REFERENCES

The author wishes to thank the management ofUnion Texas Petroleum for their support inthe publication of this study. The valuableinput and insights from D.T. Boyd and V.K.Bangia are greatly appreciated. C.D. Croweand S. Housley did a great job in preparation

of manuscript and tables.

e externalf = fractureh = horizonta'i

n = net drainhole lengthp = produced oilv = verticalW= wellbore

1. Frick, T.C., Petroleum ProductionHandbook P = 37-10 thru 37-12, MilletThe Printer, Inc. , Dallas, Tx., 1962.

2. Agulleria, R., The Uncertainty ofEvaluating Original Oil-In-Place inNaturally Fractured Reservoirs , SPWLA19th Annual Logging Symposium June 1316 1978.

3. ORYX North Dakota Industrial CommissionHearing, Case No. 5030 Exhibit 6.

4. Joshi, S.D., Production ForecastingMethods for Horizontal Wells , SPE 17580SPE International Mtg. Tianjin, ChinaNov. 1-4, 1988.

5. Nelson, R.ll., Geologic Analysis ofNatura y Fractured Reservoi rs, Chapt. 1P = 72-102 t Gulf Publishing CompanyHouston Tx., 1985.

6. King G.R., Material Balance Techniquesfor Coal Seam and Devon ian Shale GasReservoirs , SPE 20730 Annual Mtg. inNew Orleans, La., Sept. 23-26, 1990.

7. Williams Petroleum Consulting andMinerals Diversified Services, Inc., Williston Basin Bakken FormationStudies, Part I and II , Industry Reportin 1990.

8. Joshi, S.D., Methods Calculate AreaOra ined By Hori zonta1 Well s , Oi 1 and GasJournal (Sept. 17 1990), P = 77-82.

9. Joshi, S.D., Reservoir Aspects ofHorizontal Wells , SPE Short Course at

the

initial reservoir pressure, psia[kPa]bubble point pressure, psiainitial production rate, BOPD mid

= production rate at time t),BOPD[m3/d ]

= drainage radius, ft. [m]= drainage diameter, ft. [m]= recovery factor, = initial oil saturat ion, = water saturation, = viscosity, cpo [Pa s] half the side of a drainage area

which is parallel to the horizontalwell, ft. [m]

= fracture half length, ft. [m]= distance from drainage boundary to

the center of the drainhole, ft. [m]= drainage length of rectangle

(diameter), ft. [m]

= half the side of the drainage areawhich is perpendicular to thehorizontal well, ft. [m]

distance from the x axis drainageboundary to the dra inho1e, ft. [m]

= side of drainage rectangle inhorizontal plane, ft. [m]

porosity,

a

A

b

Bo

coeEUR

h

PbQiQt

= half the major axis of drainageellipse, ft. [m]

= drainage area, acres [m2]

= half the minor axis of the drainageel l ipse, t [m]

Boi = initial formation volume factor,[dimensionless]

= formation volume factor at bubblepoint, [dimensionless]

= compressibility, I/psi [I/Pa]= fracture spacing, ft. [m]= natural fracture width, [cm.]= e s t i m a t e ~ ultimate recoverable oil,

bbls. [m]= reservoir thickness, ft. [m]= effective thickness of

reservoir, ft. [m]H.D. = horizontal displacement, ft. [m]k = permeability, md.Kh = horizontal permeability, md.L = horizontal drainhole length, ft. [m]L Xe = penetration ratio, [dimensionless]N original oil in place, bbls. [m3

]

OOIPPi

Ye

w

xf w

r2revRFSoiSwu

x

2Xe

2Ye

15



8 RESERVOIR EVtlLUATION OF HORIZONTAL BAKKEN WELL PERFORMANCE SPE 2238

Annual Mtg. in New Orleans, P = 46, Sept.20; 1990:

10. Mukherjee, H., A Parametric Comparisonof Hori zonta1 and 'Vert ical Well

Performance , SPE 18303, Annual Mtg. inHouston, Tx., Oct. 2-5, 1988.11. Karcher, B J Some Practical Formulas

To Predict Horizontal Well Behavior , SPE15430, Annual Mtg. in New Orleans, La.,Oct. 5-8, 1986.

12. Joshi, S.D., Augmentation of WellProductivity With Sl ant and Hori zonta1Wells , Journal of Petroleum Technology(June 1988), P = 729-739.

13. Williams, LT Pressure TransientAnalysis of Horizontal Wells in aNaturally Fractured Reservoir , SPE20612, Annual Mtg. in New Orleans, Sept.

23-26, 1990.

APPENDIX A

EXAMPLE PROBLEM: Drainage Area of theMeridian 33-11H locatedin Sec. 11-143N-102W(Elkhorn Area)

ver tical well (320 acre [1295 E+03 mdrainage case) is 2Xe = 3474 [1059 m] and Y= 4012 [1223 m].

For a horizontal drainhole Xe

can bcalculated from equation 9

. . . . .A-

2Xe = 2082' + 2 (2106 ) = 6294 ft

The rectangular anisotropic drainage lengthfor 33-11H is calculated as 2Xe = 6294[1918 m] and 2Ye = 4012 [1223 m]. Th

r i n ~ e area is equal to 580 acres [234E+03 m] This number is consistent with thdrainage area of 646 acres [2614 E+03 m

which was calculated from equation(material balance).

METHOD 2:

The drainage area of a conventional well ian isotropic reservoir can be obtained by thequation

METHOD 1:

Solving equations A-I and A-2 simultaneously,we obtain

The calculation of the drainage area for ahorizontal drainhole in an anisotropicreservoir such as the Bakken, can be

obtained. Beginning with equations 6 and 7and solving for a 320 acre [1295 E+03 m ]

vertical drainage case (assumed)

. . . . . (A-5

. . . . . (A-6

Area = 4Xe ~

Area = EUR (Bo) (5.615)(RF) h (l-Sw)

From equation 6, the Area would be equal t Xe times 2Ye for a rectangular drainagarea. From equation 8 2Ye can be written iterms of 2Xe for an anisotropic reservoirTherefore, the area of a rectangul aanisotropic drainage area can also brepresented by the equation

. . . . . (A-I)

. . . . . (A-2)

Ye /2Xe = jXy Kx

Ye / 2Xe = 1.155

(2Xe) (2Ye) = 320 x 43560

(1/2Xe) (2Xe) (2Ye) (2Ye)= 320 x 43560 x 1.155

4Ye = 16.1 x 10

2Ye = 4012

Substituting equation A-6 into equation A-

and solving, drainage length (2Xe) i. . . . . (A-3) obtained for a well in an anisotropireservoir where the drainage area is noknown.

Substituting 4012 [1223 m] into equationA-2, 2Xe = 3474 [1059 m]. The rectangularanisotropic drainage lengths for this

4Xe2 = UR Eo 5 .615

RF He f f 0 l -SW

A-7



SP 22389 M.R. R ISZ 9

From Table 3 and 4,

4xe2 1.155) = 427,000) 1.5) 5.615) .2) 20) .04) .85)

Xe = 23922Xe = 4784

Substituting 4784 [1458 m] into equationA-2, Ye = 5526 [1684 m]. The drainage areais equal to 607 acres [2456 E+03 m2]. Thisnumber is consistent with the drainage areaof 646 acres [2614 E+03 m2], which wascalculated from equation 5.

M THO

The average of the area of an ellipse and thearea of a rectangle plus a circle will alsogive a consistent answer 669 acres [2707E+03 m2] .

The area of a rectangle plus a circle isequal to

2Xe) 2Ye) + pie r2ev) / 43560

= 6294 ) 4012 ) + pie 2106)2 / 43560= 859 acres

The average of 478 acres [1934 E+03m2] ellipse and 859 acres [3476 E+03m2] rectangle pl us ci rcl e) is equal to 669acres [2707 E+03 m2].

Area of El lips e = pie a) b)43560

a = Ln / 2 re v

1/2 of major axis1041 + 2106 = 3147

A-8)

A-9)

1/2 of minor axis A-I0)

b = 2106

Area of Ellipse = pie 3147 ) 2106 ) / 43560= 478 acres

7



T BLEKKEN RESERVE V RI BLES FROM FIELDS IN F IRW Y

CALCULATED

DATE DRAINAGE CUM OOIP

LOCATION 1ST Qi Qt CUM OIL OOIP AREA EUR OIL 2

S T FIELD WELL PROD BOPD) BOPD) MHO MHO) ACRES) MHO) EUR) MBO/MI)

1. 11-143-102 ELKHORN 33-1lH 9-87 333 133 280 2738 66 442 63.3 2639

2. 07-142-101 ASH COULEE 1-7 2-90 636 221 131 1782 572 405 32.7 1994

3. 05-142-102 ROOSEVELT 23-5H 5-90 176 51 18 368 200 93 20 1178

4. 29-143-101 ELKHORN 34-29H 8-88 267 90 137 1242 293 262 52.3 2713

5. 33-143-101 ELKHORN 12-33H 4-89 441 139 167 1364 347 337 49.6 2516

6. 27-145-101 ROUGH RIDER 14-27H 9-89 412 216 157 1735 469 425 37.6 2368

7. 33-145-101 ROUGH RIDER 21-33H 2-89 218 111 1003 217 181 61.3 2958

8. 36-145-102 BUCKHORN 36-44H2 8-89 420 89 93 761 167 200 46.5 2916

9. 19-145-103 BICENTENNIAL 33-19H 6-88 485 22 ISS 822 230 183 84.7 2287

10. 29-145-103 BICENTENNIAL 31-29H 4-89 369 41 99 633 159 145 68.3 2548

11. 29-145-103 BICENTENNIAL 33-29H 10-89 291 89 72 S 7 147 196 36.7 2207

NOTE: RECOVERY FACTOR=20



TABLE2B

TABLE 2A

Parameters orEarly Determination of Ultimate Recoveries Parameters orEarly Determination of Ultimate Recoveries

KEY CRITERIA: HORIZONTALDRAINHOLESIN TABLE 1__ ___ = === ==== _ _== ===== ===_: c

KEY CRITERIA: HORIZONTALDRAINHOLESWITH WELL PATH RANKING OF A

SORTED BY EUR

Production Data

Well location

Zonal

Penetration

ft.)

Wellbore Orientation

Pat h Az imut h)

Ranking degrees)

Fracture

Index

Qi Ot CUM. PROtO EUR

BOPO BOPO MBO) MBO)

Drainage

Area

acres)

Well Locallon

Zonal

Penetration

ft.)

Wellboro Orlentallon

Path Azimu th ) Fracture

Ranking degrees) Index

ProducUon Data

Ot Ot

BOPD BOPO

Drainage

CUM. PROtO EUR Area

MBO) MBO) acres)

Ideal Prefer> 2 of pay In opt imum direc tion

1. 33-11H 11-143-102 2082 A 161 A 333 133 290 442 664

3. 23-5H 05-142-102

1. 33-11H 11-143-102

636 221

333 133

347

170 392

167 337

123 408

139

179

180

364

639

441

88

177

164

A

A

A

2019

2858

2033

44-35H 35-144-102

44-7H 07-146-102

5. 12-33H 33-143-101

2

664

572

93

405

18

280 442

131

5176

A

166

161

E

A

73

2082

07-142-101 1-7

4. 34-29H 29-143-101 1063 A 46 267 90 137 262 293

4. 34-29H 29-143-101 1063 A 46 267 90 137 262 293

5. 12-33H 33-143-101 2033 A 164 441 139 167 337 347

31-35H 35-146-104 1100 A 70 278 96 114 232

6. 14-27H 27-145-101 1754 B 178 412 216 157 425 469

11. 33-29H 29-145-101 1905 A 107 291 69 72 196 147

7. 21-33H 33-145-101 1280 B 90 218 80 111 181 217

36-44H 36-144-103 2088 A 166 135 58 37 156

8. 36-44H 36-145-102 2242 90 420 89 93 200 167

10. 31-29H29-145-101 1761 A 71 369 41 99 146 159

9. 33-19H 19-145-103

AVERAGE EUR =

196 147

261

926

57 1 31

49

218

101

73

A

2065

19502-31H 31-145-103

43-3H 03-143-102

230

145 159

183

99

72

155

89

41

22

369

291

485

71

94

107

A

A

C18

1761

19059-145-101

29-145-101

1

0. 31-29H

11. 33-29H

AVERAGE EUR - 251



TABLE 2C

Parameters For Early Determinationof illtimate Recoveries

KEY CRITERIA: HORIZONTAl DRAINHOLES WITH >2OOO IN ZONE NETPAY)

SORTED BY EUR

_ _ ---- _ ------ -------- ------ - -- -- - -- - -- ;:::===::::=== ===== ======Production Data

Zona l WeUbo ra Ori en ta ti on ------- -------- Drainage

Penetration P at h ( Az im ut h) Fracture QI at CUM. PROD EUR Area

Well location (ft.) Rank ing (degrees ) Index (BOPD) (BOPD) (MBO) (MBO) (acres) .........== _liZ== ___

-===== ====== --_._- -- -_ .....=.

1. 33-11H 11-143-102 2082 A 161 A 333 133 260 442 664

4 4- 7H 0 7- 14 6- 10 2 2858 A 88 364 179 123 408

44-35H 35-144-102 2019 A 177 639 180 170 392

5. 12 -33H 33-143-101 2033 A 164 441 139 167 337 347

I14-35H 35-143-102 2579 77 185 96 53 202

8. 36-44H2 36-145-102 2242 90 420 89 93 200 167

36-44Hl 36-144-103 2086 A 188 135 58 37 156

33-35H 35-146-104 2000 88 220 98 64 146

43-36H 36-147-103 2450 85 171 41 48 109

43-3H 03-143-102 2085 A 73 218 41 57 103

14-33H 33-143-102 2050 27 134 22 22 39

44-23H 23-143-102 2607 92 101 3 31 35

========= ====== . .......... _- . ..... -= ..=== ======== = .- _

AVERAGE EUR • 214

TABLE 3

Meridian ~ l l H

WellParametersfor Example Problem (Appendix A)

PARAMETER SYMBOL VALUE SOURCE

====== ====== ====== ====== ====== ====== ======

Horizontal Displacement H.D. 3132 ft. MDS Williams

NetDrainhole .Ln 2082 ft. MDS .Williams

length inzone

Azimuth Azm 161 degrees MDS data

Formation thickness h 8 ft. Lng.

Effectivethickness Heff 20 ft. In house

Drainage radius of circle , 1489 ft. Calculated

(160 acre case) ev (160)





FOR320 ACREVERTICALCASE: Penetration ratio Lnl2Xe 0.331 Calculated

For 6 acre case) (0.411)

Drainagelengthalongthe 2Xe 6294 .ft. Calculated

drainholeinthex direction

Drainage lengthalong high 2Ye 4012 ft. Calculated,

permeability direction

Drainage radius of ellipse . 3147 ft. CaleuWed

major axis)

Drainage radius of ellipse b 2106 ft. Calculated

(minor axis)

Average Drainage area - A(b) 669 acres Calculated

horizontaldrainhole



TABLES

TABLE 4 BAKKENPARAMETERS

Meridian 33 IIH

FORMATION PROPERTIES

Reservoir Parameters for Example Problem Appendix APARAMETER SYMBOL VALUE SOURCE

PARAMETER SYMBOL VALUE SOURCE¢ total porosity 4.0 Core PBU Analysis

Ini tia lReservoi r p ressure Pi 4500 psi MDS data Initial R eservoir p ressure Pi 6 psi MDS data

Bubble Point pressure Pb 2500 psi MDS data

I

rUbble Point pressure Pb 2500 psi MDS data

Oil gravity 45.3 degrees MDS dataConnate w ater s aturation Swc IS Assumed

API

IIwater compressibility c w) 3 0E Q6 Assumed

Reservoir temperature T 240 degrees MDS data

F I IPermeability range K 0.2 - 1.0 md. Core

Ky .014 1 md. PBU Analysis

Gas oil ratio Rs 850 scf /s tb MDS data I I Kx 01 - .09 md.

Kv 0.9124 md.

IFormation Volume Factor I I 0.05 md.

Initial Boi 1.3 rb/stb MDS data

@Bubble point Bo 1.5 rb/stb MDS data IIAverage thickness

h 10 ft. MDS data

Heff 20 ft. Inhouse

Initial prod. rate Qi 333 BOPD MDS data

IIReservoir temperature T 240 deg ree s MDS data

Currentprod. rate Qt 151 BOPD MDS data F

Cumulative production Np 249 MBO MDS data

IUltimate recoverable EUR 427 MBO In house FLUID PROPERTIES

reserves

Recovery factor RF 20.0 MDS dataFormation VolumeFactor

Initial Boi lAO rb/stb MDS d ata

¢ t

@Bubble point Bo 1 54 rb /st b MDS data

Total porosity 4.0 Core

Oil gravity 42 degrees MDS data

API

Initial hydrocarbon Soi 85 Assumed

saturationOil viscosity at reservoir 0.3 cp MDS data

Effective permeability K 0 .2 - 1 md CoreAverage Gas oil ratio Rs 850 s cf/ stb MDS data

Ky .014- .17

IIRecovery factor RF 15.0 MDS data

x .01 09 to 20.0



BAKKEN PLAYBAKKENPARAMETERS

TABLE6

•••••••••••FRACTUREN TWOR PROPERTIES

PARAMETER SYMBOL VALUE SOURCE

= = =

HORIZONTALWELL

,/> fI.P.200-400 BOPD

Fracture porosity 0 05 to Empirical correlations200-250 MBO RECOVERABLE

I0 30

Fracture compressibility e f) 81 8E 06 Williams Petroleum I SURFACE

I IArea of

Development to

Fracture spacing D 4 ft. From Industry

IDate

100 em. IWYOM N

em. Empirical correlations I I I0

50NaturalFracturewidth e IOE-03 to t

IOE-02 MILES

Minimumwidth e IOE-OS em. L it e ra t ur e

Fracture permeability k f) 0 2 md. W ;Z 1 1 . , X ~ ~ i i t i i & . : ~ ' 4 M ( : b : : , i M b.

Figure1 • Williston Basin



Figure 7 - Group •A· : 21 WellsHorizontal Bakken Performance

Rate Va Montha From Iat Prod

Figure 8 - Bakken PlayGroup •A· Wells

1st Month Production Rate

• ~ N : . : O : . : . o : : . . : . w e : . : : : I I . = - - - - - - - - - - - - - - - - - _7

eII

4

8

2

10 L _

»80

lbtal we••••

_a.r ,

0-100 1 2 2 8 8 4 4 1 1 1

BOPD88

M I N . RATE I

II 10 2

MONTHa OF PROD

I ...... ePROD --+- MAX. RATE

1 L _ L L l _ l L . . . . l . _

o

Figure 9 - Bakken PlayGroup •A· W ells

Recoverable Reuerves

Figure 1

THE PHYSICAL MODEL

II ~ N o O:: ..:.W eI::::I.= .

4

8

2

o 1 1 1 1110-200 200-801) 8 4 400-1100

RESERVES YBO)

lbtal welle· _a.I..,h

Lo

___ Xw

... Xe

Figure - Drainage Areas

V e r t i c a l w e l l Drainage Volume Schematic

OIL r ••

Horizontal Well Drainage Volume Schematic

reservoir evaluation of horizontal wells

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