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Analytical assessment of horizontal well ef ciency with reference to improved oilrecovery of the South-East Dragon oil eld southern offshore of Vietnam

N.M. Quy a , P.G. Ranjith b ,⁎ , S.K. Choic, P.H. Giao d , D. Jasinge b

a Technology Research and Development Dept, Vietnam Petroleum Institute, Vietnamb Rock Mechanics Division, Monash University, Australiac CSIRO Petroleum, Clayton, Australiad AIT, Thailand

a b s t r a c ta r t i c l e i n f o

Article history:Received 31 January 2007Accepted 25 December 2008

Keywords:horizontal wellvertical welloil recoveryproduction rateef ciencywell length

Nowadays, improved oil recovery (IOR) becomes much needed in eld development planning, and is one of the main concerns for engineers in many reservoir management projects. Among IOR methods, horizontalwells have been widely applied in the world, and proved to be a promising technique. However, prudence isrequired in order to ensure maximum economic bene t in applying the technology.In this study, the applicability of horizontal well in the South-East Dragon eld, which is a small fracturedbasement reservoir in the southern offshore of Vietnam, was assessed. An overview of the SE Dragonreservoir characteristics was provided. The potential performance of horizontal wells was analyzed usinganalytical approaches, and the performance was compared with that predicted for vertical wells. Sensitivitystudy was conducted to investigate the effect of horizontal well length on well performance. The results of this study showed that, instead of a 350 m vertical well, drilling of a 400 m horizontal well at the samelocation could produce an additional 3,658,166 bbl of oil after 20 years. The ef ciency increasedproportionally with horizontal well length. The actual production rate can however be lower than predictedbecause of the assumptions used in the analysis.

© 2009 Published by Elsevier B.V.

1. Introduction

Horizontal wells have been successfully applied to enhanceproduction from steeply dipping reservoir (Gangle et al., 1995) andheavy oil reservoirs ( Catania, 2000 ). Horizontal wells can providesigni cant improvement of production over vertical wells ( Solimanand Boonen, 1999 ). However, success in applying the technologyrequires careful consideration of a number of factors. Some of thesefactors have been discussed by, for example, Zhang et al. (2006) .

Gangle et al. (1995) compared the eld results of horizontal wellswith the conventional wells in a steeply dipping Stevens sandreservoir in the Elk Hills eld in California. They observed higherrates, lower draw downs, and lower gas/oil ratio which will extendthe life of the project and result in higher recovery. Catania (2000)compared the actual cumulative and daily oil production with thepredicted values from the Joshi's equation. According to their results,shorter wells ( b 1000 m) showed average daily production closer toactualvalues, whereas long wells( N 1000m) showed predicted resultshigher than observed. An increase of the percentage difference wasobserved in daily production and cumulative production with increase

in well length (20% to 40% and 70% to 130% respectively). Predictedand actual oil production observed showed a signi cant divergenceafter 24 months of production. The discrepancy between predictedand observed results could be due to signi cant pressure drop alongthe well due to the high viscosity of the heavy oil being produced.Soliman and Boonen (1999) discussed the fracturing in horizontalwells. With the use of basic rock mechanics principles, reservoirengineering and operational strategies, transverse and longitudinalfractures in horizontal wells have been discussed. Also, they outlinedthe advantages and disadvantages of each type (transverse andlongitudinal) of fractures.

Stability of boreholes is quite important to gain the advantage of horizontal wells. Zhang et al. (2006) developed a wellbore modelbased on dual-porosity poroelasticity theory taking into account theimpact of solid deformation and uid ow. According to their studies,the stress concentration and stability of horizontal wells stronglydepend upon the in situ stress regime and direction of drilling.

This work mainly focuses on the analytical assessment of horizontal well ef ciency in comparison to conventional wells, withspecial reference to potential improvement in oil recovery from theSouth-East Dragon oil eld in the southern offshore of Vietnam. TheSouth-East Dragon eld is a small fractured basement reservoirlocated in the Cuu Long Basin, offshore of southern Vietnam, about20 km to the south of White Tiger eld ( Fig. 1). It was put on

Journal of Petroleum Science and Engineering 66 (2009) 75 – 82

⁎ Corresponding author.E-mail address: [email protected] (P.G. Ranjith).

0920-4105/$ – see front matter © 2009 Published by Elsevier B.V.

doi: 10.1016/j.petrol.2008.12.020

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production in 1996, and it is now at the development phase with six

vertical wells, including

ve production and one injection wells(Vietsovpetro, 1999 ). A full eld development planning is required toobtain an optimum production strategy. Horizontal well wasconsidered because of the many advantages in term of IOR. Horizontalwells have higher productivity and pay contact per well compared tovertical wells, thereby reducing the number of wells required to drainthe reservoir. Horizontal wells enable operators to take advantage of highly heterogeneous reservoirs, especially those with fractures, orwater and gas coning problems ( Joshi, 1991 ). To support the decisionof selection between conventional andhorizontal well in thenew welldrilling program, an assessment of horizontal well ef ciency has to beconducted. The main objectives of this study include a review of existing analytical solutions of ow towards a horizontal well andapplication of some suitable analytical solutions to the assessment of horizontal well ef ciency through the study of the followingparameters: drainagearea, productivityand cumulative oil productionof the well.

1.1. Drainage area

1.1.1. Drainage area of the vertical wellThe original oil in place (OOIP), based on the drainage area of the

well, can be volumetrically calculated using (in SI unit), ( Dake, 1978 ):

OOIP =Ah/ 1 − S wið Þ

Bo ð1Þwhere Ais thedrainagearea (m 2), h is the reservoir thickness (m), ϕ isthe porosity (fraction), S wi is the initial water saturation (fraction) and

B0 is the oil formation volume factor (m3

/m3

).

For single-phase ow, another form of the material balance

equation that can be used to calculate OOIP is ( Reisz, 1992 ):

OOIP =N t P

1 − Q t Q i RF

ð2Þ

where N t P is the cumulative oil production (m 3) at time t, Q t is the oilrate (m 3 /day) at time t, Q i is the initial oil rate (m 3 /day) and RF is therecovery factor (fraction).

From Eqs. (1) and (2), the drainage area of an existing vertical wellcan be obtained:

A =N t P Bo

1 − Q t Q i RF / h 1 − S wið Þ

: ð3Þ

1.1.2. Drainage area of a horizontal wellIf assuming the horizontal well drainage area is rectangular and in

a horizontal plane, then ( Reisz, 1992 ):

(1) Rectangular width, a h , is equal to the width of the drainageareaof the vertical well, a v

(2) The drainagelength, b h , is equal to the horizontal well length, L,plus drainage radius of the vertical well, r ev , at each end of thehorizontal wells.

Thus,

ah = avb

h= 2 r

ev+ L:

ð4

Þ

Fig.1. Location of the Dragon eld.

76 N.M. Quy et al. / Journal of Petroleum Science and Engineering 66 (2009) 75 –82



1.2. Productivity of the wells

In this study, the reservoir is assumed to be producing underpseudo-steady state condition, i.e. the average reservoir pressure willdecrease with time. The pseudo-steady state solution was used tocalculate the productivity of the vertical and horizontal wells.

1.2.1. Pseudo-steady state productivity of a vertical well

The pseudo-steady state productivity of a vertical well in oil

eldunit can be calculated using Eq. (5), ( Dake, 1978 ):

J v =7:08 4 10

− 3 4 h ffiffiffiffiffiffiffiffiffik xk yq μ oBo ln 0:565 ffiffiffiffiabp

r w− 0:75h i ð5Þ

where J v is vertical well productivity (bbl/day/psi), k x is thehorizontal permeability (mD) in x direction, k y is the horizontalpermeability (mD) in y direction, µo is the oil viscosity (cP), a and bare drainage width and length (ft) and r w is the wellbore radius (ft).

1.2.2. Pseudo-steady state productivity of a horizontal wellFor a horizontal well, there are several solutions available in the

literature to calculate the pseudo-steady state productivity such as:Babu and Odeh's method ( Babu and Odeh, 1988 ), Mutalik's method(Mutalik et al.,1988 ), and Kuchuk's method ( Kuchuk et al., 1988 ). Eqs.(6) – (18) were taken from the book Horizontal Well Technology by Joshi (1991) .

Kuchuk et al. (1988) expressed the horizontal well productivity byEq. (6), using approximate in nite conductivity solution. Averagepressurevalue of theuniform ux solution along thelength of thewellwas used to obtain the constant wellbore pressure.

J h =khh = 70 :6 μ oð Þ

F + h =0:5Lð Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffikh =kvp s x ð6Þ

where J h is horizontal well productivity (bbl/day/psi), F is a

dimensionless parameter which is a function of yw /2y e, xw /2x e, L/4xe and (y e/x e) ffiffiffiffiffiffiffiffiffiffiffiffiffik x =k yp , xw is the distance from the horizontal wellmid-point to the closest boundary in the x direction, yw denotes thedistance from the horizontal well to the closest boundary in the ydirection, xe is half length of side of square drainage area in x directionand ye is the half length of side of square drainage area in y direction,kh is the horizontal permeability (mD) and kv is the verticalpermeability. Value s x can be calculated as follows:

s x = ln π r wh 1+ ffiffiffiffiffikv

khs !sin π zwh " #− ffiffiffiffiffikh

kvs 2hL 1

3− zw

h +zwh

2 where L is the length of horizontal well (ft) and zw is the verticaldistance between the horizontal well and the bottom boundary.

Mutalik et al. (1988) expressed the horizontal well productivity byEq. (7). According to Mutalik et al. (1988) , when the drainage arearatio (2x e /2y e) is between 1 and 20, the shape factors and thecorresponding equivalent skin factors s CA,h for a horizontal wellshould be used.

jh =0:007078 kh = μ oBoð Þ

ln ffiffiffiffiffiffiffiffiffi A V = π p r w − A0+ s f + sm + sCA;h

− c 0 + Dqð7Þ

where s m is the mechanical skin factor (dimensionless), s f is the skinfactor of an in nite conductivity fully penetrating fracture of length L,sf = − ln[L/(4r w )], sCA,h is the shape related skin factor, c' is the shapefactorconversion constant (1.386) andA' is the drainagearea factor. A'equals 0.75 for circular area and 0.738 for square (and rectangular)

drainage area.

Babu and Odeh (1988) used the method of separation of variablesand Fourier series to solve the governing 3D ow equation. Thesolution for a horizontal well, which is of similar form to that for avertical well, is given by the following equation:

J h =7:08 4 10

− 3b ffiffiffiffiffiffiffiffik xk yq Bo μ o ln A0:5

4

r w+ lnC h − 0:75 + S r

h ið8Þ

where A⁎ is the horizontal well drainage area in the vertical plane(ft 2), C h is the shape factor of horizontal well and S r is the pseudo skinfactor due to fractional penetration. Among these methods, Babu andOdeh's method was most often used by engineers to calculate theproductivity of a horizontal well.

The geometric factor C h can be calculated using the followingequationwhich is given in theoriginal work of Babu and Odeh (1988) :

lnC h = 6 :28ah ffiffiffiffiffik y

k xs 13

− xo

a+

xo

a 2 − ln sin

180 o zo

h − 0:5lnah ffiffiffik z

k xs " #− 1:088

ð9Þwhere x o and z o are positions of horizontal well in x and z direction,respectively.

The pseudo skin factor, S r , can be calculated for the following twodifferent cases.

Case 1. a

ffiffiffiffik xp z 0:75 b

ffiffiffiffik yp N N 0:75 h

ffiffiffiffik zp where k z is the permeability in z direction (mD).

S r = P xyz + P V xy:

Here, P xyz component is a result of the degree of penetration (thevalue of L/b), and the P' xy component is a result of the well in the x – yplane, and they are given by:

P xyz =bL

− 1 lnhr w

+ 0 :25 lnk xk z

− ln sin180 o z

h − 1:84 ð10Þ

P 0 xy =2b2

Lh ffiffiffiffiffiffiffiffiffiffiffik z =k yq F L

2b + 0 :5 F 4 ymid + L

2b − F 4 ymid − L

2b ð11Þwhere y mid =0.5(y 1 +y 2)andy 1 andy 2 arethe coordinates of the twoends of the horizontal well in the y direction.

F xð Þ= − xð Þ0:145 + lnx − 0:137 xð Þ2h i

Case 2. b

ffiffiffiffik yp z 1:33 a

ffiffiffiffik xp N N 1:33 h

ffiffiffiffik zp :

In this case:

S r = P xyz + P y + P xy

where,

P y =6:28b2

ah ffiffiffiffiffiffiffiffiffik xk zp k y

13

− ymidb

+y2

mid

b2 !+ L24b

Lb

− 3 " # ð12Þand

P xy =bL

− 1 6:28ah ffiffiffiffiffiffiffiffik z =k xq 1

3− xo

a+

x2o

a2 !: ð13Þ

1.3. Cumulative oil production

1.3.1. Cumulative oil production of a horizontal wellThe cumulative oil production of a horizontal well can be

calculated using the semi-analytical solution developed by Plahn

et al.(1987) for predicting horizontal well performance in solution gas

77N.M. Quy et al. / Journal of Petroleum Science and Engineering 66 (2009) 75 –82



drive reservoirs. Their graphical correlations of the average results areas shown below for critical gas saturation between 6% and 10%

log N D =1 :2504 − 0:3903 log t D4 − 0:1097 log t D

4 2

For log t D4 V − 1:9496h ið14Þ

log N D = 1 :6663 + 0 :03701 log t D4 For log t D

4 z − 1:9469h ið15Þwhere, t D

⁎ : dimensionless producing time in oil eld unit:

t D4 = 0:00633 kkroi r wLpit

8/ μ oihx3e ð16Þ

where k roi is therelative permeability of oilat initial oilsaturation,p i isthe initial pressure (psi) and µ oi is the initial oil viscosity (cP).

N D: dimensionless recovery

N D =N P N m

4 100 ð17Þwhere N p is the cumulative oil produced at time t.

N m : the original movable oil in place

N m =2 xeð Þ

2h/ S oi− S or ð Þ

5:615 Boi ð

18

Þwhere S oi is the initial oil saturation (fraction), S or is the residual oilsaturation (fraction) and Boi is the initial oil formation volume factor(RB/STB).

2. Analytical assessment of horizontal well ef ciency

In this study, the performance of a horizontal well will be analyzedand compared with a particular existing vertical well in the SE Dragon eld. The solutions are limited to a single phase system with constantreservoir properties and without any compositional effect. Analysiswas conductedon a singlewell model with the assumptions that thereis no interaction between wells and the reservoir is producing underpseudo-steady state condition, with no supplemental energy. Theparameters of an existing vertical well will be calculated andcompared to that of a proposed horizontal well, which is assumedto be drilled at the same location with this vertical well. Both wells,therefore, have the same initial reservoir conditions.

2.1. Reservoir characteristics

The South-East Dragon reservoir is a small reservoir with the sizeof 8x7 km 2 , where the oil is produced from a naturally fracturedbasement. The porosity of the basement rock is related to fractures

and cavities caused by, for example, cooling-crystallization, weath-ering, hydrothermal action, and tectonic activities. Cavity and fracturecaused by hydrothermal action is an important porosity type of theDragon granitoid-basement reservoir ( Vietsovpetro (2003, 2004) ).The fracturing and weathering characteristics of the basement rocksvary over the area and depth of the eld. The model of the basementrock can be described as a combination of two components:

(1) The matrix part is consolidated granitic and granodioritic

blocks with negligible porosity and permeability, i.e., ϕ bb 1%,Kbb 0.1 mD.

(2) The main storage capacity includes large fractures, which weredeveloped by tectonic activities, the caverns and dense micro-fractures due to hydrothermal activities, and they are devel-oped along macro-fractures.

The maximum porosity is 10% and the minimum porosity is 0.1%.The mean porosity is 1.6%. Porosity decreases with depth. Highporosities can only be found at a depth of 100 – 200 m from thebasement surface. At greater depth, the rock is usually more intactwith low porosities.

The permeability of the basement rock varies from 5 to more than1000 mD. The mean value is 209 mD. These values are obtained bymeasurements on core samples taken from the existing wells.

The oil, gas and water samples had been taken from existing wellsfor PVT analyses in the laboratory. The results show that the crude oilhas density of 852 kg/m 3 , and the saturation pressure (bubble pointpressure) is at 1160 psi.

2.2. Reservoir production status

The SE Dragon eld was discovered in 1994 by Vietsovpetro andput on production from 1996. Five production wells, named as P1, P2,P3, P4, and P5, were drilled and put on production during 1996 – 2000.In 2001, an injector (I1) was drilled and put on operation for thepurpose of supplementing reservoir energy. The overall eld produc-tion rate is given in Fig. 2. In 2000 when all ve wells were put onproduction, the production rate increased to a peak of 610 m 3 /day.

Several well testing and well production analyses were conductedfor the production wells. The results of the well testing show that theinitial average reservoir pressure was 3973 psi. The formation damagefactor or skin factor varies from 0.197 to 1.854. The results of the welltesting are summarized in Table 1 .

2.3. Field production data

The reservoir characteristic data required for analytical solutionswere collected and summarized in Table 2 (Vietsovpetro, 2004 ).

Fig. 2. Overall eld production rate.




Among 5 existing production wells, the vertical well P1 is selectedfor assessment because of its longest production history (It has beenproducing oil continuously since 1998) with a relative stableproduction rate (see Table 3 ), and its longest well length of about350 m, compared to the others, is equal to the average thickness of theSE Dragon eld.

Because the analytical solutions are limited to single-phase system(no water injection), hence, only the production data of the well P1during 1998 to 2000, when the reservoir was produced under naturaldepletion, were used in this study.

2.3.1. Drainage area

2.3.1.1. Drainage area of the vertical well. The drainage area of anexisting vertical well can be obtained by Eq. (3). The recovery factorof the SE Dragon eld up to the year 2020, the estimated abandonmentdate of the reservoir under the natural depletion mode, was estimatedto be about 0.16 ( Vietsovpetro, 2003 ). This number was used as therecovery factor (R F) for well P1 in this study.

The production data of well P1 are taken from Table 3 . Other

parameters required for calculation such as B o, ϕ, Swi are taken fromTable 2 .Thus, the drainage area of well P1 is:

A =N t P Bo

1 − Q t Q i RF / h 1 − S wið Þ

= 2 ; 998 ; 995 m2 32 ; 280 ; 909 ft 2 :

If assuming the vertical well drainage area is rectangular then therelationship between the dimensions of the rectangle (a v and b v) and

the permeability components (k x and k y) can be represented by thefollowing equation:

bvav

= ffiffiffiffiffik y

k xs :

For a simple case when the permeability of the naturally fracturedreservoir in all directions is equal, k x =k y =k z , then well P1 can be

assumed to produce oil in a square area which has dimensions of:

av = bv = sqrt Að Þ= 1 ; 732 m 5; 682 ft ð Þ:The radius of the equivalent circular drainage area of the vertical

well is:

r ev = sqrt A = π ð Þ= 977 m 3; 206 ft ð Þ:

2.3.1.2. Drainage area of the horizontal well 2.3.1.2.0. For horizontal length of 400 m (1,312ft). From Eq. (4),

obtained:

ah = av = 1 ; 732 m 5; 682 ft ð Þbh = 2 r ev + L = 2 ; 355 m 7725 ft ð Þ:

Drainage area:

Ah = ah4 bh = 4 ; 077 ; 565 m2 43 ; 890 ; 547 ft 2 :

Similar approach wasapplied for other horizontal well lengths. Theresults of drainage area calculation are given in Table 4 and Fig. 3.

2.3.2. Productivity of the well

2.3.2.1. Pseudo-steady state productivity of the vertical well. Thepseudo-steady state productivity of a vertical well in oil eld unit was

calculated by using Eq. (5). The dimensions of the rectangular

Table 1The well testing results of the Dragon Oil Field.

No Parameters No of measuredwell

Measuredvalue range

Averagevalue

1 Initial reservoir pressure,kg/cm 2

5 256.4 – 319.9 274.8

2 Reservoir temperature, °C 4 85.2 – 96.7 87.223 Geothermal gradient,

°C/100 m4 3.8 3.80

4 Oil production rate, m3

/day 4 68.5–

1316 456.105 Gas production rate,103 m 3 /day

4 1.3 – 48.4 11.46

6 Gas oi l ratio, m 3 /m 3 4 4– 124.1 26.017 Permeability, D 4 0.0055 – 0.9305 0.218 Skin factor 4 0.197 – 1.854 0.57

Table 2Reservoir data collected for analytical solutions.

Parameter Notation SI unit Oil eld unit

Average reservoir thickness h 350 m 1148 ftAverage reservoir porosity ϕ 0.016 0.016Average reservoir permeability k 209 mD 209 mDInitial reservoir pressure p i 27.48 MPa 3984 psiOil formation volume factor B o 1.46 m 3 /m 3 1.46 RB/STBInitial oil saturation So i 0.66 0.66Irreducible water saturation Sw i 0.34 0.34Residual oil saturation So r 0.31 0.31Relative permeability of oil at initial

oil saturationkroi 0.7 0.7

Skin factor S 0.57 0.57Total compressibility C t 3.5 ⁎ 10− 3 MPa− 1 50 ⁎ 10− 6 psi − 1

Viscosity of oil at p i µo 1.05 cp 1.05 cpWellbore radius r w 0.1 m 0.33 ft

Table 3Production history of well P1.

Date Oil rate Cum. oil Date Oil rate Cum. oil

11/30/1998 768.2 23,047.15 2/28/20 01 504.3 504,215.312/31/1998 762.4 46,680.74 3/31/2001 457.6 518,401.41/31/1999 709.6 68,678.16 4/30/20 01 395.7 530,270.92/28/1999 727.2 89,039.41 5/31/20 01 504.3 545,905.53/31/1999 727.2 111,582.2 6/30/20 01 469.2 559,980.14/30/1999 697.9 132,518.2 7/31/20 01 446.3 573,816.65/31/1999 680.3 153,606.6 8/31/20 01 451.6 587,814.96/30/1999 645.1 172,959.2 9/30/20 01 439.8 601,009.97/31/1999 604 191,684.3 10/31/2001 439.8 614,644.68/31/1999 604 210,409.3 11/30/2001 428.1 627,487.7

9/30/1999 619.6 228,997.2 12/31/2001 422.2 640,577.110/31/1999 656.5 249,350.2 1/31/20 02 451.6 654,575.411/30/1999 635.7 268,421.3 2/28/20 02 457.4 667,383.312/31/1999 604 287,146.4 3/31/20 02 424.1 680,531.31/31/2000 574.7 304,962.5 4/30/20 02 510.2 695,837.42/29/2000 562.8 321,283.1 5/31/20 02 452.4 709,860.43/31/2000 545.4 338,190.2 6/30/20 02 424.9 722,606.14/30/2000 539.5 354,376 7/31/2002 543 739,440.55/31/2000 527.8 370,737.7 8/31/20 02 586.4 757,620.26/30/2000 504.3 385,867.9 9/30/20 02 576.7 774,920.27/31/2000 504.3 401,502.5 10/31/2002 586.4 793,099.98/31/2000 492.6 416,773.4 11/30/2002 574.7 810,341.39/30/2000 440.8 429,997.7 12/31/2002 572.4 828,084.710/31/20 00 486.7 445,086.8 1/31/20 03 568.8 845,71911/30/2000 510.2 460,392.9 2/28/2003 563 861,482.512/31/2000 453.8 474,459.3 3/31/20 03 537.2 878,135.11/31/2001 504.3 490,093.8 4/30/20 03 574.7 895,376.5

5/31/2003 563 912,829




drainage area (a and b) are taken from the previous result. Otherparameters needed for the calculation are taken from Table 3 .

Thus, the productivity of the vertical well P1 is:

J v = 129 STB=day = psi:

2.3.2.2. Pseudo steady state productivity of the horizontal well. TheBabu and Odeh's method was used to calculate the productivity of ahorizontal well.

2.3.2.2.0. For a 400 m horizontal well. Theresults of drainage areacalculation show that a horizontal well with length L= 1312 ft(400 m) has a box-shaped drainage volume with dimensions of a=5682 ft (1732 m), b=7725 ft (2355 m), and h=1148 ft (350 m).For simplicity, the well location is assumed to be along the y directionin the middle of the box, i.e., the well lies between y 1 =3206 ft(977m) toy 2 =4519 ft (1377 m). The x o and z o coordinates of the wellare2840 ft (866 m) and574 ft (175 m), respectively.Other parametersneeded for the calculation are taken from Table 2 .

By substituting the required parameters to Eqs. (8) – (13), theproductivity of a 400 m horizontal well was obtained:

J h =7:08 4 10

− 3b

ffiffiffiffiffiffiffiffiffik xk y

q Bo μ ln A0:5v

r w+ lnC h − 0:75 + S r h i

= 132 STB=day = psi:

Similar approachwasapplied for other horizontal well lengths.Theresults are summarized in Table 5 and Fig. 4, respectively.

In the calculations,wellbore damage was ignored and permeabilityis assumed to be isotropic. It was also assumed that the condition for

in nite conductivity holds,i.e., thepressure drop along thewell canbeignored. However, the actual production length of the horizontal wellmay be shorter than the physical length if the ow rate is very high.

2.3.3. Cumulative oil productionThe cumulative oil production of the vertical well P1 and the

alternative case of horizontal well were calculated up to the year 2020when it is estimated to be the end of the life of the reservoir under thenatural depletion mechanism.

2.3.3.1. Cumulative oil production of the vertical well. The OOIP canbe calculated using Eq. (1), where drainage area, A v, was obtained inprevious section, thus:

OOIP =Ah/ 1 − S wð Þ

Bo= 7 ; 591 ; 975 m3 :

At the abandonment time Q t =0, the cumulative oil production of vertical well P1, from 1998 up to 2020, can be calculated using Eq. (2):

N p = OOIP 4 RF = 1 ; 214 ; 716 m3 or 7; 640 ; 334 STBð Þ: 2.3.3.2. Cumulative oil production of the horizontal well. Thecumulative oil production of the horizontal well over 22 years(8030 days) was calculated in the same way as that for the verticalwell P1 by using Plahn's method (Eqs. (14) and (15)).

2.3.3.2.0. For a 400 m horizontal well. The Plahn's method is forsquare drainage area so it is needed to transform the dimension of

Fig. 3. Drainage area calculation results.

Table 4Results of drainage area calculations.

Drainage dimensions Drainage area, A A H/AV

Width Length

SI unit(m)

Oil eld unit,(ft)

SI unit(m)

Oil eld unit(ft)

SI unit(m) 2

Oil eld unit(ft) 2

Vertical well 1732 5682 1732 5682 2,998,995 32,280,909Horizontal well L=400 m 1732 5682 2355 7725 4,077,565 43,890,547 1.36

L=600 m 1732 5682 2555 8381 4,423,917 47,618,651 1.48L=800 m 1732 5682 2755 9037 4,770,270 51,346,754 1.59L=1000 m 1732 5682 2955 9693 5,116,622 55,074,857 1.71L=1200 m 1732 5682 3155 10,350 5,462,974 58,802,960 1.82L=1400 m 1732 5682 3355 11,006 5,809,326 62,531,063 1.94L=1600 m 1732 5682 3555 11,662 6,155,678 66,259,166 2.05L=1800 m 1732 5682 3755 12,318 6,502,030 69,987,269 2.17L=2000 m 1732 5682 3955 12,974 6,848,382 73,715,372 2.28




rectangular drainage area calculated in the previous section to that of an equivalent square drainage area. Other data required for thecalculation are taken from Table 2 .

The dimensionless producing time:

t 4

D =0:00633 kkroi r w Lpit

8/ μ oihx3e

= 0 :002287 :

The critical gas saturation of the SE Dragon eld is 7%, and:

logt 4

D = − 2:64 b − 1:9469 :

The correlation given by Eq. (14) was used to calculate thedimensionless recovery factor, N D.

Finally, one obtained:

N D = 32 :8N m =

2 xeð Þ2h/ S oi − S or ð Þ5:615 Boi

= 34 ; 427 ; 817 STB:

The cumulative oil production of horizontal well, N P:

N p = N D4 N mð Þ=100 = 11 ; 298 ; 500 STB or 1; 796 ; 318 m3

:

Similar approach was applied for calculating the cumulative oilproduction of the horizontal well with other well lengths. The resultsare given in Table 6 and Fig. 5.

3. Results and discussion

Horizontal well can improve well productivity and consequentlyoil recovery by a variety of mechanisms. The most basic mechanism isthe increased drainage area associated with the longer completion

interval of a horizontal well. The drainage area increases proportion-ally with horizontal length( Table 4 and Fig.3) when thepressure dropalong the well is not signi cant. Fig. 4 shows that when length isincreased, A H/AV will keep on increasing. A 400 m horizontal well hasa drainage area of 1.36 times more than that of a 350 m vertical well,while it is 2.28 for the 2000 m horizontal well. Because of the largerdrainage area of horizontal well, fewer wells are needed to achieve

similar eld ef ciency.The productivity of the horizontal well increases proportionally

with length. As can be seen in Fig. 4 and Table 5 , by increasinghorizontal well length from 400 to 2000 m, productivity could beimproved from 1.12 to 4.38 times that of a 350 m vertical well.However, the actual rate of increase maydecline when thewell is verylong and/orthe ow rate is very high, and the pressuredropalong thewell can no longer be ignored.

Having higher drainage area and higher productivity will conse-quently increase the cumulative oil production of the horizontal well.The ef ciency is also proportional to horizontal length. The results of the calculation given in Table 6 and Fig. 5 show that a 400 m horizontalwell could give an additional oil recovery of 581,602 m 3 compared to a350 m vertical well, while it is 2,201,474 m 3 for a 2000 m horizontal

well.The analytical results might be considered to be optimistic becausethe approach used a single well model with limitations of closeddrainage volume and single phase system. In reality, the production of the well could be affected by a variety of rock properties, by multi-phase ow related problems such as water coning and gas breakthrough, or by ow resistance in the well, which were not able to betaken into account in the analytical approach. Neglecting the frictionloss of ow from reservoir to wellbore and along well length could

Table 5Results of pseudo steady state productivity calculations.

Productivity, J J H/J V

SI unit(m 3/day/kg/cm 2)

Oil eld unit(STB/day/psi)

Vertical well 298 129.76Horizontal well L=400 m 303 131.48 1.02

L=600 m 442 191.73 1.49L=800 m 574 249.09 1.95

L=1000 m 701 303.95 2.39L=1200 m 822 356.59 2.81L=1400 m 939 407.25 3.22L=1600 m 1052 456.09 3.62L=1800 m 1160 503.26 4.00L=2000 m 1266 548.89 4.38

Table 6Results of cumulative oil production calculations.

Cumulative oilproduction, N P

Incremental N H/N V

SI unit(m3)

Oil eld unit(STB)

SI unit(m3)

Oil eld unit(STB)

Vertical well 1,214,716 7,640,334 0 0 -Horizontal

wellL=400 m 1,796,318 11,298,500 581,602 3,658,166 1.48L=600 m 2,048,236 12,883,015 833,520 5,242,681 1.69

L=800 m 2,268,691 14,269,637 1,053,975 6,629,303 1.87L=1000 m 2,473,892 15,560,315 1,259,176 7,919,981 2.04L=1200 m 2,670,422 16,796,446 1,455,706 9,156,112 2.20L= 1400 m 2,861,485 17,998,196 1,646,768 10,357,862 2.36L= 1600 m 3,048,836 19,176,599 1,834,120 11,536,265 2.51L=1800 m 3,233,518 20,338,214 2,018,802 12,697,881 2.66L= 2000 m 3,416,190 21,487,187 2,201,474 13,846,853 2.81

Fig. 4. Well productivity calculation results.




result in overestimation of well productivity and the drainage area of

the well. Also, wellbore damage is ignored in the calculations.However, it is likely that the effect of damage on well productivityfor a horizontal well is smaller than for a vertical well because of thelower rate of uid entry into the wellbore per unit length for ahorizontal well. On the other hand, the longer time that is required todrill a horizontal well can lead to greater degree of formation damage.Also, the horizontal well is located in a fractured basement reservoir.Both of these factors may lead to a signi cant reduction in the actualproducing length of the horizontal well.

4. Conclusions

From the result of this study, improved oil recovery in the SEDragon oil eld could be expected with the use of horizontal wells.

With a horizontal well length of 400 m, an additional 581,602 m3

of oilcould be produced. The ef ciency of horizontal well will increase withincrease in length. However, there is practical limitation on the lengthachievable due to the limitation of current drilling technology,especially drilling in fractured basement rock. Taking also into accountthe possible effect of very long well and high ow rate on friction lossalong the well on well productivity, a maximum horizontal length of 800 m is proposed as the most promising option for the SE Dragon eld.

Acknowledgement

The rst author would like to thank the Asian Institute of Technology (AIT) and Petrovietnam for providing budget that enabledhim to pursue this study.

References

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wells. J. Pet. Sci. Eng. 25, 187 – 204.Vietsovpetro, 1999. Dragon Field Outline Development Planning Report. Vung Tau.Vietsovpetro, 2003. Dragon Field Development Planning Report. Vung Tau, 2003.Vietsovpetro, 2004. Dragon Field Annual Production Report. Vung Tau, 2004.Zhang, J., Bai, M., Roegiers, J.C., 2006. On drilling directions for optimizing horizontal

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Fig. 5. Cumulative oil production calculation results.


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