PROCEEDINGS INDONESIAN PETROLEUM ASSOCIATION Twenty Fourth Annual Convention, October 1995
HORIZONTAL WELL INFLOW PERFORMANCE IN RESERVOIRS WlTH DISCONTINUOUS VERTICAL PERMEABILITY CHARACTERISTICS
Pudji Pennadi*
ABSTRACT
A large volume of publications have been available in the literature showing the benefit of horizontal wells in relatively heterogeneous reservoirs. However, a lack of attention is given to show the advantages for improving production performance in multilayer reservoirs and reservoirs that contain discontinuous shale. Many Indonesian oil reservoirs are such kind. The present study investigates the effects of vertical discontinuity in inflow performance of a horizontal well and also presents methods to forecast the oil production. These can help engineers in screening application of a horizontal well for non-homogeneous reservoirs. The major conclusions are that a horizontal well should be placed in the most permeable layer of a multilayer system, productivity decreases markedly with increasing shale density, and breakthrough time increases as effective vertical permeability decreases. Detailed results are presented and discussed.
INTRODUCTION
Attention to the use of horizontal wells for improving oil and gas recovery has been widely spreading over the world. The advantages of horizontal wells over unfractured conventional vertical wells are theoretically that inflow flux area is much larger, the drawdown required for a given rate of production is lower, and thus the reservoir energy used to produce the fluids is lower. However, horizontal well drilling and completion costs are generally higher and it is well known that its inflow performance is strongly influenced by vertical permeability of the reservoir.
A large number of papers dealing with horizontal
* Institute Technology Bandung
wells mostly relate to a single homogeneous layer, vertically anisotropic reservoir systems. Only few publications concern multilayer reservoirs (Kuchuk and Saeedi, 1992) and reservoirs with shales intercalated (Borner et al., 1988, Lien et al., 1992). In fact, due to geologic nature of deposition processes, reservoirs are basically multilayer systems with or without impervious layers within the layers. In many cases, however, a geologic unit can be considered as a single layer with randomly distributed permeability b amers .
In many depositional environments, such as point bars, distributary channel, deltaic sands, and marine sediments, sand-shale sequences are normally found (Weber, 1982). The existing shales may either be continuous (i.e., deterministic shales) or discontinuous (i.e., stochastic shales) in lateral direction (Haldorsen and Lake, 1984) (see Figures l a and lb). In the context of this study, a shale layer is said to be continuous if sand layers have no hydraulic communication within the &&age area, but it is discontinuous if the sand body has vertical flow communication. Continuous shales are not our interest in this study. The discontinuous shales may vary in length from few to more than 300 meters (see Figure 2). These discontinuous shales become obstacles to fluid flow and thus reduce vertical permeability of the reservoir. Because horizontal well inflow performance is influenced not only by horizontal permeability, but also by vertical permeability, a decrease in the latter will reduce the well productivity.
Probably, no one knows exactly the shale distribution within a pay zone. Naturally, discontinuous shales must be randomly distributed within the sand matrix. If working with such reservoir systems, a detailed geologic study is a must for estimating the shale
distribution, dimension, density, and the volumetric fraction.
Some researchers (Prats, 1972, Begg et al., 1985, Deutsch, 1989) have devoted their efforts to come up with empirical correlations for predicting effective permeability of shaly reservoirs. The correlations are very simple to use provided that net to gross, sand permeabilities, mean shale length, and number of shales per meter are known.
Because the study on the application of horizontal wells to heterogeneous reservoirs is still rare, the purpose of the present study is to investigate inflow performance of horizontal wells in intercommunicating multilayer systems and shaly reservoirs (defined here as reservoirs containing random, discontinuous shales) as wel!. To handle a problem of predicting inflow performance of a horizontal_ well in a multilayer reservoir, a new method is developed to estimate the effective permeability. A published correlation for calculating vertical permeability of a shaly reservoir is used. This study is restricted to reservoirs with no flow boundaries and also with bottom water drive.
PRODUCTIVITY INDEX
Definition
Productivity index is an index that represents the production rate of a reservoir fluid for a given drawdown. It is mathematically defined as the ratio of rate of production at stock tank condition- t o - the pressure drop within the reservoir, and for single phase as
cl J = Pr - P"f
The meaning of each symbol can be found in the Nomenclature section of this paper. The equation above is valid only for a specific condition. For two phase (gas and liquid) flow, J decreases with rate and bottomhole flowing pressure.
Vertical Well
In the context of this paper a vertical well is a well
that vertically penetrates the pay zone. Productivity index of a vertical well for circular drainage area with no flow boundaries is
0.0 0 7 0 8kh h J, = 1
6
A Horizontal Well in A Multilayer Reservoir
A horizontal well is a well with its productive portion lying horizontally within the reservoir. Many analytical solutions to estimate productivity of a horizontal well have been developed for homogeneous reservoirs. The physical models used consider only uniform vertical anisotropy. Recently, Kuchuk and Saeedi (1992) performed a study on the inflow performance of a horizontal well located. in a multilayer-bounded reservoir. They employed Green's function and Laplace transform to solve the problems. The resulting equations are so complex that they are not convenient for most practicing engineers.
The present study offers a new method which is more simple than the previous one just mentioned above. The basic physical model used in this study is the model proposed by P. Permadi (Permadi, 1993) (see Figure 3). The equations that were developed for homogeneous, vertical anisotropic reservoir have been validated using data and results of simulation studies, and field data as well (Pemadi, 1995). Excellent matches were obtained. This is the reason to continue to develop a new procedure to handle .heterogeneous reservoirs, particularly multilayer ones. The procedure is actually simple, but tedious. Basically, the confining flow region is divided into "n" equal size pie segments (see Figure 3) such that a number of grid blocks are generated as shown in Figure 4. The detailed procedure is given in Appendix A. The objective of the procedure effective permeability, k, region so that the anisotropy
is to approximate the of the confining flow factor, p, is
15
where
2 kihi - 1 kh = n
hi 1 (4)
Productivity index of the horizontal well is thus for pseudosteady-state is (Permadi, 1993)
0.00708khhL
(5)
Jh =
where
D = X, - yeE) E = [z E)
A Horizontal Well in a Shaly Reservoir
As discussed above, productivity index of a horizontal well is definitely influenced by the vertical permeability value. It is interesting, therefore, to investigate effects of shale distribution on the inflow performance.
There are some empirical correlations available in the pertinent literature (Begg et al., 1985, Deutsch, 1989) for estimating the effective vertical permeability of a reservoir containing stochastic shales. For general use, Begg et al. (1985) provide a simple equation for single layer systems,
when the shales and matrix parameters are known, then the effective vertical permeability can be calculated and the anisotropy factor p is
p = (25-)0.5
Productivity index of the horizontal well can thus be determined using Equation ( 5 ) in which "h" is now the net thickness.
PRODUCTION DECLINE AND CUMULATIVE PRODUCTION
In screening a reservoir candidate and for7 initial economic justification of a horizontal well application, a short or an intermediate term predictive tool is usually needed. Several methods empirically (Plahn et al., 1987) and analytically (Mutalik and Joshi, 1992) derived are available in the literature. Very recently, a simple method that was validated using field data (Permadi, 1995) was proposed and therefore is employed in the present study. The method should be used for depletion drive reservoirs. The equations to forecast production performance are
D - D - & i 'wf q o - 1 5.615B,,t
and
where
BREAKTHROUGH TIME FOR WATER
In most situations in which a thin oil column is underlain by water, the oil production rate is (much) higher than its critical coning rate (defined as a rate below which water will not form a cone), The reason is that higher rates are more attractive due to economic considerations.
It is known from previous studies that vertical permeability strongly affects coning performance. The presence of discontinuous shales must therefore influence the coning behavior. This paper will show how significant the influence on breakthrough time for water, particularly in a horizontal well.
One of several methods available in the literature (Permadi, 1995, Plahn et al., 1987, Mutalik and Joshi, 1992, Ozkan and Raghavan, 1988) for estimating breakthrough time is (Permadi, 1995)
16
DATA, RESULTS, AND DISCUSSION
Productivity hdex - Multilayer Systems
In this case the effect of permeability distribution in the vertical direction is examined. The reservoirs are assumed to have (i) no-flow outer boundaries, (ii) flow communication between layers, and (iii) produce oil at pseudosteady-state conditions.
Two sets of hypothetical data are obtained from published literature. One data set has a random permeability distribution, but the variation in permeability in the vertical direction is not large (see Figure 5) . Another set of data (see Figure 6 ) has a wider range of permeability values decreasing with depth and all layers have equal thickness. The reservoir and well parameters are shown in Table 1.
Productivity Index - Resewoirs with Impermeable Layers
The results in terms of horizontal-to-vertical well productivity ratio are presented in Tables 2 and 3. For a rnultilayer reservoir with intermediate permeability variation and randomly distributed, three different cases are evaluated by locating a horizontal well in layer-2, -8, and -9, respectively. Table 2 shows that a horizontal well positioned within a layer of high permeability yields higher productivity. But in this particular example, the differences are not significant because the permeability contrast is not large and the permeabilities are randomly distributed. Nevertheless, the placement of a horizontal well within layer-2 gives lower productivity although the permeability is relatively high. This is caused by so-called off- centered effects as shown in the work by P. Permadi (1 993).
Table 3 shows an extreme case for a data set exhibited in Figure 6. There is a trend of increase in productivity as the well placement moves to the higher permeability layer. In this case, a horizontal well within layer3 which has high permeability can overcome the off-centered effect. As compared to the results of the Kuchuk-Saeedi study, the present study shows similar trends. Results also imply that the horizontal well section should not be drilled within a layer with low permeability.
Examples given here assume that shales act as the discontinuous impermeable layer. The shales are randomly distributed and known from cores, well logs, and geologic interpretations. Table 4 presents the basic reservoir and well parameters. Tables 5 and 6 show results for short and long shales, respectively. Overall, these results point out that the denser and the longer the shales within a productive formation, the lower the horizontal productivity. For these particular examples, the horizontal well application still shows the benefit of increased productivity. However, since a horizontal well performance is strongly influenced by shales dimension, density, and distribution, a detailed geologic study on the depositional environment of the reservoir must be carried out before the application.
Production Decline and Cumulative Production
Estimation of productivity index is particularly useful in evaluating well performance at a specific time. Production rate as a function of time is usually nseded to analyze project economics. Equations 8 and 9 may be used to forecast production performance of a horizontal well. This paper will demonstrate the effects of shales on the performance. Some results presented in Tables 5 and 6 are used to show the production performance. The clean reservoir (Case No. 1) is selected as a reference. Cases No. 2 and 6 for short shales and Cases No. 2 and 5 for long shales are evaluated in terms of production decline and cumulative production.
Figures 7 and 8 show the declines in systems with short and long shales, respectively. The difference in production rate is clearly seen during the early period of production, but the rates will eventually be the same for all cases. The effect of shales on the performance would be better demonstrated using cumulative plots as exhibited in Figures 9 and 10. For these particular examples, small amounts of relatively short shales randomly distributed does not significantly affect a horizontal well performance. A high value of shale fraction (greater than 2.0) with a mean shale length greater than 100 feet (30 meters) aggravates the performance. These might reveal that application of a horizontal well to other cases with
17
denser and longer shales, and higher matrix anisotropy factor would not be attractive.
Bmakthmugh Time
Examples of the effect of shale distribution on breakthrough time for bottom water is illustrated in this section. Table 7 presents the reservoir and well parameters used for illustrating the idea. That table is a field data set. The given shale distribution is hypothetical. Employing a published correlation to estimate viscous drawdown AP,, the breakthrough time was determined using Eq.(l 1) and the results are given in Table 8. Inspection of Table 8, it is clear that a relatively low fraction of randomly distributed short shales would not considerably influence the breakthrough time. For short shales, denser distribution of the shales will delay the breakthrough longer although lower well productivity will be expected as described above. As the discontinuous, random shales become denser and longer, the breakthrough time would be much longer, but of course the productivity would also decrease.
CONCLUDING REMARKS
1.
2.
3.
4.
5 .
A simple method is provided to estimate productivity index of a horizontal well producing oil from a multilayer system.
For intercommunicating multilayer reservoirs, in general, a horizontal well should be placed in a layer having higher permeability.
The higher the distributed shale fraction in a reservoir the lower the effective vertical permeability and thus the lower the productivity of the horizontal well.
For a given drawdown, lower effective vertical permeability due. to existing random shales delays bottom water breakthrough.
As a rule of thumb, a productivity improvement (Jh/Jv) of about 2 to 2.5 times could provide sufficient economic justification (Crouse, 1992). The value of 2 or 2.5 is the average ratio of horizontal-to-vertical drilling and completion costs. Therefore, the benefit of horizontal well application in general would be still attractive as
long as the productivity improvement ratio is comparable with that cost ratio. The reason is that a horizontal well could accommodate a greater volume of production.
REFERENCES
1.
2.
3 .
4.
5 .
6.
7.
8.
Begg, S.H., Chang, D.M., and Haldorsen, H.H., 1985, A Simple Statistical Method for Calculating the Effective Vertical Permeability of a Reservoir Containing Discontinuous Shales, paper SPE 14271 presented at the SPE Annual Technical Conference and Exhibition, Las Vegas.
Borner, D.L., Haldorsen, H.H., Harrison, P.F., Hopwood, and MacDonald, C.J., 1988, Performance of Vertical and Horizontal Wells in Reservoirs Containing Discontinuous Shales: Numerical Studies of Two North Sea Fields, paper SPE 17600 presented at the SPE International Meeting, Tianjin.
Crouse, P., 1992, Screening and Economic Criteria for Horizontal Well Technology, paper SPE 23617 presented at the I1 LAPEC of the SPE, Caracas, Venezuela.
Gilman, J.R., 1991, Discussion of Productivity of a Horizontal Well, SPE Reservoir Engineering, February, 147-148.
Haldorsen, H.H., and Lake, L.W., 1984, A New Approach to Shale Management in Field-Scale Models, SPE Journal, August, 447-457.
Kuchuk, F.J., and Saeedi, J., 1992, Inflow Performance of Horizontal Wells in Multilayer Reservoirs, paper SPE 24945 presented at the SPE Annual Technical Conference and Exhibition, Washington, DC.
Lien, S.C., Haldorsen, H.H., and Manner, M., 1992, Horizontal Wells: Still Appealing in Formations With Discontinuous Vertical Permeability Barriers?, JPT, December, 1364- 1370.
18
9. Murphy, P.J., 1990, Performance of Horizontal Wells in the Helder Field, JPT, vo1.42, No.6, June, 792-800.
10. Mutalik, P.N., and Joshi, S.D., 1992, Decline Curve Analysis Predicts Oil Recovery from Horizontal Wells, Oil & Gas Journal, Sept. 7, 42- 48.
11. Ozkan, E., and Raghavan, R., 1988, Performance of Horizontal Wells Subject to Bottom Water Drive, paper SPE 18545 presented at the SPE Eastern Regional Meeting, Charleston.
12. Papatzacos, P., Herring, T.R., Martinsen, R., and Skjaeveland, S.M., 1989, Cone Breakthrough Time for Horizontal Wells, paper SPE 19822 presented at the SPE Annual Technical Conference and Exhibition, San Antonio.
13. Permadi, P., 1993, New Formula for Estimating Productivity of Horizontal Wells, paper IPA 93- 2.3 presented at the 22nd IPA Annual Convention, Jakarta.
14. Permadi, P., 1993, Pengaruh Posisi Sumur Horis ont al Terh ad ap Pro duktivit asny a, JT M GB , NO.3, 66-74.
15. Permadi, P., 1995, Practical Methods to Forecast Production Performance of Horizontal Wells, paper SPE 29310 presented at the SPE Asia Pacific Oil & Gas Conference, Kuala Lumpur.
16. Plahn, S.V., Startman, R.A., and Wattenbarger, R.A., 1987, A Method for Predicting Horizontal Well Performance in Solution Gas Drive Reservoirs, paper SPE 16201 presented at the SPE Production Operation Symposium, Oklahoma City.
17. Prats, M., 1972, The Influence of Oriented Arrays of Thin Impermeable Shale Lenses of Highly Conductive Natural Fractures on Apparent Permeability Anisotropy, JPT, October, 1219- 1221.
18. Weber, K.J., 1982, Influence of Common Sedimentary Structures on Fluid Flow in Reservoir Models, JPT, March, 665-672.
NOMENCLATURE
Ad
Boi B
H Jh
Jhi
JV
effective area, sq ft oil formation volume factor, bbVSTB initial oil formation volume factor, bbl/STB a constant defined by Eq.(lO) initial total compressibility, psi-1
mean horizontal extension of streamtube or a half of mean shale length, ft number of shales per meter, ft-1 fraction of shales, fraction thickness, ft thickness of layer-i, ft vertical distance from Water-Oil Contact to horizontal wellbore, ft distance measured from well axis, ft productivity index of horizontal well, STB/D/psi initial productivity index of horizontal well, STB/D/psi productivity index of vertical well, STB/D/psi effective permeability above horizontal well axis, md effective permeability below horizontal well axis, md effective permeability of the confining flow region, md horizontal permeability, md horizontal permeability of layer-i, md effective permeability of layer-i, md horizontal permeability of sands, md vertical permeability of sands, md vertical permeability, md effective vertical permeability, md vertical permeability of layer-i, md subscript for designated layer-1 horizontal well length, ft number of layers after re-arrangement original number of layers cumulative oil production, STB initial pressure, psi reservoir pressure, psi bottom hole flowing pressure, psi pressure drop due to viscous forces, psi rate of production, STBId oil production rate, STB/d radial distance as defined by Eq.(A-4), ft well radius, ft
I9
drainage radius, ft radius defined by Eq.(A-2), ft skin factor, dimensionless residual oil saturation, fraction . time, days breakthrough time, days reservoir width, ft reservoir length, ft defined by Eq.(A-28)
p = anisotropy factor, dimensionless Ay,,, = difference between hydrostatic gradients of
water and oil, psilft
P O = oil viscosity, cp P W = water viscosity, cp n = 3.1415927 4 = porosity, fraction
= defined by Eq.(A-21)
20
APPENDIX A
Procedure for Calculating Effective Permeability in Pseudo-Radial Region of a Multilayer Resemoir
1. Input data required are reservoir and well parameters, such as X,, Ye, h, (= thickness of each layer), h (= total thickness), L, r,,,, N (= number of layers), khi, hi.
2. Add one impermeable layer above the most top layer, one below the most bottom layer, and divide the layer in which the horizontal well axis is located into two layers, such that (see Figure 4).
Ih = R - h/21
lhN+2 = R - h/2] (-4-3)
3. Divide the confining flow region into semiradial segments above and below well axis and into gridblocks to determine k(ij) (see Figure 4).
4. Assign coordinate numbers for each gridblock as shown in Figure 4.
5 . Determine Arj = hj with
6. Calculate vertical distance measured from well axis.
a. Above well axis
b. Below well axis
m=l+l (A-9)
H, = R
(A-1 0)
(A-1 1)
21
Aef j = 0.5 2 R 2 arcsin(h/ZR) + h d m ) (
7. Calculate cumulative radii.
for j = 0 or j = ~ + 3
a. Above well axis
R, = R
b. Below well axis
j- 1
R~ = Arm = Rj- l + Arj-l m = l + l
% = R
8. Calculate the effective area to determine k, and kb
-1 forj#Oandj;tN+3
9. Calculate the effective radius.
10. Calculate angle between block segments.
a. Above the well
ap(i, j) = arcs in I I l al(i, j) = arcs in
(A-12)
(A- 13)
(A- 1 4)
(A-15)
(A- 1 6)
(A-17)
(A-18)
(A-19)
(A-20)
(A-2 1)
(A-22)
(A-23)
22
(A-24)
b. Below the well
al(i, j) = a r c s i n R j + l + R j
1 1. Calculate permeability in radial direction.
12. Calculate permeability of radial segments.
a. Above the well
1
~ k . 3 = a(i, j)k(i, j) + a ( j r I) i=j+l
4
b. Below the well
; i # j
; i = j
; i # j
; j = O
; j # l
; j = 1
kj = 1 [ 2 2a(i, j)k(i , j)] ; j = N + 2 - a ( N + 5 N + 2) i = l + l
(A-25)
(A-26)
(A-27)
(A-28)
(A-29)
(A-3 0)
(A-3 1 )
(A-32)
(A-33)
(A-34)
23
13. Calculate the effective permeability.
a. Above the well
( R e f l + l = r w l
b. Below the well
I i = l + l I
; j # l - t l
; j = l + l
~~
14. Determine the effective permeability of the pseudo-radial region.
Ik,,, = 0.5(ka + k,) l
(A-35)
(A-3 6)
(A-3 7)
(A-3 8)
(A-3 9 )
(A-40)
24
Well Length
(ft)
TABLE 1 MULTILAYER RESERVOIR AND WELL PARAMETERS
(AFI'ER KUCHUK AND SAEEDI, 1991)
Horizontal-to-Vertical-Well Productivity Ratio Jh/Jv in STB/D/psi
This Study's Well Location Kuchuk & Saeedi's Well Location
Layer-2 Layer-8 Layer-9 Layer-2 Layer-8 Layer-9
Reservoir length, ft Reservoir width, ft Reservoir thickness, ft Oil viscosity, cp Formation volume factor, bbl/STB Radius of wellbore, ft
1.9 2.1 2.4 2.8 3.1 3.5 3.7 4.1 4.6
4000 4000
98 1 .o 1 .o
0.33
2.3 2.4 3.5 3.5 - 4.5 4.4
TABLE 2 RESULTS FOR MULTILAYER RESERVOIR WITH RANDOMLY DISTRIBUTED
PERMEABILITY
1000 1500 2000
2.6 3.7 4.7
TABLE 3 RESULTS FOR MULTILAYER RESERVOIR WITH PERMEABILITY
DECREASES DOWNWARD
I I .-, 2000
Horizontal-to-Vertical Well Productivity Ratio Jh/Jv in STB/D/psi
This Study's Well Location Layer-;! Layer-8 Layer-9
Kuchuk & Saeedi's Well Location Layer-2 Layer-8 Layer-9
1.6 1.5 0.5 2.4 2.2 0.7 3.2 2.9 0.9
2.2 1.8 0.6 3.2 2.6 0.9 4.0 3.4 1.3
1 I
25
TABLE 4 BASIC RESERVOIR AND WELL PARAMETERS
(AFTER GILMAN, 1991)
2640 2640 1475 45 350 70
1.05 7.5
0.33 1 x loJ (assumed)
TABLE 5
RESERVOIR CONTAINING SHORT SHALES HORIZONTAL-TO-VERTICAL WELL PRODUCTIVITY RATIO :
26
K, (Eq.6) (md)
70 7.9 7.4 6.1 3.4
TABLE 6
RESERVOIR CONTAINING LONG SHALES HORIZONTAL-TO-VERTICAL WELL PRODUCTIVITY RATIO :
Jh 1 J"
5.7 3.8 3.5 2.9 2.0
(fraction)
0 0.05 0.1 0.1 0.2
f (# / ft)
0 1/20 1/20 1/10 1/10
0 100 100 100 200
TABLE 7 RESERVOIR AND WELL PARAMETERS BOTTOM WATER DRIVE RESERVOIR
(AFTER MURPHY, 1990)
2000 2700 2700 1348
0.354 3680 2944
53 63
0.30 0.29 1.06 28.9 0.6
0.88 1.07
27
Fs f 1 K, (fraction) (# 1 ft) (ft) (Eq.6)
(m4
0.05 1/100 2 2354 0.1 3/10 5 946
0.2 5/10 10 224 0.1 1 120 100 252 0.2 1/10 200 24
TABLE 8 WATER BREAKTHROUGH TIME FOR VARIOUS SHALES DENSITY
