Compositional gradient: its role in near-critical reservoir development

Journal of Petroleum Science and Engineering 45 (2004) 193 – 201 www.elsevier.com/locate/petrol

Compositional gradient: its role in near-critical reservoir development Shanqiang Luoa,*, Maria A. Barrufetb a

Schlumberger, College Station, TX, USA Department of Petroleum Engineering, Texas A&M University, College Station, TX, USA

b

Abstract In thick reservoirs, gravity force can generate variation in composition along the hydrocarbon column. For near-critical reservoirs, compositional gradient can be appreciable, and as a result, it can significantly influence reservoir development strategy. Through simulation study, this paper investigates the effect of isothermal compositional gradient on the estimation of initial in situ hydrocarbon, prediction of gas/oil contact (GOC) location, and reservoir production performance. D 2004 Elsevier B.V. All rights reserved. Keywords: Compositional gradient; Near-critical reservoir; Simulation

1. Introduction Muskat (1930) used a simplified equation of state (EOS) to conduct compositional gradient calculations, with results showing negligible effect of gravity on compositional variations in reservoirs. Sage and Lacey (1938) used a more accurate EOS to research compositional gradients and concluded that compositions may change greatly with depth in reservoir systems, especially in near-critical systems. Schulte (1980) used a Cubic EOS to perform a series of calculations and suggested that binary interaction coefficients used and the aromatic content of oil can also affect the compositional gradient. * Corresponding author. E-mail addresses: [email protected] (S. Luo)8 [email protected] (M.A. Barrufet). 0920-4105/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2004.07.005

Montel and Gouel (1985) presented a new method of predicting fluid compositional variation with depth. Wheaton (1991) developed a theoretical treatment of composition variations with depth in hydrocarbon reservoirs and provided some applications in several North Sea gas-condensate fields. And, Hoier and Whitson (1998) investigated the miscibility condition variations for a number of reservoir fluid systems exhibiting compositional gradients due to gravity/chemical equilibrium. All of these researches provided solid theoretical background about modeling compositional gradient effect. Will and how will this compositional gradient phenomenon influence production performance in near-critical reservoir development? Through simulation study, this paper investigates the role of isothermal compositional gradient in near-critical reservoir development.

194

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

2. Equilibrium criteria in a gravitational field

3. Simulation model and data

The Gibbs free energy under a gravitational field is (Firoozabadi, 1999):

3.1. Reservoir parameters

dG ¼  SdT þ V dP þ mgdh þ

Nc X

ðli þ Mi hgÞdni

i¼1

ð1Þ where G is the Gibbs free energy, S is entropy energy, T is temperature, V is volume, P is pressure, m is mass, g is gravity constant, h is height, i is the component number, N c is the number of total component, l i is the component chemical potential, M i is the component molecular weight, and n is the component moles. At equilibrium, dG must vanish. Pressure and height (h) are related through the hydrostatic head equation as V dP þ mgdh ¼ 0

Some basic reservoir parameters refer to paper bThird SPE Comparative Solution Project: Gas Cycling of Retrograde Condensate ReservoirsQ (Kenyon and Behie, 1987). Table 1 indicates the characteristics of the synthetic reservoir used for this study. 3.2. Fluid PVT properties

ð2Þ

The sample fluid initially had 36 components and was lumped into seven pseudocomponents by using Whitson’s stepwise characterization procedure. This fluid represented a gas condensate field from Colombia, and no attempt was made to calibrate the EOS model to the experimental data. The lumping was conducted to reduce the computational time. Table 2 contains the description of the fluid model used.

ð3Þ

4. Simulation results and discussions

ð4Þ

Based on the above reservoir model and fluid properties, a set of numerical simulations was made to investigate the effect of compositional gradient.

For an isothermal system dT ¼ 0 then, Eq. (1) becomes  d li þ Mi hgÞT ¼ 0

i ¼ 1; N ; Nc

This expression provides the Gibbs sedimentation equation 

dli þ Mi gdhÞT ¼ 0

i ¼ 1; N ; Nc

ð5Þ

Expressing the chemical potential l i in terms of fugacities f i , where (dl i =RTdln f i )T and integrating this from a reference depth of zero to h gives 

fi ¼ fi0 exp 

Mi gh RT

 i ¼ 1; N ; Nc

ð6Þ

Eq. (6) provides the fugacity calculation of component i in a given phase as a function of the vertical position h. The Peng–Robinson EOS is used to calculate fugacity in this work. Given the pressure and compositions at a reference depth, the composition and pressure at any depth can be calculated.

4.1. Effect of compositional gradient on fluid properties 4.1.1. Fluid composition change versus depth Fluid composition change versus depth is shown in Fig. 1. The profile shows obviously that the lightest Table 1 Reservoir parameters used in this study Case Number of grids in Number of grids in Number of grids in Dimensions (ft) X Dimensions (ft) Y Dimensions (ft) Z Porosity Permeability (md) Kv/Kh Reservoir reference Reservoir reference

X direction Y direction Z direction

depth (ft) pressure (psia)

Coarse

Fine

9 9 4 300 300 1000 0.13 100 0.1 12000 6200

9 9 40 300 300 100 0.13 100 0.1 12000 6200

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

195

Table 2 Properties of the seven pseudocomponents used in the fluid model MW Mole fraction Tc (R) Pc (psia) x

PC1

PC2

PC3

PC4

PC5

PC6

PC7

16.1 0.620 342.6 667.1 0.013

34.6 0.141 549.3 827.4 0.140

44.1 0.051 665.6 615.8 0.152

69.6 0.067 829.1 505.4 0.228

125.1 0.074 986.6 304.3 0.818

244.5 0.034 1260.9 190.6 1.082

409.7 0.013 1652.1 160.5 1.272

and the heaviest components have the largest compositional gradient, and intermediate components have smaller gradient. Also, as a result of gravity segregation, heavy fractions increase while light fractions decrease with depth. 4.1.2. Saturation pressure change versus depth Saturation pressure change versus depth is shown in Fig. 2. With increasing depth, it is observed that the bubble point pressure decreases, while dew point pressure increases. This is in sharp contrast with the fixed saturation pressure that would result by ignoring the compositional gradient and using a single reference composition for the entire depth. 4.2. Effect of compositional gradient on the estimation of in-place hydrocarbon content First, by assuming the fluid sample reference depth is in the middle of the reservoir (12,000 ft), we obtain the in-place oil and gas reserve surface volumes, as indicated in Fig. 3. It is apparent that the oil surface

volume considering the gradient is larger than that when the gradient is ignored, and consequently, the gas surface volume with gradient is smaller than that without gradient. Three reference depths were analyzed for the reference composition: one in the middle of the reservoir, one at the top of the reservoir, and the third at the bottom of the reservoir. The resulting oil and gas surface volumes for these three cases are shown in Fig. 3. When the reference depth is at the top of the reservoir, the estimated oil surface volume with gradient is bigger than without gradient, and consequently, the estimated gas surface volume of the gradient case is smaller than that of the nongradient case. This is apparent because the oil composition will become richer in the heavier compounds with depth, while it would remain constant when the gradient is ignored. When the reference depth is at the bottom of the reservoir, the estimated oil surface volume of gradient case is smaller than that of nongradient case, and consequently, the estimated gas surface volume of gradient case is bigger than that of the no-gradient case.

Fig. 1. Compositional gradient profile generated from the PR EOS – The reference sample composition used is at 12,000 ft depth (T reservoir=280 8F).

196

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

Fig. 2. Saturation pressure change due to compositional gradient (T reservoir=280 8F).

The fluid composition of the entire column can erroneously be taken constant either at an optimistically high percentage of heavier components (bottom reference) or at an extremely conservative low percentage of heavier components (top reference). Both scenarios provide incorrect estimates of the inplace hydrocarbons. A reference composition located in the middle offsets partially these discrepancies. 4.3. Effect of compositional gradient on the depletion production recovery As shown earlier, compositional gradients can greatly affect fluid properties and in-place hydrocarbon estimation. Therefore, a practical concern may

be bwill compositional gradient influence the field depletion production recovery?Q Coarse and fine grids in the vertical direction were used in further simulations to answer this question. And the reference sample is in the middle of the reservoir. The resulting depletion liquid recovery profile is shown in Fig. 4, which shows that gradient case will have a much optimistic liquid recovery than the nongradient case will. To secure the accuracy, other two situations changing reservoir temperature from 280 8F (gas-condensate case) to 240 and 200 8F (volatile oil cases) were simulated, and the results are indicated in Figs. 5 and 6, which also indicate that gradient cases yield a much higher depletion liquid recovery than the nongradient cases do.

Fig. 3. Comparison of hydrocarbon surface volumes by using reference sample compositions at different depths (T reservoir=280 8F).

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

197

Fig. 4. Depletion liquid recovery (Coarse grid, T reservoir=280 8F).

Over so large a reservoir interval (4000 ft), using so coarse grids in the vertical direction (four layers) may not capture the proper physical behavior. Therefore, finer grids, as discussed before, were used to repeat the above simulations. Production constraint is the same as in the coarse grid cases. The results from these simulations are shown in Figs. 7–9. The results seem very interesting because three simulations consistently show that depletion liquid recovery with compositional gradient is almost the same as the depletion liquid recovery without the compositional gradient cases. This is attributed to using a reference composition in the middle of the reservoir that offsets the compositional variations to the top and the bottom

of the reservoir. These results would not coincide if the reference depth and composition were taken at the top or the bottom of the reservoir. Because the same compositional gradient data were used in both coarse and fine grid simulations, it is apparent that coarse grids oversimplify the description of compositional gradient in the fluid column because the reservoir simulator considers initial fluid compositions to be the same in the same layer (although initial compositions are different in different layers). The size of the fine grid used may not be sufficiently accurate, and the objective of this paper is to illustrate these differences and the necessity to investigate the proper grid size on an individual case-by-case basis.

Fig. 5. Depletion liquid recovery (Coarse grid, T reservoir=240 8F).

198

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

Fig. 6. Depletion liquid recovery (Coarse grid, T reservoir=200 8F).

4.4. Effect of compositional gradient on the gasinjection production recovery Early discussion shows that depletion liquid recovery is almost insensitive to compositional gradient, provided that the reference sample is taken near the middle of the reservoir. Production practices often require the injection of gas to maintain reservoir pressure and achieve higher recovery. Our concern is whether compositional gradient will affect the liquid recovery from gasinjection processes. Because a fine grid simulation provides a more accurate description of the reservoir dynamics, we used the fine grid model (40 vertical grid layers) to analyze the effect of including or

ignoring the compositional gradient in gas injection processes. Considering the reservoir temperature to be 280 8F (gas condensate), two situations were analyzed: one with gas injection in the top first layer and the other with gas injection in the top 10 layers, and in both situations, all the produced gas is reinjected into the reservoir. Results are shown in Figs. 10 and 11. Both situations show that the compositional gradient has a profound effect on the liquid recovery by gas injection. The reason is that if significant compositional gradient occurs at different depth in-place fluid properties, such as saturation pressure change, the minimum miscible pressure (MMP) will change when gas is injected (Hoier and Whitson, 1998). Hence, in practical gas-

Fig. 7. Depletion liquid recovery (Fine grid, T reservoir=280 8F).

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

Fig. 8. Depletion liquid recovery (Fine grid, T reservoir=240 8F).

Fig. 9. Depletion liquid recovery (Fine grid, T reservoir=200 8F).

Fig. 10. Liquid recovery with gas injection (Fine grid, T reservoir=280 8F; top 1 layer injecting produced gas).

199

200

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201

Fig. 11. Liquid recovery with gas injection (Fine grid, T reservoir=280 8F; top 10 layers injecting produced gas).

injection production, ignoring compositional gradient will result in very different liquid recovery.

5. Conclusions (1)

(2)

(3)

Compositional gradient has significant impact on the in-place hydrocarbon estimation and fluid properties prediction, but has little effect on liquid depletion recovery if the reference fluid composition is taken near the middle of the reservoir. Optimistic or pessimistic estimation of the inplace hydrocarbon content depends upon what reference depth for sample fluid you take. The oil composition of the entire column can erroneously be taken constant either at an optimistically high percentage of heavier components (bottom reference) or at an extremely conservative low percentage of heavier components (top reference). Both scenarios provide incorrect estimates of the in-place hydrocarbons. A reference composition located in the middle offsets partially these discrepancies. When significant compositional gradient occurs, a sensitivity analysis should be conducted to define the proper grid size in the vertical direction when conducting simulations. A compromise should be achieved between a more accurate description of in-place fluid content and production performance and computational overhead.

(4)

Compositional gradient has great effect on gasinjection liquid recovery. Further analysis should be conducted to analyze the effect of completions in producer and injector wells to asses whether ignoring a compositional gradient provides always overly optimistic liquid recoveries.

Acknowledgment The authors gratefully acknowledge the financial support provided by the Petroleum Engineering Department at Texas A&M University for this research work. References Firoozabadi, A., 1999. Thermodynamics of Hydrocarbon Reservoirs. McGraw-Hill, New York. Hoier, L., Whitson, C.H., 1998. Miscibility variation in compositionally grading reservoirs. SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, (SPE49269). Kenyon, D.E., Behie, G.A., 1987. Third SPE comparative solution project: gas cycling of retrograde condensate reservoirs. Journal of Petroleum Technology, 981 – 997. Montel, F., Gouel, P.L., 1985. Prediction of compositional grading in a reservoir fluid column. The 60th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers. The Society of Petroleum Engineers, Las Vegas, NV. SPE14410. Muskat, M., 1930. Distribution of non-reacting fluids in the gravitational field. Physical Review 35, 1384 – 1393.

S. Luo, M.A. Barrufet / Journal of Petroleum Science and Engineering 45 (2004) 193–201 Sage, B.H., Lacey, W.N., 1938. Gravitational concentration gradients in static columns of hydrocarbon fluids. Trans. AIME 132, 120 – 131. Schulte, A.M., 1980. Compositional variations within a hydrocarbon column due to gravity. The 55th Annual Fall Technical Conference and Exhibition of the Society of Petroleum

201

Engineers. The Society of Petroleum Engineers, Dallas, TX. (SPE9235). Wheaton, R.J., 1991. Treatment of variations of composition with depth in gas-condensate reservoirs. SPE Reservoir Engineering, 239 – 244.