SPE A Pseudo-Black-Oil Method for Simulating Gas Condensate Reservoirs S.-W. Wang, SPE, and I. Harmawan, SPE, Unocal Indonesia Co.

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1 SPE A Pseudo-Black-Oil Method for Simulating Gas Condensate Reservoirs S.-W. Wang, SPE, and I. Harmawan, SPE, Unocal Indonesia Co. Copyright 2005, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 2005 Asia Pacific Oil & Gas Conference and Exhibition held in Jakarta, Indonesia, 5 7 April This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box , Richardson, TX , U.S.A., fax Abstract A method was developed to estimate the composition of heavy end by matching MDT pressure gradient when downhole sample or reliable recombined surface sample is not available. After adjusting the heavy end or C7+ composition, an equation-of-state was used to match (1) MDT pressure gradient from calculated gas density, (2) dew point, (3) surface condensate yield, and (4) API gravity of condensate. The fine tuned equation-of-state was then converted into a pseudo black oil PVT table. This method allows reservoir engineers to study production from retrograde gas condensate reservoirs without using equation-of-state to handle complex phase behavior and commingled production from multiple reservoirs. Three examples are included to illustrate the proposed method. The first two examples give detailed description of step by step procedures. The third example incorporates a 3D reservoir simulation model and a pipeline to form an integrated model. The reservoir model consists of two separate reservoirs to be produced by two subsea wells, which are linked to a surface pipeline tied back to West Seno FPU. The advantages and disadvantage of this method are discussed at the end of this paper. Introduction This paper presents a method which tries to estimate liquid yield and phase behavior when there is lack of good downhole sample but good MDT pressure gradient is available. If we have good downhole sample or good recombined surface sample, the fluid composition and phase behavior can be determined in laboratory. However, if downhole sample is not available or only the composition of separator gas is available, then the true reservoir fluid composition can not be accurately determined. The main difference between a downhole sample and a separator gas sample is the missing of heavy end or condensate in separator gas. The mole fraction of C7+ in a good downhole sample, assuming no contamination, is known with certainty and should not be adjusted during regression of equation-of-state (EOS). On the contrary, separator gas is devoid of heavy end or C7+. Therefore, the main objective of this method is to estimate the mole fraction and/or molecular weight of the heavy end, C7+, so that the adjusted composition will yield a gas density at reservoir condition to match MDT pressure gradient. The adjusted fluid composition is considered to represent the true composition at initial reservoir condition. Algorithm The general principle of the proposed algorithm is summarized as follows: (1) Adjust composition and/or molecular weight of C7+ so that the gas density, ρ, matches MDT pressure gradient, P/h, at reservoir temperature and pressure as shown in equation (1). ρg = P/h = MDT pressure gradient (1) where ρ is gas density, g is gravity constant, P is initial reservoir pressure, and h is subsea vertical depth. (2) Based on adjusted C7+, calculate non-ideal gas factor, Z, to satisfy MDT gradient in equation-1 and gas PVT in equation-2 simultaneously. P*M w = ρ ZRT (2) where M w is gas molecular weight, Z is nonideal gas deviation factor, T is reservoir temperature, and R is universal gas constant. (3) Select appropriate parameters from a chosen equation-of-state (EOS) and tune EOS to match (a) gas density corresponding to MDT pressure gradient, (b) estimated dew point, and (c) condensate yield and API gravity at surface condition. (4) If the result in (3) is not satisfactory, then the EOS in step (3) is saved and reloaded back to the previous EOS as a new starting point for further fine tuning with a new set of parameters. This step is called successive substitution.

2 2 SPE More detailed description of the proposed methodology is presented in the following examples. Example-1 In this example, downhole sample is not available, nor is the composition of recombined surface sample. However, MDT pressure gradient, separator gas composition, and separator liquid yield at surface condition are available. MDT gradient is shown in Figure-1, which yields a pressure gradient of psia/ft. Table-1 shows the initial compositions of three separator gas samples from Bangka Upper Channel reservoir. Reservoir temperature is F and initial reservoir pressure is 4415 psia. Liquid yield at surface separator is approximately 29 B/MMSCF and 50 0 API gravity. In order to fine tune gas composition, we have to estimate the true composition of the heavy end or C7+ since recombined oil and gas sample is not available. Step-1: The first step is to calculate average gas composition from three surface gas samples, which have been stripped of condensate as shown in columns 3 though 6 of Table-1. Step-2 is to substitute calculated average gas composition into an EOS such as Peng-Robinson EOS to calculate gas density at prevailing reservoir temperature and pressure. This process usually will not match MDT pressure gradient right away without further adjustment of C7+, which is lost in the gas phase. Adjustment of C7+ mole fraction and/or its molecular weight is a trial-and-error process. The molecular weight of C7+ usually is reported in the gas composition analysis. If it is not available, C7+ molecular weight can be estimated from condensate API through correlations. When C7+ mole% is adjusted, the mole% of the rest components needs to be adjusted accordingly in order to maintain the total mixture s composition equal to 100% as shown in the last column of Table-1. We then substitute adjusted overall gas composition into an EOS to calculate gas density at reservoir condition, which can be converted into MDT gradient according to equation-1. Strictly speaking, an EOS may not be necessary at this step since all it takes is to calculate a new Z-factor for the adjusted gas composition. Any appropriate Z-factor correlation or program should do equally well. Note precise matching of gas density is not absolutely necessary since all we need is a good approximation in the first pass so that we can proceed to step- 3. Step-3 requires integrating all pertinent data together, which includes estimated dew point, separator conditions, condensate yield ratio, API gravity of condensate, and gas density back calculated from MDT pressure gradient via equation-1. Dew point pressure can be determined from the intersection of MDT pressure gradients. If the intersection point is not available, then dew point needs to be estimated by analogy or from other published literature. Step-4 is fine-tuning EOS parameters in order to match all observed data as listed in step-3. Further adjustment of C7+ mole% and its molecular weight would depend on the matching results of gas density, separator API gravity, and condensate yield. For instance, if API is too low, which means the fluid density is high, and then C7+ mole fraction and/or molecular weight may have to be reduced. Step-5 is extension of step-4. A major limitation of step-4 is the number of EOS parameters which can be adjusted each time must be less than or equal to the number of data points. One way to overcome this limitation is to use successive substitution. For instance, if Ω A and Ω B are chosen for regression in step-4, we can load their values after first iteration back into the original EOS as new initial values of Ω A and Ω B, and regress them again in second interaction until satisfactory result is obtained. Or we can select different EOS parameters such as binary coefficient, T c, P c, or accentric factor in second iteration until satisfactory result is obtained. Step-6 converts EOS parameters into pseudo black oil PVT by means of R v to represent retrograde gas condensate behavior. R v represents the amount of vaporized oil molecules present in the gas phase. In example-1, Peng-Robinson EOS was selected to match MDT pressure gradient. The fine tuned Peng-Robinson EOS predicts a gas density of g/cc for Upper Channel reservoir at F and 4400 psig. The predicted gas density yields an equivalent pressure gradient of psi/ft for Upper Channel reservoir, which is in excellent agreement with MDT gradient, psi/ft, the slope of pressure gradient shown in the left hand side of Figure 1. Tables-2 and 3 show the key parameters and binary interaction coefficient of Peng-Robinson EOS, respectively. Table 3 only shows half of the binary interaction coefficients because of symmetry. Table-4 shows comparison between predicted values by this method and the observed MDT pressure gradient (via gas density), dew point, condensate yield and API gravity. If the agreement is satisfactory, then the information in tables 2 and 3 are used to generate black oil PVT as shown in Table-5 for Upper Channel reservoir. Notice that the conversion process generates a small difference in dew point and condensate yield between EOS and pseudo black oil conversion as shown in Tables 4 and 5. For instance, the dew point and condensate yield are predicted to be 4437 psia and 26.3 B/MMSCF, respectively by EOS as opposed to 4434 psia and 26.6 B/MMSCF by pseudo black oil PVT. Example 2 Example-2 is similar to example-1, where downhole sample is not available, nor is the composition of recombined surface sample. However, MDT pressure gradient, separator gas composition, and separator liquid yield at surface condition are available. MDT gradient is shown in the right hand side of Figure-1, which yields a pressure gradient of psia/ft or an equivalent gas density of g/cc. Table-6 shows the initial compositions of two surface gas samples from Bangka Lower Channel reservoir. Reservoir temperature is F and initial reservoir pressure is 4850 psia. Liquid yield at surface separator is approximately 36 B/MMSCF and 50 0 API gravity. Following the same procedures as outlined in example-1, the predicted gas density is g/cc, which yields an equivalent pressure gradient of psi/ft for Lower Channel. The equivalent pressure gradient is in excellent

3 SPE agreement with MDT gradient, psi/ft, the slope of pressure gradient shown in the right hand side of Figure 1. Tables-7 and 8 show the key parameters and binary interaction coefficient of Peng-Robinson EOS, respectively. Table-9 shows comparison between calculated and observed parameters such as MDT pressure gradient (via gas density), dew point, condensate yield, and API gravity of condensate. Table-10 shows the converted pseudo black oil PVT for Lower Channel reservoir. Example 3 This example uses pseudo PVT properties to estimate liquid yield of a mixed well stream from two wells. Well-1 has an initial condensate yield of B/MMSCf and well-2 has an initial condensate yield of For instance, if both wells produce at the same rate, say 50 MM SCF/D, then the mixed well stream would be 100 MMSCF/D. Reservoir simulation shows an average daily codensate yield at B/MMSCF, which is equivalent to the weighted average condensate yield of each contributing well stream. In other words, the simulated condensate yield is the same as calculated by (30.66* *50)/( ) = B/MMSCF. Note each well s rate needs not be identical as shown in this example. Pseudo black oil method will predict a mixture s yield by using linear weighting factor proportional to each well s rate ratio in a mixture or commingled well stream. Although the concept of pseudo black oil PVT may not yield very accurate in predicting the condensate yield of mixed or commingled well streams, it is considered to be even more difficult to solve the same problem with an EOS since we usually do not have laboratory tests based on mixed well streams. It could also be quite difficult to use a single EOS to model the phase behavior of multiple well streams from multiple reservoirs starting at different temperature, pressure, and condensate yield. Conclusion This paper presents a method which can be used to estimate phase behavior of a retrograde condensate reservoir when there is lack of downhole or recombined surface sample to accurately account for the heavy end fraction. This method attempts to adjust C7+ mole fraction and its estimated molecular weight so that the gas density at reservoir condition would yield a pressure gradient which matches MDT pressure gradient. Once a reasonable C7+ composition and molecular weight can be obtained, we can proceed to incorporate other observed data such as dew point, condensate yield, and condensate API gravity to tune a selected EOS. If dew point can not be directly determined from MDT pressure gradient, an estimated dew point would have to be used. After successful matching of the observed data with an EOS, the EOS parameters are converted into pseudo black oil PVT properties by means of R v, oil vapor in the gas phase, to predict condensate yield as a function of reservoir pressure. This process offers the following advantages over fully compositional EOS approach: (1) it is very fast in computation when compared to fully compositional approach, (2) it can be used to predict yield for commingled production or multiple wells from multiple reservoirs since it is considered to be quite difficult to predict the phase behavior of mixed well streams from multi-reservoirs at different temperature and pressure, (3) it provides approximate yield in the pipeline as pressure loss due to friction. The disadvantages of this method include (1) it can not be used for gas re-injection operation and (2) it does not have temperature dependency, which can underestimate liquid drop out in subsea pipeline. If downhole or recombined surface sample can be obtained successfully, then the trial-an-error step to tune C7+ can be avoided. Acknowledgment The authors thank Unocal Indonesia Company for permission to publish this paper. Nomenclature Rs: solution gas/oil ratio Ω A : constant in cubic EOS Ω B : constant in cubic EOS µ: viscosity ω: accentric factor Table-1: Initial and Adjusted Composition, Bangka Upper Channel Reservoir Comp Mol Wt Sample No. 1 Sample No. 2 Sample No. 3 Average After C7+ adj Name Mol % Mol % Mol % Mol % Mol % CO N C C C ic nc ic nc C C Total Avg M W SpGr

4 4 SPE Table 3: EOS Binary Interaction Coefficient for Upper Channel Reservoir CO2 N2 C1 C2 C3 IC4 NC4 IC5 NC5 NC6 C7+ CO N C C C IC NC IC NC5 0 0 NC6 0 C7+ Table 2: EOS Parapters for Upper Channel Reservoir COMP Mw T C P C Z C ω Ω A Ω B PCHOR 0 Name F psia CO N C C C IC NC IC NC NC C Table-4: Comparison between Predicted and Observed Data, Upper Channel Reservoir Parameter Unit This Method Observed Remark Gas Density g/cc MDT Dew Point psia GOC Yield b/mmscf Separator API Separator Table 5: Pseudo Black Oil PVT for Upper Channel Reservoir P R s B o µ o ρ o Z o B g µ g Z g ρ g R v psia scf/stb rb/stb cp g/cc rcf/scf cp g/cc stb/mmscf Table-6: Initial and Adjusted Composition, Bangka Lower Channel Reservoir Comp Mol Wt Sample Sample After Average No. 1 No. 2 C7+ adj Name Mol % Mol % Mol % Mol % CO N C C C ic nc ic nc C C Total Avg M W SpGr

5 SPE Table 7: EOS Parapters for Lower Channel Reservoir COMP Mw T C P C Z C ω Ω A Ω B PCHOR 0 Name F psia CO N C C C IC NC IC NC NC C Table 8: EOS Binary Interaction Coefficient for Lower Channel Reservoir CO2 N2 C1 C2 C3 IC4 NC4 IC5 NC5 NC6 C7+ CO N C C C IC NC IC NC5 0 0 NC6 0 C7+ Table-9: Comparison between Predicted and Observed Data, Lower Channel Reservoir Parameter Unit This Method Observed Remark Gas Density g/cc MDT Dew Point psia GOC Yield b/mmscf Separator API Separator

6 6 SPE Table 10: Pseudo Black Oil PVT for Lower Channel Reservoir P R s B o µ o ρ o Z o B g µ g Z g ρ g R v psia scf/stb rb/stb cp g/cc rcf/scf cp g/cc stb/mmscf Figure 1: Bangka Field MDT Pressure Data Bangka Field by Wells Depth, SS ft Upper Channel: Y = *X Lower Channel: Y = *X ,300 4,400 4,500 4,600 4,700 4,800 4,900 5,000 Pressure, Psia Bangka-1 Bangka-2 Bangka-4 Aton-1 Aton-1ST Current Well