Correspondence pubs.acs.org/IECR
Cite This: Ind. Eng. Chem. Res. 2019, 58, 12896−12897
Reply to “Comment on ‘Multiphase Equilibrium Calculation Framework for Compositional Simulation of CO2 Injection in LowTemperature Reservoirs’” Huanquan Pan,*,† Michael Connolly,‡ and Hamdi Tchelepi† †
Department of Energy Resources Engineering, Stanford University, Stanford, California 94305, United States McKinsey & Company, 609 Main Street, Houston, Texas 77002, United States
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‡
W
publication4 in which two additional K-value estimates
e thank Luigi Raimondi for expressing interest in our work on phase equilibrium calculations for compositional simulation of CO2 injection in low temperature reservoirs. It appears that Raimondi has misunderstood our position. Raimondi confuses the characterization of a three-phase reservoir fluid with the development of three-phase equilibrium calculations. Khan et al.1 is the only paper cited. As the title of the paper indicates, it focuses on procedures to characterize mixtures of a reservoir fluid + CO2. In the fluid characterization process a mixture is first grouped into several defined and pseudocomponents. Thermodynamic properties are estimated for each pseudocomponent. The binary interaction coefficients are then adjusted to match experimental data. Fluid characterization is carried out prior to compositional reservoir simulation. Compositional reservoir simulation is performed with predefined fluid properties. Our research focuses on the development of phase behavior algorithms for reservoir simulation. To be clear, the characterization of fluids is completed prior to reservoir simulation, and thermodynamic fluid properties are specified as an input. Our objective was never to match experimental data. We do not compare results with experimental data because we are using a fluid that has already been characterized. We validated our algorithm by comparing results with those from commercial software packages. We compared our detailed results (mole fraction and composition of each phase) with CMG WinProp2 and PVTSim3 for all nine fluids. At minimum, we used dozens of comparison points for each fluid. This vetting exercise is essential when testing a new phase behavior algorithm. In the interests of brevity, we did not report the comparison with commercial software packages in our paper, nor did researchers in other recent publications.4,5 Raimondi’s letter notes the absence of an explicit comparison with established phase behavior algorithms. Herein we present our results vis-à-vis those obtained with CMG WinProp at three different conditions where the mixture of JEMA and injected CO2 gives rise to single phase, two-phase, and three-phase behavior, respectively. PR-EOS6 is used in the calculations. Table 1 lists the comparison of phase mole fractions at these different conditions. Table 2 compares the calculated three-phase equilibrium compositions. Raimondi states that our publication does not present a single case where the framework succeeds and previously developed methods fail. This is not true. We show erroneous results obtained using previously developed methods in Figures 8, 9, 10, and 11. The results are taken from a recent © 2019 American Chemical Society
K iWilson and 1/ 3 K iWilson are used besides the full set of initial estimates proposed by Michelsen.7,8 Raimondi misattributes research to Khan et al.1 The threephase equilibrium calculations used by Khan et al.1 were developed by Perschke9 who implemented the three-phase equilibrium calculations proposed by Michelsen.7,8 The full set of initial estimates Michelsen7,8 proposed for phase-stability is , 1/KWilson , KPure‑j (j = 1, ..., Nc), KIdeal , KAverage }. As { KWilson i i i i i 4 shown in the Li and Firoozabadi paper and in our publication, three-phase equilibrium conditions may incorrectly be identified as two-phase because the initial estimates 3
CO ‑95 are not used in phase K iWilson , 1/ 3 K iWilson and Ki 2 stability testing calculations. In Perschke’s algorithm,9 only one equilibrium phase is tested for two-phase stability testing. Figures 8, 9, and 10 of our publication show that reliable detection of a third equilibrium phase requires stability testing of each of the two phases present. Raimondi claimed that his three-phase equilibrium algorithm developed 20 years ago can identify the three-phase region for both the NWE and JEMA fluids. As we emphasized in our publication, it is necessary to perform very high-resolution numerical tests which traverse the entire three-phase region. In Figures 8, 9, 10, and 11 of our publication we show that it is very difficult to diagnose shortcomings in previous approaches to stability testing unless high resolution tests are performed. In our tests we constructed phase diagrams by traversing the Px parameter space in steps of Δx = 0.001, ΔP = 0.02 bar for both JEMA and NWE. We used 203 401 test points for JEMA and 630 450 test points for NWE. Most of the erroneous results we identify using prior approaches are not located at the extreme edge of the threephase region. This is important to note because most software packages focus on identifying phase boundaries, rather than rigorous quantification of phase equilibrium across the entire parameter space. Phase labeling is a postprocessing step which follows phase equilibrium calculations. Each hydrocarbon phase is labeled as vapor or liquid prior to calculation of relative permeability. This occurs upon completion of the phase equilibrium calculations in reservoir simulation. For two-hydrocarbon phase systems, the commonly used phase labeling for a hydrocarbon phase is the Li-correlation which represents a weighted average of the component critical temperatures in reservoir simulation.10 The other less frequently used method 3
Published: July 3, 2019 12896
DOI: 10.1021/acs.iecr.9b03349 Ind. Eng. Chem. Res. 2019, 58, 12896−12897
Industrial & Engineering Chemistry Research
Correspondence
Table 1. Phase Mole Fractions at Different Test Points for JEMA Fluid at 316.48 Ka Pan et al.12
WinProp pressure (bar)
xCO2
L1
L2
V
L1
L2
V
84.7 84.7 84.7
0.523 0.568 0.673
1.0 0.951071 0.650905
0 0 0.241087
0 0.048929 0.108007
1.0 0.951048 0.650899
0 0 0.241053
0 0.048952 0.108048
a
L1, L2, and V represent the oil-rich liquid phase, CO2-rich liquid phase, and vapor phase, respectively. xCO2 is the mole fraction of injected CO2 in the mixture.
Table 2. Compositions of Each Phase at 84.7 bar, xCO2 = 0.673 and 316.48 Ka Pan et al.12
WinProp component
z
xL1
xL2
y
xL1
xL2
y
CO2 C1 C2−3 C4−6 C7−16 C17−29 C30+
0.679278 0.022661 0.056963 0.063569 0.102613 0.050652 0.024263
0.588684 0.016626 0.058319 0.076354 0.145721 0.07703 0.037267
0.832315 0.027497 0.0576 0.049319 0.031116 0.002126 2.65 × 10−05
0.883615 0.04823 0.047381 0.018339 0.002426 8.9 × 10−06 0
0.58869 0.016627 0.058318 0.076352 0.145717 0.077029 0.037267
0.832312 0.027498 0.057599 0.049319 0.031119 0.002127 2.65 × 10−05
0.883615 0.048232 0.04738 0.018338 0.002426 8.94 × 10−06 1.57 × 10−09
a
z, xL1, xL2 and y represent compositions of feed, oil-rich liquid phase, CO2-rich liquid phase, and vapor phase, respectively.
was proposed by Grosset et al.11 Neither method is completely robust, and an alternate approach is required for lowtemperature hydrocarbon−CO2 mixtures in a three-hydrocarbon phase reservoir simulation. Perschke9 labeled the phases using a phase tracking algorithm, beginning with the initial fluid in each cell during the simulation. To the best of our knowledge, reliable phase labeling for low-temperature hydrocarbon−CO2 mixtures is still an open problem in reservoir simulation. Phase labeling must be integrated with a solution of the flow equations starting with the initial reservoir fluid.
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(9) Perschke, D. R. Equation-of-state phase-behavior modeling for compositional simulation. Ph.D. Thesis, Texas University, Austin, TX, USA, 1988. (10) Intersect Technical Description, version 2013.1; Schlumberger, 2013. (11) Gosset, R.; Heyen, G.; Kalitventzeff, B. An Efficient Algorithm to Solve Cubic Equations of State. Fluid Phase Equilib. 1986, 25, 51− 64. (12) Pan, H.; Connolly, M.; Hamdi Tchelepi, H. Multiphase Equilibrium Calculation Framework for Compositional Simulation of CO2 Injection in Low-Temperature Reservoirs. Ind. Eng. Chem. Res. 2019, 58, 2052−2070.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Huanquan Pan: 0000-0003-4229-971X Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Khan, S.; Pope, G.; Sepehrnoori, K. Fluid characterization of three-phase CO2/oil mixtures. SPE/DOE Enhanced Oil Recovery Symposium; Society of Petroleum Engineers: Richardson, TX, USA, 1992. (2) WinProp, version 2013; Computer Modeling Group, 2013. (3) PVTSim Nova 3; CalSep, 2018. (4) Li, Z.; Firoozabadi, A. General strategy for stability testing and phase-split calculation in two and three phases. SPE Journal 2012, 17, 1096−1107. (5) Petitfrere, M.; Nichita, D. V. Robust and efficient trust-region based stability analysis and multiphase flash calculations. Fluid Phase Equilib. 2014, 362, 51−68. (6) Robinson, D. B.; Peng, D.-Y. The characterization of the heptanes and heavier fractions for the GPA Peng-Robinson programs; Gas Processors Association: Tulsa, OK, USA, 1978. (7) Michelsen, M. L. The isothermal flash problem. Part I. Stability. Fluid Phase Equilib. 1982, 9, 1−19. (8) Michelsen, M. L. The isothermal flash problem. Part II. Phase split calculation. Fluid Phase Equilib. 1982, 9, 21−40. 12897
DOI: 10.1021/acs.iecr.9b03349 Ind. Eng. Chem. Res. 2019, 58, 12896−12897
