Application of Multiple-Mixing-Cell Method To Improve Speed and Robustness of Compositional Simulation

Summary Standard equation-of-state-based phase equilibrium modeling in reservoir simulators involves computationally intensive and time-consuming iterative calculations for stability analysis and flash calculations. Therefore, speeding up stability analysis and flash calculations and improving robustness of the calculations are of utmost importance in compositional reservoir simulation. Prior knowledge of the tie-lines traversed by the solution of a gas-injection problem translates into valuable information with significant implications for speed and robustness of reservoir simulators. The solution of actual-gas-injection processes follows a very complex route because of dispersion, pressure variations, and multidimensional flow. The multiple-mixing-cell (MMC) method, originally developed to calculate minimum miscibility pressure of a gas-injection process, accounts for various levels of mixing of the injected gas and initial oil. This observation suggests that the MMC tie-lines developed upon repeated contacts may represent a significant fraction of the actual simulation tie-lines encountered. We investigate this idea and use three tie-line-based K-value-simulation methods for application of MMC tie-lines in reservoir simulation. In two of the tie-line-based K-value-simulation methods, we examine tabulation and interpolation of MMC tie-lines in a framework similar to the compositional-space adaptive-tabulation (CSAT) method. In the third method, we perform K-value simulations based on inverse-distance interpolation of K-values from MMC tie-lines. We demonstrate that for the displacements examined, the MMC tie-lines are sufficiently close to the actual simulation tie-lines and provide excellent coverage of the simulation compositional route. The MMC-based methods are then compared with the computational time by use of other methods of phase-equilibrium calculations, including a modified application of CSAT (an adaptive tie-line-based K-value simulation), a method using only heuristic techniques, and the standard method in an implicit-pressure/explicit-concentration-type reservoir simulator. The results show that tabulation and interpolation of MMC tie-lines significantly improve phase equilibrium and computational time compared with the standard approach, with acceptable accuracy. The results also show that computational performance of the MMC-based methods with only prior tie-line tables is very close to that of CSAT, which requires flash calculations during simulation. The K-value simulations by use of MMC-based tie-line-interpolation methods improve the total computational time up to 51% in the cases studied, with acceptable accuracy. The results suggest that MMC tie-lines represent a significant fraction of the actual tie-lines during simulation and can be used to significantly improve speed and robustness of phase-equilibrium calculations in reservoir simulators.

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Multiple-Mixing-Cell Method for MMP Calculations

SPE Journal ◽

10.2118/116823-pa ◽

2011 ◽

Vol 16 (04) ◽

pp. 733-742 ◽

Cited By ~ 44

Author(s):

Kaveh Ahmadi ◽

Russell T. Johns

Keyword(s):

Analytical Methods ◽

Oil And Gas ◽

Equilibrium Phase ◽

Variable Number ◽

Simulation Methods ◽

Displacement Efficiency ◽

Fractional Flow ◽

Cell Method ◽

Multiple Mixing ◽

Tie Lines

Summary The minimum miscibility pressure (MMP) is a key parameter governing the displacement efficiency of gasfloods. There are several methods to determine the MMP, but the most accurate methods are slim-tube experiments, analytical methods, and numerical-simulation/cell-to-cell methods. Slim-tube experiments are important to perform because they use actual crude oil, but they are costly and time consuming. Analytical methods that use the method of characteristics (MOC) are very fast and help to understand the structure of gasfloods. MOC, however, relies on finding the unique and correct set of key tie lines in the displacements, which can be difficult. Slim-tube simulation methods and their simplified cell-to-cell derivatives require tedious fluid and rock inputs, and their MMP estimates can be clouded by dispersion. This paper presents a simple and accurate multiple-mixing-cell method for MMP calculations that corrects for dispersion, and is faster and less cumbersome than 1D simulation methods. Unlike previous mixing-cell methods, our cell-to-cell mixing model uses a variable number of cells, and is independent of gas/oil ratio, volume of the cells, excess oil volumes, and the amount of gas injected. The new method only relies on robust P/T flash calculations using any cubic equation-of-state (EOS). The calculations begin with only two cells and perform additional cell-to-cell contacts between resulting equilibrium-phase compositions based on equilibrium gas moving ahead of the equilibrium liquid phase. We show for a variety of oil and gas compositions that all key tie lines can be found to the desired accuracy, and that they are nearly identical to those found using analytical MOC methods. Our approach, however, is more accurate and robust than those from MOC because we do not make approximations regarding shocks along nontie-line paths, and the unique set of key tie lines converges automatically. The MMP using our mixing-cell method can be calculated in minutes using an Excel spreadsheet and is estimated from a novel bisection method of the minimum tie-line lengths observed in the cells at four or five pressures. Our multiple-mixing-cell method can calculate either the MMP or the minimum miscibility for enrichment (MME) independent of the number of components in the gas or oil. Our approach further supports the notion that the MMP is independent of fractional flow because we obtain the same key tie lines independent of how much fluid is moved from one cell to another.

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Four-Phase Equilibrium Calculations of Carbon Dioxide/Hydrocarbon/Water Systems With a Reduced Method

SPE Journal ◽

10.2118/154218-pa ◽

2013 ◽

Vol 18 (05) ◽

pp. 943-951 ◽

Cited By ~ 15

Author(s):

Saeedeh Mohebbinia ◽

Kamy Sepehrnoori ◽

Russell T. Johns

Keyword(s):

Carbon Dioxide ◽

Phase Equilibrium ◽

Phase Behavior ◽

Water Systems ◽

Computational Time ◽

General Strategy ◽

Recovery Processes ◽

Carbon Dioxide Co2 ◽

Almost All ◽

Equilibrium Calculations

Summary Three hydrocarbon phases can coexist at equilibrium at relatively low temperatures in many carbon dioxide (CO2) floods. The formation of an aqueous phase in contact with hydrocarbon phases is inevitable in almost all recovery processes, because of the permanent presence of water in the reservoirs either as injection fluid or as initial formation water. As the number of phases increases, flash calculations become more difficult and time-consuming. A possible approach to reduce the computational time of the phase-equilibrium calculations is to use reduced methods. This paper presents a general strategy to model the phase behavior of CO2/ hydrocarbon/water systems in which four equilibrium phases occur by use of a reduced-flash approach. The speedup obtained by a reduced-flash algorithm compared with the conventional-flash approach is demonstrated for a different number of components and phases. The results show a significant speedup in the Jacobian-matrix construction and in Newton-Raphson (NR) iterations by use of the reduced method when four phases are present. The computational advantage of the reduced method increases rapidly with the number of phases and components. The developed four-phase reduced-flash algorithm is used to investigate the effect of introducing water on the phase behavior of two west Texas oil/CO2 mixtures. The results show changes in the phase splits and saturation pressures by adding water to these CO2/hydrocarbon systems.

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