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Compositional simulation of miscible processes
Prediction of a miscible flood is best done with a compositional reservoir simulator. The simulation must be able to predict the phase behavior as well as the sweep behavior in the reservoir to forecast such quantities as incremental oil recovery, miscible-solvent requirement, and solvent utilization efficiency and to optimize such variables as solvent composition, operating pressure, slug size, water-alternating-gas (WAG) ratio, injection-well placement, and injection rate.
The compositional reservoir simulator calculates the flow in up to three dimensions of solvent, oil, and water phases as well as n components in the solvent and oil phases. It also computes the phase equilibrium of the oil and solvent phases (i.e., the equilibrium compositions and relative volumes of the solvent and oil phases) in each gridblock of the simulator. In addition, it computes solvent- and oil-phase densities. The equilibrium compositions and densities are calculated with an equation of state (EOS). From knowledge of the phase compositions and densities, solvent and oil viscosity and other properties such as interfacial tension are estimated from correlations.
Predicting phase behavior
Phase behavior can be predicted by:
Phase behavior (from both methods) provides valuable inputs to the reservoir simulator.
Advantages of using a compositional simulator
A compositional simulator is the most mechanistically accurate simulator for solvent compositional processes. When the EOS is tuned properly to appropriate experimental data, it computes realistic phase behavior. Thus, the appropriate phase behavior for flooding with enriched hydrocarbon solvent, lean hydrocarbon solvent, N2, and CO2 all can be taken into account. Compositional simulators predict the effect of changing pressure and injection-solvent composition on a displacement without the need to enter approximations into the simulator for these effects (except as the EOS itself is an approximation). The compositional simulator is capable of computing realistic behavior when pressure is well below the minimum miscibility pressure (MMP) of the injection solvent, is near but still below the MMP, or is well above the MMP. For this reason, it is ideally suited to study optimum operating conditions.
In addition to these advantages, a compositional simulation, to a large degree, removes the need for a user-defined miscible flood residual oil saturation, as it naturally computes the amount of residual oil left after the interaction of phase behavior and dispersion and distributes this residual saturation realistically as a varying saturation instead of an input, constant saturation.
A compositional simulation can have other aspects of mechanistic reality besides phase behavior. The mechanisms of molecular diffusion and convective dispersion may be included in the equations solved by the simulator. Although grid-refinement sensitivity (described later), or numerical dispersion, may dwarf the effects of these mechanisms in many simulations, they may be important to include in the finely gridded reference simulations (also described later).
Another physical mechanism that can be included in compositional simulations is the effect of interfacial tension (IFT) on solvent/oil relative permeability and capillary pressure. Although one cannot readily foresee the impact of a particular mechanism in the complex compositional simulation of solvent flooding, inclusion of the IFT mechanism seems prudent.
When an appropriate relative permeability treatment is included, compositional simulation predicts realistic solvent trapping, especially the trapping of solvent by crossflowing oil. Oil crossflow into a solvent-swept zone immiscibly displaces the solvent in a compositional simulation and leaves the solvent as a residual saturation consistent with the phase behavior.
Disadvantages of using a compositional simulator
The primary disadvantages of a compositional simulator are the degree of grid refinement often required to compute oil recovery with satisfactory accuracy and the computing time required for fine-grid simulations. These factors generally preclude using a compositional simulator directly for full-field simulations unless some kind of scaling-up technique is used to transfer the information developed from fine-grid reference-model simulations on a limited reservoir scale to coarse-grid simulations on the full-field-model scale. The predicted benefit of compositionally enhanced solvent flooding can be substantially in error if the simulation is made directly with a full-field model with typical coarse grids. This is illustrated by Fig. 1, which shows the results of an enriched-solvent-drive reservoir study. In this figure, simulations were made for two one-fourth nine-spot models that represented the same reservoir description.
- One model had a fine grid (30×30×31 cells in the x-, y-, and z- directions)
- The other had the same grid as that used in the full-field model (5×5×17).
The incremental recovery in this figure is the difference between solvent-flood and waterflood simulations in each model. The direct full-field simulation overpredicted incremental recovery by a factor of two.
Fig. 1 – Predictions with reference model and corresponding model with full-field grid size (after Jerauld).
There also are some additional data requirements for predicting solvent trapping and solvent relative permeability hysteresis that are not found in black-oil waterflood simulations.
Fine-grid reference models
Fine-grid reference models are used to reduce the grid refinement sensitivity problems in compositional simulators.Grid-refinement sensitivity is an extremely troublesome problem in many compositionally enhanced solvent simulations. The problem manifests itself by the predicted behavior changing as the grid is refined (i.e., as the gridblocks become smaller and smaller). This behavior can be caused by truncation error or numerical dispersion that results from representing derivatives by finite differences; by the inability to accurately resolve the size of solvent tongues or fingers with large gridblocks; and by the inability to represent with large gridblocks some features of reservoir description that have an important effect on solvent sweep, such as discontinuous shales, thin high-permeability strata, or thief zones.
Importance of minimizing grid refinement error
Fig. 2 shows the incremental recovery computed for two different 3D models, one representing one-eighth of a nine-spot pattern, the other representing one-fourth of a nine-spot. Each model had a different geostatistical distribution of correlated permeability with scattered, discontinuous shales represented by zero vertical permeability between gridblocks. Permeability and porosity were scaled up by the renormalization method from the model with the smallest gridblocks to the other models.
The base model for the one-eighth nine-spot has a grid of 20×20×40. Gridblocks were 93 ft on a side and 1 ft thick. The gridding of the one-fourth nine-spot model was 20×20×80, with gridblocks also 93 ft on a side and 1 ft thick.
Incremental recovery in this figure is plotted vs. 1/NX, where 1/NX is the dimensionless x-direction gridblock size. However, in this problem the dimensionless gridblock sizes in the other two directions also vary directly with the x-direction gridblock size. It is apparent that as the gridblock size is refined, the predicted incremental recovery decreases for what is supposed to be the same reservoir problem.
Fig. 2 illustrates the importance of minimizing grid-refinement error and explicitly including reservoir-description details that affect flow in an important way. Generally, minimizing the error from grid refinement and accounting for important reservoir-description details adequately requires small gridblocks. Layers that are 1 ft or no more than a few feet thick and have at least 20 to 40 lateral gridblocks between wells are desirable. Unfortunately, such fine gridding is not feasible for full-field simulations, for most 3D simulations of a single pattern, or perhaps even for some 3D repeating elements of a pattern. Because of this, field predictions need to be made in two steps—with reference models that can be gridded finely enough to accomplish the objectives summarized above, and with scaleup models that incorporate the information derived from reference models into field predictions that account for fieldwide reservoir description, multiple patterns, and operating realities and constraints.
Although it is desirable to make 3D reference-model simulations gridded so finely that the computed answer is adequately close to the converged answer, the discussion above shows that in general, it may not be feasible to do this. A reasonable alternative may be to make finely gridded 2D cross-section simulations to study the grid-refinement issue because for many problems, grid refinement has a larger effect on the computed outcome than the areal effects captured by a coarser-gridded 3D model. Variable-width 2D cross sections sometimes adequately represent the behavior of 3D pattern-segment models with the same fine gridding. In these cross sections, the width is smaller near the injector and producer and increases in the interwell region. This causes flow rate to be greatest near the wells and lowest midway between wells, as it would in a 3D displacement. Even when a fine-grid cross section does not realistically model a fine-grid 3D displacement, it still may predict incremental recovery better than a simulation in a more coarsely gridded 3D model. Moreover, 2D cross-section simulations are well suited for scaleup with the segment and streamline/streamtube models discussed in the next section.
A potential procedure for developing a 3D reference model is first to make a 3D simulation of a pattern element with the finest-grid refinement that is practical. Then, well-to-well cross sections are taken from this model, and the cross sections are refined further. Pseudoproperties are developed for the original cross sections that predict the performance of the more finely gridded cross sections. Then, these pseudoproperties are used in the moderately gridded 3D model to approximate the effect of further grid refinement.
Scaleup to the full field from a fine grid model is the next step in understanding the behavior of a miscible flood.
- Jerauld, G.R. 1998. A Case Study in Scaleup for Multicontact Miscible Hydrocarbon Gas Injection. SPE Res Eval & Eng 1 (6): 575–582. SPE-53006-PA. http://dx.doi.org/10.2118/53006-PA
- Christie, M.A., Mansfield, M., King, P.R. et al. 1995. A Renormalisation-Based Upscaling Technique for WAG Floods in Heterogeneous Reservoirs. Presented at the SPE Reservoir Simulation Symposium, San Antonio, Texas, 12-15 February 1995. SPE-29127-MS. http://dx.doi.org/10.2118/29127-MS
Noteworthy papers in OnePetro
Adepoju, O. O., Lake, L. W., & Johns, R. T. (2013, January 30). Investigation of Anisotropic Mixing in Miscible Displacements. Society of Petroleum Engineers. doi:10.2118/159557-PA
Johns, R. T., & Garmeh, G. (2010, October 1). Upscaling of Miscible Floods in Heterogeneous Reservoirs Considering Reservoir Mixing. Society of Petroleum Engineers. doi:10.2118/124000-PA
Johns, R. T., Sah, P., & Solano, R. (2002, February 1). Effect of Dispersion on Local Displacement Efficiency for Multicomponent Enriched-Gas Floods Above the Minimum Miscibility Enrichment. Society of Petroleum Engineers. doi:10.2118/75806-PA
Johns, R. T., Fayers, F. J., & Orr, F. M. (1994, April 1). Effect of Gas Enrichment and Dispersion on Nearly Miscible Displacements in Condensing/Vaporizing Drives. Society of Petroleum Engineers. doi:10.2118/24938-PA
Li, Y., & Johns, R. T. (2006, October 1). Rapid Flash Calculations for Compositional Simulation. Society of Petroleum Engineers. doi:10.2118/95732-PA
Okuno, R., Johns, R. T., & Sepehrnoori, K. (2010, September 1). Three-Phase Flash in Compositional Simulation Using a Reduced Method. Society of Petroleum Engineers. doi:10.2118/125226-PA
Okuno, R., Johns, R. T., & Sepehrnoori, K. (2010, March 1). Application of a Reduced Method in Compositional Simulation. Society of Petroleum Engineers. doi:10.2118/119657-PA
McGuire, P. L., & Stalkup, F. I. (1995, May 1). Performance Analysis and Optimization of the Prudhoe Bay Miscible Gas Project. Society of Petroleum Engineers. doi:10.2118/22398-PA
Newley, T. M. J., & Merrill, R. C. (1991, November 1). Pseudocomponent Selection for Compositional Simulation. Society of Petroleum Engineers. doi:10.2118/19638-PA
Perschke, D. R., Pope, G. A., & Sepehrnoori, K. (1989, January 1). Phase Identification During Compositional Simulation. Society of Petroleum Engineers.
Rathmell, J. J., Stalkup, F. I., & Hassinger, R. C. (1971, January 1). A Laboratory Investigation of Miscible Displacement by Carbon Dioxide. Society of Petroleum Engineers. doi:10.2118/3483-MS
Stalkup, F. I. (1987, January 1). Displacement Behavior of the Condensing/Vaporizing Gas Drive Process. Society of Petroleum Engineers. doi:10.2118/16715-MS
Stalkup, F. (1998, January 1). Predicting the Effect of Continued Gas Enrichment Above the MME on Oil Recovery in Enriched Hydrocarbon Gas Floods. Society of Petroleum Engineers. doi:10.2118/48949-MS
Stalkup, F. L. (1990, November 1). Effect of Gas Enrichment and Numerical Dispersion on Enriched-Gas-Drive Predictions. Society of Petroleum Engineers. doi:10.2118/18060-PA
Todd, M.R. and Longstaff, W.J. 1972. The Development, Testing, and Application of a Numerical Simulator for Predicting Miscible Flood Performance. J Pet Technol 24 (7): 874–882. SPE-3484-PA. http://dx.doi.org/10.2118/3484-PA
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