Effect of Including Composition-Dependent K Values To Generate Data for a Modified Beta-Type Simulator (includes associated papers 6418 and 6419)
Authors: Henry Richard L. 
Published: December 2007

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Introduction
Cook et al. presented a modified beta-type reservoirsimulatorforapproximatingcompositionaleffectsduring simulation of dry-gas injection into an oil orrich-gas-condensate reservoir. A composition parameterrepresenting the cumulative volume of dry gas per volume of oil(G) was incorporated into a standard beta-type simulator to make that simulator behave as a compositional modelwith a reported substantial reduction in computer time.The composition parameter and fluid properties requiredby the beta-type simulator were obtained from a linear cell-to-cell model. The parameter was plotted vs thefluid properties, and the result was a set of curves for eachfluid property that was independent of cell number in thelinear model. Therefore, the curves would beindependent of the space dimension in a reservoir model.This was important because incorporating position-dependentcurves into a beta-type model would significantly complicate this model, resulting in a loss of model simplicityand computer-time advantage.
The cell-to-cell model used by Cook et al.incorporated K values that were a function of pressure only; theK values were independent of fluid composition. Theauthors suggested their model for simulation of drygas injection. However, the results presented are for arelatively rich gas (9.3 1-percent C -C). Compositiondependence of K values would be minimal for this gas, which supports the fair agreement between performancepredicted by the modified beta-type model and thecompositional model.
For complex fluid systems, such as dry-gas injectioninto a volatile oil or a rich-gas condensate, K values arehighly dependent on fluid composition. This paperpresents results demonstrating that composition-dependent K values yield fluid properties that are dependenton cell number or location within the reservoir.Consequently, the modified beta-type model should not be usedfor reservoir simulations where large changes in fluidcomposition are anticipated.

Discussion
A study was initiated to determine the effects ofcomposition-dependent K values on reservoir propertiesduring dry-gas injection into a volatile oil reservoir.The gas and oil compositions and their physical properties aregiven in Table 1. A cell-to-cell model, similar to the oneused by Cook et al., was used to obtain the compositionparameter. Gi, and the phase properties. This modeldiffered from Cook et al.'s, however, in that it used theRedlich-Kwong equation of state matched experimentallyequilibria. The equation of state matched experimentallydetermined volumetric data of the volatile oil and ofmixtures of a lean gas with the gas condensate thatis in equilibrium with this oil at reservoir conditions, The matching of these volumetric data results incomposition-dependent K values; and to match thesedata, composition-dependent K values were predicted by the equation of state. These results suggest the equationof state can be used to simulate dry-gas injection into thevolatile oil.
The computation logic of the cell-to-cell model hasbeen presented in Refs. 4 and 5. Each cell of the modelused in this study contained 1 bbl of equilibrated reservoiroil at the reservoir temperature of 265 deg. F and a pressure of4,000 psia.
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