A Treatment of the Gas Percolation Problem in Simulation of Three-Dimensional, Three-Phase Flow in Reservoirs
Authors: Coats K.H. 
Published: December 2007

Coats, K.H., Member AIME, The U. of Texas, Austin, Tex.

Abstract
This paper describes an approximate technique for handling the problem of percolation of evolved gas upwards through the oil column in computer simulation of natural depletion. This technique has been incorporated into a general model for simulating three-phase flow in one, two or three dimensions. The mathematical model for performing these calculations is described in detail in a separate article. While vertical gas percolation occurs during natural depletion in a reservoir of any configuration, it is especially pronounced in the pinnacle reef or bioherm. The reef may have an areal extent less than one section with a thickness of up to 800 ft. The upward percolation of evolved gas often limits the time step in calculations as little as one day. Using this small time step, computer expense for a single 30- to 40-year simulation on even a one-dimensional basis has exceeded $2,000. The method described here for handling the percolation allows time steps of 60 days or more percolation allows time steps of 60 days or more (depending on reservoir size and production rate), resulting in a considerable reduction in computing expense. The method also allows calculations in which secondary gas caps build up in tight zones of the oil column below the main gas cap. The validity of the method is indicated in connection with an example pinnacle reef field. Calculated results using a 2-day time step (where the method in question is not needed and not invoked) are compared with results using the method and a 60-day time step. The comparison shows good agreement. Results from one- and two-dimensional simulations of the reef are presented along with the corresponding computing times on the CDC 6600 computer. A three-dimensional simulation was also performed and the required computing time is given

Introduction
A general analysis for simulating three-dimensional, three-phase flow in reservoirs has been developed. In applying this model to reservoirs undergoing natural depletion, a time-step restriction was encountered due to the flow of evolved gas upwards through the oil column and toward the gas cap. A remedy for this problem has been incorporated in the analysis and is described here. The time-step restriction is encountered only in calculations which include flow in the vertical or near vertical direction. The restriction occurs to some extent in reservoirs of any geometrical configuration, but it is especially pronounced in the pinnacle reef or bioherm where the ratio of thickness to areal extent is unusually large. This paper describes the problem, a method of handling paper describes the problem, a method of handling it, incorporation of the method in the three-dimensional, three-phase model, and, finally, a test of the method's validity in an application to an example pinnacle reef reservoir.

THE PROBLEM
During the early stages of reservoir depletion, pressure falls below bubble point in progressively pressure falls below bubble point in progressively lower regions of the oil column. Continuing production results in evolution of dissolved gas production results in evolution of dissolved gas throughout the oil column. This gas then percolates upwards toward the top of the reservoir. If the gas encounters a sufficiently low permeability zone in its travel upward, then it can accumulate and form a secondary gas cap. If no zones are encountered which are tight enough to hold gas against the gravity forces, then the gas travels on until it reaches the top of the sand or the main gas cap. Numerical simulation of multiphase flow in reservoirs is generally performed with time steps such that the flow of a fluid into or out of a block in one time step is a fraction (considerably less than one) of the total amount of that fluid present in the block.
SPEJ
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