A Treatment of the Gas Percolation Problem in Simulation of Three-Dimensional, Three-Phase Flow in Reservoirs

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 /or performing these calculations is described in detail in a separate article. 1 While vertical gas percolation occurs daring natural depletion in a reservoir of any configuration, it is especially pronounced in the pinnacle ree~ or bioberrm 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 30to 40-year simulation on even a onedirnensionai basis has exceeded J2,000. The method described here for handling the 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 calcrdat ions 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 [ield. ;Calculat ed results using a 2-day time step (where the method in question is not needed and no: invoked) are compared with results using the method and a 60-day time step. The comparison shows good agreement. Results /rorn oneand two-dimensional simulations of the reef are presented along with the corresponding computing times on the CDC 6600 computer. A three-dimensional simulation was Original manuscript received in f$ociety of P etrol cum Engineers off ice March 12, 1968. Revised manuscript received Aug. 9, 4966. Paper (SPE 203S) was presented at SPE Symposium on Numerical Simulation of Reservoir Performance held irr Dallas, Tex., April 22.23, 196S. @ Copyright 196S American Inetitute of Mining, Metallurgical, and Petroleum Engineers, Inc. preferences given et end of paper. ‘ This paper will be printed in Traneactfok volume 243, which will cover 1968. DECEMBER, 196S I \ THE U. OF TEXAS AUSTIN, TEX. also performed and the required computing time is given.