A Simple Method for Controlling Gas Percolation in Numerical Simulation of Solution Gas Drive Reservoirs
Authors: McCreary J.G. 
Published: December 2007

Abstract
The gas percolation problem occurs in finite difference simulation of solution gas drive reservoirs with several cells or nodes in the vertical direction. As the pressure drops in the vicinity of a producing well near the bottom of the oil column, gas comes out of solution. Because of the low density of The gas in comparison with the oil, there is a high potential gradient for upward gas flow. Since the potential gradient for upward gas flow. Since the gas viscosity is low, the upward flow rate of gas is often big enough to deplete all the gas in the finite cell during a time step. In fact, more gas may flow out of the cell than actually is present. This phenomenon causes a numerically calculated phenomenon causes a numerically calculated negative gas saturation at the end of the time step. The result is oscillations in the saturations and numerical instability. A method for controlling this numerical phenomenon is presented that retards vertical gas flow to the amount available within the cells. The amount of gas available within each cell is calculated at the beginning of each time step and compared with the expected flow rate based on the last time-step values for gas potential gradients. If the predicted flow is greater than the amount present, the vertical gas transmissibility is adjusted to retard the flow. The solution calculated by this method is compared with the solution without control and the solutions calculated by a method recently suggested by Coats.* The method of this paper is shown to be superior in numerical stability. The comparisons are made with a one-dimensional vertical simulation of natural depletion, solution gas drive, of a pinnacle reef structure. pinnacle reef structure

Introduction
The problem of gas percolation in multidimensional, multiphase mathematical reservoir simulators is concerned with the extremely unstable conditions that exist when low density, low viscosity gas is percolating upward through less mobile oil. In many percolating upward through less mobile oil. In many cases, the gas being released from solution is flowing upward while the oil is flowing down toward a well perforation. This problem often severely limits the size of the time steps used in the simulation and therefore greatly increases the number of time steps, the computer time and the cost of simulation. Basically, this problem arises when large volumes of fluid, in time-varying-phase ratios, flow through a relatively small finite volume of reservoir. A typical problem is as follows. Consider an oil reservoir simulation, with a production well completed near the bottom of the oil column, without any gas or water injection to maintain reservoir pressure. As oil is produced, the pressure drops in pressure. As oil is produced, the pressure drops in the cell containing the well and gas is released from solution to partially replace the volume of oil produced. Initially, the gas in the producing cell is produced. Initially, the gas in the producing cell is present below the critical gas saturation and is present below the critical gas saturation and is therefore immobile. Gradually, this gas accumulates to the point where the gas saturation is above the critical saturation and the gas phase becomes mobile. Because of the large difference in density of oil and gas, there is a large gravitational effect which causes the gas to rise through the oil column from one cell to the next. In addition, since the viscosity of gas is very low in relation to the viscosity of oil, even though the relative permeability to gas is low, there is a large mobility for gas flow. At the beginning of the finite time step, conditions exist that specify a large flow rate of gas upward in the producing cell. If the relative permeability is calculated explicitly and left at time step initial conditions, this flow rate is not cut back as the cell is depleted of gas. If the time step is too large, this large flow rate completely depletes the gas and in the extreme case even more gas may flow than is actually present. This leads to calculated oil saturations greater than 100 percent.
SPEJ
P. 85