Transient flow of ideal and real gases through porous media

Abstract

The effects of variations of pressure-dependent viscosity and gas law deviation factor on the flow of real gases through porous media are considered. Numerical solutions of the gas flow equation, which is a non-linear partial differential equation, are obtained for constant and variable rate performance. Results indicate that prediction of gas well performance utilizing current methods based on flow of ideal gases can lead to serious errors. To obtain a unique solution to the rigorous gas flow equation a new method of linearization is proposed. A new real gas flow equation has been developed by means of a change of variable which couples pressure, viscosity and gas law deviation factor. This substitution, called the real gas pseudo-pressure, leads to simple equations describing gas flow which do not involve the assumption of small pressure gradients leads to errors in estimating pressure distributions for tight formations and to inaccurate interpretation of data obtained from present well testing methods. Production performance of real gasses obtained from finite difference solution can be correlated with the liquid flow solutions of van Everdingen and Hurst, and the ideal gas flow solutions of Aronofsky and Jenkins. Application of the new method of solution to radial flow system under transient, stead or pseudo-steady state injection or production has been considered. The method can be applied, also, for one-dimensional flow of real gases. Superposition of linearized real gas flow solutions to generate variable rate performance is investigated and found satisfactory. This provides justification for pressure build-up testing. The concept of the real gas pseudo-pressure will lead to improved interpretation of gas well performance tests, and improved forecasting of gas production.