The Effect of High-Pressure Gradients on Gas Flow

Abstract

ABSTRACT The flow of gases through homogenous porous media is governed by non-linear differential equations when expressed in squares of pressure. In the usual analysis the equations are linearized by assuming small changes in pressure, and thus in fluid properties. The results thus yield a linear relationship between pressure drop and flow rate. At high flow rates, experiments and well tests show deviations from the behavior predicted by the linear theory. These deviations are usually attributed turbulence, inertial effects and other factors, all of which are usually thought to render Darcy's law invalid. Quadratic and higher order equations are then used to characterize this type of flow, with the nonlinear coefficients determined empirically. However, this study has found that an alternative to using empirically determined non-Darcy effects is to correctly account for the consequences of the assumptions used to linearize the flow equations. In this study the flow of real gases through porous media was analyzed by incorporating some of the nonlinearities present in the flow equations. It is shown that deviations from linearity, of the form observed in field tests and in laboratory experiments, can result from the nonlinearities inherent in the basic formulation. Thus, a lack of proportionality between pressure drop and flow rate does not necessarily imply or indicate a deviation from Darcy flow. In laboratory examples it has been possible to correctly determine the observed Forchheimer coefficients, based on the derivation from first principles. This is achieved with only Darcy's law, without reference to any non-Darcy effects.