Numerical study of the effect of inertia terms in the equation of motion on gas flow in porous media

Abstract

In describing the motion of a gas in a fissured-porous medium, empirical, experimentally established laws, the linear and quadratic dependences of the pressure gradient of a gas on the velocity [1], are used instead of Euler's equation with allowance for the drag forces. For the majority of soluble problems in the flow of a fluid and a gas in porous media, this replacement cannot evoke any doubts. A large number of experimental and theoretical studies have been devoted to the investigation of this fact. However, in the description of the motion of a gas through intensely disturbed media under the influence of high pressure gradients the flow laws do not hold in the first stage of the process. The present study considers problems of the motion of a gas in a porous medium, and as equation of motion it uses both Euler's equation with a friction force, and empirical dependences — Darcy's linear law and the two-term drag law. The numerical solutions so obtained are compared and the characteristic times are established, as also are the characteristic lengths of the porous medium for which the solutions agree.