Nonlinear effects in gas filtration

The existence of considerable deviations from the linear Darcy filtration law has been established for numerous systems consisting of a fluid and a porous medium. One of the manifestations of this nonlinearity is the existence of a limiting (initial) pressure gradient—the minimum value of the pressure gradient for which fluid motion occurs. (As a rule, fluid motion still takes place for subcritical values of the pressure gradient, but very slowly; on reaching the limiting value of the pressure gradient there is a marked acceleration of the filtration. The limiting-gradient concept thus provides a good approximation for velocities which are not too low.)We would also expect nonlinear effects in the motion of a Newtonian liquid or gas in a porous medium containing some amount of fluid which does not participate in the main motion. These effects can take the form of layers enclosing the particles of the porous medium and partly or completely blocking the pore channels. For sufficiently high pressure gradients rearrangement of these layers must begin, accompanied by a change of the hydrodynamic resistance of the porous medium.As a result of this restructuring it is natural to expect a disproportionately fast increase of the filtering-fluid flow rate with increase of the pressure differential; i.e., the filtration law of a Newtonian fluid in a medium containing a. layer of bound fluid having elasticity will have the form which is characteristic for pseudoplastic non-Newtonian fluids. In particular, if the initial attached-fluid content is so large that all the pore channels are blocked in the initial state, then the motion of the liquid (gas) being externally pumped begins only after the attached fluid layers are partly ruptured. Therefore, under these conditions the appearance of a limiting (initial) pressure gradient for filtration of a Newtonian fluid is possible. This can occur in filtration of a gas in argillous rocks containing connate water, since the water and the clay particles form a colloidal suspension which has some shear strength.This phenomenon may be of importance in the development of gas deposits which are associated with argillous rocks, particularly in determining the possible current and final gas yield. In fact, the most characteristic property of flows with an initial gradient is the formation of impermeable blocks; if the deposits have the usual nonuniformity the incompleteness of the gas extraction from the reservoir will manifest itself in both microscopic and macroscopi scales.In the following study we present relations describing gas filtration under such conditions and results of laboratory experiments which confirm the concepts described. Hydrodynamic estimates are also made of the possible effects of the initial gradient.The authors wish to thank I. I. Eremina for assistance in making the calculations, A. Sh. Asadov and Sh. S. Aslanov for assistance in conducting the experiments.