The phenomenon of colmatage as a generalization of filtration

In this paper various models of the process of colmotage are presented. Three kinds of kinetics are discussed, describing the course of this phenomenon, and the relevant systems of partial differential equations. Examples of the solutions of these equations (2.2), (2.3); (2.2), (2.4); (2.2), (2.5) are given and the function of porosity of a medium during the colmatage process (2.7), (2.11), (2.15) is determined from these equations. Besides, by introducing the adequate equation of motion (2.17), the way of determining the pressure distribution in a medium when the flow proceeds at the assumed discharge (2.19) and at the constant difference of pressure, Eq (3.3), is presented. In the latter case the discharge of flow as a decreasing function of time Eq (3.2) is additionally determined.

Calculations are made for each kinetics. The diagram enclosed illustrates the distribution of pressure versus time t when the flow proceeds at a constant pressure difference. It should be noticed that the distribution obtained from the theory of colmatage at the moment t=0 agrees with that obtained when Darcy's law is applied.