Pressure Distribution in a Porous Medium During the Colmatage Phenomenon Accurring According to the First Kinetics without Linearization of the Expression Defining the Porosity of the Considered Medium as a Function of Position and Time

Abstract

The phenomenon of colmatage occurs in nature wherever there is a flow of fluid carrying suspended solid particles through porous media.
Even the "cleanest" water flowing into the well after some period of time will become clogged and therefore its efficiency will decrease,
which is a negative phenomenon. Research conducted in our center, since the 1960s [1,4-14], has led to: a theoretical description of the
phenomenon of colmatage [4-8,13,14] and a number of experiments verifying it [9-14]. The obtained results were used during tests to seal
the rock mass around a mining excavation [12].
This article attempts to determine the area К in the case of the colmatage phenomenon occurring in accordance with the first kinetics, and
to identify/formulate relationships describing the pressure distribution h(x,t) for the flow without colmatage and with colmatage without
linearization of the expression ε(x,t)-3 in the surroundings εo, where ε determines the porosity of the medium as a function of position and
time. Determining the area К allows us to clearly derive the exact pressure distribution h(x,t) during flow with colmatage through a porous
medium without linearization, and then compare the solutions of the system of colmatage equations using the linearization method and
the exact method using the dimensionless form of the ξ function. During the experimental research, the attempt to match the actual phenomenon
with the developed mathematical model was burdened with high uncertainty, probably resulting from the use of linearization
of the ε(x,t)-3 term. In the article, the authors explain what generates the deviation of the approximate method from the exact solution and
point out that the exact solution better reflects the physical meaning of the mathematical model for describing the phenomenon and the
defined colmatation coefficients, the parameter εo, in particular.