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.