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Colmatage, flows with substance exchange of its volume |
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Colmatage, flows with substance exchange of its volume Authors: A. Trzaska, K. Sobowska
In this paper a certain model of the process of colmatage is discussed in which the swelling (multiplication) of particles in a porous medium proceeds. It is assumed that the process in question consists of two stages. During stage one, suspension which dispersed colmatant is forced into the porous medium; the colmatant settles in the medium pores. This stage has been described by a system of partial differential equations (1), (2) with initial-boundary conditions (4), (5). Following from the solution of this system, the function of the colmatant distribution in the medium at an arbitrary moment t, and at moment t sub 1 at which this stage is finished, is obtained. During the other stage, a liquid in which a substance dissolved or dispersed causing the swelling (multiplication) of the colmatant settled earlier, is forced into medium. The volume concentration of the substance transported by the liquid and settled in the medium at stage two is found when a system of equations (10), (11) with initial-boundary conditions (12), (13) is solved. Next, the distribution of the above mentioned substance being determined, we find the function of position and swelling (multuplication) of the colmatant during stage two of the process. We use here equation (16) with the condition (17). In this paper, the distribution of pressure during stage two of the process has been also determined. These computations have been carried out on the basis of the equation of motion (20) and on the assumption that - firstly - the flow proceeds at an assigned and at constant discharge of flow, and at constant difference of pressure at points x = 0 and x = L. In the latter case implicit function of the flow discharge (31) has been obtained.
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2011