Flows with substance exchange and change of its volume in radial geometry

Authors: A. Trzaska, K. Sobowska

The subject of this paper is a certain model of the process of eolmatage in which the swelling of colmatant settled in a porous medium proceeds. An axi-symmctric flow is considered.

The paper is a continuation of the article (Trzaska, Sobowska 2000) in which a similar problem for the one-dimensional case was examined.

It is assumed that the swelling occurs when colmatant contacts a certain substance. In the accepted model it is assumed that suspension carrying solid particles of the colmatant is initially forced into the porous medium.

The particles settle in the pores.

This part of the process is conventionally called its first stage.

The stage is described by a system of balance-transport (1) and kinetics (2) equations. The obtaining of a certain distribution of colmatant P0(r) settled in the porous medium (16) is the result of stage one of the process.

During stage two, substance which can cause the swelling of the colmatant settled earlier is forced into the medium. Part of this substance stays in the medium pores reacting on the colmatant and leading to the increase of its volume.

This stage of the process is described by equations (17), (18), (24). The distribution of the colmatant in the medium pores P(r,t) is obtained in the form (25).

In this paper computations arc made which help to determine the distribution of pressure in the medium during stage two of the process.

The equation of motion (26) was used. The flow at known discharge q(t) was examined. The distribution of pressures h(r,t) is expressed then by formula (29).