Model of acid solution flow in a porous half-space

Abstract

To increase oil recovery of weakly permeable carbonate rock, acid treatments with a weakly concentrated aqueous solution of hydrochloric acid are used. There can be various modes of dissolution of rocks depending on the injection rate of the acid solution in the breed from complete dissolution of the skeleton of the rock with a solid front at low speeds the injection to the emergence of long, single wormhole at high speeds of injection. A one-dimensional unsteady model of the flow of an aqueous hydrochloric acid solution in a porous carbonate rock is developed taking into account the movement of the front of the carbonate rock dissolution reaction. The boundary conditions under which the obtained system of equations is reduced to a self-similar system of equations of the fifth order are found. In contrast to self-similar filtration of a Newtonian fluid in the half space, the degree of dependence of self-similar independent variable is equal to − 3/2, and the dependent variables are the porosity and rate of filtration depend on the exponent of the dependence of rock permeability from changes in porosity after acid treatment. A one-dimensional non-stationary model of the flow of an aqueous solution of hydrochloric acid in a porous carbonate rock was developed taking into account the movement of the front of the dissolution reaction of carbonate rock. Boundary conditions are found under which the resulting system of equations reduces to a self-similar system of fifth-order equations. Unlike self-similar filtering of Newtonian fluid in half-space, the degree of dependence of the self-similar independent variable is −3/2, and the dependent variables (porosity and speed) of filtration depend on the degree of dependence of rock permeability on the change in porosity after acid treatment.