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The problem of modeling the acid treatment of the dolomitic collector of an oil formation bottom-hole zone is considered with account of rock colmatation. Themodeling is performedwithin the framework of mechanics of multicomponent and multiphase flows using the mean values of the reservoir porosity and permeability with account of kinetics of the acid digestion of the dolomitic rock. A mathematical model of the process that allows for liquid seepage flow and the chemical reaction of the acid with the rock matrix proceeding in the kinetic regime is presented. On the basis of the model proposed the motion of an active admixture and the variation in the filtration parameters of the formation in the process of the reactant pumping are investigated. The rock colmatation effect on the acidizing process is estimated. Numerical calculations are performed and the process characteristics are determined.

The model of two-phase seepage flow occurring when oil is displaced by an acid solution in the neighborhood of a horizontal well is considered with account for flow in the well bore. The effect of acid activation and acid fracturing is studied. The influence of the phase permeability variations accompanying the rock break-up on the treatment result is estimated. The nonuniformity of the inflow distribution along the horizontal bore is shown to increase as a result of the acidizing. Numerical calculations are carried out for actual situations.

The process of inflow of an oil-bearing fluid from an infinite region of porous soil into a cavity (reservoir) and its subsequent pumping into a well located at the center of the reservoir is investigated. The cavity is chosen from the class of flattened ellipsoids of revolution. Thus, a combined problem of the optimization of the shape of a cavity of given volume for which the maximum seepage flow is achieved and the approximate determination of the additional constraints on the cavity dimensions necessary to ensure the outflow of the oil-bearing fluid is considered.

Free percolation and seepage flows from natural and artificial watercourses with curvilinear profiles are considered. The rigorous hydrodynamic solution of the problem of free percolation and seepage flow from a watercourse is obtained by representing the watercourse profiles in the plane of the Joukowski variable by means of the equation of a family of lemniscates and using the conformal mapping method. The calculated dependences for determining all the necessary parameters of the seepage flows and constructing the curvilinear watercourse profiles are given. In the case of a circular basis for the shape of the watercourse profile in the plane of the Joukowski variable these dependences coincide with the well-known exact dependences.

Unsteady problems concerning the displacement of gas and oil deposits in a seepage flow of stratal water are of specific interest to oil and gas hydrogeology, and in the planning and analysis of the processes of reservoir exploitation. Firstly, a change of the hydrogeological environment in a region of already formed deposits involves their displacement. Secondly, when one of two adjacent deposits is developed, a displacement of the other occurs in the artificial flow of stratal water which is produced. Papers [1–3] investigate the steady configuration of gas—water or water—oil contacts in the presence of a seepage flow of stratal water under the deposit. The unsteady problem considered below is a generalization of the problem in paper [3]. Its characteristic property is the presence of mobile boundaries separating the regions with flow of different fluids in the horizontal plane.

Seepage under a flat apron in a two-layer ground consisting of homogeneous isotropic layers of equal thickness was investigated by means of the analytic theory of linear differential equations by Polubarinova-Kochina [1]. An approximate solution of the same problem for layers of different thickness by the methods of the variational calculus was given in [2]. The solution to such a problem for homogeneous anisotropic layers of different thickness by means of a special complex variable representation and linear conjugation was given in [3] by Prusov and the author of the present paper. The method of [3] is now used to investigate two-dimensional steady seepage flow under two aprons in a multilayer ground consisting of n homogeneous anisotropic layers of different thickness, the principal directions of anistropy of each layer having an arbitrary position relative to the horizontal.