O. Yu. Dinariev

Modeling of surface phenomena in the presence of surface-active agents on the basis of the density-functional theory

Within the framework of the density-functionalmethod in multiphase multicomponent mixture hydrodynamics, the possibility of modeling surface-active agents on a “fluid-fluid” phase interface is shown. The method is based on the continuum description of multiphase mixtures with introducing terms quadratic in component density gradients to entropy or free energy. The determining equations are derived. Hydrodynamic model problems which demonstrate certain typical phenomena (the accumulation of surface-active agents on the phase interface, the corresponding decrease in surface tension, and the Gibbs and Marangoni effects) are solved numerically.

Gas and liquid transport in porous media with fractal geometry

The applications of fractal geometry in the theory of flow through porous media are reviewed.

Flow in a fractured medium with fractal fracture geometry

A model of a fractured porous medium in which the fracture system forms a fractal with Hausdorff-Bezikovich dimension d is proposed. The fractal is immersed in a saturated porous medium with the dimension D (D ≥ d, D=2, 3). The rock skeleton is assumed to be nondeformable. The system of flow equations is written out for cylindrically (D=2) and spherically (D=3) symmetrical flows. When D=d the model reduces to the well-known Barenblatt-Zheltov model. Certain particular solutions, which make it possible to determine the phenomenological parameters of the model experimentally, are obtained.

Modeling of isothermal processes in porous materials on the basis of the concept of an ensemble of pores

A class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometric parameters (for example, the pore size) is considered. The cases of pores saturated with single-and two-phase multicomponent liquid mixtures are investigated. The properties of equilibrium states of the mixture are derived from the minimum free energy condition and the transfer laws from the decreasing free energy condition. The hydrodynamic connectivity of the pores is described by two types of kernels: one describes the spatial connectivity and the other the connectivity in an elementary macrovolume. Analytically and numerically, the one-dimensional problems of establishment of a steady-state regime, propagation of a passive admixture, and two-phase flow (an analog of the Buckley-Leverett problem) are investigated. A relationship between the models in question and relaxational filtration models is demonstrated. A simple model of capillary hysteresis related with the non-monotonicity of the pore area to volume ratio function is proposed.

Multicomponent Mixture Flow in an Axisymmetric Capillary in the Presence of a Mobile Surface Phase

Within the framework of the density-functional method, the hydrodynamics of a multicomponent mixture in the presence of a mobile surface phase is investigated. A system of interrelated three- and two-dimensional hydrodynamic equations for isothermal volume and surface flows is formulated. For flow in a thin axisymmetric capillary, the principal term of the asymptotic expansion of the solution in powers of the characteristic capillary radius to length ratio is obtained. For slow motion, the solution is found in quadratures.

Modeling of retrograde condensation in the process of steady radial flow through a porous medium

The problem of the steady axisymmetric two-phase flow of a multicomponent mixture through a porous medium with phase transitions is considered. It is shown that the system of equations for the two-phase multicomponent flow process, together with the equations of phase equilibrium, reduces to a system of two ordinary differential equations for the pressures in the gas and liquid phases. A family of numerical solutions is found under certain assumptions concerning the pressure dependence of the molar fraction of the liquid phase.

Some solutions of the problem of plane steady flow of a gas condensate mixture through a porous medium

The plane problem of steady two-phase flow of a multicomponent mixture through a porous medium with phase transitions is considered. It is shown that the system of equations for the two-phase multicomponent flow process, together with the equations of phase equilibrium, can be solved in quadratures if the solution of two auxiliary problems is known. These are the problem of conformal mapping of the neighborhood of a well onto a rectangle and the purely physicochemical problem of the description of the mechanical and thermodynamic properties of a mixture. The solutions for a vertical well with a barrier and for a horizontal well in a finite productive stratum are found under certain assumptions concerning the properties of the mixture.

Relaxation effects associated with the flow of a dense gas through a porous medium

Unsteady processes of gas and Newtonian liquid flow through porous media are usually described within the framework of the standard elastic regime model [1, 2]. At the same time, from general theoretical considerations it is clear that for fairly small characteristic times of variation of the pressure and the seepage velocity the elastic regime model loses its validity and more general relaxation flow models [3, 4] must be employed. It is therefore important to determine the limits of applicability of the elastic regime model. For this purpose the unsteady process of gas flow from one vessel to another through a porous medium has been investigated theoretically and experimentally for small pressure differences and absolute pressures up to 50 MPa. It is shown that the experimental results diverge sharply from the theoretical predictions based on the elastic regime model. It is therefore proposed that for unsteady processes a generalization of Darcys law with a relaxation kernel be employed. From the results of the experiments it is possible to determine the parameters of the kernel characterizing the internal relaxation processes in the porous medium-dense gas system.