Multi-fluid model of suspension filtration in a porous medium

In the framework of a three-fluid approach, a new model of suspension filtration in a porous medium is constructed with account for the formation of a dense packing of trapped particles with finite permeability and porosity. The following three continua are considered: the carrier fluid, the suspended particles, and the deposited particles. For a one-dimensional transient flow of suspension, a system of equations for the concentrations of the suspended and deposited particles, the suspension velocity, and the pressure is constructed. Two cases of the flow in a porous medium are considered: plane and radial. Numerical solution is found using a finite-difference method. Numerical calculations are shown to be in agreement with an analytical solution for the simplest case of filtration with a constant velocity and constant porosity and permeability. A comparison is performed with the classic filtration models for five sets of experimental data on the contamination of a porous sample. It is shown that near the inlet boundary, where an intense deposition of particles takes place, the new model describes the concentration profile of the deposited particles more accurately than the classical model.     

One-dimensional filtration of immiscible liquids in a nonuniform porous medium

As is known, the differential equation for two-phase filtration with account for capillarity was obtained in [1], and later integrated numerically for the case of a uniform stratum of finite length in [2]. Other versions of the solution of the Rapoport-Leas equation or the system which is equivalent to it are known [3, 4]. This article presents the results of a numerical solution of an analogous problem with account for nonuniform permeability of the stratum.The authors wish to thank T. V. Startsev and L. Kh. Aminov for assistance in performing the calculations on the Ural-3 computer.     

Numerical study of single-phase gas filtration in a porous medium

This paper describes a method for numerical solution of single-phase nonstationary gas filtration in a porous medium. Linearization of the classical Leibenzon equation is performed. To solve the resulting linear equation, an efficient numerical algorithm was constructed without saturation over spatial variables and time.     

Experimental study of viscous instability in a porous medium

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 79–84, July–August, 1989.     

Mathematical model of deep-bed filtration of a two-component suspension through a porous medium

A model of deep-bed filtration of a two-component suspension through a porous medium with formation of two types of the deposit which have different structures and properties is constructed. The influence of the parameters of fluid and particle flux densities which determine mass transfer between different components of the suspension and deposits on the filtration characteristics and properties of the resulting deposits is estimated on the basis of numerical experiments for the suspensions with contrast particle fractions.     

Experimental investigation in filtration of hydrocarbons with mass transfer

The results are given of an experimental investigation into the process of extraction from a porous medium of a liquid hydrocarbon (precipitated condensate) filling part of the pore space by means of hydrocarbon solvents.Translated from Izyestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 167–170, September–October, 1979.     

Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium

In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the stress jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the stress jump boundary condition is investigated. It is shown that accounting for a jump in the shear stress at the interface essentially influences velocity profiles.     

Experimental and theoretical studies of convective heat transfer in a cylindrical porous medium

Convective heat transfer at constant heat flux through unconsolidated porous media has been studied both experimentally and theoretically. Heat transfer measurements have been performed for convective heat transfer over a wide range of operational parameters at constant heat fluxes. In addition to heat transfer coefficients, pressure drop and temperature profiles both in radial and axial direction have been recorded. The equations of motion and energy which account for the non-Darcian effect are used to describe the flow and convective heat transfer through the porous medium. Mathematical models for the prediction of heat transfer coefficients and temperature profiles are presented which predict the experimental data with good accuracy.     

Experimental validation of heat transfer models for flow through a porous medium

Unsteady heat transfer in a fluid saturated porous medium contained in a tube is studied. The porous medium is a bed of uniform diameter spheres, made of glass or steel, while the flowing fluid is water. The flow field is time invariant in the simulation as well as experiments. Step response of the bed when the temperature of the incoming water is suddenly increased, and oscillatory response when hot and cold fluids alternately flow through the tube are studied. Heat transfer models are based on thermal equilibrium between the fluid and the solid phase (one-equation) and thermal non-equilibrium (two-equation) between the two phases. The predictions of these models are compared against experiments conducted in a laboratory-scale apparatus. The comparison is in terms of time evolution of temperature profiles at selected points in the bed, as well as global properties of the temperature distribution such as attenuation and phase lag with respect to the boundary perturbations. The range of Peclet numbers considered in the study is 500–4,000, for which the flow can be considered laminar. Results show that the predictions of the two-equation model are uniformly superior to the one-equation model over the range of Peclet numbers studied. The differences among the three approaches diminish when the thermophysical properties of the solid and fluid phases are close to one another. The differences also reduce in the step response test as steady state is approached.     

Spin-up in a saturated porous medium

It is shown that, on the Brinkman model, spin-up is confined to boundary layers whose thickness is of order k ^1/2, and the spin-up is established in a time of order k/, where k, , and denote permeability, density, porosity and dynamic viscosity, respectively.     

Theoretical investigation on submicron particle penetration through circular tubes inside a porous medium

The analytical infinite series solution of submicron particle transport in a circular tube bounded by a porous wall, such as a pinhole, is determined under the slip velocity boundary condition, and the solution is verified by using the experimental data in the previous studies for the specific cases. The results show that particle penetration rate increases with the increase of the porous parameter, the axial pressure drop, and the pinhole radius, whereas it decreases with increasing the pinhole length. The penetration rate of nano-particles are more sensitive to the variation of these parameters. However, the differences between the penetrations of particles ranging from 0.3 μm to 1 μm are not evident because the diffusion becomes weak gradually in this size range. In addition, a further comparison is performed between the analytical solution and the existing studies, and approximate expressions are presented for accurate calculation of particle penetration rate through pinholes appearing in porous materials including filter devices and masks.     

Experimental data on the displacement of a gas from a porous medium by a gas

In connection with the exploitation of gas-condensate deposits by the method of the reverse injection of a dry gas, the article gives the results of an experimental investigation of the displacement of a gas by a gas, carried out in tubular models of homogeneous porous media with differing permeabilities.     

Flow of electrolytes in a porous medium

A two-scale model of ion transfer in a porous medium is obtained for one-dimensional horizontal flows under the action of a pressure gradient and an external electric field by the method of homogenization. Steady equations of electroosmotic flows in flat horizontal nano-sized slits separated by thin dielectric partitions are averaged over a small-scale variable. The resultant macroequations include Poisson’s equation for the vertical component of the electric field and Onsager’s relations between flows and forces. The total horizontal flow rate of the fluid is found to depend linearly on the pressure gradient and external electric field, and the coefficients in this linear relation are calculated with the use of microequations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 162–173, July–August, 2008.