Numerical simulation of the miscible displacement of radionuclides in a heterogeneous porous medium

The aim of this paper is to model and simulate the displacement of radioactive elements in a saturated heterogeneous porous medium. New schemes are proposed to solve accurately the convection–diffusion–reaction equations including nonlinear terms in the time derivative. Numerical tests show the stability and robustness of these schemes through strong heterogeneities of the medium. Finally the COUPLEX 1 benchmark concerning the far field simulation of a polluted flow by a leak of a nuclear waste disposal is performed and compared with the results available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

Macrokinetic model of the trapping process in two-phase fluid displacement in a porous medium

A microinhomogeneity-averaged model of the kinetics of the trapping process is proposed for a porous medium in which two fluids are mutually displaced. The traps are treated as a new hydrodynamic phase, and the trapping process as a phase transition. Kinetic relations for the average trapping process are obtained. The structure and quantitative values of the kinetic coefficients are obtained for a model of a porous medium in the form of a system of doublets. The dependence of the characteristic time of the process on the degree of inhomogeneity of the medium is investigated. A variant of the macroscopic model of the process of two-phase flow, in which the kinetic relations obtained are used as the closing relations, is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 92–101, May–June, 1995.     

Stability of the replacement of a non-Newtonian fluid layer in a porous medium

When petroleum is extracted from strata by replacing it with other fluids, the question arises of the stability of the interface. Uniformity in the injection horizons is in practice achieved by such methods as using polymer additives to thicken the replacing fluid or introducing an intermediate layer with non-Newtonian properties between the replacing fluid and the fluid being replaced. In this article the stability of the interface of non-Newtonian fluids being filtered exponentially is investigated in a linear formulation. The condition governing the stability of the interface of two non-Newtonian fluids is found and the influence of the thickness of the intermediate layer on the stability is also demonstrated. The presence of the layer is found to be essential for certain parameters of fluids moving in a porous medium if the replacement is to be stable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 183–186, March–April, 1976.The author wishes to thank V. N. Nikolaevskii for suggesting the subject for this investigation and A. T. Listrov for his constant interest in the work.     

Scaling mixing during miscible displacement in heterogeneous porous media

This paper discusses scaling of mixing during miscible flow in heterogeneous porous media. In large field systems dispersivity appears to depend on system length due to heterogeneities. Three types of scaling are discussed to investigate the heterogeneous effects. Dimensional analysis of mixing during flow through geometerically scaled heterogeneous models is illustrated using measured dispersion. Fractal analysis of mixing in statistically scaled heterogeneous porous media is discussed. Analog scaling of pressure transients in heterogeneous porous media is suggested as an in-situ method of estimating dispersion.Notation L Length - M mass - t time, (1) indicates dimensionless - a dispersivity (L) - V local velocity (L/t) - c concentration (l). - v velocity (L/t) - C₁ fluid compressibility (Lt²/M) - v time averaged velocity (LJt) - D dispersion VA) - W width (L) - D fractional dimension (1) - x coordinate (L) - d Euclidean dimension (1) - Y Y=In \-k (l) - \-d average particle size (L) - y coordinate (L) - g acceleration due to gravity (L/t2) - _c fractal cutoff (L) - \-k average permeability (L2) - viscosity (LM/t) - L length (L) - porosity (1) - L correlation scale (1/L) - density (N/L³) - N Number of sites (l) - ² variance (dimension depends on variable) - p pressure (W/t²L) - spectral exponent (l) - [R] randomnumber (1) - r radius (L) - t time (t)     

Horizontal displacement of miscible fluids from fractured porous media

The equations of horizontal displacement of miscible fluids from thin fractured porous formations are derived with allowance for all three mechanisms of mass transfer between the blocks and the fractures. The effect of the difference in the densities of oil and gas and the displacement velocity on oil production is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 87–95, May–June, 1992.The author is grateful to A. K. Kurbanov for useful discussions and his intererst in the work and also to G. D. Istomin for carrying out the numerical calculations.     

Influence of the heterogeneity of the solutions on the parameters of miscible displacement in saturated porous medium

The aim of this study is the investigation of the effects of density and viscosity contrasts on miscible displacements when the regime is stable. It has been possible to quantify these effects by using an empirical model which takes into account both the physical properties of the liquids and the hydrodynamic parameters in different configurations of a miscible displacement involving distilled water and a calcium chloride solution. The introduction of a method for measuring electrical conductivities within the porous medium itself (without disturbing the flow) has enabled us to monitor the change in the mixing zone throughout the entire length of the flow path. A stability criterion based on hydrodynamic parameters has been established that depends on two dimensionless numbers.     

Efficiency of diffusion controlled miscible displacement in fractured porous media

Experiments were performed to study the diffusion process between matrix and fracture while there is flow in fracture. 2-inch diameter and 6-inch length Berea sandstone and Indiana limestone samples were cut cylindrically. An artificial fracture spanning between injection and production ends was created and the sample was coated with heat-shrinkable teflon tube. A miscible solvent (heptane) was injected from one end of the core saturated with oil at a constant rate. The effects of (a) oil type (mineral oil and kerosene), (b) injection rates, (c) orientation of the core, (d) matrix wettability, (e) core type (a sandstone and a limestone), and (f) amount of water in matrix on the oil recovery performance were examined. The process efficiency in terms of the time required for the recovery as well as the amount of solvent injected was also investigated. It is expected that the experimental results will be useful in deriving the matrix–fracture transfer function by diffusion that is controlled by the flow rate, matrix and fluid properties.     

Stability analysis of soret-driven double-diffusive convection of Maxwell fluid in a porous medium

Stability analysis of double-diffusive convection for viscoelastic fluid with Soret effect in a porous medium is investigated using a modified-Maxwell-Darcy model. We use the linear stability analysis to investigate how the Soret parameter and the relaxation time of viscoelastic fluid effect the onset of convection and the selection of an unstable wavenumber. It is found that the Soret effect is to destabilize the system for oscillatory convection. The relaxation time also enhances the instability of the system. The effects of Soret coefficient and relaxation time on the heat transfer rate in a porous medium are studied using the nonlinear stability analysis, the variation of the Nusselt number with respect to the Rayleigh number is derived for stationary and oscillatory convection modes. Some previous results can be reduced as the special cases of the present paper.     

Stability of the displacement front and development of “fingering” in a porous medium

The effect of random disturbances at the fluid interface on the formation and development of fingering in the immiscible displacement of liquid hydrocarbons by water is experimentally investigated in a modified Hele-Shaw cell.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 101–106, September–October, 1989.     

Filtration of two miscible liquids in a fractured porous medium in a gravity field

The article discusses the one-dimensional problem of the displacement of a liquid (petroleum), saturating a fractured porous medium, by another liquid miscible with it in all ratios, in a gravity field. A system of two nonlinear equations in partial derivatives, of the hyperbolic type, is obtained for the concentration of one of the liquids in fractures and blocks. The system is integrated numerically by the method of characteristics. On the basis of the results universal dependences are obtained for the distribution of the concentrations over the stratum and the yield of petroleum.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–168, March–April, 1973.The authors axe grateful to V. M. Entov for his evaluation of the work.     

One-dimensional simulation of viscous fluid displacement from a porous medium with consideration of lateral inflow

A one-dimensional model of fluid displacement in a porous medium is discussed with consideration of lateral inflow. The time period required for the complete displacement of an initially injected fluid from a region is studied. Some numerical results obtained for two formulations of the problem are given; these results are in good agreement with the estimates considered in this paper. The problem under study is of interest in practice for enhancing the oil recovery from oil fields.     

Fingering associated with immiscible displacement in a two-layer porous medium

The effect of capillary cross flows on the structure of the displacement front in a two-layer porous medium with different layer permeabilities is examined. It is shown that capillary cross flows along the curved displacement front may lead to stabilization of the displacement. Approximate expressions are obtained for the limiting finger length and the oil displacement coefficient at the moment of breakthrough of the water as functions of the displacement parameters and the form of the functional parameters of the two-phase flow in the porous medium; the results obtained are compared with the results of numerical calculations and the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 98–104, January–February, 1991.     

Compressibility effects under conditions of convective stability of miscible fluids in a porous medium

The effect of compressibility on the convective stability of equilibrium of a binary mixture in a homogeneous porous medium is analyzed. It is shown that the contribution of compressibility significantly increases the equilibrium stability with respect to oscillatory perturbations.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–23, January–February, 1995.     

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.     

Barothermal effect in the displacement of oil from a porous medium

The formation of the temperature field due to the barothermal effect when oil is displaced from a porous medium by water is investigated in the piston displacement and two-phase flow approximations. The approach of the displacement front to the outlet from the porous medium leads to a sharp increase in temperature and the temperature anomalies are observed to depend on the saturation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 104–109, May–June, 1992.     

Stability of a stationary steam-water front in a porous medium

The instability of a plane front between two phases of the same fluid (steam and water) in a porous medium is considered. The configuration is taken to be initially stationary with the more dense phase overlying the less dense phase. The frontal region is assumed sharp, so that macroscopic boundary conditions can be utilized. This assumption precludes the existence of dispersion instabilities. The stabilizing influence of phrase transition as well as the implication of different macroscopic pressure boundary conditions on the stability of the front are discussed and illustrated.     

Surface deposition from fluid flow in a porous medium

The changes to porosity and permeability resulting from surface deposition and early dissolution in an initial rhombohedral array of uniform spheres are studied. Very rapid decreases in permeability result from early deposition, with 48 percent reduction predicted in permeability from 8 percent reduction in porosity. After deposition has caused about a 1 percent increase in the radii of the spherical array, relative permeability reductions vary approximately as the square of relative changes in porosity. These theoretical results are matched with experimental data of Itoi et al. and Moore et al. on deposition of silica. Satisfactory results are obtained in some cases, but for other cases a more complex model of the porous medium is needed.     

Plane waves in a semi-infinite fluid saturated porous medium

The field equations governing the propagation of waves in an incompressible liquid-saturated porous medium are investigated and a general solution is presented. It has been revealed that coupled longitudinal and transverse waves propagate in the porous medium. The propagation of transverse waves in the fluid phase is completely due to the interaction between the solid and fluid phases. The dispersion relationship and attenuation features are discussed. Unlike other investigations, all explicit forms of the arguments are derived. The reflection of the plane harmonic waves at the plane, traction-free boundary, which shows the influence of the dissipation on the velocity, and the attenuation coefficients of the reflected waves is studied. It is of interest that pore pressure is produced in the process of reflection, even in the case of the incidence of transverse waves.     

Micromechanics of residual saturation formation during immiscible displacement in a porous medium

The process of displacement of a nonwetting fluid has been studied experimentally on a transparent model of a porous medium for various percolation velocities in the stable front regime, when the viscosity of the displacing fluid is greater than that of the fluid displaced. The flow structures in the final displacement regime, when the nonwetting phase is distributed in the pore space in the form of individual drops or ganglia, have been visually investigated. Imbibition is numerically modeled on a two-dimensional network model with allowance for various microdisplacement mechanisms. The effect of the initial displacing phase saturation on the magnitude and structure of the residual displaced fluid saturation is demonstrated. The fractal dimensionality of the displacement boundary is measured.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 116–121, May–June, 1994.