Averaging a granular medium with spherical packing

The problem of averaging three-component media consisting of rigid grains, a viscous or elastic deformable meterial occupying the intergranular gaps and an inviscid pore liquid (or gas) is examined. When the deformable material completely fills the gaps, the medium is reduced to two-component form. The volume of the interlayers is comparable with the volume of the grains (the grains are spherical and the distance between the nearest points on neighboring spheres is small as compared with the diameter).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–81, May–June, 1990.     

Hydraulic radius and transport in reconstructed model three-dimensional porous media

Methods for reconstructing three-dimensional porous media from two-dimensional cross sections are evaluated in terms of the transport properties of the reconstructed systems. Two-dimensional slices are selected at random from model three-dimensional microstructures, based on penetrable spheres, and processed to create a reconstructed representation of the original system. Permeability, conductivity, and a critial pore diameter are computed for the original and reconstructed microstructures to assess the validity of the reconstruction technique. A surface curvature algorithm is utilized to further modify the reconstructed systems by matching the hydraulic radius of the reconstructed three-dimensional system to that of the two-dimensional slice. While having only minor effects on conductivity, this modification significantly improves the agreement between permeabilities and critical diameters of the original and reconstructed systems for porosities in the range of 25–40%. For lower porosities, critical pore diameter is unaffected by the curvature modification so that little improvement between original and reconstructed permeabilities is obtained by matching hydraulic radii.     

Percolation models of the permeability properties of media

Models that describe the permeability of media with allowance for the structure of the pore space are considered. It is proposed to use percolation theory to describe the topology of the pore space. If the distribution of the pore channels in the medium is random, percolation theory makes it possible to determine the percolation threshold, and also to estimate the fluid conductivity of the cluster that then results. Results obtained for models of granular, porous, and cracked media are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–86, May–June, 1984.     

Exchange model of displacement in porous media

A displacement model constructed on the assumption of the exchange of components between the volumes of the pore space moving and not moving in the direction of displacement is considered. The theoretical solution is shown to be in good agreement with the actual results of the displacement of oil by water. Criterial equations for predicting the interphase exchange coefficient and the relation between the nonmoving and moving volumes of the pore space are constructed on the basis of a series of experiments in uncemented porous media.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97. January–February, 1991.     

Application of the Carman–Kozeny Correlation to a High‐Porosity and Anisotropic Consolidated Medium: The Compressed Expanded Natural Graphite

The Carman–Kozeny correlation is applied to a medium which is consolidated, highly porous and anisotropic: the expanded then compressed natural graphite. The effective textural properties (i.e. the mean pore diameter, porosity and tortuosity) have been measured by a mercury porosimeter and a heterogeneous diffusion cell. The texture and the permeability (according to the Darcy's law) measured for the two main directions of these orthotropic porous media change over a very wide range depending on their apparent mass densities. Experimental data show that only a part of the total porosity participates in the gas flow in steady state conditions.     

Calculation of a stratum saturated with liquid under pressure as a hydraulic seismograph

The reaction of the pore pressure of a stratum completely saturated with liquid to periodic long-wavelength variations in the stressed state of a rock mass is a alyzed. The amplitude-frequency characteristic of the stratum used as a hydraulic sensor is found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 81–86, July–August, 1984.     

Conditions op mobilization of the nonwetting phase in a porous medium

The characteristics of the motion of individual ganglia in a model of a hydrophilic porous medium have been experimentally investigated. On the basis of a probability analysis the ganglion mobilization data obtained are generalized with allowance for the structure of the pore space.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 104–111, November–December, 1988.     

Micromodel Observation of the Role of Oil Layers in Three-Phase Flow

We have studied the flow of a non-aqueous phase liquid (NAPL, or oil), water and air at the pore scale using a micromodel. The pore space pattern from a photomicrograph of a two-dimensional section through a Berea sandstone was etched onto a silicon wafer. The sizes of the pores in the micromodel are in the range 3–30,m and are the same as observed in the rock from which the image was taken. We conducted three-phase displacement experiments at low capillary numbers (in the order of 10^-7) to observe the presence of predicted displacement mechanisms at the pore scale. We observed stable oil layers between the wetting phase (water) and the non-wetting phase (gas) for the water–decane–air system, which has a negative equilibrium spreading coefficient, as well as four different types of double displacements where one fluid displaces another that displaces a third. Double imbibition and double drainage are readily observed, but the existence of an oil layer surrounding the gas phase makes the other double displacement combinations very unlikely.     

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.     

An Analysis of Three-Phase Pore Occupancies and Relative Permeabilities in Porous Media with Variable Wettability

In three-phase flow, the macroscopic constitutive relations of capillary pressure and relative permeability as functions of saturation depend in a complex manner on the underlying pore occupancies. These three-phase pore occupancies depend in turn on the interfacial tensions, the pore sizes and the degree of wettability of the pores, as characterised by the cosines of the oil–water contact angles. In this work, a quasi-probabilistic approach is developed to determine three-phase pore occupancies in media where the degree of wettability varies from pore to pore. Given a set of fluid and rock properties, a simple but novel graphical representation is given of the sizes and oil–water contact angles underlying three-phase occupancies for every allowed combination of capillary pressures. The actual phase occupancies are then computed using the contact angle probability density function. Since a completely accessible porous medium is studied, saturations, capillary pressures, and relative permeabilities are uniquely related to the pore occupancies. In empirical models of three-phase relative permeability it is of central importance whether a phase relative permeability depends only on its own saturation and how this relates to the corresponding two-phase relative permeability (if at all). The new graphical representation of pore sizes and wettabilities clearly distinguishes all three-phase pore occupancies with respect to these saturation-dependencies. Different types of saturation-dependencies may occur, which are shown to appear in ternary saturation diagrams of iso-relative permeability curves as well, thus guiding empirical approaches. However, for many saturation combinations three-phase and two-phase relative permeabilities can not be linked. In view of the latter, the present model has been used to demonstrate an approach for three-phase flow modelling on the basis of the underlying pore-scale processes, in which three-phase relative permeabilities are computed only along the actual flow paths. This process-based approach is used to predict an efficient strategy for oil recovery by simultaneous water-alternating-gas (SWAG) injection.     

Inertia and drag of cylinders oscillating in a fluid

The results of an experimental investigation of the hydrodynamic forces acting on a circular cylinder oscillating horizontally in water at rest parallel to the free surface are presented. The coefficients of the hydrodynamic forces — the inertia force proportional to the acceleration and the viscous drag proportional to the square of the velocity -are determined. The force coefficients are shown to depend significantly on the dimensionless (divided by the cylinder diameter) amplitude of the oscillations on the interval of variation from 0.5 to 10. In the experiments the maximum values of the Reynolds numbers, calculated from the maximum velocity and the cylinder diameter, were 2.10³–8.10⁴.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 111–115, July–August, 1989.     

Forced capillary breakup of liquid jets

The characteristics of the forced capillary breakup (FCB) of liquid jets have been investigated over a broad range of variation of the breakup parameters: jet orifice diameter (34–527 m), flow rate (10^–5–1 cm³/sec), and excitation amplitude and frequency. The theory is compared with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–61, March–April, 1988.The authors are grateful to E. V. Ametistov for his constant interest and assistance.     

Contribution of capillary forces to the volume of residual oil pillars

Equations for calculating the limiting equilibrium shapes of the residual oil pillars in homogeneous and stratified inhomogeneous reservoirs of varying wettability are written within the framework of a two-phase displacement model with allowance for capillary pressure. Comparative calculations for an individual well in a circular reservoir show that, in general, the effect of capillary pressure on the shape and volume of the pillars is not negligibly small and may reach 10% of the pore volume.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 114–123, January–February, 1991.     

A Two-Dimensional Network Model to Simulate Permeability Decrease Under Hydrodynamic Effect of Particle Release and Capture

A model was developed to simulate permeability decrease induced by hydrodynamic effects when injecting a fluid in a reservoir with respect to particle release and capture mechanisms and the parameters of the fluid–rock system. The kinetics of particle release and capture were integrated after computing the initial permeability of the porous medium with a square lattice of a two–dimensional network model. The rate of particle release is related to the difference between a microscopic velocity of the fluid and a critical velocity. The permeability decrease shows a direct link to the reduction of pore throat radii by three mechanisms of particle capture: straining and particle accumulation through direct interception or diffusion. Comparison between the simulations and the experimental results shows that the model reproduces the physics of the permeability decrease phenomenon, although the values are overestimated. The difference between the two sets of results can be explained by the fact that the simulations are realized at constant pressure whereas the experiments are realized at constant flow rate, and that re–entrainment of the trapped particles was not taken into account in the model.     

Transient analysis of ionic replacements in elastic–plastic expansive clays

Chemically active saturated clays are considered in a two-phase framework. The solid phase contains clay particles, absorbed water and dissolved ions, Na⁺, K⁺ and Cl⁻. The fluid phase, or pore water, contains free water and the same ionic species. Water and ions can transfer between the two phases. In addition, they diffuse through the porous medium. A global understanding of all phenomena, mass transfer, diffusion/advection and deformation is provided. The coupled constitutive equations associated to these phenomena are developed. Emphasis is laid on the electro-chemo-mechanical constitutive equations in an elastic–plastic setting.A finite element formulation embodying all the above aspects is proposed and simulations of oedometer tests are presented and commented. Of particular interest are the consolidation and swelling that occur during salinization and desalinization of an external reservoir in contact with the specimen, and the more subtle, but important effects of replacing an NaCl pore solution by a KCl pore solution, and conversely.     

Nonlinear evolution of waves in forced decaying capillary jets

The investigation of nonlinear waves in decaying capillary jets is of great interest both from the point of view of nonlinear wave processes in media and for practical applications associated with the generation and propagation of flows of monodisperse droplets [1–4]. The formation and dynamics of satellite droplets are particularly important in the study of the decay of thin capillary jets [5–8]. Investigation of the conditions of formation of satellites open up important prospects for the preparation of monodisperse microscopic granules with diameters appreciably less than the diameter of the original jet. This is of great importance in modern technologies based on the use of materials in disperse form [9–13]. The present paper is devoted to the investigation of nonlinear waves in decaying capillary jets.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 54–60, May–June, 1993.     

Shock adiabats of porous metals

In this paper we investigate the shock compression and also the unloading of shock-loaded metals, taking into account the air in the pore spaces between the grains of continuous metal. We study the range of pressures and temperatures of the air during the shock compression, wherein the contribution of the thermal radiation of the air to the pressure and energy is still unimportant. The experimental results, obtained in the pressure range 40–850 kbar for Ni, Cu, and W, agree within experimental error with calculated data. We give the experimental results for the unloading of porous copper from a pressure state of 485 kbar.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 101–105, March–April, 1971.     

Numerical Study of Hydrodynamics and Heat and Mass Transfer of a Ducted Gas–Vapor‐Droplet Flow

A computational model has been developed to predict heat and mass transfer and hydrodynamic characteristics of a turbulent gas–vapor–droplet flow. Turbulent characteristics of the gas phase are computed using the k– model of turbulence. It is shown that, with increasing inlet droplet diameter, the rate of heat transfer between the duct surface and the vapor–gas mixture decreases appreciably, whereas the wall friction increases only insignificantly. The predicted values agree fairly well with available experimental and numerical data     

Pore-Level Modeling of Gas and Condensate Flow in Two- and Three-Dimensional Pore Networks: Pore Size Distribution Effects on the Relative Permeability of Gas and Condensate

We present a mechanistic model of retrograde condensation processes in two- and three-dimensional capillary tube networks under gravitational forces. Condensate filling-emptying cycles in pore segments and gas connection–isolation cycles are included. With the pore-level distribution of gas and condensate in hand, we determine their corresponding relative permeabilities. Details of pore space and displacement are subsumed in pore conductances. Solving for the pressure field in each phase, we find a single effective conductance for each phase as a function of condensate saturation. Along with the effective conductance for the saturated network, the relative permeability for each phase is calculated. Our model porous media are two- and three-dimensional regular networks of pore segments with distributed size and square cross-section. With a Monte Carlo sampling we find the optimum network size to avoid size effects and then we investigate the effect of network dimensionality and pore size distribution on the relative permeabilities of gas and condensate.