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.     

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.     

Gas-gas displacement in a fractured porous reservoir

The results of an experimental investigation of the process of miscible displacement of a gas from a fractured porous reservoir by another gas are presented. It is established that the displacement process is influenced by convective and molecular diffusion. The displacement coefficient depends both on the reservoir properties of the formation and on the technological displacement parameters. The experiments revealed a decrease in the displacement coefficient with increase in the permeability ratio of the joints and the blocks and with decrease in formation pressure. The dependence of the displacement coefficient on the average gas velocity in the reservoir, i.e., the ratio of the gas flow rate to the product of the flow area and the total reservoir porosity coefficient (including the blocks and the joints), is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–79, May–June, 1991.     

Nonlinear flow in fractured porous media

Conventional models of filtration in fractured porous bodies involve certain unwarrantable assumptions related to the definition of basic equations and the underestimation of a connection between the effective properties of a body and both the stress system and the pressure of a flowing fluid. A new theory is developed with the help of reconsidering those underlying assumptions and of a conception of the body being subject to elastic deformations. The theory is illustrated by means of studying a particular problem of stationary filtration.     

Wave propagation in fractured porous media

A theory of wave propagation in fractured porous media is presented based on the double-porosity concept. The macroscopic constitutive relations and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. In microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law in fractured porous media. The macroscopic constitutive relations of elastic porous media saturated by one or two fluids and saturated fractured porous media can be obtained from the constitutive relations developed in the paper. In the simplest case, the final set of governing equations reduce to Biot's equations containing the same parameters as of Biot and Willis.Now at Izmir Institute of Technology, Anafartalar Cad. 904, Basmane 35230, Izmir, Turkey.     

Structure of saturation jumps in nonequilibrium displacement from porous media

The nonequilibrium displacement characteristics are investigated experimentally and by numerical calculation of the nonequilibrium percolation equations under various conditions of wetting of the porous medium by the displacing and displaced fluids. A scheme for calculating the disequilibrium parameter is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 97–104, November–December, 1990.     

Traveling liquid bridges in unsaturated fractured porous media

Interplay between capillary, gravity and viscous forces in unsaturated fractures gives rise to a range of complex flow phenomena. Evidence of highly intermittent fluxes, preferential and sustainable flow pathways lead to potentially significant flow focusing of concern for regulatory and management of water resources in fractured rock formations. In previous work[Ghezzehei TA,Or D.: Water Resour. Res. In Review(2005)] we developed mechanistic models for formation, growth and detachment of liquid bridges in geometrical irregularities within fractures. Such discrete and intermittent flows present a challenge to standard continuum theories. Our focus here is on predicting travel velocities of detached liquid elements and their interactions with fracture walls. The scaling relationships proposed by Podgorski et al. [Podgorski, T., et al.: Phys. Rev. Lett. 8703(3), 6102-NIL_95 (2001)] provide a general framework for processes affecting travel velocities of discrete liquid elements in fractures, tubes, and in coarse porous media. Comparison of travel velocity and distance by discrete bridges relative to equivalent continuous film flow reveal significantly faster and considerably larger distances traversed by liquid bridges relative to liquid films. Coalescence and interactions between liquid bridges result in complex patterns of travel times and distances. Mass loss on rough fracture surfaces shortens travel distances of an element; however, results show that such retardation provides new opportunities for coalescence of subsequent liquid elements traveling along the same path, resulting in mass accumulation and formation of larger liquid elements traveling larger distances relative to smooth fracture surfaces. Such flow focusing processes may be amplified considering a population of liquid bridges within a fracture plane and mass accumulation in fracture intersections.     

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.     

Experimental investigation of the displacement of viscous fluids from porous media

The results of experimental investigations of different-viscosity and immiscible Newtonian fluid flows through porous media are presented. The investigations were carried out for a Hele-Shaw cell occupied by a porous medium. The basic difference from the previous studies is the observation of the flow after break-through of the displacing fluid into the sink. A series of qualitative and quantitative results which clarify the physics of immiscible fluid flows through capillaries and porous media were obtained in the course of the experimental investigations.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 124–131. Original Russian Text Copyright © 2005 by Baryshnikov, Belyaev, and Turuntaev.     

Solution of some problems of flow through fractured porous media

Problems of fluid flow through a fractured porous medium consisting of fractures and blocks with different filter characteristics are solved. The mass exchange between fractures and blocks is assumed to be proportional to the pressure difference between them. The porosity in the fractures is assumed to be negligibly small. Under these assumptions the determination of the pressure fields reduces to the integration of a system of linear differential equations. The solution is found by the operational method using the Efros theorem. The cases of oil reservoir operation by means of both galleries and wells are considered. The solutions are obtained in an analytical form convenient for calculations.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 94–102, January–February, 1995.     

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)     

Laws of viscoplastic fluid flow in anisotropic porous and fractured media

In invariant tensor form, the laws of viscoplastic fluid flow are formulated for capillary and fractured media with a periodic microstructure that has orthotropic and transversely isotropic symmetry in the flow properties. An analysis of the laws of viscoplastic fluid flow in transversely isotropic and orthotropic porous and fractured media shows that in formulating the equations it is necessary to distinguish between the permeability tensor and the limiting gradient tensor, which may differ in the symmetry of the flow characteristics, and that the flow law is multivariant and admits one-, two-, and three-dimensional flows.     

Self-similar solutions for displacement of non-Newtonian fluids through porous media

This paper presents a class of self-similar solutions describing piston-like displacement (single-phase flow is included as a special case) of one slightly compressible non-Newtonian, power-law, dilatant fluid by another through a homogeneous, isotropic porous medium. These solutions can be used to evaluate the validity and accuracy of existing approximate solutions, such as the assumption of constant flow rate at each radial distance that Ikoku and Ramey use to linearize the partial differential equation for the flow of non-Newtonian, power-law fluid through a porous medium.Nomenclature a parameter, defined by (A8) - A cross-section area of linear reservoir - B constant - c fluid compressibility - c _f formation compressibility - c _t system compressibility - c t dimensionless system compressibility, defined by (24) - C constant of integration - D _I dimensionless coefficient, directly proportional to injection rate, for linear displacement case, defined by (22). - D ₂ dimensionless coefficient, directly proportional to injection rate, for radial displacement case, defined by (55) - erf(x) error function - ercf(x) complementary error function - Ei(x) exponential integral - f dimensionless pressure, defined by (10) - h formation thickness - k permeability - l linear location of moving boundary between the displacing and displaced fluids - n flow behavior parameter - p pressure - p _i injection pressure - p ₀ initial pressure; reference pressure - p ₀ dimensionless initial pressure, defined by (19) - q injection rate - r radial distance - R radial location of moving boundary between the displacing and displaced fluids - t time - u superficial velocity - U substitution of variable - x linear distance - _e effective viscosity - _e dimensionless effective viscosity, defined by (24) - dimensionless variable, defined by (9) or (45) - _i0 value of corresponding to the location of the moving boundary between the displacing and displaced fluids - density - ₀ value of density at reference pressure - porosity - ₀ value of porosity at reference pressure - 1 displacing fluid - 2 displaced fluid     

Body waves in fractured porous media saturated by two immiscible newtonian fluids

A study of body waves in fractured porous media saturated by two fluids is presented. We show the existence of four compressional and one rotational waves. The first and third compressional waves are analogous to the fast and slow compressional waves in Biot's theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. The effects of fractures on the phase velocity and attenuation coefficient of body waves are numerically investigated for a fractured sandstone saturated by air and water phases. All compressional waves except the first compressional wave are diffusive-type waves, i.e., highly attenuated and do not exist at low frequencies.Now at Izmir Institute of Technology, Faculty of Engineering, Gaziosmanpasa Bulvari, No.16, Cankaya, Izmir, Turkey.     

Fluid flow in fractured and fracturing porous media: A unified view

Fluid flow in fractures that pre-exist or propagate in a porous medium can have a major influence on the deformation and flow characteristics. With the aim of carrying out large-scale calculations at reasonable computing costs, a sub-grid scale model has been developed. While this model was originally embedded in extended finite element methods, thereby exploiting some special properties of the enrichment functions, we will herein show that, using proper micro–macro relations, in particular for the mass balance, sub-grid scale models can be coupled to a range of discretisation methods at the macroscopic scale, from standard interface elements to isogeometric finite element analysis.     

A solution of steady-state fluid flow in multiply fractured isotropic porous media

Herein a plane, steady-state fluid flow solution for fractured porous media is first presented. The solution is based on the theory of complex potentials, the theory of Cauchy integrals, and of singular integral equations. Subsequently, a numerical method is illustrated that may be used for the accurate estimation of the pore pressure and pore pressure gradient fields due to specified hydraulic pressure or pore pressure gradient acting on the lips of one or multiple non-intersecting curvilinear cracks in a homogeneous and isotropic porous medium. It is shown that the numerical integration algorithm of the singular integral equations is fast and converges rapidly. After the successful validation of the numerical scheme several cases of multiple curvilinear cracks are illustrated.     

Solute diffusion in fractured porous media with memory effects due to adsorption

Modelling of solute transport in fractured porous media is a subject of intensive research in many engineering disciplines, such as petroleum engineering, water resources management, civil engineering. Recent field and laboratory experiments show that, in presence of strong adsorption, the behaviour of solute penetrating into the fractured porous medium diverges from classical hypotheses, rendering impossible the adjustment of classical transport models. The aim of this paper is to develop a mathematical continuous model of solute transport, when strong adsorption of solute occurs on the grains of the porous matrix. The macroscopic model is obtained by upscaling the pore and the fracture behaviours, by using the multiple scale expansion method. We obtain a non-standard diffusion behaviour of solute which shows local non-equilibrium between transport in the fractures and in the porous matrix, as well as memory effects. To cite this article: J. Lewandowska et al., C. R. Mecanique 330 (2002) 879–884.     

LBM simulation of fluid flow in fractured porous media with permeable matrix

To analyze and depict complicated fluid behaviors in fractured porous media with variably permeable matrix, an integrated discrete computational algorithm is proposed based on lattice Boltzmann method (LBM). This paper combines with the external force model and statistical material physics to effectively describe the feature changes while the fluid passes through the fractures within the permeable matrix. As an application example, a two dimensional rock sample is reconstructed using the digital image and characterized with different feature values at each LBM grid to distinguish pores, impermeable and permeable matrix by stating its local physical property. Compared with the conventional LBM, the results demonstrate the advantages of proposed algorithm in modeling fluid flow phenomenon in fractured porous media with variably permeable matrix.     

Numerical study of the linear stability of immiscible displacement in porous media

In this paper the linear stability of immiscible displacement in porous media is examined by numerical methods. The method of matched initial value problems is used to solve the eigenvalue problem for displacement processes pertaining to initially mobile phases. Both non capillary and capillary displacement in rectilinear flow geometries is studied. The results obtained are in agreement with recent asymptotic studies. A sensitivity analysis with respect to process parameters is carried out. Similarities and differences with the stability of Hele-Shaw flows are delineated.This is a revised version of paper SPE 13163, presented at the 59th Annual Technical Conference of the Society of Petroleum Engineers, Houston, Texas, 16–19 Sept. 1984.