Cracked Porous Medium Research Articles

Love-Type Wave Propagation in an Inhomogeneous Cracked Porous Medium Loaded by Heterogeneous Viscous Liquid Layer

Love-type wave propagation through inhomogeneous dual porous layer has been investigated in this present article. The heterogeneous fluid-saturated dual porous stratum is bounded by a non-homogeneous viscous liquid layer and an isotropic half-space. Impacts of viscosity, inhomogeneity, matrix porosity along with fracture porosity have been calculated in detail. Navier–Stokes equation has been used to acquire the velocity component in heterogeneous viscous liquid layer. Separable variable method has been performed to convert partial differential equations into ordinary differential equations. Elimination of arbitrary constants from boundary conditions leads to complex dispersion relation of Love-type wave propagation. The complex equation consists of Whittaker functions and their derivatives which are expanded up to second term by approximating large parameters. Dispersion and attenuation equations of Love-type wave have been decoupled for implementing several graphs which illustrate reverberations of heterogeneity parameter, porosity, volume fraction of fractures, density on dispersive and damping nature of Love-type wave. Fundamental mode and higher modes of Love-type wave are observed through graphical execution. Effects of inhomogeneity parameters are also portrayed through surface plotting. Correlation of liquid layer and fractured porous layer in crustal region has been established both analytically and graphically which is also validated by applying particular conditions. Heterogeneity parameter, volume fraction of fractures, porosity, density have major impact on dispersion and attenuation of Love-type wave propagating in dual porous medium. This solid–liquid collaborative study unlocks a different area of future research.

Contaminant Flow and Transport Simulation in Cracked Porous Media using Locally Conservative Schemes

The purpose of this paper is to analyze some features of contaminant flow passing through cracked porous medium, such as the influence of fracture network on the advection and diffusion of contaminant species, the impact of adsorption on the overall transport of contaminant wastes. In order to precisely describe the whole process, we firstly build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation; the other is reactive transport equation. The first equation is used to describe the total flow of contaminant wastes, which is based on Darcy law. The second one will characterize the adsorption, diffusion and convection behavior of contaminant species, which describes most features of contaminant flow we are interested in. After the construction of numerical model, we apply locally conservative and compatible algorithms to solve this mathematical model. Specifically, we apply Mixed Finite Element (MFE) method to the flow equation and Discontinuous Galerkin (DG) method for the transport equation. MFE has a good convergence rate and numerical accuracy for Darcy velocity. DG is more flexible and can be used to deal with irregular meshes, as well as little numerical diffusion. With these two numerical means, we investigate the sensitivity analysis of different features of contaminant flow in our model, such as diffusion, permeability and fracture density. In particular, we study Kd values which represent the distribution of contaminant wastes between the solid and liquid phases. We also make omparisons of two different schemes and discuss the advantages of both methods.

Numerical Study on the Characteristics of Multipole Acoustic Logging While Drilling in Cracked Porous Medium

AbstractCracks and pores universally exist in earth formation rocks, significantly affecting logging while drilling (LWD) acoustic waves. Using a cracked porous medium elastic wave theory, we derive the LWD acoustic wave field for a fluid‐filled borehole containing a drill collar and study the velocity dispersion, attenuation, and sensitivity of multipole wave modes (e.g. Stoneley, flexural and quadrupole waves) as a function of crack density and gas saturation. Increasing crack concentration and gas saturation can produce significant velocity change and attenuation. Relatively speaking, the velocity is more sensitive to crack density, while the attenuation is more sensitive to gas saturation. The dispersive LWD dipole and quadrupole waves characterized by a “Airy Phase” are strongly attenuated by gas saturation. This phenomenon can be used to detect the presence of gas in tight formations. The modeling and analysis results of this study are in agreement with analysis of field LWD data.

Contaminant Flow and Transport Simulation in Cracked Porous Media Using Locally Conservative Schemes

AbstractThe purpose of this paper is to analyze some features of contaminant flow passing through cracked porous medium, such as the influence of fracture network on the advection and diffusion of contaminant species, the impact of adsorption on the overall transport of contaminant wastes. In order to precisely describe the whole process, we firstly build the mathematical model to simulate this problem numerically. Taking into consideration of the characteristics of contaminant flow, we employ two partial differential equations to formulate the whole problem. One is flow equation; the other is reactive transport equation. The first equation is used to describe the total flow of contaminant wastes, which is based on Darcy law. The second one will characterize the adsorption, diffusion and convection behavior of contaminant species, which describes most features of contaminant flow we are interested in. After the construction of numerical model, we apply locally conservative and compatible algorithms to solve this mathematical model. Specifically, we apply Mixed Finite Element (MFE) method to the flow equation and Discontinuous Galerkin (DG) method for the transport equation. MFE has a good convergence rate and numerical accuracy for Darcy velocity. DG is more flexible and can be used to deal with irregular meshes, as well as little numerical diffusion. With these two numerical means, we investigate the sensitivity analysis of different features of contaminant flow in our model, such as diffusion, permeability and fracture density. In particular, we studyKdvalues which represent the distribution of contaminant wastes between the solid and liquid phases. We also make omparisons of two different schemes and discuss the advantages of both methods.

Relaxation Filtration of Homogeneous Fluids in Cracked-Porous Media

Equations of relaxation filtration of homogeneous fluids in cracked-porous media are derived. From a general system of equations, systems of “truncated” and simplified equations of filtration are obtained, for which the laws of smearing of pressure jumps are studied and the ranges of convergence of their solutions to the solution of the general system of equations are established.

The pressure build-up curve for a fractal cracked porous medium. Linear theory

The long-term asymptotic behaviour of the pressure build-up curve is found using the fractal model of a cracked medium (CPM) [1]. All processes are assumed to be isothermal.

Filtration of a non-newtonian fluid through a cracked-porous medium

Basic processes of fluid filtration in an elastically compressible cracked-porous material in the presence of an initial filtration gradient are considered.

Mass transfer during filtration of solutions in cracked-porous media

We obtain and study an analytical solution for the one-dimensional problem of the filtration of a solution in cracked-porous media with allowance for the dependence of the saturation concentration on the composition of the solution.

Numerical solution of problems of the filtration of a liquid in elastically deformable cracked-porous media

Results are presented from a numerical study of problems concerning filtration in cracked-porous reservoirs whose exploitation is accompanied by substantial deformation of the main flow channels (cracks).

Determination of the effective permeability of a cracked-porous medium

Formulas are derived to calculate the effective permeability of periodic, highly nonuniform porous structures. Also, methods are developed to calculate the parameters of the medium from data from studies of wells.

Fingero Imbibition in Artificial Replenishment of Ground Water Through Cracked Porous Medium

The present paper analytically discusses a theoretical model of groundwater replenishment in a cracked porous medium, with simultaneous occurrence of the phenomena of fingering and imbibition under certain conditions. We assume that the injection of water bodies is initiated by imbibition, and the ‘injected’ and ‘native’ water form two immiscible liquid phases of different salinities with small viscosity difference [Bear and Martin, 1965]. If we consider only the average behavior of fingering, we solve the nonlinear differential equation by a perturbation technique. An expression for the average cross‐sectional area occupied by fingers has been obtained.