Effective stress principle for saturated fractured porous media

An effective stress principle for saturated fractured porous media is proposed based On the double-porosity representation. Both the solid grains and the fractured porous medium are assumed to be linearly elastic materials. The derivation employs volume averaging technique to obtain macroscopic scale expressions. Two parameters, the bulk modulus of the fractured medium and bulk modulus of the porous matrix, are introduced in the formulation. The final expression reduces to the one obtained by Blot and Willis [1957], Skempton [1960], Nur and Byeerle [1971], and Verruijt [1984] when the volume fraction of the fractures vanishes, that is, for a nonfractured porous medium

Wave propagation in fractured porous media saturated by two immiscible fluids

A study of wave propagation in fractured porous media saturated by two immiscible fluids 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. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law in fractured porous media. In the simplest case, the final set of governing equations reduce to Blot's equations containing the same parameters as Blot and Willis. Then, we demonstrate the existence of four compressional waves and one rotational wave. The first and third compressional waves are analogous to the fast and slow compressional waves in Blot'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. All compressional waves, except the first, are diffusive-type waves, i.e., highly attenuated and nonexistent at low frequencies

A SEMIANALYTICAL ANALYSIS OF COMPRESSIBLE ELECTROPHORETIC CAKE FORMATION

Leaks in geomembrane liners of waste landfills and liquid impoundments cause chemical contaminants to leak into the subsurface environment. A mathematical model is presented to simulate electrophoretic sealing of impoundment leaks. The model describes the formation of a compressible clay cake because of electrical and gravitational forces. The model includes mass balance equations for the solid-particles and liquid phase, modified Darcy's law in an electrical field, and Terzaghi's definition of effective stress. The formulation is presented in the Eulerian coordinates. The resulting second-order, nonlinear partial differential equation and the lower boundary condition are linearized to obtain an analytical solution for time-dependent settlement. After discretizing in time the analytical solution is applied to simulate compression of an accreting Sediment. In the; simulation of an accreting sediment, solid fluxes on either side of suspension/sediment interface are coupled using a no-jump condition. The velocity of a discrete particle in the suspension zone is assumed to be equal to the algebraic sum of electrophoretic and Stoke's settling velocities. An empirical relationship available in the literature is used to account for the effect of concentration on the velocity of solid particles in the suspension zone. The validity of the semianalytical approach is partially verified using an exact steady state solution for self-weight consolidation. The simulation results obtained for a set of material parameters are presented graphically. It is noted that the electrokinetic consolidation of sediment continues even after the completion of electrophoretic settling of all clay particles. An analysis reveals that the electrophoretic cake formation process is quite sensitive to voltage gradient and the coefficient of compressibility

Landfill settlement with decomposition and gas generation

A one-dimensional multiphase numerical model is developed to simulate the vertical settlement involving liquid and gas flows in a deformable.(settling) municipal solid waste (MSW) landfill. MSW is represented by a chemical composition, and a global stoichiometric reaction is used to estimate the maximum yield of gas generation. Following the general assumption accepted in the literature, the gas generated by waste decomposition is assumed to comprise of in I ethane (CH4)and carbon dioxide (CO2). The gas generation rate follows an exponentially decaying function of time. The gas generation model developed based on a first-order kinetic single-bioreactor approach includes the governing equations of gas migration, liquid flow, and landfill deformation. The. Galerkin finite element method is used to solve the resulting equations. The model developed can be used to estimate the transient and ultimate settlements due to waste decomposition and gas generation in MSW landfills. The proposed model can estimate the waste porosity, gas pressure, liquid pressure, gas saturation, liquid saturation, and stress distributions in settling landfills. The results obtained for a deformable landfill are compared with a landfill having a rigid solid skeleton. Due to settlement, the depth of waste is 27% smaller in deformable landfills than that of the rigid ones

Rise velocity of an air bubble in porous media: Theoretical studies

[1] The rise velocity of injected air phase from the injection point toward the vadose zone is a critical factor in in-situ air sparging operations. It has been reported in the literature that air injected into saturated gravel rises as discrete air bubbles in bubbly flow of air phase. The objective of this study is to develop a quantitative technique to estimate the rise velocity of an air bubble in coarse porous media. The model is based on the macroscopic balance equation for forces acting on a bubble rising in a porous medium. The governing equation incorporates inertial force, added mass force, buoyant force, surface tension and drag force that results from the momentum transfer between the phases. The momentum transfer terms take into account the viscous as well as the kinetic energy losses at high velocities. Analytical solutions are obtained for steady, quasi-steady, and accelerated bubble rise velocities. Results show that air bubbles moving up through a porous medium equilibrate after a short travel time and very short distances of rise. It is determined that the terminal rise velocity of a single air bubble in an otherwise water saturated porous medium cannot exceed 18.5 cm/s. The theoretical model results compared favorably with the experimental data reported in the literature. A dimensional analysis conducted to study the effect of individual forces indicates that the buoyant force is largely balanced by the drag force for bubbles with an equivalent radius of 0.2-0.5 cm. With increasing bubble radius, the dimensionless number representing the effect of the surface tension force decreases rapidly. Since the total inertial force is quite small, the accelerated bubble rise velocity can be approximated by the terminal velocity

Sealing leaks in geomembrane liners using electrophoresis

An innovative method was demonstrated to seal leaks in geomembrane liners by attracting clay particles to the leaks using electrophoresis. Electrophoresis is the movement of electrically charged particles suspended in a liquid by the action of an electric field. A direct-current voltage impressed across the liner causes electrical current to flow through the leaks. The current produces a strong electric field at leaks. When a clay slurry is dispersed into the liquid in the impoundment, electrophoresis attracts the clay particles to the leaks, thereby sealing them. The method can seal leaks in liquid impoundments without removing the liquid or locating or accessing the leaks. The laboratory and full-scale test results were remarkable in that electrophoresis sealed the leaks completely when a layer of geofabric was under the liner, and electrophoresis reduced the leakage rate through holes as large as 10 mm in diameter by a factor of 1600 in the field test with gravel under the liner, and by a factor of 1667 in the laboratory basin with geonet under the liner.link_to_subscribed_fulltex