Poromechanics Response of Inclined Wellbore Geometry in Fractured Porous Media

This paper presents the poromechanics/poroelastic analytical solution for stress and pore pressure fields induced by the action of drilling and/or the pressurization of an inclined/horizontal wellbore in fractured fluid-saturated porous media, or naturally fractured fluid-saturated rock formations. The model which is developed within the framework of the coupled processes in the dual-porosity/dual-permeability approach accounts for coupled isothermal fluid flow and rock/fractures deformation. The solution to the inclined/horizontal wellbore problem is derived for a wellbore drilled in an infinite naturally fractured poroelastic medium, subjected to three-dimensional in situ state of stress and pore pressure. The dual-porosity analytical solution is first reduced to the limiting single-porosity case and verified against an existing single-porosity solution. A comparison between single-porosity and dual-porosity poroelastic results is conducted and displayed in this work. Finally, wellbore stability analyses have been carried out to demonstrate possible applications of the solution.     

Poromechanics Response of Inclined Wellbore Geometry in Chemically Active Fractured Porous Media

The porochemoelastic analytical models and solutions have been used to describe the response of chemically active saturated porous media such as clays, shales, and biological tissues. To date, all existing solutions are only applicable to single-porosity and single-permeability model, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fractures. This work summarizes the general linear dual-porosity and dual-permeability porochemoelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active fractured formation, such as fractured shale, subjected to a three-dimensional in situ state of stress. The analytical solution to this geometry incorporates coupled matrix-fracture deformation, simultaneous fluid flows, solute transports and interporosity exchanges induced by the combined influences of stress variation, fluid pressure and solute chemical salinity gradients under isothermal conditions. The fracture system is modeled as a secondary porosity porous continuum following Biot’s formulation while using mixture theory and the pore fluid is a binary solution comprised of a solvent and a solute. Results for the transient stresses and dual pore pressure distributions due to the coupled fracture and hydrochemical effects are plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic counterparts. Finally, wellbore stability analyses are carried out to demonstrate applications of the solutions to field drilling operations.     

Coupled Consolidation and Contaminant Transport in Compressible Porous Media

This paper presents an experimental and numerical investigation of coupled consolidation and contaminant transport in compressible porous media. Numerical simulations were performed using the CST2 computational model, in which a dual-Lagrangian framework is used to separately follow the motions of fluid and solid phases during consolidation. Diffusion and large strain consolidation-induced transport tests were conducted on composite specimens of kaolinite slurry consisting of an upper uncontaminated layer and a lower layer contaminated with potassium bromide. Assessment of the importance of the consolidation process on solute transport is based on measured and simulated solute breakthrough curves and final contaminant concentration profiles. CST2 simulations closely match the experimental data for three different loading conditions. Diffusion and consolidation-induced advection made important contributions to solute transport and mass outflow in this study. Additional simulations indicate that consolidation-induced contaminant transport may also be affected by specimen boundary drainage and initial concentration conditions.     

Breakthrough Curves and Simulation of Virus Transport through Fractured Porous Media

In this paper, an advective dispersive virus transport equation, including first-order adsorption and an inactivation constant, is used for simulating the movement of viruses in fractured porous media. The implicit finite-difference numerical technique is used to solve the governing equations for viruses in the fractured porous media. In this work, the focus is (1)?to investigate the transport processes of the movement of viruses in both fractured rock and porous rock without fracture and (2)?to simulate the experimental data of biocolloids through a fractured aquifer model. It is seen that movement of the contaminant is faster in the fractured rock than in the porous rock formation. Higher values of diffusion coefficient, matrix porosity, mass transfer constant, and inactivation rate reduce both temporal and spatial virus concentrations in the fracture. Also, experimental data of biocolloids in the fractured aquifer model with constant and time-dependent inactivation rates were simulated successfully.     

Energy Equation for Volatile Liquid Transport in Porous Media

Two energy balance equations widely used to describe simultaneous transfer of heat and mass in porous media are inconsistent with control volume energy conservation. Potential energy, enthalpy, and internal energy terms are involved in the discrepancies. Energy within a volume is properly counted as the sum of internal, potential, and kinetic energy. However, one equation uses enthalpy where internal energy should have been used. In the other, potential energy and shifts in internal energy associated with heat of wetting are not included. Energy conservation for a control volume dictates summing convective fluxes of internal, potential, and kinetic energy at the control volume surface along with conducted heat and work crossing the boundary. The pressure–volume (pv) work at the volume surface may be combined with internal energy convection so that flow of enthalpy is used in the flux term. Examples of energy change versus work input in adiabatic processes illustrate the error introduced when enthalpy rather than internal energy is used to compute control volume energy content. For porous media flows kinetic energy can be dropped. A consistent equation based on the control volume approach is presented. It includes effects due to internal energy, potential energy, heat of wetting, conducted heat, non-pv work, enthalpy, and mass flow. Substantial temperature changes due to heat of wetting have been found experimentally in a separate work. A comparison is needed of the experiments and a numerical simulation based on the new equation.     

Improving Fluid Flow in Clarifiers Using a Highly Porous Media

The theory behind ideal sedimentation tanks assumes that the fluid moves in uniform flow. Numerous studies have shown numerous nonuniform flow patterns, which explains why the solids removal efficiency of real clarifiers does not match theory predictions. This problem gets worse when the influent flow rate exceeds what the clarifier was designed to handle. This research shows that introducing a highly porous bed of “dendrite” fibers into clarifiers designed for the pulp and paper industry removed some of the nonuniformities as shown in a residence time distribution (RTD). These clarifiers have RTDs that are similar to their waste treatment counterparts. So, it is expected that the new technology will have similar effects in waste treatment systems. The bed acts as a resistor to nonaxial flow, reducing radial and angular components of velocity. It is also shown that the greatest effect on the bulk flow patterns occurs when the bed is positioned such that all of the overflow passes through it. Increasing the bed thickness also increases the effect. Analysis of these results was performed with a new model for RTDs based on the Weibull distribution, which is mathematically similar to the equation for a mixed flow RTD.     

Analytical Solutions for Contaminant Diffusion in Double-Layered Porous Media

Analytical solutions for conservative solute diffusion in one-dimensional double-layered porous media are presented in this paper. These solutions are applicable to various combinations of fixed solute concentration and zero-flux boundary conditions (BC) applied at each end of a finite one-dimensional domain and can consider arbitrary initial solute concentration distributions throughout the media. Several analytical solutions based on several initial and BCs are presented based on typical contaminant transport problems found in geoenvironmental engineering including (1) leachate diffusion in a compacted clay liner (CCL) and an underlying stratum; (2) contaminant removal from soil layers; and (3) contaminant diffusion in a capping layer and underlying contaminated sediments. The analytical solutions are verified against numerical solutions from a finite-element method based model. Problems related to leachate transport in a CCL and an underlying stratum of a landfill and contaminant transport through a capping layer over contaminated sediments are then investigated, and the suitable definition of the average degree of diffusion is considered.     

Experimental Investigations of Colloidal Silica Grouting in Porous Media

This paper presents the results of an experimental investigation performed to understand the processes influencing the injection of colloidal silica grout into porous media. Based on the combined analysis of grout injection pressures and the visually observed grout distribution patterns, three major processes, gelation, shear, and viscous fingering, have been identified to occur during grout injection. The results demonstrate the dynamic interplay between grout viscosity variations and the resulting flow instabilities.     

Parametric Study of One-Dimensional Solute Transport in Deformable Porous Media

Formulation for the effect of dissipation of excess pore water pressure on one-dimensional advective-diffusive transport of solutes in clays is presented. The formulation is based on the effect of the rate of consolidation or swelling and excess pore pressure or suction dissipation on transient, nonlinear advective component of transport through clay. One partial differential equation is presented for advective diffusive transport that is dependent upon soil/solute properties and transient hydraulic head gradient, which is calculated from the Terzaghi consolidation equation. Finite difference method is used to solve the system of partial differential equations for consolidation and solute transport. Four hypothetical cases are evaluated to demonstrate the effect of consolidation under loading and swelling under hydraulic gradient on advective-diffusive transport and breakthrough in single and double drainage clay layer. The results show that consolidation in doubly drained clay impacts concentration profiles, but does not significantly impact breakthrough of the diffusive flux. Consolidation under single drainage conditions, significantly impacts the diffusional flux. When drainage path is the same as the diffusional flux, consolidation accelerates transport and breakthrough time can be less than 5% of the diffusional breakthrough time under no consolidation. Swelling under hydraulic gradient application can either accelerate or retard the advective diffusive flux, depending upon the ratio of the effective diffusion coefficient relative to the coefficient of consolidation. Higher the effective diffusion coefficient and lower the coefficient of consolidation result in an increase in the effect of pressure dissipation on transport.     

Extended Boussinesq Equations for Water-Wave Propagation in Porous Media

This paper presents a new Boussinesq-type model equations for describing nonlinear surface wave motions in porous media. The mathematical model based on perturbation approach reported by Hsiao et al. is derived. The drag force and turbulence effect suggested by Sollitt and Cross are incorporated for observing the flow behaviors within porous media. Additionally, the approach of Chen for eliminating the depth-dependent terms in the momentum equations is also adopted. The model capability on an applicable water depth range is satisfactorily validated against the linear wave theory. The nonlinear properties of model equations are numerically confirmed by the weakly nonlinear theory of Liu and Wen. Numerical experiments of regular waves propagating in porous media over an impermeable submerged breakwater are performed and the nonlinear behaviors of wave energy transfer between different harmonics are also examined.     

Retardation of Nonlinearly Sorbed Solutes in Porous Media

The impact of the assumption of linear sorption on retardation of nonlinearly sorbed solutes in porous media is numerically explored in this paper. Breakthrough data of nonlinearly sorbed solutes are generated using the BIO1D simulation code along with the Freundlich-type nonlinear sorption model. Retardation coefficients (R) from generated breakthrough curves are estimated using first-moment analysis. Variations of R with experimental conditions revealed that R of a nonlinearly sorbed solute is a function of the input concentration, the injection period and the pore-water velocity but is independent of the length scale. This study also showed that it is appropriate to estimate R of a nonlinearly sorbed solute using a linearized isotherm if all soil particles experience sorption with liquid concentration equal to the induced concentration. Otherwise, the estimated linearized R will be either under- or overestimated depending on the applied experimental conditions and Freundlich parameters. The study further revealed that inability to account for sorption nonlinearity may in some cases erroneously be interpreted as evidence of the presence of transport nonequilibrium. A method is suggested to determine nonlinear sorption parameters from miscible displacement experiments.     

Effect of Convergence on Nonlinear Flow in Porous Media

The behavior of flow through porous media has been the subject of study for a long time. The relationship relating friction factor and Reynolds number using the square root of intrinsic permeability as the characteristic length is examined for flow in porous media with converging boundaries. An experimental investigation of the effect of convergence of streamlines on the linear and nonlinear parameters for different radial flow lines in a converging permeameter for different ratios of radii of the test section is also studied. In the present case, crushed rocks of sizes 11.64 and 4.73 mm were used as media and water as fluid, to develop curves relating friction factor and Reynolds number for different radial flow lines with different ratios of radii of the test section of the permeameter.     

Reaction Kinetics of Ozone in Variably Saturated Porous Media

A kinetic model based on the mass balance principle with equilibrium partitioning of gaseous ozone into pore water was developed to delineate the reactions of ozone in variably saturated porous media contaminated with phenanthrene. Dimensionless fraction factors were used in the kinetic model to account for the reactions of ozone with soil organic matter (SOM), metal oxide (MO), and phenanthrene as a function of water saturation. The enhanced removal of phenanthrene resulting from heterogeneous catalytic reactions between ozone and soil organic matter and metal oxide was incorporated as lumped parameters in the reaction rate coefficients of gaseous and dissolved ozone with phenanthrene. Laboratory experiments employing 5 cm long mini column reactor systems were conducted to estimate the reaction constants for three porous medium types (glass beads, baked field soil, and field soil) at various water-saturation levels. Water saturation and SOM were found to significantly affect the decomposition of gaseous ozone in both uncontaminated and contaminated porous media. It was found that water saturation over 75% completely eliminates gas-to-solid interfacial ozone reactions with SOM and MO. The kinetic model, with the reaction parameters estimated in this study, predicted reasonably well the experimental data obtained from both the mini column reactor and 20 cm long columns packed with field soil, suggesting that the kinetic model would be suitable for describing the fate and reactions of ozone in variably saturated porous media for soil types and experimental conditions similar to those tested in this study.     

Retardation of Nonlinearly Sorbed Solutes in Porous Media

The impact of the assumption of linear sorption on retardation of nonlinearly sorbed solutes in porous media is numerically explored in this paper. Breakthrough data of nonlinearly sorbed solutes are generated using the BIO1D simulation code along with the Freundlich-type nonlinear sorption model. Retardation coefficients (R) from generated breakthrough curves are estimated using first-moment analysis. Variations of R with experimental conditions revealed that R of a nonlinearly sorbed solute is a function of the input concentration, the injection period, and the pore–water velocity but is independent of the length scale. This study also showed that it is appropriate to estimate R of a nonlinearly sorbed solute using a linearized isotherm if all soil particles experience sorption with liquid concentration equal to the induced concentration. Otherwise, the estimated linearized R will be either under- or overestimated depending on the applied experimental conditions and Freundlich parameters. The study further revealed that inability to account for sorption nonlinearity may in some cases erroneously be interpreted as evidence of the presence of transport nonequilibrium. A method is suggested to determine nonlinear sorption parameters from miscible displacement experiments.     

Temporal Moment Analysis for Volatile Organic Compounds in Dual-Porosity Porous Media: Loss Fractions and Effective Parameters

Using transform techniques, analytical expressions for potential losses by volatilization and degradation are developed for several organic compounds in dual porosity porous media. A sensitivity analysis is conducted to study the importance of different physical/chemical processes on volatilization, degradation, and leaching losses. To obtain estimates for overall solute behavior, expressions for effective Péclet numbers and degradation rates for organic contaminants are presented using method of moments. Results indicate that large fractions of many organic compounds are likely to volatilize into the atmosphere for sandy and clayey soils under typical flow conditions. It is found that nondimensional degradation influences both advective and dispersive effects. Thus, the Péclet number from effective-parameter equation tends to be enhanced when the nondimensional degradation is rather high. The simple expressions for moments and effective parameters can be used as screening tools to assess the behavior of volatile compounds in vadoze zone of soils.     

Intake Shape Factors for Entry Points in Porous Media with Transversely Isotropic Hydraulic Conductivity

The intake shape factors for spherical and disc-shaped entry points located within a hydraulically transversely isotropic porous medium of infinite extent are presented in exact closed form. Implications of these results on a methodology for the in situ evaluation of the principal hydraulic conductivities are discussed.     

Application of UVP within Porous Beds

Standard measurement devices do not normally provide detailed information about flows in porous media because either they are too intrusive (e.g., hot/film wire anemometers) or because the solid phase impedes their physical access to the flow as in the case of laser Doppler anemometers or particle image velocimetry (PIV). In this study, a Metflow ultrasonic velocity profiler (UVP) is used to measure instantaneous velocity fields within porous media composed of plastic balls packed in a cubic pattern. Simple considerations of the ultrasound beam properties and propagation, plus a comparison with measurements performed by a PIV system, demonstrate that UVP devices are suitable for such a purpose.     

Colloidal Silica Transport through Liquefiable Porous Media

Mitigation of liquefaction potential in loose granular soil can theoretically be achieved through permeation and subsequent gelation of dilute colloidal silica stabilizer. However, practical application of this technique requires efficient and adequate delivery of the stabilizer to the liquefiable soil prior to gelation. The purpose of this research was to evaluate colloidal silica transport mechanisms and to determine if an adequate concentration can be delivered to a soil column prior to gelation. The laboratory work consisted of grouting 15 short (0.9 m) columns tests packed with Nevada No. 120, Ottawa 20/30, or graded silty sand to identify the variables that influence stabilizer transport through porous media. It was found that colloidal silica can be successfully delivered through 0.9-m columns packed with loose sand efficiently and in an adequate concentration to mitigate the liquefaction potential. Transport occurs primarily by advection with limited hydrodynamic dispersion, so Darcy’s law can be used to predict flow. The Kozeny-Carmen equation can be used to include the effect of increasing viscosity on transport by incorporating the power law mixing rule of Todd. The primary variables influencing stabilizer transport were found to be the viscosity of the colloidal silica stabilizer, the hydraulic gradient, and the hydraulic conductivity of the liquefiable soil.     

Turbulent Flow Over and Within a Porous Bed

The characteristics of turbulent flow in open channels with a porous bed are studied numerically and experimentally. The “microscopic” approach is followed, by which the Reynolds-averaged Navier-Stokes equations are solved numerically in conjunction with a low-Re k-ε turbulence model above and within the porous bed. The latter is represented by a bundle of cylindrical rods of certain diameter and spacing, resulting in permeability K ranging from 5.5490×10?7 to 4.1070×10?4?m2 and porosity ? from 0.4404 to 0.8286. Mean velocities and turbulent stresses are measured for ? = 0.8286 using hot-film anemometry. Emphasis is given to the effect of Darcy number Da on the flow properties over and within the porous region. Computed and experimental velocities in the free flow are shown to decrease with increasing Da due to the strong momentum exchange near the porous medium/free flow interface and the corresponding penetration of turbulence into the porous layer for highly permeable beds. Computed discharge indicates the significant reduction of the channel capacity, compared to the situation with an impermeable bed. On the contrary, laminar flow computations, along with analytical solutions and measurements, indicate opposite effects of the porous medium on the free flow.     

Immiscible Displacement Model for Anisotropic and Correlated Porous Media

Immiscible flow governs the macroscopic behavior of aqueous and non-aqueous phase liquids inside the porous media. Ganglia generation and movement of the advancing front during fluid displacement can only be described by means of microscopic models. In this study, a pore network cellular automata is used to simulate the displacement of a nonaqueous phase liquid by water inside a porous media. Pore sizes are generated using random and stochastic fields. The numerical model captures the evolution of interfaces and fluid movement for each pressure applied to the displacing fluid. Observed trends suggest that ganglia size and shape, and fingering are directly related to anisotropy, pore size spatial variability and correlation length. The results show that micro- and mesoscale porous media properties control the nonaqueous phase residual saturation and observed macoscopic behavior.