Radon Emanation in Partially Saturated Porous Media

Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.     

NMR Measurements of Tortuosity in Partially Saturated Porous Media

The tortuosity (τ), defined in the present context as the ratio of the free diffusion coefficient to the restricted diffusion coefficient of a contained fluid, is an important but difficult to measure characteristic of a porous medium, particularly when it is partially saturated with water. We develop and apply methodology, based on nuclear magnetic resonance (NMR) pulsed field gradient techniques, to measure τ for various sandstone rock cores as a function of residual water fraction. The NMR methodology requires the use of bipolar pulsed field gradient stimulated echo pulse sequences to avoid systematic errors due to magnetic susceptibility differences and D₂O as a stationary immiscible water phase; this was selected as it provides no ¹H NMR signal. Tortuosity of the free pore space was successfully measured using liquid ethane as a probe fluid for three different sandstones over the full accessible range of residual water saturation. Generally, the tortuosity was observed to increase with residual water (D₂O) content; however, significant variations were observed between the different sandstones.     

Wave Dynamics of Saturated Porous Media and Evolutionary Equations

Nonlinear wave dynamics of an elastically deformed saturated porous media is investigated following the Biot approach. Mathematical models under research are the Biot model and its generalization by consideration of viscous stresses inside liquids. Using two-scales and linear WKB methods, the classical Biot system is transformed to a first-order wave equation. To construct the solution of the other system, an asymptotic modified two-scales method is developed. Initial system of equations is transformed to a nonlinear generalized Korteweg–de Vries–Burgers equation for quick elastic wave. Distinctions of wave propagation in the context of the Biot model and its generalization are shown.     

Predicting Vertical Flow Barriers Using Tracer Diffusion in Partially Saturated,Layered Porous Media

Sudden changes in isotopic tracer concentration in pore waters have been interpreted as indicating barriers to vertical advective flow through porous rocks in the subsurface, e.g. step changes in \(^{87}\hbox {Sr}/^{86}\) Sr ratio are often used in the oil and gas industry as a signature of reservoir compartmentalisation. This study shows that this is not necessarily the case. It can take millions of years for such step changes to equilibrate by diffusion if there is no flow resulting from pressure or density gradients even in high permeability, high porosity rocks, particularly if the water saturation is low. Changes in tracer concentration gradients can be good indicators of changes in porosity (or water saturation) between layers. In contrast changes in sorption without a change in porosity are almost impossible to identify. The time taken for concentration gradients to equilibrate is affected by the layer properties but can be quickly estimated from the harmonic average of the effective diffusion coefficient for each layer and a simple analytical expression for a homogeneous system. This was achieved by performing a sensitivity analysis on different layer properties (porosity contrast, saturation contrast, sorption contrast, thickness ratio) using existing analytical solutions for diffusion in layered systems.     

Analytical Solution for the Effect of Viscous Dissipation on Mixed Convection in Saturated Porous Media

A new analytical solution is introduced for the effect of viscous dissipation on mixed convection flow and heat transfer about an isothermal vertical wall embedded in Darcy and non-Darcy porous media with uniform free stream velocity. The effect of viscous dissipation on mixed convection in both regimes has been analyzed for both the aiding and opposing flows using Gebhart number, Ge _x =gx/c _p. The governing parameters are Re, Ra, Pe and Ge _x . The case of Re=0 corresponds to Darcy mixed convection region and Re/Pe is identified as the mixed convection governing parameter, Ra=0 leading to pure forced convection. A good agreement was found between the numerical and analytical solutions. It was found from the Nusselt number results that viscous dissipation lowers the heat transfer rate in both Darcy and Forchheimer flow regimes for aiding as well as opposing flows.     

Comparison of Iterative Methods for Improved Solutions of the Fluid Flow Equation in Partially Saturated Porous Media

Abstract. The Picard and modified Picard iteration schemes are often used to numerically solve the nonlinear Richards equation governing water flow in variably saturated porous media. While these methods are easy to implement, they are only linearly convergent. Another approach to solve the Richards equation is to use Newton's iterative method. This method, also known as Newton–Raphson iteration, is quadratically convergent and requires the computation of first derivatives. We implemented Newton's scheme into the mixed form of the Richards equation. As compared to the modified Picard scheme, Newton's scheme requires two additional matrices when the mixed form of the Richards equation is used and requires three additional matrices, when the pressure head-based form is used. The modified Picard scheme may actually be viewed as a simplified Newton scheme.Two examples are used to investigate the numerical performance of different forms of the 1D vertical Richards equation and the different iterative solution schemes. In the first example, we simulate infiltration in a homogeneous dry porous medium by solving both, the h based and mixed forms of Richards equation using the modified Picard and Newton schemes. Results shows that, very small time steps are required to obtain an accurate mass balance. These small times steps make the Newton method less attractive.In a second test problem, we simulate variable inflows and outflows in a heterogeneous dry porous medium by solving the mixed form of the Richards equation, using the modified Picard and Newton schemes. Analytical computation of the Jacobian required less CPU time than its computation by perturbation. A combination of the modified Picard and Newton scheme was found to be more efficient than the modified Picard or Newton scheme.     

Flow and Heat Transfer of Viscous Fluids Saturated in Porous Media over a Permeable Non-isothermal Stretching Sheet

The present paper deals with the flow and heat transfer of a viscous fluid saturated in a porous medium past a permeable and non-isothermal stretching sheet with internal heat generation or absorption and radiation. Closed-form solutions to steady, two dimensional momentum equations with neglecting quadratic inertia terms and heat transfer equation are found using a similarity transformation. Asymptotic expressions of the temperature functions are also presented valid for both very large and very small modified Prandtl numbers. Attention is focused on the effects of porous parameter K, suction parameter R, radiation parameter Nr, viscosity ratio Λ, internal heat parameter α and Prandtl number P to the characteristics of flow and heat transfer.     

Acoustics of Rotating Deformable Saturated Porous Media

We investigate wave propagation in elastic porous media which are saturated by incompressible viscous Newtonian fluids when the porous media are in rotation with respect to a Galilean frame. The model is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For Kibel numbers A A(1), the acoustic filtration law resembles a Darcys law, but with a conductivity which depends on the wave frequency and on the angular velocity. The bulk momentum balance shows new inertial terms which account for the convective and Coriolis accelerations. Three dispersive waves are pointed out. An investigation in the inertial flow regime shows that the two pseudo-dilatational waves have a cut-off frequency.     

Osmotic Mechanism of Fracture Growth in Saturated Porous Media

Fracture growth in saturated porous bodies under the action of the osmotic pressure developed in the fracture by a solute for which the fracture surface represents a semipermeable membrane is considered. This mechanism of fracture growth, which follows directly from the basic laws of fracture mechanics and physical chemistry, should be a fairly general effect of significance in a number of geochemical and technological processes. In particular, the role of osmosis in well flushing and cementing processes was noted in study by N. G. Avetisyan, Choice of type of drill solution for drilling in unstable rocks, published in: Review Information. Drilling [in Russian], VNIIOENG (1983) and the mechanism was briefly discussed in monograph by A. Kh. Mirzadzhanzade and V. M. Entov, Drilling Hydrodynamics [in Russian], Nedra, Moscow (1985).In study by R. V. Gol'dshtein, V. M. Entov, and B. P. Pavlovskii, Model of the development of hydrogen fractures in metal, Dokl. Acad. Nauk SSSR, Vol. 237, 828 (1977) a comparable mathematical model was proposed for explaining the hydrogen embrittlement of metals. Finally, in study by J. P. Sargent and K. H. G. Ashbee, The contribution of osmosis to dimensional instability of adhesive joints, J. Adhesion, Vol. 17, 83 (1984) a very similar mechanism of fracture development in polymeric materials due to the osmotic splitting of internal joints as a result of the release in the joints of a substance dissolved in the solid polymer was discussed and visual observation data were given.The property of semipermeability of the fracture surface (permeability for water and impermeability for dissolved salts), which is fundamental to our study, is taken as a basic hypothesis and will not discussed in what follows. Many arguments could be advanced to show that natural semipermeable membranes can develop in rocks, especially in argillaceous ones. However, these arguments are not definite and clearly lie beyond the competence of the authors whose task is to trace the possible mechanical consequences of the presence of semipermeable membranes and draw them to the attention of the specialists.     

Stress Generated During Drying of Saturated Porous Media

The article is a contribution for the modelling of heat and mass transfers coupled to strain–stress equations during drying of deformable two-phase media. Both unidirectional and bidirectional configurations are examined. In order to compare the results, one assumes the material of a convectively dried clay slab in two configurations. Numerical calculations of the temperature, drying curves variations and the spatio-temporal distributions of moisture, temperature and drying induced stresses are evaluated. A significant difference was observed between the results obtained for both configurations particularly in intensity of the shear stress that caused cracking.     

Numerical Modeling of Salt Transport and Precipitation in Non-Isothermal Partially Saturated Porous Media Considering Kinetics of Salt Phase Changes

Water and salts strongly influence the durability of porous materials. One of the most adverse phenomena which is related to the salt and moisture presence in the pore system of building materials is salt crystallization. The process is associated with the supersaturation ratio. The salt phase change kinetics is taken into account during the modeling of coupled moisture, salt, and heat transport. To solve the set of governing, differential equations the finite element and the finite difference methods are used. Three different rate laws are assumed in modeling the salt phase change. The drying, cooling, and warming of the cement mortar sample, during which the salt phase change occurs, have been simulated using the developed software. The changes of salt concentration in the pore solution and the amount of precipitated salt due to variation of boundary conditions are presented and discussed. The results obtained in the numerical simulation assuming the first, second, and fourth order rate low indicate that the higher order of the rate law the longer time delay between the change of boundary conditions and the salt precipitation. Such an analysis might be very useful during the determination of the material parameters by solving the inverse problem.     

Thermodynamic Correction for Salts in Variably Saturated Porous Media

Using thermodynamic principles, the general relationship describing the equilibrium vapor content in the gas phase above a saline liquid and across a curved liquid–gas interface is developed. Since high salt concentration affects the intensive and extensive liquid properties, it is also necessary to account for these effects in liquid water content/liquid water pressure relationship curves so that experimentally derived curves for pure water may be useful for elevated salt concentrations. The appropriate thermodynamic relationships are derived to describe the salt effects on liquid and vapor properties. The resulting equations are valid for salt concentrations between zero and saturation, and for any temperatures that nominally occur in nearsurface geologic materials.     

A Pore-Scale Investigation of Low-Salinity Waterflooding in Porous Media: Uniformly Wetted Systems

The potential of low-salinity (LS) water injection as an oil recovery technique has been the source of much recent debate within the petroleum industry. Evidence from both laboratory and field-level studies has indicated significant benefits compared to conventional high-salinity (HS) waterflooding, but many conflicting results have also been reported and, to date, the underlying mechanisms remain poorly understood. In this paper, we aim to address this uncertainty by developing a novel, steady-state pore network model in which LS brine displaces oil from a HS-bearing network. The model allows systematic investigation of the crude oil/brine/rock parameter space, with the goal of identifying features that may be critical to the production of incremental oil following LS brine injection. By coupling the displacement model to a salinity-tracking tracer algorithm, and assuming that a reduction of water salinity within the pore network leads to localised wettability alteration, substantial perturbations to standard pore filling sequences are predicted. The results clearly point to two principal effects of dynamic contact angle modification at the pore scale: a “pore sequence” effect, characterised by an alteration to the distribution of displaced pore sizes, and a “sweep efficiency” effect, demonstrated by a change in the overall fraction of pores invaded. Our study indicates that any LS effect will depend on the relative (scenario-dependent) influence of each mechanism, where factors such as the initial wettability state of the system and the pore size distribution of the underlying network are found to play crucial roles. In addition, we highlight the important role played by end-point capillary pressure in determining LS efficacy.     

An Experimental Method to Measure Gaseous Diffusivity in Tight and Partially Saturated Porous Media via Continuously Monitored Mass Spectrometry

Transport in Porous Media -     

Asymptotic Research of Nonlinear Wave Processes in Saturated Porous Media

The problem of nonlinear wave dynamics of a fluid-saturated porous medium is investigated. The mathematical model proposed is based on the classical Frenkel--Biot--Nikolaevskiy theory concerning elastic wave propagation and includes mass, momentum, energy conservation laws, as well as rheological and thermodynamic relations. The model describes nonlinear, dispersive, and dissipative medium. To solve the system of differential equations, an asymptotic modified two-scales method is developed and a Cauchy problem for initial equations system is transformed to a Cauchy problem for nonlinear generalized Korteweg--de Vries--Burgers equation for modulated quick wave amplitudes and an inhomogeneous set of equations for slow background motion. Stationary solutions of the derived evolutionary equation that have been constructed numerically reflect different regimes of elastic wave attenuation: diffusive, oscillating, and soliton-like.     

Hydromechanical Modelling of Experimentally Compacted Saturated Argillaceous Porous Media

In order to model the experimental compaction of clays as completely as possible, it is necessary to use the hydromechanical coupled three-dimensional theory for saturated porous media. The proposed formulation is based on elastoplasticity, more precisely on modified Cam-clay model. The identification of the parameters of the model is made by special oedometric experiments at steady state. The compaction experiments are simulated with accuracy in transient and steady states and complement those obtained in a recent study based only on steady state.     

A Numerical Study of the Distribution of Water in Partially Saturated Porous Rock

The distribution of water and air phases in small blocks of porous sandstone is examined by using a simulated annealing technique that finds the minimum interfacial energy distributions at different saturations. Simulations are based on existing sandstone microstructures that were determined by X-ray microtomography. At low saturations, some of the water is distributed in films along the walls of larger pore spaces, and connects to pendular structures in the crevices and smaller pores. As the amount of water in the pores increases the water films become thicker and pores fill from the pendular structures. The distribution of water voxels in the pore space is examined by calculating interfacial areas, by classifying water voxels as to whether they lie within films or clusters, and by determining the size and distribution of these film clusters. An exponential relationship is found between the fraction of water voxels in the films and the degree of saturation. In addition, the dependency of small-sample electrical conductivity on saturation is examined by using a random walk method.     

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.     

Comments on ‘Analytical Solution for the Effect of Viscous Dissipation on Mixed Convection in Saturated Porous Media’, Transport in Porous Media 41, 197–209, 2000

Transport in Porous Media -     

Diffusion of Randon in Porous Media Saturated with Gels and Emulsions

The effective diffusion coefficient of radon was determined in polymer/silicate gels and clay suspension used as sealing materials in environmental protection. On the basis of the experimental findings, it was concluded that both materials drastically decrease the convective mass transport in porous media. Simultaneously, the effective diffusion coefficient was reduced significantly. Thus, the radon flux might be decreased by 5 to 6 orders of magnitude in porous systems originally having gas or low water saturation by injection of gel-forming materials or placement of clay suspensions. At high water saturation, however, the diffusion transport of radon can be slightly restricted in consolidated and unconsolidated porous media. The laboratory studies may firmly allow us to conclude that hydrogels and clay suspensions are prospective candidates in an integrated environmental technology to be used for restriction of radon migration in subsurface regions.