Accumulation and Precipitation of Salts during Groundwater Evaporation and Flow

A mathematical model for the precipitation of dissolved salts during groundwater evaporation is proposed. An asymptotic solution of the problem is obtained for a specified flow law. It is shown that there are two different regimes of solute precipitation which are determined by the evaporation front velocity and the groundwater flow rate. The dependence of the precipitated salt mass on the soil surface temperature, the atmospheric humidity, the initial solute concentration and the filtration rate is illustrated.     

Calculation of Groundwater Flows in Coastal Pressurized Reservoirs

A model of a fresh groundwater flow through a rectangular horizontal pressurized reservoir toward a salt-water sea (basin, reservoir, trench, etc.) is examined within the framework of two-dimensional steady-state flow theory. In order to study the model, a mixed multi-parameter boundary value problem of the theory of analytic functions is formulated and solved using the Polubarinova-Kochina method. The structure and the characteristic features of the simulated process and the effect of all the determining physical parameters of the model on the nature of the flow are analyzed using the analytic dependences obtained and numerical calculations. An approximate hydraulic solution of the problem is compared with the exact solution obtained.     

Hydrodynamic Investigation of Certain Groundwater Flows in Coastal Pressurized Aquifers

Mathematical models of certain fresh groundwater flows through a semi-infinite pressurized aquifer toward a salt-water sea (basin, reservoir, etc.) are examined within the framework of two-dimensional steady-state flow theory. In order to study the models, mixed boundary value problems of the theory of analytic functions are formulated and solved using the Polubarinova-Kochina method. Algorithms for calculating the flows are developed on the basis of these models for situations in which groundwater streams arrive at the sea from one side or from below. Both the structure and the characteristic features of the simulated processes and the effect of all the physical characteristics of the models on the nature of the flow are analyzed in detail using the exact analytic dependences obtained and numerical calculations. The calculation results for the two inflow schemes are compared and features of the flows that depend on the initial position of the fluid contact are discussed.     

On Analytical Solutions of Advective Transport by Infiltration–Redistribution Gravitational Flow

Contaminant transport in the upper layers of soil during the multiple cycles of short infiltration and prolonged redistribution is investigated. Analytical solutions for the two typical problems encountered in agricultural engineering are derived. The first problem considers the penetration of fertilizer initially applied at the soil surface. The second one is the propagation of contaminant injected with the applied water. Explicit analytical expressions for the solute concentration are obtained under assumptions of one-dimensional gravitational flow and advective solute transport under equilibrium conditions. The properties of the solute penetration are analyzed for the case of contaminant initially applied at the soil surface and picked up by the water flow during ten infiltration–redistribution cycles. P. Indelman - (deceased)     

Numerical solutions for the transient flow in the homogenous closed circle reservoirs

There are many fault block fields in China. A fault block field consists of fault pools. The small fault pools can be viewed as the closed circle reservoirs in some case. In order to know the pressure change of the developed formation and provide the formation data for developing the fault block fields reasonably, the transient flow should be researched. In this paper, we use the automatic mesh generation technology and the finite element method to solve the transient flow problem for the well located in the closed circle reservoir, especially for the well located in an arbitrary position in the closed circle reservoir. The pressure diffusion process is visualized and the well-location factor concept is first proposed in this paper. The typical curves of pressure vs time for the well with different well-location factors are presented. By comparing numerical results with the analytical solutions of the well located in the center of the closed circle reservoir, the numerical method is verified.     

Review on Scale Dependent Characterization of the Microstructure of Porous Media

The paper discusses local porosity theory and its relation with other geometric characterization methods for porous media such as correlation functions and contact distributions. Special emphasis is placed on the charcterization of geometric observables through Hadwigers theorem in stochastic geometry. The four basic Minkowski functionals are introduced into local porosity theory, and for the first time a relationship is established between the Euler characteristic and the local percolation probabilities. Local porosity distributions and local percolation probabilities provide a scale dependent characterization of the microstructure of porous media that can be used in an effective medium approach to predict transport.     

剧变截面圆管内渗流的数值计算方法

对于剧变截面圆管的渗流问题写出不可压缩渗流的基本方程组,对直接求解原始变量(速度和压力)的数值计算方法作出改进。先由非主流方向的运动方程计算压力,后由主流方向的运动方程计算主流方向的速度分量,再由连续性方程计算非主流方向的速度分量。这样可以避免在一般的求解原始变量方法中由连续性方程计算压力时出现的困难和麻烦。根据本方法和剧变截面圆管的特点,采用半交错不等距非正交贴体混合网格系。本文详细写出差分方程和迭代计算公式,对剧变截面圆管内的渗流算例进行数值计算。本方法的优点是简单和实用,在工程上具有较大的应用价值。     

Simulation of flow through porous anode in MFC at higher power density

Microbial fuel cell (MFC) is a novel environmental friendly energy device which has received great attention due to its technology for producing electricity directly from organic or inorganic matter by using bacteria as catalyst. To date, many experiments have been carried out to achieve the maximum power output with advective flow through porous anode to the cathode in the MFC. However, the precise mechanical mechanism of flow through anode and the quantified relationship between electrode spacing and MFC performance are not yet clearly understood. It has been found experimentally that the power output can be increased apparently at certain electrode spacing configuration. Based on these available experimental data, this paper investigates the effect of spacing between electrodes, the Darcy number of porous anode and the Reynolds number on the power production performance of MFC by using lattice Boltzmann method. The numerical simulation results present that the distance between electrodes significantly influences the flow velocity and residence time of the organic matter attached to the anode in the MFC. Moreover, it is found that the Darcy number of porous anode and the Reynolds number can regulate the output efficiency of MFC. These results perform better understanding of the complex phenomena of MFC and will be helpful to optimize MFC design.     

New Considerations on Analytical Solutions Employed in Tracer Flow Modeling

A methodology commonly used to obtain analytical and semi-analytical solutions to describe spike and finite-step tracer injection tests is discussed. In these cases, solutions to the diffusion–convection equation are derived from the solution of a different problem, namely the continuous injection of a tracer. Within this procedure, spike injection results from the time derivative of this solution, and finite-step injection from the superposition of two solutions shifted in time. In this paper we show that although this methodology is mathematically correct, attention should be paid to the properties of the solutions. Their boundary conditions may not represent physically acceptable situations, since these conditions are inherited from a different problem. The application of the methodology to a simple one-dimensional case of a tracer pulse diffusing in a homogeneous, semi-infinite reservoir shows serious problems regarding boundary conditions and mass conservation. These problems has not probably been found before since tracer breakthrough curves are not very sensitive to them. However, the problems clearly show up when the tracer distribution in space is analyzed. We conclude that the traditional methodology should not be employed. Equations should be solved imposing the specific boundary and initial conditions corresponding to the original system under consideration.     

Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium

In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the stress jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the stress jump boundary condition is investigated. It is shown that accounting for a jump in the shear stress at the interface essentially influences velocity profiles.     

Salt Water Intrusion in a Three-dimensional Groundwater System in The Netherlands: A Numerical Study

Salt water intrusion is investigated in a coastal groundwater system in the northern part of the province Noord-Holland, The Netherlands. Density dependent groundwater flow is modeled in three-dimensions with MOCDENS3D. This computer code is a version of MOC3D (Konikow et al., 1996) that has been adapted to simulate transient density-driven groundwater flow. Results from the model suggests that in this Dutch hydrogeologic system a severe and irreversible salinisation is already occurring. Within a few tens to hundreds of years, the salinity of the shallow aquifer is estimated to increase substantially. This salinisation process is a result of human activities such as the reclamation of the low-lying areas during the past centuries. Without changing the present boundary conditions, seepage into the low-lying areas will decrease slightly because of predicted increases in groundwater salinity. However, the rate in salt load through the Holocene aquitard into the low-lying areas will increase significantly due to an increase in salinity in the shallow aquifer. In addition, a relative sea level rise of 0.5m per century will intensify the salinisation process, causing an enormous increase in salt load in all low-lying areas in this part of The Netherlands.     

Experimental investigation of capillary pressure effects on immiscible displacement in lensed and layered porous media

This paper reports the results of extensive experimental studies of the effects of well-defined heterogeneous porous media on immiscible flooding. The heterogeneities were layers and lenses, with some of the lenses being a wettability contrast. Drainage and imbibition displacements, with and without an initial residual fluid saturation, were carried out at a variety of flow rates on layered and lensed two-dimensional glass beads models of the size of a typical large core test (58×10×0.6 cm). These displacements were followed photographically and the effluent saturation profiles recorded. In most of the experiments the glass beads were water-wet, but in some the lens beads were coated with a water repellent chemical. In all experiments, the displacement fronts became highly irregular due to the different capillary pressures acting in the different areas of the models. In this paper, these displacements are fully reported and their implications for reservoir simulation and for interpretation of laboratory core tests, where the inner heterogeneities are not known, are discussed.     

Flow behaviour in the presence of wettability heterogeneities

The physical processes occurring during fluid flow and displacement within porous media having wettability heterogeneities have been investigated in specially designed heterogeneous visual models. The models were packed with glass beads, areas of which were treated with a water repellent to create wettability variations. Immiscible displacement experiments show visually the effect of wettability heterogeneities on the formation of residual oil and recovery due to capillary trapping. This work demonstrates by experiment the importance of incorporating reservoir heterogeneity into pore displacement analysis, essential for the correct interpretation of core data and for directing the route for scale-up of the processes to reservoir scale.     

Modeling of Two-Phase Flow in Fractured Porous Media on Unstructured Non-Uniformly Coarsened Grids

In this article, we investigate two strategies for coarsening fractured geological models. The first approach, which generates grids that resolve the fractures, is referred to as explicit fracture-matrix separation (EFMS). The second approach is based on a non-uniform coarsening strategy introduced in Aarnes et al. (Adv Water Resour 30(11):2177–2193, 2007a). A series of two-phase flow simulations where the saturation is modeled on the respective coarse grids are performed. The accuracy of the resulting solutions is examined, and the robustness of the two strategies is assessed with respect to number of fractures, degree of coarsening, well locations, phase viscosities, and fracture permeability. The numerical results show that saturation solutions obtained on the non-uniform coarse grids are consistently more accurate than the corresponding saturation solutions obtained on the EFMS grids. The numerical results also reveal that it is much easier to tune the upscaling factor with the non-uniform coarsening approach.     

Modelling the Density-Driven Discharge of Sandstone Blocks

The density-driven discharge of salt-laden sandstone blocks has been studied to provide a knowledge basis for the prediction of the contaminant release of abandoned mines when they are flooded. To this end the results of a model experiment, of simplified analytical models and of numerical simulations in 1D, 2D and 3D have been analysed. Simple analytical functions have been found which approximately describe the time-dependent discharge of salt mass at complete saturation. They depend on the material parameters, the dimensions and the outflow geometry of the blocks. The discharge through the basal face is described well by an exponential behaviour. If the outflow occurs solely through the lateral block faces an algebraic function has been fitted to the simulated curves. In this case similarities to directed transport models of statistical physics have been pointed out. The results facilitate the superposition of discharge functions for single sandstone blocks to yield the discharge behaviour of the whole mine.     

Effect of flows between formations and capillary forces on the process of oil displacement in a stratified inhomogeneous bed

The results of a numerical investigation of the process of oil displacement in a stratified inhomogeneous formation on the basis of the two-phase flow model with account for capillary forces are presented. It is shown that in many cases the vertical inhomogeneity of oil reservoirs may not be a cause of nonuniform displacement and the non-recovery of large oil reserves by the time of water breakthrough to the extraction surface. The action of the capillary forces is an additional factor leading to equalization of the water propagation front in the inhomogeneous formation, water breakthrough delay, and intensification of the mass transfer between the layers with different permeabilities. Analysis of the contribution of the interlayer flows to the water flooding of low-permeability formation intervals calls into question the practicability of blocking high-permeability inclusions in the neighborhood of pumping wells.     

Modelling fluid flow in cross-bedded sections

Beadpack experiments and numerical simulations have been carried out to study flow displacements, effluent profiles and streamline patterns for layered systems with flow not parallel to the layers. The effects of layer thickness, permeability contrast, angle of layer to flow direction, mobility ratio and flood rate have been examined. Each of these parameters influence the displacement profiles, and disperse the flood front. Such real effects must be considered when subsuming reservoir heterogeneities in average reservoir parameters in simulation studies, or interpreting core tests.     

Global behavior of compressible three-phase flow in heterogeneous porous media

The homogenization method is used to analyze the equivalent behavior of a compressible three-phase flow model in heterogeneous porous media with periodic microstructure, including capillary effects. Asymptotic expansions lead to the definition of a global or effective model of an equivalent homogeneous reservoir. The resulting equations are of the same type as the points equations, with effective coefficients. The method allows the determination of these effective coefficients from a knowledge of the geometrical structure of the basic cell and its heterogeneities. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method.