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1.
Barr DW 《Ground water》2001,39(5):646-650
The pressure driving flow through porous media must be equal to the viscous resistance plus the inertial resistance. Formulas are developed for both the viscous resistance and the inertial resistance. The expression for the coefficient of permeability consists of parameters which describe the characteristics of the porous medium and the permeating fluid and which, for unconsolidated isotropic granular media, are all measurable. A procedure is proposed for testing for the occurrence of turbulence and calculating the effective permeability when it occurs. The formulas are applied to a set of data from 588 permeameter runs ranging from laminar to highly turbulent. The equations fit the data from the permeameter closely through the laminar flow conditions and quite closely through the turbulent conditions. In the turbulent range, the plotting of the data separates into three distinct lines for each of the three shapes of particles used in the tests. For the porous medium and fluid of these tests, turbulence begins at a head gradient of about 0.1.  相似文献   

2.
The knowledge of hydraulic and electric properties of porous media and the relations between them is essential for the quantitative evaluation of electric well logs and the solution of other reservoir engineering problems. The state of the art in this field is not yet satisfying. Theories still show considerable discrepancies with practice due to oversimplified model approaches. Empirical relations are either too coarse, not fully determined, or valid under specific geological and geographical conditions only. This article deals with the development of a general theory of the electric and hydraulic resistance behavior of porous media on the basis of a very general statistical network model. A general solution of the relations between formation factor, permeability, and porosity is presented by means of a rigorous mathematical treatment of two limiting cases of such a network. The solution shows that the product of the formation factor and the permeability can be expressed in the expectation values and the variation coefficients of pore channel cross section and shape factor and by a network factor, that depends on the mesh texture of the network. This network factor is in the range zero to one. It is further shown that the path length increase enters both the electric and the hydraulic tortuosity by its square.  相似文献   

3.
Complexity of the pore geometry and the random nature of flow velocity make it difficult to predict and represent post laminar flow through porous media. Present study experimentally investigates the applicability of Forchheimer and Wilkins equations for post laminar flow where Darcy’s law is invalid due to predominant inertial effect. It is observed that both porosity and media size have significant influence over the coefficients of the Forchheimer coefficients. To incorporate the effect of porosity and media size, behaviour of Forchheimer coefficients are investigated with hydraulic radius as characteristic length. An inversely proportional variation trend is found for all the present and earlier reported data. A new empirical relation between Forchheimer coefficients and hydraulic radius is obtained which can be universally applicable for all media size and porosity. Coefficients of the Wilkins equation are found to be non-deviating for different hydraulic radius in the present study and in the reported literature validating its applicability in predicting the non laminar flow through porous media. Further the Wilkins equation is modified after incorporating the correction factors for better applicability on the field.  相似文献   

4.
The migration and entrapment of dense nonaqueous phase liquids (DNAPLs) in aquifer formations is typically believed to be controlled by physical heterogeneities. This belief is based upon the assumption that permeability and capillary properties are determined by the soil texture. Capillarity and relative permeability, however, will also depend on porous medium wettability characteristics. This wettability may vary spatially in a formation due to variations in aqueous phase chemistry, contaminant aging, and/or variations in mineralogy and organic matter distributions. In this work, a two-dimensional multiphase flow simulator is modified to simulate coupled physical and chemical formation heterogeneity. To model physical heterogeneity, a spatially correlated permeability field is generated, and then related to the capillary pressure-saturation function according to Leverett scaling. Spatial variability of porous medium wettability is assumed to be correlated with the natural logarithm of the intrinsic permeability. The influence of wettability on the hysteretic hydraulic property relations is also modeled. The simulator is then employed to investigate the potential influence of coupled physical and chemical heterogeneity on DNAPL flow and entrapment. For reasonable ranges of wettability characteristics, simulations demonstrate that spatial variations in wettability can have a dramatic impact on DNAPL distributions. Higher organic saturations, increased lateral spreading, and decreased depth of infiltration were predicted when the contact angle was varied spatially. When chemical heterogeneity was defined by spatial variation of organic-wet solid fractions (fractional wettability porous media), however, the resultant organic saturation distributions were more similar to those for perfectly water-wet media, due to saturation dependent wettability effects on the hydraulic property relations.  相似文献   

5.
Permeability of porous media in subsurface environments is subject to potentially large uncertainties due to the heterogeneity of natural systems. In this study, a first-order reliability method (FORM) is combined with a lattice Boltzmann method (LBM) to estimate the permeability of randomly generated porous media. The proposed procedure provides an increased ease of addressing complex pore structures by employing LBM to model fluid flow, while inheriting the computational efficiency from FORM. Macroscale-equivalent permeability can thus be estimated with significantly reduced computational efforts, while maintaining a connection to the complex microscale fluid dynamics within a pore structure environment. Implemented on several randomly generated porous media domains, the proposed method provides 13–120 times the efficiency compared to Monte Carlo methods.  相似文献   

6.
The matrix–fracture transfer shape factor is one of the important parameters in the modeling of fluid flow in fractured porous media using a dual-porosity concept. Warren and Root [36] introduced the dual-porosity concept and suggested a relation for the shape factor. There is no general relationship for determining the shape factor for a single-phase flow of slightly compressible fluids. Therefore, different studies reported different values for this parameter, as an input into the flow models. Several investigations have been reported on the shape factor for slightly compressible fluids. However, the case of compressible fluids has not been investigated in the past. The focus of this study is, therefore, to find the shape factor for the single-phase flow of compressible fluids (gases) in fractured porous media. In this study, a model for the determination of the shape factor for compressible fluids is presented; and, the solution of nonlinear gas diffusivity equation is used to derive the shape factor. The integral method and the method of moments are used to solve the nonlinear governing equation by considering the pressure dependency of the viscosity and isothermal compressibility of the fluid. The approximate semi-analytical model for the shape factor presented in this study is verified using single-porosity, fine-grid, numerical simulations. The dependency of the shape factor on the gas specific gravity, pressure and temperature are also investigated. The theoretical analysis presented improves our understanding of fluid flow in fractured porous media. In addition, the developed matrix–fracture transfer shape factor can be used as an input for modeling flow of compressible fluids in dual-porosity systems, such as naturally fractured gas reservoirs, coalbed methane reservoirs and fractured tight gas reservoirs.  相似文献   

7.
Fractures in porous media have been documented extensively. However, they are often omitted from groundwater flow and mass transport models due to a lack of data on fracture hydraulic properties and the computational burden of simulating fractures explicitly in large model domains. We present a MATLAB toolbox, FracKfinder, that automates HydroGeoSphere (HGS), a variably saturated, control volume finite-element model, to simulate an ensemble of discrete fracture network (DFN) flow experiments on a single cubic model mesh containing a stochastically generated fracture network. Because DFN simulations in HGS can simulate flow in both a porous media and a fracture domain, this toolbox computes tensors for both the matrix and fractures of a porous medium. Each model in the ensemble represents a different orientation of the hydraulic gradient, thus minimizing the likelihood that a single hydraulic gradient orientation will dominate the tensor computation. Linear regression on matrices containing the computed three-dimensional hydraulic conductivity (K) values from each rotation of the hydraulic gradient is used to compute the K tensors. This approach shows that the hydraulic behavior of fracture networks can be simulated where fracture hydraulic data are limited. Simulation of a bromide tracer experiment using K tensors computed with FracKfinder in HGS demonstrates good agreement with a previous large-column, laboratory study. The toolbox provides a potential pathway to upscale groundwater flow and mass transport processes in fractured media to larger scales.  相似文献   

8.
A precise value of the matrix-fracture transfer shape factor is essential for modeling fluid flow in fractured porous media by a dual-porosity approach. The slightly compressible fluid shape factor has been widely investigated in the literature. In a recent study, we have developed a transfer function for flow of a compressible fluid using a constant fracture pressure boundary condition [Ranjbar E, Hassanzadeh H, Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Adv Water Res 2011;34(5):627-39. doi:10.1016/j.advwatres.2011.02.012]. However, for a compressible fluid, the consequence of a pressure depletion boundary condition on the shape factor has not been investigated in the previous studies. The main purpose of this paper is, therefore, to investigate the effect of the fracture pressure depletion regime on the shape factor for single-phase flow of a compressible fluid. In the current study, a model for evaluation of the shape factor is derived using solutions of a nonlinear diffusivity equation subject to different pressure depletion regimes. A combination of the heat integral method, the method of moments and Duhamel’s theorem is used to solve this nonlinear equation. The developed solution is validated by fine-grid numerical simulations. The presented model can recover the shape factor of slightly compressible fluids reported in the literature. This study demonstrates that in the case of a single-phase flow of compressible fluid, the shape factor is a function of the imposed boundary condition in the fracture and its variability with time. It is shown that such dependence can be described by an exponentially declining fracture pressure with different decline exponents. These findings improve our understanding of fluid flow in fractured porous media.  相似文献   

9.
A numerical procedure for the analysis of Rayleigh waves in saturated porous elastic media is proposed by use of the finite element method. The layer stiffness matrix, the layer mass matrix and the layer damping matrix in a layered system are presented for the discretized form of the solid-fluid equilibrium equation proposed by Biot. In order to consider the influence of the permeability coefficient on the behavior of Rayleigh waves, attention is focused on the following states: ‘drained’ state, ‘undrained’ state and the states between two extremes of ‘drained’ and ‘undrained’ states. It is found from computed results that the permeability coefficient exerts a significant effect on dispersion curves and displacement distributions of Rayleigh waves in saturated porous media.  相似文献   

10.
Prediction of CO2 injection performance in deep subsurface porous media relies on the ability of the well to maintain high flow rates of carbon dioxide during several decades typically without fracturing the host formation or damaging the well. Dynamics of solid particulate suspensions in permeable media are recognized as one major factor leading to injection well plugging in sandstones. The invading supercritical liquid-like fluid can contain exogenous fine suspensions or endogenous particles generated in situ by physical and chemical interactions or hydrodynamic release mechanisms. Suspended solids can plug the pores possibly leading to formation damage and permeability reduction in the vicinity of the injector. In this study we developed a finite volume simulator to predict the injectivity decline near CO2 injection wells and also for production wells in the context of enhanced oil recovery. The numerical model solves a system of two coupled sets of finite volume equations corresponding to the pressure-saturation two-phase flow, and a second subsystem of solute and particle convection-diffusion equations. Particle transport equations are subject to mechanistic rate laws of colloidal, hydrodynamic release from pore surfaces, blocking in pore bodies and pore throats, and interphase particle transfer. The model was validated against available laboratory experiments at the core scale. Example results reveal that lower CO2 residual saturation and formation porosity enhance CO2-wet particle mobility and clogging around sinks and production wells. We conclude from more realistic simulations with heterogeneous permeability spanning several orders of magnitude that the control mode of mobilization, capture of particles, and permeability reduction processes strongly depends on the type of permeability distribution and connectivity between injection and production wells.  相似文献   

11.
Managed aquifer recharge is an effective method for utilizing excess flood flows, but clogging of porous media is a limiting factor in the implementation of this water storage technique. In recent years, much research on the physical clogging of porous media during artificial recharge has been conducted. However, the understanding of clogging due to silt‐sized suspended solids (SS) is still inadequate, especially under varying physical conditions. Here, we subjected sand columns to controlled rates of flow and SS suspensions to investigate the influence of media size, SS size, SS concentration, and flow velocity on the clogging of porous media by silt‐sized SS. The results show that the diameter ratio of SS particles to sand grains is the dominant factor influencing the position of physical clogging. As pore velocity increased, the mobility of silt‐sized SS was enhanced and retention in the porous media decreased noticeably. The spatial retention profiles in the porous media were found to vary greatly at different flow velocities. The SS concentration of the infiltrating suspension also dramatically influenced the mobility and deposition of silt‐sized SS particles, such that high concentrations accelerated the clogging process. As the different physical factors changed, the breakthrough curves and retention profiles of silt‐sized SS particles changed obviously and the mechanisms of retention differed. On the whole, clogging position is mainly determined by particle size ratio, but clogging rate is dominated by a variety of factors including particle size ratio, SS concentration, and flow velocity.  相似文献   

12.
Hydraulic displacement is a mass removal technology suitable for stabilization of a dense, nonaqueous phase liquid (DNAPL) source zone, where stabilization is defined as reducing DNAPL saturations and reducing the risk of future pool mobilization. High resolution three-dimensional multiphase flow simulations incorporating a spatially correlated, heterogeneous porous medium illustrate that hydraulic displacement results in an increase in the amount of residual DNAPL present, which in turn results in increased solute concentrations in groundwater, an increase in the rate of DNAPL dissolution, and an increase in the solute mass flux. A higher percentage of DNAPL recovery is associated with higher initial DNAPL release volumes, lower density DNAPLs, more heterogeneous porous media, and increased drawdown of groundwater at extraction wells. The fact that higher rates of recovery are associated with more heterogeneous porous media stems from the fact that larger contrasts in permeability provide for a higher proportion of capillary barriers upon which DNAPL pooling and lateral migration can occur. Across all scenarios evaluated in this study, the ganglia-to-pool (GTP) ratio generally increased from approximately 0.1 to between approximately 0.3 and 0.7 depending on the type of DNAPL, the degree of heterogeneity, and the imposed hydraulic gradient. The volume of DNAPL recovered as a result of implementing hydraulic displacement ranged from between 9.4% and 45.2% of the initial release volume, with the largest percentage recovery associated with 1,1,1 trichloroethane, the least dense of the three DNAPLs considered.  相似文献   

13.
A three-dimensional, reactive numerical flow model is developed that couples chemical reactions with density-dependent mass transport and fluid flow. The model includes equilibrium reactions for the aqueous species, kinetic reactions between the solid and aqueous phases, and full coupling of porosity and permeability changes that result from precipitation and dissolution reactions in porous media. A one-step, global implicit approach is used to solve the coupled flow, transport and reaction equations with a fully implicit upstream-weighted control volume discretization. The Newton–Raphson method is applied to the discretized non-linear equations and a block ILU-preconditioned CGSTAB method is used to solve the resulting Jacobian matrix equations. This approach permits the solution of the complete set of governing equations for both concentration and pressure simultaneously affected by chemical and physical processes. A series of chemical transport simulations are conducted to investigate coupled processes of reactive chemical transport and density-dependent flow and their subsequent impact on the development of preferential flow paths in porous media. The coupled effects of the processes driving flow and the chemical reactions occurring during solute transport is studied using a carbonate system in fully saturated porous media. Results demonstrate that instability development is sensitive to the initial perturbation caused by density differences between the solute plume and the ambient groundwater. If the initial perturbation is large, then it acts as a “trigger” in the flow system that causes instabilities to develop in a planar reaction front. When permeability changes occur due to dissolution reactions occurring in the porous media, a reactive feedback loop is created by calcite dissolution and the mixed convective transport of the system. Although the feedback loop does not have a significant impact on plume shape, complex concentration distributions develop as a result of the instabilities generated in the flow system.  相似文献   

14.
Permeability changes in layered sediments: impact of particle release   总被引：8，自引：0，他引：8  
One of the mechanisms of sudden particle release from grain surfaces in natural porous media is a decrease in salt concentration of the permeating fluid to below the critical salt concentration. Particle release can cause a change in hydraulic conductivity of the matrix, either by washing out the fines and thus increasing the pore sizes or by the plugging of pore constrictions. The phenomenon of permeability changes as a result of particle detachment was investigated in a series of column experiments. Coarse and fine sediments from the Hanford Formation in southeast Washington were tested. Columns were subject to a pulse of highly saline solution (NaNO3) followed by a fresh water shock causing particle release. Outflow rates and changes in hydraulic head as well as electric conductivity and pH were monitored over time. No permeability decrease occurred within the coarse matrix alone. However, when a thin layer of fine sediment was embedded within the coarse material (mimicking field conditions at the Hanford site), permeability irreversibly decreased to 10% to 20% of the initial value. Evidence suggests that most of this permeability decrease was a result of particles detached within the fine layer and its subsequent clogging. An additional observation was a sudden increase in pH in the outflow solution, generated in situ during the fresh water shock. Because layered systems are common in natural settings, our results suggest that alteration between sodium solution and fresh water can lead to particle release and subsequently reduce the overall permeability of the matrix.  相似文献   

15.
A common way to simulate fluid flow in porous media is to use Lattice Boltzmann (LB) methods. Permeability predictions from such flow simulations are controlled by parameters whose settings must be calibrated in order to produce realistic modelling results. Herein we focus on the simplest and most commonly used implementation of the LB method: the single-relaxation-time BGK model. A key parameter in the BGK model is the relaxation time τ which controls flow velocity and has a substantial influence on the permeability calculation. Currently there is no rigorous scheme to calibrate its value for models of real media. We show that the standard method of calibration, by matching the flow profile of the analytic Hagen-Poiseuille pipe-flow model, results in a BGK-LB model that is unable to accurately predict permeability even in simple realistic porous media (herein, Fontainebleau sandstone). In order to reconcile the differences between predicted permeability and experimental data, we propose a method to calibrate τ using an enhanced Transitional Markov Chain Monte Carlo method, which is suitable for parallel computer architectures. We also propose a porosity-dependent τ calibration that provides an excellent fit to experimental data and which creates an empirical model that can be used to choose τ for new samples of known porosity. Our Bayesian framework thus provides robust predictions of permeability of realistic porous media, herein demonstrated on the BGK-LB model, and should therefore replace the standard pipe-flow based methods of calibration for more complex media. The calibration methodology can also be extended to more advanced LB methods.  相似文献   

16.
Traditional analysis methods used to determine hydraulic properties from pumping tests work well in many porous media aquifers, but they often do not work in heterogeneous and fractured‐rock aquifers, producing non‐plausible and erroneous results. The generalized radial flow model developed by Barker (1988) can reveal information about heterogeneity characteristics and aquifer geometry from pumping test data by way of a flow dimension parameter. The physical meaning of non‐integer flow dimensions has long been a subject of debate and research. We focus on understanding and interpreting non‐radial flow through high permeability conduits within fractured aquifers. We develop and simulate flow within idealized non‐radial flow conduits and expand on this concept by simulating pumping in non‐fractal random fields with specific properties that mimic persistent sub‐radial flow responses. Our results demonstrate that non‐integer flow dimensions can arise from non‐fractal geometries within aquifers. We expand on these geometric concepts and successfully simulate pumping in random fields that mimic well‐test responses seen in the Culebra Dolomite above the Waste Isolation Pilot Plant.  相似文献   

17.
Effect and mechanism of stresses on rock permeability at different scales   总被引：1，自引：0，他引：1  
1 Introduction Unlike general solids, rocks are porous materialswhich include different scales of pores, such as pores, cracks, fractures, capillary and disfigurement in the crystal, tiny pores and cracks between crystal grains at micro-scale, in which the fluid is water, oil or gas. Thedifferences between rocks and solids can be seen in two aspects, one is stresses bearing states. Solids are only subjected to external stresses, while rocks are subjected to external stresses σ ij (i, j=1,2,3)…  相似文献   

18.
A model of wave propagation in fluid-saturated porous media is developed where the principal fluid/solid interaction mode affecting the propagation of the acoustic wave results from the conjunction of the Biot and the Squirt flow mechanism. The difference between the original Biot/Squirt (BISQ) flow theory and the new theory, which we call the reformulated BISQ, is that the average fluid pressure term appearing in the dynamic equation for a two component solid/fluid continuum is independent of squirt flow length. P-velocity and attenuation relate to measurable rock physical parameters: the Biot's poroelastic constants, porosity, permeability, pore fluid compressibility and viscosity. Modelling shows that velocity and attenuation dispersion obtained using the reformulated BISQ theory are of the same order of magnitude as those obtained using the original BISQ theory. Investigation on permeability effect on velocity and attenuation dispersion indicate that the transition zone in velocity and attenuation peak, occurring both at the relaxation frequency, shifts toward high frequency when permeability decreases. This behaviour agrees with Biot's theory prediction.  相似文献   

19.
Synopsis

The dynamic equation of motion that governs the laminar flow of water through soils is the empirical equation of Darcy. According to Darcy's equation the velocity of the flowing water is proportional to the hydraulic gradient under which the water is flowing, with the constant of proportionality being the coefficient of permeability. The interesting question arising is whether or not the coefficient of permeability is a scalar quantity (having only a magnitude) or a vector (having both magnitude and direction). It is proved, in the present paper, that the permeability coefficient is neither a scalar nor a vector but a symmetric tensor of second rank. The fact that the permeability tensor is symmetric gives rise to great simplifications and permits a simple graphical construction of the tensor ellipsoid. Having the tensor ellipsoid, the determination of the direction at which the water will flow under a known imposed hydraulic gradient can be found graphically. In case of isotropic soils (the permeability coefficient has the same value along any direction) the ellipsoid reduces to a sphere and the tensor becomes a scalar. In the general case of anisotropic soils the permeability tensor is an entity with nine elements, six of which are independent representing pure extension or contraction along the three principal coordinate axes, thus transforming the permeability sphere into an ellipsoid and vice versa. It should be noted that in anisotropic soils the only directions along which the flow takes place in the direction of the hydraulic gradient are those of the principal axes of the tensor ellipsoid.

Permeability tests were conducted on anisotropic sandstone samples taken at different directions with respect to rectangular coordinates. The permeability coefficient values plotted on a two-dimensional polar coordinate graph paper give rise to an ellipse substantiating therefore the tensor concept of the permeability coefficient. The graphical construction of the tensor ellipse and the use of it in order to obtain the direction of flow by knowing the direction of the hydraulic gradient is also shown.  相似文献   

20.
In this paper we consider one-dimensional capillary redistribution of two immiscible and incompressible fluids in a porous medium with a single discontinuity. We study a special time-dependent solution, a similarity solution, which is found when the initial saturation is discontinuous at the same point as the permeability and porosity, and is constant elsewhere. The similarity solution can be used to validate numerical algorithms describing two-phase flow in porous media with discontinuous heterogeneities. We discuss the construction of the similarity solution, in which we pay special attention to the interface conditions at the discontinuity, both for media with positive and zero entry pressure. Moreover, we discuss some qualitative properties of the solution, and outline a numerical procedure to determine its graph. Examples are given for the Brooks-Corey and Van Genuchten model. We also consider similarity solutions for unsaturated water flow, which is a limit case of two-phase flow for negligible nonwetting phase viscosity.  相似文献   

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