Non-isothermal Permeability Impairment by Fines Migration and Deposition in Porous Media including Dispersive Transport

Particle migration and deposition, and resulting permeability impairment occurring in porous media are described by a practical phenomenological model considering temperature variation and particle transport by advection and dispersion. Variation of the filter coefficient and permeability of porous matrix by temperature and particle deposition, and other essential factors are considered by means of the special correlations of the relevant variables and dimensionless numbers. Comparison of the numerical results, obtained using a finite-difference numerical scheme with and without considering the dispersion mechanism and temperature variation, reveals the significance of such effects on fines migration and deposition, and consequent permeability impairment in porous media. Improved model presented in this article can be instrumental for scientifically guided experimentation, analysis, and optimal design of processes involving in transport of colloidal and fine particles through geological subsurface formations.     

Smoothed Particle Hydrodynamics Model for Diffusion through Porous Media

A smoothed particle hydrodynamics (SPH) model is presented for the study of diffusion in spatially periodic porous media. The method of SPH is formulated to solve the convection–diffusion equation for tracer diffusion under steady state and transient conditions. Solutions obtained using SPH are compared with other available solutions and the model is used to calculate diffusion coefficients of spatially periodic porous media for the steady state diffusion problem. Diffusion coefficients are then used to calculate nondimensional diffusivities of the media. The effects of media properties on the values of nondimensional diffusivity are also presented.     

多孔介质渗透率的一种新分形模型

多孔介质的渗流特性是油气藏工程、地下水资源利用、高放废物深地质处置等实际工程领域的热门研究问题．基于分形理论及多孔介质由一束面积大小不等的椭圆形毛细管组成的假设,本文建立了流体在分形多孔介质中渗流时的绝对渗透率及相对渗透率的分形渗透率模型．结果表明,绝对渗透率是最大和最小孔隙面积、分形维数、形状因子ε的函数,且当ε =1时,本文模型可以简化成Yu与Cheng模型;而非饱和多孔介质的相对渗透率与饱和度和多孔介质微结构参数有关．将本文提出的渗透率分形模型预测与实验测量数据及其他模型结果进行对比,显示它们整体吻合很好．     

Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects

We have studied the transport and capture of non-Brownian particles in porous media, when the particles are mainly submitted to hydrodynamic and weak inertial effects. Visualization experiments have been performed using several models of porous media which consist of transparent etched networks of interconnected channels. Typical particle deposits have been observed at the corners of the grains of the porous medium. Their shape and their orientation were dependent on flow rate and on the anisotropy of the flow field. A trajectory analysis model has been applied to a porous medium made of a doubly periodic array of rectangular grains very close to the experimental model. This numerical model has been used to localize particle deposits and to determine particle capture efficiency on the grains over a range of low Stokes numbers, grain aspect ratios and flow-field anisotropy ratios. The results have been interpreted in terms of shape of particle deposits and compared successfully to experimental observations.     

Modified Particle Detachment Model for Colloidal Transport in Porous Media

Particle detachment from the rock during suspension transport in porous media was widely observed in laboratory corefloods and for flows in natural reservoirs. A new mathematical model for detachment of particles is based on mechanical equilibrium of a particle positioned on the internal cake or matrix surface in the pore space. The torque balance of drag, electrostatic, lifting and gravity forces, acting on the particle from the matrix and the moving fluid, is considered. The torque balance determines maximum retention concentration during the particle capture. The particle torque equilibrium is determined by the dimensionless ratio between the drag and normal forces acting on the particle. The maximum retention function of the dimensionless ratio (dislodging number) closes system of governing equations for colloid transport with particle release. One-dimensional problem of coreflooding by suspension accounting for limited particle retention, controlled by the torque sum, allows for exact solution under the assumptions of constant filtration coefficient and porosity. The explicit formulae permit the calculation of the model parameters (maximum retention concentration, filtration and formation damage coefficients) from the history of the pressure drop across the core during suspension injection. The values for maximum retention concentration, as obtained from two coreflood tests, have been matched with those calculated by the torque balance on the micro scale.     

A Simple Model for the Variation of Permeability due to Partial Saturation in Dual Scale Porous Media

The main focus of this work is to model macroscopically the effects of partial saturation upon the permeability of dual scale fibrous media made of fiber bundles when a Newtonian viscous fluid impregnates it. A new phenomenological model is proposed to explain the discrepancies between experimental pressure results and analytical predictions based on Darcy's law. This model incorporates the essential features of relative permeability but without the necessity of measuring saturation of the liquid for its prediction. The model is very relevant for the small scale industrial systems where a liquid is forced to flow through a fibrous porous medium. It requires four parameters. Two of them are the two permeability values based on the two length scales. One length scale is of the order of magnitude of the individual fiber radius and corresponds to the permeability of the completely staurated medium, the other is of the order of magnitude of the distance between the fiber bundles and corresponds to the permeability of the partially saturated medium. The other two parameters are the lengths of the two partially saturated regions of the flow domain. The two lengths of the partially saturated region and the permeability of the fully saturated flow domain can be directly measured from the experiments. The excellent agreement between the model and the experimental results of inlet pressure profile with respect to time suggests that this model may be used to describe the variation of the permeability behind a moving front in such porous media for correct pressure prediction. It may also be used to characterize the fibrous medium by determining the two different permeabilities and the relative importance of the unsaturated portion of the flow domain for a given architecture.     

Experimental and Numerical Study of Gel Particles Movement and Deposition in Porous Media After Polymer Flooding

Gel particle, a promising conformance control technology, is recently applying to after-polymer-flooding reservoirs by reusing the remaining polymer in porous media. However, there is no available numerical model which is useful for simulating the conformance control. A series of lab experiments are conducted to explore the main characters of gel particles movements after polymer flooding. Four main mechanisms, namely, swelling, synergy with remaining polymer, shear breaking, and deformation migration, are recognized and described by mathematical formulas. Based on the physical experiments, a numerical model is established to simulate gel particles propagation after polymer flooding. In particular, gel particles are treated as an additional component in aqueous phase. The interaction between the particle gels and the remaining polymer is simplified by aqueous viscosity relationship and particle gel grain size variation. Two transport forms, plugging and deformation migration, are embodied in the model, and the local pressure gradient controls which form the propagation belongs to. The retention of particle gels will cause pore volume decrease and therefore reduce the permeability of thief zones to bypassing water to less swept zones. An iterative method is employed to decouple the gel particle profile control model, which is robust and fairly time-saving. In particular, the flow model is numerically solved by the IMPSAT method and the gel particles continuity equation is explicitly solved by using an operator splitting technique. The newly developed model is validated by history matching results of 1D experiments and actual application case. The results suggest that the presented model is helpful to optimize parameters for profile control for gel particle profile control technology.     

A New Model for Viscous Dissipation in Porous Media Across a Range of Permeability Values

In this paper a unified mathematical theory for the viscous dissipation term in the governing Brinkman equation is derived. This term has, unlike other models, the correct asymptotic behaviour in both the fully Darcy and Newtonian fluid flow limits.     

Permeability Impairment Study Due to Asphaltene Deposition: Experimental and Modeling Approach

This fact is well known that during any scenario of production, asphaltene deposition in porous media has a substantial effect on oil flow. But a clear understanding of asphaltene deposition mechanisms can help to minimize asphaltenic problem in oil-bearing formations. In this study, the experimental results of three dynamic CO₂ miscible injection tests were investigated. Regarding the effects of adsorption, mechanical entrapment, and sweeping mechanisms on permeability behavior, a mathematical mass and permeability variation model were developed. According to the experimental results asphaltene deposition causes a 70% loss of sand stone initial permeability while the loss is significantly low in carbonate cores, about 30%. The model validation shows that the main particulate processes of Asphaltene deposition in sandstone cores are the cake forming and adsorption while in the case of carbonate cores, are the gradual pore blocking and pore sweeping. Obtained results from mass model provide that entrainment and deposition coefficients in square mass model lead to a more flexible trend than the linear variation of general model.     

Permeability of the Fluid-Filled Inclusions in Porous Media

In this article, we propose an approach to obtain the equivalent permeability of the fluid-filled inclusions embedded into a porous host in which a fluid flow obeys Darcy’s law. The approach consists in the comparison of the solutions for one-particle problem describing the flow inside the inclusion, firstly, by the Stokes equations and then by using Darcy’s law. The results obtained for spheres (3D) and circles (2D) demonstrate that the inclusion equivalent permeability is a function of its radius and, additionally, depends on the host permeability. Based on this definition of inclusion permeability and using effective medium method, we have calculated the effective permeability of the double-porosity medium composed of the permeable matrix (with small scale pores) and large scale secondary spherical pores.     

Analytical Solutions to Gas Flow Problems in Low Permeability Porous Media

In most of conventional porous media the flow of gas is basically controlled by the permeability and the contribution of gas flow due to gas diffusion is ignored. The diffusion effect may have significant impact on gas flow behavior, especially in low permeability porous media. In this study, a dual mechanism based on Darcy flow as well as diffusion is presented for the gas flow in homogeneous porous media. Then, a novel form of pseudo pressure function was defined. This study presents a set of novel analytical solutions developed for analyzing steady-state and transient gas flow through porous media including effective diffusion. The analytical solutions are obtained using the real gas pseudo pressure function that incorporates the effective diffusion. Furthermore, the conventional assumption was used for linearizing the gas flow equation. As application examples, the new analytical solutions have been used to design new laboratory and field testing method to determine the porous media parameters. The proposed laboratory analysis method is also used to analyze data from steady-state flow tests of three core plugs. Then, permeability (k) and effective diffusion coefficient (D _e) was determined; however, the new method allows one to analyze data from both transient and steady-state tests in various flow geometries.     

The Effective Permeability of Cracks and Interfaces in Porous Media

The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface.

     

Sensitivity of Intrinsic Permeability to Electrokinetic Coupling in Shaly and Clayey Porous Media

Classical Darcy’s law assumes that the intrinsic permeability of porous media is only dependent on the micro-geometrical and structural properties of the inner geometry of the medium. There are, however, numerous experimental evidences that intrinsic permeability of shaly and clayey porous material is a function of the fluid phase used in the experiments. Several pore-scale processes have been proposed to explain the observed behavior. In this study, we conduct a detailed investigation of one such mechanism, namely the electrokinetic coupling. We have developed a numerical model to simulate this process at the pore-scale, incorporating a refined model of the electrical double layer. The model is used to conduct a detailed sensitivity analysis to elucidate the relative importance of several chemical–physical parameters on the intensity of the electrokinetic coupling. We found that permeability reduction due to this mechanism is likely to occur only if the effective pore-radius is smaller than 10⁻⁶ m. We also observed that electrokinetic coupling is strongly sensitive to electrophoretic mobility, which is normally reduced in clays compared to free-water conditions. Based on these findings, we set up a suite of stochastic pore-network simulations to quantify the extent of permeability reduction. We found that only if the effective pore-radius is ranging from 5 × 10⁻⁷ m to 5 × 10⁻⁸, electrokinetic coupling can be responsible for a 5–20% reduction of the intrinsic permeability, and, therefore, this mechanism has a minor impact on situations of practical environmental or mining interest.     

A Multi-Scale Approach to Model Two-Phase Flow in Heterogeneous Porous Media

The immiscible displacement of a wetting fluid by a non-wetting one in heterogeneous porous media is modeled using a multi-scale network-type analysis: (1) The pressure-controlled immiscible displacement of water by oil in pore-and-throat networks (1st length scale ~ 1?mm) is simulated as a capillary-driven process. (2) The pressure-controlled immiscible displacement in uncorrelated cubic lattices (2nd length scale ~ 1?cm) is simulated as a site percolation process governed by capillary and gravity forces. At this scale, each node represents a network of the previous scale. (3) The rate-controlled immiscible displacement of water by oil in cubic networks (3rd length scale ~ 10?cm), where each node represents a lattice of the previous scale, is simulated by accounting for capillary, gravity, and viscous forces. The multi-scale approach along with the information concerning the pore structure properties of the porous medium can be employed to determine the transient responses of the pressure drop and axial distribution of water saturation, and estimate the effective (up-scaled) relative permeability functions. The method is demonstrated with application to data of highly heterogeneous soils.     

Mechanisms of Particle Transport Acceleration in Porous Media

Experimental data show that the groundwater transport of radionuclides in porous media is frequently facilitated when accompanied with colloid particles. This is usually explained by the size exclusion mechanism which implies that the particles move through the largest pores where the flow velocity is higher. We call attention to three other mechanisms which influence the colloid particle motion, while determining both the probable transport facilitation and retardation. First of all, it is shown that the transport facilitation may be significantly reduced and even transformed into a retardation due to the growth of the effective suspension viscosity (a friction-limited facilitation). Secondly, we will show that the transport of particles through the largest pores can be retarded due to a reduced connectivity of the large-pore cluster (a percolation-breakup retardation). Thirdly, we highlight the Fermi mechanism of acceleration known in statistical physics which is based on the elastic collisions between particles. All three effects are analyzed in terms of the velocity enhancement factor, by using statistical models of porous media in the form of a capillary bundle and a 3D capillary network. Optimal and critical regimes of velocity enhancement are quantified. Estimations show that for realistic parameters, the maximal facilitation of colloid transport is close to the experimentally observed data.     

Opportunities for Particles and Particle Suspensions to Experience Enhanced Transport in Porous Media: A Review

Transport in Porous Media - The possibility of broaching, or the release of fluids at the seafloor due to a damaged or faulty well, is a hazard that must be assessed in the well permitting process....     

Stochastic Estimation of the Slip Factor in Apparent Permeability Model of Gas Transport in Porous Media

Transport in Porous Media - In this paper, we introduce an estimation of the random Klinkenberg slip coefficient in the apparent permeability model using a chaos decomposition technique. The...     

A Subgrid-Scale Model for Turbulent Flow in Porous Media

Transport in Porous Media - Given the analogy between the filtered equations of large eddy simulation and volume-averaged Navier–Stokes equations in porous media, a subgrid-scale model is...     

A New Model for Immiscible Displacement in Porous Media

Immiscible displacement is regarded as the superposition of forward flows of both water and oil, due to injection of water into the medium, and of additional forward flow of water coupled with reverse flow of oil, caused by the existence of capillary pressure gradients. The model has been evaluated numerically for the prediction of the evolution of saturation profiles in waterfloods covering a wide range of water injection rates. In agreement with experimentation, saturation profiles ranging from a completely flat shape to piston-shape, depending on the injection rate, have been obtained. Also in agreement with experimentation, numerical evaluation of the model for the case of a closed system with an initial step-function saturation profile has predicted a gradual spreading of the piston front into S-shaped profiles with an increasing variance. The final profile corresponds to uniform saturation everywhere in the medium.