ANALYSIS OF PERMEABILITY FOR ELLIS FLUID FLOW IN FRACTAL POROUS MEDIA

This work studies the flow characteristics of Ellis fluid in saturated porous media. A fractal model is developed for the effective permeability of Ellis fluid flow in porous media based on the assumptions that porous media consist of a bundle of tortuous capillaries, whose size distribution and tortuosity follow the fractal scaling laws. The average flow velocity and the effective permeability for Ellis fluid flow in porous media are derived. The proposed fractal model does not contain any empirical constant, and every parameter in the model has clear physical meaning. The model predictions are compared with the measured data, and good agreement between them is obtained.     

A THREE DIMENSIONAL NETWORK MODEL FOR CONSOLIDATED POROUS MEDIA. BASIC STUDIES

A three-dimensional porous medium model that pertains to consolidated permeable porous rocks and similar structures is proposed. The porous medium is considered as a network of chambers connected through long narrow throats and it is approximated as a network of unit cells of the constricted tube type. The skeleton of the network can be either regular or randomized, and the throat-to-chamber coordination number can be varied by randomly removing a number of throats. The sizes of contiguous chambers and throats can be cither independent random variables, or they can be correlated. This correlation can be positive (large chambers preferring large throats), or negative (large chambers preferring small throats). The permeability of the network is found to be minimal when the chambers and throats are completely uncorrected. The degree of correlation also affects the throat-to-chamber size ratio, a parameter which is very important in two-phase flows through porous media. A substantial correlation between the local intensity of the flow field on one hand and the local porosity and throat diameter on the other is found. @KEYWORDS: Pore network model, Consolidated porous media.     

SINGLE FLUID FLOW IN POROUS MEDIA

A comprehensive study on single fluid flow in porous media is carried out. The volume averaging technique is applied to derive the governing flow equations. Additional terms appear in the averaged governed equations related to porosity ε, tortuosity τ, shear factor F and hydraulic dispersivity D _h. These four parameters are uniquely contained in the volume averaged Navier-Stokes equation and not all of them are independent. The tortuosity can be related to porosity through the Brudgemann equation, for example, for unconsolidated porous media.

The shear factor models are reviewed and some new results are obtained concerning high porosity cases and for turbulent flows. It is known that there are four regions of flow in porous media: pre-Darcy's flow, Darcy's flow, Forchheimer flow and turbulent flow. The transitions between these regions arc smooth. The first region, the pre-Darcy's flow region represents the surface-interactive flows and hence is strongly dependent on the porous media and the flowing fluid. The other flow regions are governed by the flow strength of inertia. For Darcy's flow, the pressure gradient is found to be proportional to the flow rate. The Forchheimer flow, however, is identified by a strong inertia! effects and the pressure gradient is a parabolic function of flow rate. Turbulent flow is unstable and unsteady flow characterized by chaotic flow patterns. The pressure drop is slightly lower than that predicted using the laminar flow equation.

The hydraulic dispersivity is a property of the porous media. It may be considered as the connectivity of the pores in a porous medium. It characterizes the dispersion of mementum, heat and mass transfer. In this paper, only the dispersion of momentum is studied.

Single fluid flow through cylindrical beds of fibrous mats and spherical particles has been used to show how to solve the single fluid flow problems in porous media utilizing the knowledge developed in this communication. Both the pressure drop and axial flow velocity profiles are computed using the developed shear factor and hydraulic dispersion models. Both the predicted velocity profile and pressure drop compare fairly well with the published experimental data.     

POWER-LAW FLUIDS IN POROUS MEDIA

An analysis is presented to describe the parallel flow of power-law fluids within a channel bounded by porous media. It is shown that there is an excess flow above the Darcy's law prediction for the porous medium region adjacent to the channel/ porous medium boundary. This also leads to a higher flow rate in the channel. The excess flow increases with a decreasing value of the power law index, and with increasing permeability. The excess flow is found to reach a maximum at an intermediate value of the dimensionless channel width (=½H/K^½and it vanishes in the limit of h→∞and h→0. Experimental evidence is also presented to demonstrate the excess flow. The experimental data are found to be in reasonable agreement with the proposed flow model.     

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.’     

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.'     

OSCILLATORY FLOW OF FOURTH-ORDER FLUID IN A POROUS HALF SPACE

This work describes the incompressible flow of fourth-order fluid in a porous half space. The flow in the porous space is caused by the porous plate oscillations in its own plane. Modified Darcy's law has been taken into account to discuss the flow characteristics in a porous space. Numerical solution of the governing nonlinear problem is obtained and the effects of various pertinent parameters are discussed.     

多孔介质中流体流动的格子气自动机模拟

介绍了 13-Bit正六边形多速格子气自动机模型的特点 ,讨论了多孔介质流体流动的格子气自动机模型的渗透率等参量算方法 ,应用该模型对计算机产生的多孔介质几何构型和焦炭多孔介质中的流体流动进行了模拟 ,其结果既可以给出多孔介质中的流动细节 ,也可统计得到表征多孔介质宏观流动特征的物理参量 .初步研究表明 :格子气自动机模型可用于模拟复杂边界条件下多孔介质的流体流动     

CAPILLARY NETWORK MODELS FOR TRANSPORT IN PACKED BEDS: CONSIDERATIONS OF PORE ASPECT RATIO

The conventional analysts for the estimation of the tortuosity factor for transport in porous media is modified here to account for the effect of pore aspect ratio. Structural models of the porous medium are also constructed for calculating the aspect ratio as a function of porosity. Comparison of the model predictions with the extensive data of Currie (1960) for the effective diffusivity of hydrogen in packed beds shows good agreement with a network model of randomly oriented intersecting pores for porosities upto about 50 percent, which is the region of practical interest. The predictions based on this network model are also found to be in better agreement with the data of Currie than earlier expressions developed Tor unconsolidated and grainy media.     

用三维网络模型模拟多孔介质的吸着回路

在简单立方网络框架的基础上构造了具有规整和随机特性的三维网络模型,并引入了周期边界条件.采用Weibull分布作为孔尺寸参数的分布函数,模拟了不同配位数和孔尺寸范围下氮在多孔介质中的等温吸附和脱附过程.着重考察了多孔介质网络模型的几何性质和拓扑性质对吸着等温回路的影响.结果发现,影响吸着等温线回路形状的主要因素是孔喉的半径和网络的配位数.     

MICROSCOPIC DETERMINATION OF TRANSPORT PARAHETERS IN DRYING POROUS MEDIA

ABSTRACT

The flow and distribution of liquid and vapor in the pore space of drying porous media are represented by a simple network model that incorporates the microscopic mechanisms. A method akin to Monte Carlo and molecular dynamics approaches is described for calculating from any such model the macroscopic, ‘volume- averaged’, or effective transport parameters: relative permeabilities for pressure-driven flow, effective diffusivities for molecular diffusion, and so on.

The method is to map representative small samples of pore space onto regular networks that have equivalent mean coordination and are made up of biconical pore segments intersecting in pore bodies, all dimensions being drawn from measured or estimated distributions. Evaporation and meniscus curvature, vapor movement by diffusion away from menisci and viscous flow toward them are described by one-dimensional local approximations. The resulting large set of ordinary differential and algebraic equations is solved by computer. Solutions from several such realizations are averaged to determine relative permeability to liquid, capillary pressure, and effective diffusivity of vapor as functions of liquid saturation and drying history. The results are to be used for interpreting, interpolating, and extrapolating experimental measurements of the same quantities.     

SIMULTANEOUS HEAT AND FLUID FLOW IN POROUS MEDIA: CASE STUDY: STEAM INJECTION FOR TERTIARY OIL RECOVERY

Heat transfer and fluid flow in porous media occur simultaneously in thermal enhanced oil recovery and significantly increase the rate of energy transfer. The purpose of this investigation was to take advantage of such contemporary transfers and to study heavy oil recovery efficiency using hot-water flooding, cold-water flooding, and steam injection into porous media. A set of multistage laboratory tests was performed to find the temperature profile during steam injection as a means of tertiary oil recovery. Sand-packed models were utilized to investigate the oil recovery efficiency during cold and hot water injection as well as steam flooding for both secondary and tertiary oil production stages. An oil bank was formed in steam injection during the tertiary oil recovery from a vertical standing sand-packed model, resulting in very high oil recovery efficiency. Steam injection was found to be very effective, compared to cold- and hot-water flooding, for the recovery of heavy oil. Based on the principles of transport phenomena in porous media, a mathematical model was developed to predict the temperature profile during the steam injection process. Satisfactory agreement is achieved between the temperature profile predicted from the model and the experimental results.     

SIMULTANEOUS HEAT AND FLUID FLOW IN POROUS MEDIA: CASE STUDY: STEAM INJECTION FOR TERTIARY OIL RECOVERY

Heat transfer and fluid flow in porous media occur simultaneously in thermal enhanced oil recovery and significantly increase the rate of energy transfer. The purpose of this investigation was to take advantage of such contemporary transfers and to study heavy oil recovery efficiency using hot-water flooding, cold-water flooding, and steam injection into porous media. A set of multistage laboratory tests was performed to find the temperature profile during steam injection as a means of tertiary oil recovery. Sand-packed models were utilized to investigate the oil recovery efficiency during cold and hot water injection as well as steam flooding for both secondary and tertiary oil production stages. An oil bank was formed in steam injection during the tertiary oil recovery from a vertical standing sand-packed model, resulting in very high oil recovery efficiency. Steam injection was found to be very effective, compared to cold- and hot-water flooding, for the recovery of heavy oil. Based on the principles of transport phenomena in porous media, a mathematical model was developed to predict the temperature profile during the steam injection process. Satisfactory agreement is achieved between the temperature profile predicted from the model and the experimental results.     

TRANSIENT FLOW OF A COMPRESSIBLE FLUID THROUGH BEDS OF SOLID PARTICLES OR POROUS MATERIALS

The problem of transient gas flow through porous structures is a typical one in many practical applications e.g. gas production from an underground reservoir, gas flow through the soil after an underground nuclear explosion or gas flow through a packed column. This later application is important for separation processes called Rapid Pressure Swing Adsorption (RPSA) and Pressure Swing Adsorption (PSA) where the course of the column pressurization strongly affects the mass transfer between the gas and either the adsorbent or the molecular sieve.

A mathematical model for the isothermal transient flow of an ideal gas through a solid bed or porous material has been compared with experimental results both in Darcy's region and in the high velocity region. Numerical simulations have been used to study the effect of the fixed bed characteristic parameters on the pressurization course of a fixed bed column closed at one end and connected to the constant pressure vessel on the other end. In four limiting cases the results have been interpreted using simple algebraic equations.

The theoretical analysis proved that for the particles being tested (d_p smaller than 0·7  mm) the effect of macroscopic inertia forces and nonisothermal effects are negligible under the following conditions: Input pressure smaller than 600  kPa and the ratio of inlet to initial pressure smaller than 20.     

多孔介质中三组分气体扩散的网络分析

采用有效介质理论和平滑域近似的方法 ,对乙烯、氩气和二氧化碳在γ -Al2 O3 内的三组分扩散进行了网络分析 ,同时又用定态扩散实验加以验证 .研究结果表明 ,在确定了多孔介质孔结构参数 (平均配位数 )和孔尺寸参数 (孔径分布 )的前提下 ,通过网络分析的方法就可以获得有关多孔介质中多组分气体扩散的信息 .从而 ,建立起了用多孔介质微观性质描述宏观扩散过程的基本方法     

DEVELOPMENT OF RADIAL MODELS FOR FORMATION DAMAGE IN POROUS MEDIA

The continuously changing velocities in radial geometry have a significant effect on process characteristics, making it an intellectually challenging problem. In practical operations, fluid is generally pumped down injection wells from where it flows radially outward. Simulating this radial system with linear models is definitely restrictive. Consequently, the need for developing radial models for flow and particle entrapment in porous media is both fundamental and applied.

A radial network model, covering a 120° angle, has been developed to simulate formation damage due to deep bed filtration (DBF) of injected suspensions. The models draws upon our previously developed concepts of “wave-front movement” and “flow-biased probability” for linear systems. Systematic studies have been performed on formation damage using monodispersed and polydispersed suspensions. Case studies have been presented for constant flow rate and constant pressure injections, and comparisons are made between linear and radial systems.

Results show that the results obtained from linear models are conservative in comparison to those obtained from radial models. Furthermore, the use of monodispersed particles in mathematical models would show smaller differences between linear and radial predictions than would actually occur for polydispersed particles.     

HEAT AND MASS TRANSFER IN STAGNATION-POINT FLOW OF A POLAR FLUID TOWARDS A STRETCHING SURFACE IN POROUS MEDIA IN THE PRESENCE OF SORET,DUFOUR AND CHEMICAL REACTION EFFECTS

This work is focused on the numerical solution of steady boundary-layer stagnation-point flow of a polar fluid towards a stretching surface embedded in porous media in the presence of the effects of Soret and Dufour numbers and first-order homogeneous chemical reaction. The governing boundary-layer equations of the problem are formulated and transformed into a self-similar form. The obtained equations are solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. Both assisting and opposing flow conditions are considered. Comparisons of the present numerical results with previously published work under limiting cases are performed and found to be in excellent agreement. Representative results for the fluid velocity, angular velocity, temperature, and solute concentration profiles as well as the local heat and mass transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.     

A NON-FICKIAN SURFACE EXCESS MODEL FOR CHEMICAL TRANSPORT THROUGH FRACTURED POROUS MEDIA

The transport of a solute through fractured rock domains is of major concern in various disciplines. The transport of chemicals in a porous medium is not a very well understood phenomenon, especially if the meidum is fractured. A study was conducted to invertigate the transport process of three selected chemicals in a fractured porous medium. A series of laboratory flow experiments was conducted in silica sand packs using a single fracture. Forty six runs were conducted to investigate the effects of chemical concentration, flow rate, and fractures in the transport process. A numerical model was developed that employed a one-dimensional transport equation combined with the surface excess concept to describe absorption equilibrium in the solid/liquid interface. Functional forms of the dispersion parameter (λ) and the kinetic desorption constant (k₂) were used to take into account the effect of the fracture on the porous medium. This non-fickian simulation results showed excellent agreement with experimental results. The developed model accommodates various interactions between the solid and the liquid phases. Therefore, it can be used for different chemical and rock types with little modification.     

EVAPORATION FROM POROUS MEDIA: A CAPILLARY MODEL OF A PENETRATING FRONT

A capillary tube model was solved to investigate the influence of mass transfer coefficient, temperature, and front depth on the evaporation rate during the penetrating-front period of water-filled porous media dried in hot air. The results show that increasing the flow rate of the drying air is not so efficient as increasing the sample temperature. Due to attenuating diffusion rate, the rate of liquid front migration decreases with time. The calculations explain the falling rate period behavior of sandstone heated at 121°C. Trends depicted by the model may be useful for the design of heating conditions for drying processes.     

AN ARTIFICIAL NEURAL NETWORK APPROACH TO CAPILLARY RISE IN POROUS MEDIA

An artificial neural network (ANN) was used to analyze the capillary rise in porous media. Wetting experiments were performed with 15 liquids and 15 different powders. The liquids covered a wide range of surface tension (15.45-71.99 mJ/m²) and viscosity (0.25-21 mPa.s). The powders also provided an acceptable range of particle size (0.012-45 μm) and surface free energy (25.5-62.2 mJ/m²). An artificial neural network was employed to predict the time of capillary rise for a known given height. The network's inputs were density, surface tension, and viscosity for the liquids and particle size, bulk density, packing density, and surface free energy for the powders. Two statistical parameters, the product moment correlation coefficient (r²) and the performance factor (PF/3), were used to correlate the actual experimentally obtained times of capillary rise to: (i) their equivalent values as predicted by a designed and trained artificial neural network; and (ii) their corresponding values as calculated by the Lucas-Washburn equation as well as the equivalent values as calculated by its various other modified versions. It must be noted that for a perfect correlation r² = 1 and PF/3 = 0. The results showed that only the present ANN approach was able to predict with superior accuracy (i.e., r² = 0.92, PF/3 = 51) the time of capillary rise. The Lucas-Washburn calculations gave the worst correlations (r² = 0.15, PF/3 = 1002). Furthermore, some of the modifications of this equation as proposed by different workers did not seem to conspicuously improve the relationships, giving a range of inferior correlations between the calculated and experimentally determined times of capillary rise (i.e., r² = 0.27 to 0.48, PF/3 = 112 to 285).