NETWORK SIMULATION OF RELATIVE PERMEABILITY CURVES USING A BOND CORRELATED-SITE PERCOLATION MODEL OF PORE STRUCTURE

This paper deals with the conductivity and relative conductivity properties of irregular 3-D networks of pores that represent the continua of the oil phase and the aqueous phase respectively, during steady slate two phase flow in porous media. The relative conductivity properties presented, correspond to the saturation history defined by the drainage, imbibition and secondary drainage capillary pressure curves respectively. Use has been made of the pore accessibility history of a 20 × 20 × 20 network and a 10 × 10 × 10 nodes core portion of the network is used to write the flow equations. A set of 1001 linear equations is solved using the Preconditioned Conjugate Gradients Method for the conductivities of the wetting phase and the non-wetting phase respectively, as a function of network saturation and saturation history. The effects of pore throat size distribution and pore body size distribution on relative permeability behaviour has been investigated. Furthermore, the effect of conductivity function q(D) proportional to Dⁿ (n = 0, 1, 2, 3, 4) on relative permeability behaviour was investigated, where D stands for pore throat diameter and n is an exponent depending on pore geometry.

The results of this work are very significant in elucidating the following points that are not clearly stated in the literature: 1) using the bypassing as the only trapping mechanism, the primary drainage and secondary drainage relative permeability curves are in agreement with experimental findings; 2) more realistic displacement mechanisms in secondary imbibition are required to have better agreement with experimental findings; 3) the correlated network models after the site type problem of percolation theory are realistic models of pore structure; 4) the conductivity function q(D) proportional to D³ is the most appropriate pore throat conductivity function because of lamelar like pore geometries; and 5) accurate prediction of the effective permeability requires knowledge of the porosity and the detailed pore geometry in the pore network, in addition to pore size distributions used in the network simulation.     

ESTIMATION AND MEASUREMENT OF THE DISTRIBUTION OF TENSILE MODULI IN INJECTION MOLDED THERMOPLASTICS

A variety of techniques have been employed to study anisotropic behavior, as a result of processing, in injection molded parts. The techniques include density, sonic modulus, birefringence, wide-angle X-ray diffraction, infrared dichroism and mechanical testing.

Generally, maximum density is observed in the core of the molding and near the gate, while minimum density is observed near the surface. Maximum orientation occurs at or near the surface, as indicated by both birefringence and sonic measurements. X-ray diffraction suggests a complex pattern of orientation for the three cyslallographic axes. The crystallographic a-axis tends to be oriented in the flow direction as shown by both the X-ray and infrared techniques. In general, raising the molding temperature has only a marginal influence on crystallinity and orientation. However, the two resins included in the study exhibited substantial differences in the distribution of these properties. Both elongation at break and at yield exhibit maxima near, but not at, the surface. On the other hand, tensile stress at yield tends to increase monotonically from the surface towards the centre.

The results of crystallinity and orientation are combined to predict the distribution of tensile moduli using available theories. Good agreement is obtained between the calculated and measured values.     

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.'     

APPLICATION OF THE PRECONDITIONED CONJUGATE GRADIENTS METHOD IN THE SIMULATION OF RELATIVE PERMEABILITY PROPERTIES OF POROUS MEDIA

A model that is after the determination of the relative permeability characteristics of porous media is presented. It is part of a general model that deals with the simulation of capillary phenomena and immiscible fluid flow behaviour in porous media. The relative permeability characteristics in a water wet porous medium are simulated with the use of three-dimensional (3-D) network models of pore structure with pore body and pore throat size distributions. The major assumption involved is that a cubic network of pore bodies connected by pore throats with pore body and pore throat size distribution respectively, is a realistic representation of the pore structure of a porous medium. The physical laws that apply in real media are simulated in the network analysis, and the computed results are compared with experimental findings. A new algorithm was developed that leads to the solution of a large set of linear equations, with a sparse and positive definite coefficient matrix. Results obtained with the application of the Preconditioned Conjugate Gradients method and numerical aspects of the simulation are presented and discussed. Comparison of this method with other available numerical methods is also made. It is concluded that the Preconditioned Conjugate Gradients method is advantageous for large networks with regards to time of solution, convergence, and accuracy. The validity of the algorithm is tested against other methods in the literature.     

EXPERIMENTAL DETERMINATION OF THE PERMEABILITY AND RELATIVE VISCOSITY FOR FINE LATEXES AND YEAST SUSPENSIONS

The specific cake resistances of thin layers of fine latexes and of yeast cells have been determined from flux data for pressure drops of up to 100 kPa in a static filtration device. A single correlation has been developed that relates the cake resistance to particle diameter for monodisperse rigid latex spheres with diameters between 1.0 and 6.7 μm. The specific resistance of the yeast cell layers was found to be almost 50 times larger than that of the rigid latex spheres of the same median diameter

The relative viscosities of a 7.3 μm latex and yeast cell suspensions have been measured in a cone-and-plate viscometer. Empirical correlations relating the relative viscosity to the solids volume fraction were developed from linear regression of the data for each suspension. A correlation was also developed that relates the relative viscosity of the yeast cell suspension to the cell count. The effective shear-viscosities were not observed to exhibit a significant shear-rate dependence. However, an apparent viscosity increase with time was observed. This is attributed to radial migration of the particles as a result of interactions with the surface of the cone.     

Prediction of pressure drop and liquid holdup in trickle bed reactor using relative permeability concept in CFD

A Computational Fluid Dynamics (CFD) model based on porous media concept is presented to model the hydrodynamics of two-phase flow in trickle-bed reactors (TBRs). The aim of this study is to develop a comprehensive CFD based model for predicting hydrodynamic parameters in trickle-bed reactors under cold-flow conditions. The two-phase Eulerian model describing the flow domain as a porous region has been used to simulate the macroscale multiphase flow in trickle beds operating under trickle flow regime using FLUENT 6.2 software. The closure terms for phase interactions have been addressed by adopting the relative permeability concept [Sàez, A.E., Carbonell, R.G., 1985. Hydrodynamic parameters for gas-liquid cocurrent flow in packed beds. A.I.Ch.E. Journal 31, 52-62]. The model has been evaluated by comparing predictions with the data (collected under a varied set of laboratory conditions) available in the open literature. It is shown that while being relatively simple in structure, this CFD model is flexible and predictive for a large body of experimental data presented in the open literature.     

Dynamic effects in capillary pressure-saturations relationships for two-phase flow in 3D porous media: Implications of micro-heterogeneities

The capillary pressure-saturation (P^c-S) relationships are essential in characterising two-phase flow behaviour in porous media. However, these relationships are not unique and depend on the flow dynamics, i.e., steady state or dynamic, among other factors. It has been shown that empirical models describing two-phase flow processes in porous media may be inadequate to account fully for the physics of flow in dynamic conditions. New capillary pressure relationships have been proposed which include an additional term to account for the dependence of capillary pressure on saturation and time derivative of saturation (∂S/∂t). This parameter is a capillary damping coefficient, also known as dynamic coefficient (τ), which establishes the speed at which flow equilibrium is reached. The dependence of P^c-S relationships on ∂S/∂t is called dynamic effects.In most laboratory experiments for measuring two-phase flow properties, it is implicitly assumed that the sample is homogeneous. However, this is not the case and micro-heterogeneities with their distinct multiphase flow properties may exist within the domain. They affect the dynamics of the multiple fluid phases and saturation distributions in the domain. These issues have been studied individually but the combination of dynamic effects and micro-scale heterogeneities on the P^c-S relationships has not been quantified accurately, particularly in 3D domains. Consequently, there are significant uncertainties on the reported values of τ in the literature.In this work, we have carried out a numerical study to investigate how the presence of micro-scale heterogeneities affects the dynamics of dense non-aqueous phase liquid (DNAPL) and water flow in porous domain. The relative significance of the variations in nature, intensity and distribution of micro-scale heterogeneities on dynamic flow conditions are manifested on P^c-S curves which are quantified in terms of the dynamic coefficient, τ. There is a complex interplay of various factors (e.g., dynamic flow conditions, distribution and intensity of micro-heterogeneity, pore size distribution, domain size and geometry and media anisotropy) which affects P^c-S curves. However, our results show that as the intensity of heterogeneity increases the dynamic coefficient at a given saturation increases, provided all other factors remain the same. The effects of domain shapes (cylindrical vs. rectangle), aspect ratios, dimensionality (2D vs. 3D), permeability anisotropy on τ are also analysed in order to generalise their effects as far as possible. We envisage that our simulations will minimise some of the inconsistencies on the reported data on τ in the literature.     

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.     

A numerical study of capillary pressure–saturation relationship for supercritical carbon dioxide (CO2) injection in deep saline aquifer

Carbon capture and sequestration (CCS) is expected to play a major role in reducing greenhouse gas in the atmosphere. It is applied using different methods including geological, oceanic and mineral sequestration. Geological sequestration refers to storing of CO₂ in underground geological formations including deep saline aquifers (DSAs). This process induces multiphase fluid flow and solute transport behaviour besides some geochemical reactions between the fluids and minerals in the geological formation. In this work, a series of numerical simulations are carried out to investigate the injection and transport behaviour of supercritical CO₂ in DSAs as a two-phase flow in porous media in addition to studying the influence of different parameters such as time scale, temperature, pressure, permeability and geochemical condition on the supercritical CO₂ injection in underground domains. In contrast to most works which are focussed on determining mass fraction of CO₂, this paper focuses on determining CO₂ gas saturation (i.e., volume fraction) at various time scales, temperatures and pressure conditions taking into consideration the effects of porosity/permeability, heterogeneity and capillarity for CO₂–water system. A series of numerical simulations is carried out to illustrate how the saturation, capillary pressure and the amount of dissolved CO₂ change with the change of injection process, hydrostatic pressure and geothermal gradient. For example, the obtained results are used to correlate how increase in the mean permeability of the geological formation allows greater injectivity and mobility of CO₂ which should lead to increase in CO₂ dissolution into the resident brine in the subsurface.     

A two-phase Eulerian approach using relative permeability concept for modeling of hydrodynamics in trickle-bed reactors at elevated pressure

Most commercial trickle-bed reactors (TBRs) employed in hydroprocessing and other industrially relevant operations normally operate at elevated pressures. Two-phase pressure drop and liquid holdup are two foremost important hydrodynamic parameters to consider for analysis and design of a TBR, including those operating at higher pressures. Even after several decades of research efforts directed towards the development of TBR technology, know-how about the hydrodynamics of two-phase flow in a TBR especially operating at high-pressure conditions has been inadequate. In this study, an effort has been made to assess the complex hydrodynamics of high-pressure TBR through the development of a Computational Fluid Dynamics (CFD) based model to predict pressure drop and liquid saturation. A two-phase Eulerian CFD model envisaging the flow field as porous region has been utilized for evaluating these hydrodynamic parameters. Different combinations of relative permeability correlations in the closure terms have been exercised to realize the best fit. The comparisons between model predictions and numerous experimental data, collected from different independent sources under a varied set of operating conditions, lead to the favourable implementation of this less computationally intensive, yet first-principle based CFD model to forecast the two-phase hydrodynamics for high-pressure TBRs.     

Upscaling multi-component two-phase flow in porous media with partitioning coefficient

This paper deals with the upscaling of multicomponents two-phase flow in porous media. In this paper, chemical potential equilibrium at the interface between both phases is assumed to be described by a linear partitioning relationship such as Raoult or Henry's law. The resulting macro-scale dispersion model is a set of two equations related by a mass transfer coefficient and which involves several effective coefficients. These coefficients can be evaluated by solving closure problems over a representative unit-cell. The proposed model is successfully validated through direct analytical and numerical calculations.     

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.     

IDENTIFICATION OF LIQUID-LIQUID FLOW PATTERN IN A HORIZONTAL PIPE USING ARTIFICIAL NEURAL NETWORKS

Identification of flow pattern during the simultaneous flow of two immiscible liquids requires knowledge of the flow rate of each fluid as well as knowledge of other physical parameters like conduit inclination, pipe material, pipe diameter, viscosity of the oil, wetting characteristics of the pipe, design of the entry mixer, and fluid-fluid interfacial tension. This article presents an artificial neural network (ANN)-based novel technique to determine the liquid-liquid flow regime. This approach uses phase superficial velocities as input parameters, which are obtained from a specific set of data obtained from experimental investigations. Both experimental and ANN-based determinations of liquid-liquid flow pattern have been undertaken for a common data set and the results are compared to prove the effectiveness of ANNs in pattern recognition. A unique ANN architecture is identified with three hidden layers, and the inputs and outputs are modeled into binary form. Levenberg-Marquardt (LM) learning algorithm is used for training this neural network. The design details of the ANN, parameter modeling, and training aspects are presented.     

相态逆转及其密度波的不稳定性

在长度／直径比为1250的水平管内研究了液液相态逆转现象及其对油水两相流和油气水多相流水动力特性的影响．以双流体模型为基础,考虑悬浮相所受的雷诺应力,提出了描述气液两相流和液液两相流中密度波不稳定性的通用模型．模型计算结果表明,“水包油”流型与“油包水”流型之间的相态逆转在悬浮相体积分数为0.3左右发生,与经验性结论相吻合,揭示了相态逆转的机理．     

VARTM工艺中多层玻纤织物渗透规律研究与工艺优化

本文主要通过径向法测量VARTM工艺中不同铺层厚度玻纤单向织物的渗透率,研究分析了VARTM成型工艺中厚铺层织物的渗透规律以及在多层织物中顶层与底层及其在三维方向流动的特性,并对工艺进行优化设计,通过实验结果对比分析确定了优化设计的可行性,对于制造厚铺度构件提供了解决途径.     

气体通过颗粒层突破压力和达西渗透率的关系

对空气通过窄筛分球型颗粒层和窄筛分沙粒在水中自然沉积层孔隙率和突破压力进行实验,发现随着多孔颗粒层内的流通通道的微细化,即使在常压下,气流也会出现速度滑移的稀薄性效应,并且颗粒越小速度滑移的影响越显著,使得实验测量结果不再与平均粒径(或平均孔隙直径)的平方成正比,而受制于Kn_p数的大小.给出了考虑这种速度滑移影响的数据综合方法.     

煤的孔隙结构与容渗性

采用宏观分析方法观测和测定煤的割理及渗透率,并结合扫描电镜和孔隙义分析煤的微观孔隙结构以及等温吸附试验分析微孔结构方法,定性和定量分析了煤的容积性和渗透性特征。     

DEVELOPMENT OF A NEUTRON- RADIOGRAPHIC TECHNIQUE FOR INVESTIGATING PHYSICAL MODELS OF FLUIDIZED BEDS

This paper describes the results of the application of neutron radiography to the study of a two-phase medium, and the resulting technique can be extended to the study of two-phase flow in a fluidized bed. Neutron radiography allows the nonintrusive visualization of a sand/air bed enclosed in aluminum walls. This capability exceeds what others have been able to observe using conventional optical or radiographic techniques.

A static 15 cm thick sand model was constructed and examined by the radiographic technique. The technique employed a collimated thermal column of neutrons, an image intensifier, and conventional photography. To simulate a fluidized bed, spherical voids of several centimeters in diameter were created by placing thin-walled empty aluminum shells in the sand bed. Also, hollow tubes were inserted in the bed. As a function of neutron fluence, high contrast images of the voids inside the 15 cm thick bed were obtained and analyzed. This technique can be extended to the study of dynamic beds by using the neutron source, i.e., the nuclear reactor, in the pulsed mode. Also, contrast agents may be used to extend the range of experimental situation under which high contrast images may be obtained.     

Numerical and microfluidic pore networks: Towards designs for directed water transport in GDLs

Based on a pore network representation of porous media, numerical and experimental methods are employed to explore the design of gas diffusion media in order to control and direct water transport. Randomized pore networks with structured biasing in both diagonal and radial directions show a marked influence on liquid water transport through the two-dimensional media. Radial biasing is shown to have the beneficial effect of decreasing the network saturation, which is a desirable quality in fuel cell gas diffusion layers. Similar flow patterns are obtained from both numerical simulations and experiments, and it is found that relatively small radial biasing can yield a 43% decrease in average saturation compared to pore networks without a prescribed radial gradient.