Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network

A stochastic approach to network modelling has been used to simulate quasi-static immiscible displacement in porous media. Both number-based and volume-based network saturation results were obtained. Number-based results include: number-based saturation curves for primary drainage, secondary imbibition and secondary drainage, fluid distribution data, and cluster trapping history. Using pore structure data of porous media, it is possible to convert the number-based curves to capillary pressure — saturation relationships. Pore size distribution functions and pore shapes which are thought to closely represent Berea sandstone samples were used to predict the capillary curves. The physical basis of these calculations is a one-to-one correspondence between the cumulative node and bond index fractions in the network analysis, and the cumulative number-based distributions of pore body and pore throat diameters, respectively. The oil-water capillary pressure curve simulated for primary drainage closely resembles those measured experimentally. The agreement between the simulated and the measured secondary imbition and secondary drainage curves is less satisfactory.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

多孔介质中稳定泡沫的流动计算及实验研究

将多孔介质简化为一簇变截面毛管束,根据多孔介质的颗粒直径、颗粒排列方式、孔喉尺度比及束缚水饱和度,计算出变截面毛细管的喉道半径和孔隙半径. 在考虑多孔介质喉道和孔隙中单个气泡的受力和变形基础上,利用动量守恒定理,推导出单个孔隙单元内液相的压力分布和孔隙单元两端的压差计算公式,最终得到多孔介质的压力分布计算公式. 利用长U型填砂管对稳定泡沫的流动特性进行了实验研究. 研究结果表明:稳定泡沫流动时多孔介质中的压力分布呈线性下降,影响泡沫在多孔介质中流动特性的因素包括:多孔介质的孔喉结构、泡沫流体的流量和干度、气液界面张力、气泡尺寸,其中孔喉结构和泡沫干度是影响泡沫封堵能力的主要因素.关键词: 稳定泡沫;多孔介质;变截面毛管;流动;表观粘度;压力分布;实验研究      

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.     

Pore-Scale Analysis of NAPL Blob Dissolution and Mobilization in Porous Media

A pore-scale analysis of nonaqueous phase liquid (NAPL) blob dissolution and mobilization in porous media was presented. Dissolution kinetics of residual NAPLs in an otherwise water-saturated porous medium was investigated by conducting micromodel experiments. Changes in residual NAPL volume were measured from recorded video images to calculate the mass transfer coefficient, K and the lumped mass transfer rate coefficient, k. The morphological characteristics of the blobs such as specific and intrinsic area were found to be independent of water flow rate except at NAPL saturations below 2%. Dissolution process was also investigated by separating the mass transfer into zones of mobile and immobile water. The fractions of total residual NAPL perimeters in contact with mobile water and immobile water were measured and their relationship to the mass transfer coefficient was discussed. In general, residual NAPLs are removed by dissolution and mobilization. Although these two mechanisms were studied individually by others, their simultaneous occurrence was not considered. Therefore, in this study, mobilization of dissolving NAPL blobs was investigated by an analysis of the forces acting on a trapped NAPL blob. A dimensional analysis was performed to quantify the residual blob mobilization in terms of dimensionless Capillary number (Ca _I). If Ca _I is equal to or greater than the trapping number defined as , then blob mobilization is expected.     

Volume Conservation of the Intermediate Phase in Three-Phase Pore-Network Models

Quasi-static rule-based network models used to calculate capillary dominated multi-phase transport properties in porous media employ equilibrium fluid saturation distributions which assume that pores are fully filled with a single bulk fluid with other fluids present only as wetting and/or spreading films. We show that for drainage dominated three-phase displacements in which a non-wetting fluid (gas) displaces a trapped intermediate fluid (residual oil) in the presence of a mobile wetting fluid (water) this assumption distorts the dynamics of three-phase displacements and results in significant volume errors for the intermediate fluid and erroneous calculations of intermediate fluid residual saturations, relative permeabilities and recoveries. The volume errors are associated with the double drainage mechanism which is responsible for the mobilization of waterflood residual oil. A simple modification of the double drainage mechanism is proposed which allows the presence of a relatively small number of partially filled pores and removes the oil volume errors.     

An Analysis of the Movement of Wetting and Nonwetting Fluids in Homogeneous Porous Media

The movement of wetting and nonwetting fluid flow in columns packed with glass beads is used to understand the more complicated flows in homogeneous porous media. The motion of two immiscible liquids (oil and water) is observed with different surfactants. Through dimensional analyses, fluid velocity is well correlated with interfacial tension and less dependent on particle size. In water–oil (W/O) experiments, finger pattern flows are observed if water is the displacing fluid that flows in an oil-filled porous media, whereas oil ganglia tend to form if oil is the displacing fluid in the water-wetted porous media. The results are well described by a simple model based on an earlier theory of flow in a tube.     

Effects of Precursor Wetting Films in Immiscible Displacement Through Porous Media

A computer-aided simulator of immiscible displacement in strongly water-wet consolidated porous media that takes into account the effects of the wetting films is developed. The porous medium is modeled as a three-dimensional network of randomly sized unit cells of the constricted-tube type. Precursor wetting films are assumed to advance through the microroughness of the pore walls. Two types of pore wall microroughness are considered. In the first type of microroughness, the film advances quickly, driven by capillary pressure. In the second type, the meniscus moves relatively slowly, driven by local bulk pressure differences. In the latter case, the wetting film often forms a collar that squeezes the thread of oil causing oil disconnection. Each pore is assumed to have either one of the aforementioned microroughness types, or both. The type of microroughness in each pore is assigned randomly. The simulator is used to predict the residual oil saturation as a function of the pertinent parameters (capillary number, viscosity ratio, fraction of pores with each type of wall microroughness). These results are compared with those obtained in the absence of wetting films. It is found that wetting films cause substantial increase of the residual oil saturation. Furthermore, the action of the wetting films causes an increase of the mean volume of the residual oil ganglia.     

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

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

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.     

Impact of Rock Heterogeneity on Interactions of Microbial-Enhanced Oil Recovery Processes

Residual oil saturation reduction and microbial plugging are two crucial factors in microbial-enhanced oil recovery (MEOR) processes. In our previous study, the residual saturation was defined as a nonlinear function of the trapping number, and an explicit relation between the residual oil saturation and the trapping number was incorporated into a fully coupled biological (B) and hydrological (H) finite element model. In this study, the BH model is extended to consider the impact of rock heterogeneity on microbial-enhanced oil recovery phenomena. Numerical simulations of core flooding experiments are performed to demonstrate the influences of different parameters controlling the onset of oil mobilization. X-ray CT core scans are used to construct numerical porosity-permeability distributions for input to the simulations. Results show clear fine-scale fingering processing, and that trapping phenomena have significant effects on residual oil saturation and oil recovery in heterogeneous porous media. Water contents and bacterial distributions for heterogeneous porous media are compared with those for homogenous porous media. The evolution of the trapping number distribution is directly simulated and visualized. It is shown that the oil recovery efficiency of EOR/MEOR will be lower in heterogeneous media than in homogeneous media, largely due to the difficulty in supplying surfactant to unswept low-permeability zones. However, MEOR also provides efficient plugging along high-permeability zones which acts to increase sweep efficiency in heterogeneous media. Thus, MEOR may potentially be more suited for highly heterogeneous media than conventional EOR.     

A Dynamic Network Model for Two-Phase Flow in Porous Media

We present a dynamic model of immiscible two-phase flow in a network representation of a porous medium. The model is based on the governing equations describing two-phase flow in porous media, and can handle both drainage, imbibition, and steady-state displacement. Dynamic wetting layers in corners of the pore space are incorporated, with focus on modeling resistivity measurements on saturated rocks at different capillary numbers. The flow simulations are performed on a realistic network of a sandpack which is perfectly water-wet. Our numerical results show saturation profiles for imbibition in agreement with experiments. For free spontaneous imbibition we find that the imbibition rate follows the Washburn relation, i.e., the water saturation increases proportionally to the square root of time. We also reproduce rate effects in the resistivity index for drainage and imbibition.     

Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media

As a typical multiphase fluid flow process, drainage in porous media is of fundamental interest both in nature and in industrial applications. During drainage processes in unsaturated soils and porous media in general, saturated regions, or clusters, in which a liquid phase fully occupies the pore space between solid grains, affect the relative permeability and effective stress of the system. Here, we experimentally study drainage processes in unsaturated granular media as a model porous system. The distribution of saturated clusters is analysed by optical imaging under different drainage conditions, with pore-scale information from Voronoi and Delaunay tessellation used to characterise the topology of saturated cluster distributions. By employing statistical analyses, we describe the observed spatial and temporal evolution of multiphase flow and fluid entrapment in granular media. Results indicate that the distributions of both the crystallised cell size and pore size are positively correlated to the spatial and temporal distribution of saturated cluster sizes. The saturated cluster size is found to follow a lognormal distribution, in which the generalised Bond number (\( Bo^{*} \)) correlates negatively to the scale parameter (μ) and positively to the shape parameter (σ). With further consideration of the total surface energy obtained based on liquid–air interfaces, we were able to include additional grain-scale information in the constitutive modelling of unsaturated soils using both the degree of saturation and generalised Bond number. These findings can be used to connect pore-scale behaviour with overall hydro-mechanical characteristics in granular systems.     

Numerical Calculation of Effective Diffusion in Unsaturated Porous Media by the TRT Lattice Boltzmann Method

Numerical models that solve transport of pollutants at the macroscopic scale in unsaturated porous media need the effective diffusion dependence on saturation as an input. We conducted numerical computations at the pore scale in order to obtain the effective diffusion curve as a function of saturation for an academic sphere packing porous medium and for a real porous medium where pore structure knowledge was obtained through X-ray tomography. The computations were performed using a combination of lattice Boltzmann models based on two relaxation time (TRT) scheme. The first stage of the calculations consisted in recovering the water spatial distribution into the pore structure for several fixed saturations using a phase separation TRT lattice Boltzmann model. Then, we performed diffusion computation of a non-reactive solute in the connected water structure using a diffusion TRT lattice Boltzmann model. Finally, the effective diffusion for each selected saturation value was estimated through inversion of a macroscopic classical analytical solution.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Simulation of the dynamic (frequency-dependent) permeability and electrical conductivity in porous materials based on the concept of an ensemble of pores

The class of models of porous media based on the concept of an ensemble of pores with a certain distribution of the main geometrical parameters (e.g., pore size) is studied. The case of the saturation of the pore space with a single-phase multicomponent fluid mixture is studied with and without taking into account the transfer of electric charges. Transfer laws are derived from the condition of decreasing free energy. The hydrodynamic connectivity of pores (and electrical conductivity) is described by two kernels: one kernel describes the connectivity of pores in space, and the other describes the connectivity of pores in the elementary macrovolume. The frequency dependences of the dynamic permeability determined in laboratory experiments and the electrical conductivity of the porous medium were determined using the concept of an ensemble of pores. The relationship between the models considered and relaxation filtration models is established.     

Similarity solutions for immiscible phase migration in porous media: an analysis of free boundaries

A fuel pollutant migrating in a water flow throughout a porous medium is distributed between the moving (continuous) and residual (discontinuous) phases. Usually, there is an equilibrium condition between these phases. In this study, the migration of a fuel slug confied within free boundaries moving in the porous medium is considered. This type of fuel migration pertains to circumstances in which convective fuel transport dominates fuel dispersion when fuel saturation approaches zero. A one-dimensional self-similar model is developed, describing the movement of fuel saturation fronts in a porous medium against and with the water flow direction. Several analytical solutions are found revealing the effects of the pore size, fuel viscosity, fuel mass, and the capillary number on the fuel migration in the porous medium.     

Radon Emanation in Partially Saturated Porous Media

Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.     

Numerical Analysis of Imbibition Front Evolution in Fractured Sandstone under Capillary-Dominated Conditions

Fractures serve as primary conduits having a great impact on the migration of injected fluid into fractured permeable media. Appropriate transport properties such as relative permeability and capillary pressure are essential for successful simulation and prediction of multi-phase flow in such systems. However, the lack of a thorough understanding of the dynamics governing immiscible displacement in fractured media, limits our ability to properly represent their macroscopic transport properties. Previous experimental observations of imbibition front evolution in fractured rocks are examined in the present study using an automated history-matching approach to obtain representative relative permeability and capillary pressure curves. Predicted imbibition front evolution under different flow conditions resulted in an excellent agreement with experimental observations. Sensitivity analyses, in combination with direct experimental observation, allowed exploring the competing effects of relative permeability and capillary pressure on the development of saturation distribution and imbibing front evolution in fractured porous media. Results show that residual saturations are most sensitive to matrix relative permeability to oil, while the ratio of oil and water relative permeability, rock heterogeneity, boundary condition, and matrix–fracture capillary pressure contrast, affect displacement shape, speed, and geometry of the imbibing front.