Anomalous Dispersion in Pore-Scale Simulations of Two-Phase Flow

Transport in Porous Media - We investigate anomalous dispersion in steady-state two-phase flow though a random, artificial porous domain. A natural distribution of trapped wetting-phase fluid was...     

Shear Rate Determination from Pore-Scale Flow Fields

Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order to predict the Darcy-scale effective viscosity \(\mu _{\mathrm{eff}} \) required for practical applications often, semi-empirical correlations such as the Cannella or Blake–Kozeny correlation are employed. These correlations employ an empirical constant (“C-factor”) that varies over three orders of magnitude with explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons for this dependency are not very well understood. The semi-empirical correlations are derived under the assumption that the porous media can be approximated by a capillary bundle for which exact analytical solutions exist. The effective viscosity \(\mu _{\mathrm{eff}} (v_{\mathrm{Darcy}} )\) as a function of flow velocity is then approximated by a cross-sectional average of the local flow field resulting in a linear relationship between shear rate \(\gamma \) and flow velocity. Only with such a linear relationship, the effective viscosity can be expressed as a function of an average flow rate instead of an average shear rate. The local flow field, however, does in general not exhibit such a linear relationship. Particularly for capillary tubes, the velocity is maximum at the center, while the shear rate is maximum at the tube wall indicating that shear rate and flow velocity are rather anti-correlated. The local flow field for a sphere pack is somewhat more compatible with a linear relationship. However, as hydrodynamic flow simulations (using Newtonian fluids for simplicity) performed directly on pore-scale resolved digital images suggest, flow fields for sandstone rock fall between the two limiting cases of capillary tubes and sphere packs and do in general not exhibit a linear relationship between shear rate and flow velocity. This indicates that some of the shortcomings of the semi-empirical correlations originate from the approximation of the shear rate by a linear relationship with the flow velocity which is not very well compatible with flow fields from direct hydrodynamic calculations. The study also indicates that flow fields in 3D rock are not very well represented by capillary tubes.     

Pore-Scale Displacement of Heavy Crude Oil During Low Salinity Water Flooding

Transport in Porous Media - To date, most studies about low salinity water flooding (LSWF) have been conducted at the Darcy scale, taking into account mixed-wet conditions, although a limited...     

Predictive Pore-Scale Modeling of Single and Multiphase Flow

We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. The pore space is represented by a topologically disordered lattice of pores connected by throats that have angular cross-sections. We successfully predict single-phase non-Newtonian rheology, and two and three-phase relative permeability for water-wet media. The pore size distribution of the network can be tuned to match capillary pressure data when a network representation of the system of interest is unavailable. The aim of this work is not simply to match experiments, but to use easily acquired data to estimate difficult to measure properties and to predict trends in data for different rock types or displacement sequences.     

Pore-Scale Simulation of Interphase Multicomponent Mass Transfer for Subsurface Flow

A simulation framework is proposed to simulate multicomponent multiphase flow in porous media at the pore scale. It solves equations for the species concentrations in the framework of the volume-of-fluid approach including thermodynamics equilibrium at the fluid/fluid interface. Particular attention is paid to the derivation of the boundary condition for the concentration at the solid walls. The method is validated by comparison with analytical solutions of simple setups. Then, the approach is used to investigate and upscale mass transfer across interfaces in different configurations, including the drainage of water in a tube by a gas carrying a contaminant, mass transfer in thin films, and mass transfer in complex porous structures under various flow conditions.     

Pore-Scale Simulation of Shear Thinning Fluid Flow Using Lattice Boltzmann Method

The present work attempts to identify the roles of flow and geometric variables on the scaling factor which is a necessary parameter for modeling the apparent viscosity of non-Newtonian fluid in porous media. While idealizing the porous media microstructure as arrays of circular and square cylinders, the present study uses multi-relaxation time lattice Boltzmann method to conduct pore-scale simulation of shear thinning non-Newtonian fluid flow. Variation in the size and inclusion ratio of the solid cylinders generates wide range of porous media with varying porosity and permeability. The present study also used stochastic reconstruction technique to generate realistic, random porous microstructures. For each case, pore-scale fluid flow simulation enables the calculation of equivalent viscosity based on the computed shear rate within the pores. It is observed that the scaling factor has strong dependence on porosity, permeability, tortuosity and the percolation threshold, while approaching the maximum value at the percolation threshold porosity. The present investigation quantifies and proposes meaningful correlations between the scaling factor and the macroscopic properties of the porous media.     

Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element simulations of the Stokes equations for assemblies of 8–200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients.     

High-Resolution Temporo-Ensemble PIV to Resolve Pore-Scale Flow in 3D-Printed Fractured Porous Media

Transport in Porous Media - Fractures are conduits that can enable fast advective transfer of (fluid, solute, reactant, particle, etc.) mass and energy. Such fast transfer can significantly affect...     

Pore-Scale Simulations of Single- and Two-Phase Flow in Porous Media: Approaches and Applications

Transport in Porous Media - We present a review of pore-scale simulations of immiscible fluid transport with focus on two of the most popular approaches: lattice Boltzmann modeling for direct...     

Finite Element-Based Characterization of Pore-Scale Geometry and Its Impact on Fluid Flow

We present a finite element (FEM) simulation method for pore geometry fluid flow. Within the pore space, we solve the single-phase Reynold’s lubrication equation—a simplified form of the incompressible Navier–Stokes equation yielding the velocity field in a two-step solution approach. (1) Laplace’s equation is solved with homogeneous boundary conditions and a right-hand source term, (2) pore pressure is computed, and the velocity field obtained for no slip conditions at the grain boundaries. From the computed velocity field, we estimate the effective permeability of porous media samples characterized by section micrographs or micro-CT scans. This two-step process is much simpler than solving the full Navier–Stokes equation and, therefore, provides the opportunity to study pore geometries with hundreds of thousands of pores in a computationally more cost effective manner than solving the full Navier–Stokes’ equation. Given the realistic laminar flow field, dispersion in the medium can also be estimated. Our numerical model is verified with an analytical solution and validated on two 2D micro-CT scans from samples, the permeabilities, and porosities of which were pre-determined in laboratory experiments. Comparisons were also made with published experimental, approximate, and exact permeability data. With the future aim to simulate multiphase flow within the pore space, we also compute the radii and derive capillary pressure from the Young–Laplace’s equation. This permits the determination of model parameters for the classical Brooks–Corey and van-Genuchten models, so that relative permeabilities can be estimated.     

Pore-Scale Monitoring of Wettability Alteration by Silica Nanoparticles During Polymer Flooding to Heavy Oil in a Five-Spot Glass Micromodel

It is well known that the oil recovery is affected by wettability of porous medium; however, the role of nanoparticles on wettability alteration of medium surfaces has remained a topic of debate in the literature. Furthermore, there is a little information of the way dispersed silica nanoparticles affect the oil recovery efficiency during polymer flooding, especially, when heavy oil is used. In this study, a series of injection experiments were performed in a five-spot glass micromodel after saturation with the heavy oil. Polyacrylamide solution and dispersed silica nanoparticles in polyacrylamide (DSNP) solution were used as injected fluids. The oil recovery as well as fluid distribution in the pores and throats was measured with analysis of continuously provided pictures during the experiments. Sessile drop method was used for measuring the contact angles of the glass surface at different states of wettability after coating by heavy oil, distilled water, dispersed silica nanoparticles in water (DSNW), polyacrylamide solution, and DSNP solution. The results showed that the silica nanoparticles caused enhanced oil recovery during polymer flooding by a factor of 10%. The distribution of DSNP solution during flooding tests in pores and throats showed strong water-wetting of the medium after flooding with this solution. The results of sessile drop experiments showed that coating with heavy oil, could make an oil-wet surface. Coating with distilled water and polymer solution could partially alter the wettability of surface to water-wet and coating with DSNW and DSNP could make a strongly water-wet surface.     

Direct Numerical Simulation of Pore-Scale Trapping Events During Capillary-Dominated Two-Phase Flow in Porous Media

Transport in Porous Media - This study focuses on direct numerical simulation of imbibition, displacement of the non-wetting phase by the wetting phase, through water-wet carbonate rocks. We...     

An Orthorhombic Lattice Boltzmann Model for Pore-Scale Simulation of Fluid Flow in Porous Media

One application of the lattice Boltzmann equation (LBE) models is in combination with tomography to simulate pore-scale flow and transport processes in porous media. Most LBE models in the literature are based on cubic lattice, and if the voxels in a tomography image are not cubic or cannot be divided into cubes due to computational limitations, these models will lose most of their advantages. How to deal with such images is, hence, an interest in use of the LBE model to simulate pore-scale processes. In this paper, we present an orthorhombic LBE model based on the single-relaxation time approach with the relaxation parameter varying with lattice directions. The equilibrium distribution functions in the standard LBE model were modified to correct the anisotropy induced by the non-cubic lattice, and the calculations of the fluid density and momentum were also redefined in order to maintain the conservation of mass and momentum during the collision. We tested the model against analytical solution for fluid flow in a tube, and against the standard cubic-based LBE model for fluid flow in a duct with an island inside. The model was then applied to simulate fluid flow in a 3D image in attempts to analyse the errors if the voxels in the image are not cubic but are assumed to be cubic.     

Pore-Scale Modeling of Electrokinetics in Geomaterials

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials developed on the application of an external voltage and pressure difference, respectively. This model is used to predict the macroscale permeabilities of geomaterials via the widely used Carmen–Kozeny equation and through the electrokinetic coupling coefficients. The permeability results for a two-dimensional X-ray tomography-derived sand microstructure are within the same order of magnitude as the experimentally calculated values. The effect of the particle aspect ratio and orientation on the electrokinetic coupling coefficients and subsequently the electrical and hydraulic tortuosity of the porous media has been determined. These calculations suggest a highly tortuous geomaterial can be efficient for applications like decontamination and desalination.

     

Pore-Scale Modelling of Rate Effects in Waterflooding

We develop a rate-dependent network model that accounts for viscous forces by solving for the wetting and non-wetting phase pressure and which allows wetting layer swelling near an advancing flood front. The model incorporates a new time-dependent algorithm by accounting for partial filling of elements. We use the model to study the effects of capillary number, mobility ratio and contact angle distribution on waterflood displacement patterns, saturation and velocity profiles. By using large networks, generated from a new stochastic network algorithm, we reproduce Buckley–Leverett profiles directly from pore-scale modelling thereby providing a bridge between pore-scale and macro-scale transport.     

Experimental Investigation of Synergy of Components in Surfactant/Polymer Flooding Using Three-Dimensional Core Model

Surfactant/polymer (SP) floods have significant potentials to recover remaining oil after water flooding. Their efficiency can be maximized by fully utilizing synergistic effect of polymer and surfactant. Various components adsorbed on the rock matrix due to chromatographic separation can significantly weaken the synergistic effect. Due to scale and dimensional problems, it is hard to investigate chromatographic separation among various components using one-dimensional natural cores. This study compared the adsorption difference between artificial and natural cores and developed a three-dimensional artificial core model of a 1/4 5-spot configuration to simulate oil recovery in multilayered reservoirs with high, middle and low permeability for each layer. Sampling wells were established to monitor pressures, and effluent fluids were acquired to measure interfacial tension (IFT) and viscosity. Then, distances of synergy of polymer and surfactant in three layers were evaluated. Meanwhile, electrodes were set in the model to measure oil saturation variation with resistance changes at different locations. Through comparison with IFT values, the contribution of improved swept volume and oil displacement efficiency to oil recovery during SP flooding could be known. Results showed that injected 0.65 PV of SP could improve oil recovery by 21.56% when water cut reached 95% after water flooding. The retention ratio of polymer viscosity was kept 55.3% at the outlet, but IFT was only 2 mN/m within the 3/10 injector–producer spacing during SP injection. Although subsequent water flooding could result in surfactant desorption and the IFT became 10^?2?mN/m within the 3/10 injector–producer spacing, the IFT turned to 2?mN/m at the half of the model. The enhanced displacement efficiency by reducing IFT only worked within three-tenth location of the model in the high permeability layer, while the enlarged swept volume contributed much in the other areas.

     

Three-Phase Flow Modelling Using Pore-Scale Capillary Pressures and Relative Permeabilities for Mixed-Wet Media at the Continuum-Scale

When regions of three-phase flow arise in an oil reservoir, each of the flow parameters, i.e. capillary pressures and relative permeabilities, are generally functions of two phase saturations and depend on the wettability state. The idea of this work is to generate consistent pore-scale based three-phase capillary pressures and relative permeabilities. These are then used as input to a 1-D continuum core- or reservoir-scale simulator. The pore-scale model comprises a bundle of cylindrical capillary tubes, which has a distribution of radii and a prescribed wettability state. Contrary to a full pore-network model, the bundle model allows us to obtain the flow functions for the saturations produced at the continuum-scale iteratively. Hence, the complex dependencies of relative permeability and capillary pressure on saturation are directly taken care of. Simulations of gas injection are performed for different initial water and oil saturations, with and without capillary pressures, to demonstrate how the wettability state, incorporated in the pore-scale based flow functions, affects the continuum-scale displacement patterns and saturation profiles. In general, wettability has a major impact on the displacements, even when capillary pressure is suppressed. Moreover, displacement paths produced at the pore-scale and at the continuum-scale models are similar, but they never completely coincide.     

Upscaling of Anomalous Pore-Scale Dispersion

Transport in Porous Media - We study the upscaling of advective pore-scale dispersion in terms of the Eulerian velocity distribution and advective tortuosity, both flow attributes, and of the...