Multiphase Flow In Porous Media Research Articles

Prediction of live reservoir fluid interfacial tension from dead oil measurements

The interfacial tension (IFT) between crude oil and water governs the multiphase flow in porous media and is therefore of paramount importance for understanding reservoir behavior. IFT data is commonly, but inadequately, acquired at ambient conditions using samples of dead oil, because live crude oil samples are limited in availability and measurements under high pressure and temperature conditions are complex. In this study, ten live crude oil samples were used to establish the first correlation allowing to predict live crude oil interfacial tension based on dead oil IFT values and conventional PVT data. IFT experiments were executed for all samples at different pressure and temperature conditions. A common trend of IFT increase from the dead oil at ambient to the live oil at reservoir conditions was noted in the experiments. Based on the measured data, a correlation was established to predict live oil IFT at reservoir conditions from dead oil IFT at ambient condition, using dead oil viscosity and molecular weight, as well as gas to oil ratio and fluid densities as input parameters. The correlation showed a strong coefficient of determination (R2 = 0.98) and was validated using three additional live crude oils from different fields. The IFT values at reservoir conditions were well predicted with average errors below 5%.

Utilization of Nonequilibrium Phase Change Approach to Analyze the Nonisothermal Multiphase Flow in Shallow Subsurface Soils

AbstractThe prediction of coupled nonisothermal multiphase flow in porous media has been the subject of many theoretical and experimental studies in the past half a century. In particular, the evaporation phenomenon from the shallow subsurface has been extensively studied based on the notion of equilibrium phase change between liquid water and water vapor (i.e., instantaneous phase change). One of the frequent assumptions in equilibrium phase change approach is that liquid water is hydraulically connected throughout the vadose zone. Furthermore, classical soil‐water retention curves (e.g., van Genuchten model), which have been extensively used in the literature to model evaporation process, are only valid for high and intermediate saturation degrees. Although these limitations have been addressed and improved in separate studies, they have not yet been rigorously incorporated in the numerical modeling of nonisothermal multiphase flow in shallow subsurface of in‐field soils. Therefore, the aim of this study is to investigate the coupled heat, liquid, and vapor flow in soil media through the Hertz‐Knudsen‐Schrage (HKS) phase change model and by incorporating a water retention model which captures the soil‐water characteristics from full to oven‐dried saturation degrees. A numerical model is developed and validated against the in‐field experimental data. Reasonable agreements between the calculated and measured values of water contents at all depths, as well as the temperature, and cumulative evaporation are observed. Results also confirm that the contribution of the film flow in overall mass flow in the medium is required for accurate modeling and cannot be ignored.

On the Performance of the Node Control Volume Finite Element Method for Modeling Multi-phase Fluid Flow in Heterogeneous Porous Media

In this paper, we critique the performance of the node control volume finite element (NCVFE) method for modeling multi-phase fluid flow in heterogeneous media. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them. Material properties are defined on elements, while transport is simulated on the control volumes. These two meshes are not aligned producing inaccurate results and artificial fluid smearing when modeling multi-phase fluid flow in heterogeneous media. We perform numerical tests to quantify and visualize the extent of this artificial fluid smearing in domains with different material properties. The domains are composed of tetrahedron finite elements. Large artificial fluid smearing is observed in coarse meshes; however, it decreases with the increase in mesh resolution. These findings prompt the use of high-resolution meshes for the method and the need for development of novel numerical methods to address this unphysical flow.

The role of the spatial heterogeneity and correlation length of surface wettability on two-phase flow in a CO2-water-rock system

This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO2 (scCO2)-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO2). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO2 and showed that the variations in the relative permeability curves for both water and scCO2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. The impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.

Micro-Sweep Characteristics of CO2 Flooding

In this paper a micro multi-phase flow equation is built based on the mechanism of a multi-phase fluid flow in porous media. The authors consider the impact of convection diffusion and the improved component mixing rule. In order to accurately evaluate the fluid flow in a low permeability reservoir, two models are established to simulate simple pore throat structure and complex pore throat structure. The predicted residual oil distribution characteristics of CO2 flooding in low permeability reservoir, calculated by finite element microsimulation, have been further verified by experiment. Furthermore, we analyze the effect of different wettability on microflow characteristics of CO2 flooding. The results show that CO2 flooding improving microsweep volume by convective diffusion is more evident in low permeability reservoirs than in high permeability reservoirs. The residual oil is mainly distributed following a pattern of prismatic, wedge-shape, or membrane microstructure. With decrease in the wetting angle on the fluid-rock boundary, the efficiency of oil displacement is further improved.

X-ray microcomputed imaging of wettability characterization for multiphase flow in porous media: A review

With the advent of X-ray micro-computed tomography which is now routinely used, pore- scale fluid transport and processes can be observed in three-dimensional (3D) at the micro-scale. Multiphase flow experiments that are conducted under in situ imaging scanning conditions can be utilized to study the pore-scale physics relevant to subsurface techno- logical applications. X-ray micro-tomographic imaging is a non-destructive technique for quantifying these processes in 3D within confined pores. This paper presents a review for the usage of X-ray micro-computed tomography experiments to investigate wettability effect on multiphase flow. The fundamental workflow of combining experiments with pore-scale in situ imaging scanning such as equipment requirements, apparatus design and fluid systems are firstly described. Then imaging analysis toolkit is presented for how to quantify interfacial areas, curvatures, contact angles, and fluid properties through these images. Furthermore, we show typical examples, illustrating recent studies for the wettability characterization by using X-ray micro-computed imaging. Cited as : Zou, S., Sun, C. X-ray microcomputed imaging of wettability characterization for multiphase flow in porous media: A review. Capillarity, 2020, 3(3): 36-44, doi: 10.46690/capi.2020.03.01

A 6M digital twin for modeling and simulation in subsurface reservoirs

A 6M digital twin for modeling and simulation in subsurface reservoirs

Direct numerical simulation of trapped-phase recirculation at low capillary number

Understanding multiphase flow in porous media, especially how velocity is distributed at the pore-scale, has been the aim of several studies. However, these studies address the recirculation behavior inside the trapped phase experimentally without any comprehensive numerical study of the impact of different governing mechanisms related to the fluid configurations and properties, including drag force and capillary number analysis at low capillary number regime. In this study, we analyzed the recirculation phenomenon inside the trapped phase for various displacement mechanisms, fluid configurations, and dynamic properties. To simulate the pore-scale displacement at low capillary number, we used a filtered surface-force formulation of volume of fluid method, which was implemented in a separately available solver for OpenFoam package. The results showed that within the ranges of capillary number of invading phase analyzed in this study (in the order of 1 × 10−7 to 1 × 10−2), the recirculation phenomenon exists in trapped phases. During the imbibition mechanism, two stagnant regions are created adjacent to the fluid-fluid interface inside the invading fluid. Drag-force analysis on fluid-fluid interfaces shows that during imbibition the maximum force is exerted near the center of the interface, whereas during drainage more force is applied on two elongated interface tails on a solid surface. The centroids are elongated parallel to the interface during drainage and perpendicularly during imbibition, which is in concordance with drag-force distribution along with the interface. The existence of a solid surface near the fluid-fluid interface affects the recirculation process in a way that one or more centroids can be created depending on displacement mechanisms. When the ratio of trapped-phase radius to cavity depth is lower, two simultaneous recirculation zones are formed inside the invading and trapped phases While the changes in viscosity ratio and interfacial tension shifted the centroid location inside the trapped zone, the center of rotation seems to be independent of injection velocity. The average velocity of trapped phase is individually a logarithmic function of the surface tension and fluids viscosity ratio. The stationariness of centroid results in a linear relationship between the average velocity inside the trapped zone and injection velocity. For all ranges of viscosity ratios, a linear relationship between the capillary number of invading and trapped phase is obtained. The findings of this study lead to a better understanding of trapping and mobilization mechanisms in microchannels where various forces are acting on fluid-fluid interfaces.

Coupled fine-scale modeling of the wettability effects: Deformation and fracturing.

Multiphase flow in porous media has been thoroughly studied over the years and its importance is encountered in several areas related to geo-materials. One of the most important parameters that control multiphase flow in any complex geometry is wettability, which is an affinity of a given fluid toward a surface. In this paper, we have quantified the effects of wettability on deformation in porous media, along with other parameters that are involved in this phenomenon. To this end, we conducted numerical simulations on a porous medium by coupling the exchanged forces between the fluid and solid. To include the effect of wettability in the medium, we used the Fictitious Domain methodology and coupled it with volume of fluid through which one can model more than one fluid in the system. To observe the effect of wettability on dynamic processes in the designated porous medium, such as deformation, particle-particle contact stresses, particle velocity, and injection pressure, a series of systematic computations were conducted where wettability is varied through five different contact angles. We found that wettability not only controls the fluid propagation patterns but also affects drag forces exerted on the particles during injection such that larger deformations are induced for particles with lower wettability. Our results are also verified against experimental tests.

Wettability control on deformation: Coupled multiphase fluid and granular systems.

Understanding of multiphase flow in porous media is important for a wide range of applications such as soil science, environmental remediation, energy resources, and CO_{2} sequestration. This phenomenon depends on the complex interplay between the fluid and solid forces such as gravitational, capillary, and viscous forces, as well as wettability of the solid phase. Such interactions along with the geometry of the medium give rise to a variety of complex flow regimes. Although much research has been done in the area of wettability, its mechanical effect is not well understood, and it continues to challenge our understanding of the phenomena on macroscopic and microscopic scales. In this paper, therefore, the effect of wettability on the deformation of porous media and fluid-fluid patterns is studied through a series of three-dimensional (3D) simulations. To this end, the discrete element method (DEM) and volume of fluid (VOF) are coupled to accurately model free-surface flow interaction in a cylindrical pack of spheres. The fluid-particle interactions are modeled by exchanging information between DEM and VOF, while the effect of wettability is considered to study how it controls fluid displacement. The results indicate that the drag force and deformation in the pack vary with the change in wettability and capillary number. To demonstrate the effect of both wettability and capillary number, a series of numerical experiments were conducted with two capillary numbers and three wettability conditions. Our results show that the drag force was greatest for near extreme wettability conditions, which resulted in a larger deformation.

An Automatic In Situ Contact Angle Determination Based on Level Set Method

AbstractA novel level set‐based approach is presented to calculate in situ contact angle distribution, θ, from pore‐scale immiscible fluids and rock configuration directly imaged with micro‐computed tomography (micro‐CT) techniques. We first identify interfaces of the fluid‐fluid and fluid‐solid by their zero level set functions. This is accomplished by reinitializing the level set functions with a signed distance function. Then the three‐phase contact line is determined at the crossover of the two zero level set functions that represent the two interfaces. The normal vectors of both surfaces are calculated directly using the two level set functions, and the contact angle is found from the dot product of these vectors where they meet at the contact line. We first validated our newly proposed method for the semianalytically calculated fluid configurations in a 2‐D tube and then tested the algorithm on a synthetic spherical oil droplet residing on a tilted flat solid surface where the contact angle is analytically defined. It was then used to measure the in situ contact angle of droplets directly imaged by micro‐CT, and the results are compared with the manually and other available automatically measured results. Compared with other available automatic approaches, our approach is mathematically well defined, and it does not require any other complicated tuning procedures for surface smoothing. This proposed approach allow us to accurately characterize local in situ pore‐scale wettability, which is essential to model multiphase flow in porous media and eventually help us to design and assess optimal processes, such as hydrocarbon recovery and carbon dioxide storage.

Evaluation of Relative Permeability From Resistivity Data for Fractal Porous Media

The characteristics of multiphase flow in porous media are of great significance to various applications, such as reservoir evaluation and engineering geology. The analogy between fluid flow and electric flow provides a new idea for studying multiphase flow properties from geophysical resistivity data. However, a theoretical relationship between relative permeability and resistivity index, which is the key to the successful joint interpretation of multiphase flow and rock electric characteristics in porous media, is poorly understood. Based on fractal theory, a relative permeability-resistivity index model is developed to accurately describe the link between the rock electric and multiphase flow characteristics. The relative permeability is found not only to be related to fluid saturation and resistivity index, but also to be affected by structural parameters, such as the tortuosity fractal dimension, pore fractal dimension, water-phase fractal dimension, and tortuosity ratio. The proposed model reveals the significant effect of structural parameters on the resistivity index and relative permeability, on the other hand, the study provides an effective method to calculate the relative permeability from the resistivity data. By applying the relative permeability-resistivity index model to real cases, it shows that the predicted relative permeability results calculated by our model are in good agreement with experimental data.

Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

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We present continuum-scale modeling of multiphase compressible flow in porous media with applications to hydrocarbon reservoir engineering. A new black-oil model is developed and compared with a fully compositional simulator to model the thermodynamic phase behavior. In the context of black-oil modeling, where components are lumped into a gas and liquid pseudocomponent with only the gas transferring between liquid and gas phases, we allow for a variable bubble point pressure (e.g., when gas enters an undersaturated zone). Traditionally, a primary variable switching strategy has been used, which is known to be prone to convergence and phase identification issues. Instead, we adopt an overall molar composition-based framework that can robustly model phase appearance or disappearance. Phase properties across a broad range of pressures for different black-oil compositions are constructed from compositional phase split calculations to correctly model the phase transition. Mass transport is updated explicitly by a locally mass conserving multilinear discontinuous Galerkin method. Globally continuous pressure and velocity fields are obtained through an implicit mixed hybrid FE scheme. The robustness and accuracy of our FE simulator are demonstrated in several problems, where we have attained considerable speed-up and maintained the accuracy with the new black-oil model.

Two-phase multiscale numerical framework for modeling thin films on curved solid surfaces in porous media

Complex solid geometries, subgrid thin films, and interfacial deformations are critical for studying multiphase flows in porous media. However, it is challenging to accurately predict the flow evolution in porous media because of the difficulties in capturing the fluid-solid and fluid-fluid interactions in complex-shaped confinements at the pore-scale. In this work, we propose a multiscale continuum framework enabling the accurate simulation of the multiphase flow physics in complex porous media. Within this framework, we couple an efficient and accurate incompressible Navier-Stokes solver developed on a fixed Cartesian grid with a level-set method designed for capturing the interface between immiscible two-phase flows at low Capillary numbers. To capture the effects of complex solid boundaries on the flow dynamics, we employ an immersed boundary method based on a direct forcing approach. Most importantly, we develop a subgrid-scale thin-film model on a cylindrical coordinate around the curved solid surfaces to resolve the thin liquid films below the grid resolution and capture their effects on the fluid-fluid interfaces. The proposed multiscale framework illustrates how the embedded subroutines such as the level-set approach, the immersed boundary method, and the thin-film model can be coupled in order to capture the crucial physics involved in multiphase flow within porous media at different length scales.

Analytical model for gravity segregation of horizontal multiphase flow in porous media

Simultaneous horizontal injection of two immiscible fluids into a porous medium gives rise to three regions of constant saturation. Due to gravity impact, the region with fluid saturation reflecting the volume fraction and viscosity ratio of the injected fluids morphs into two horizontal layers fully saturated with one fluid or the other. The location of the discontinuity separating constant saturation regions is often estimated with the Stone–Jenkins (SJ) formula. Our numerical simulations of multiphase flow in porous media demonstrate that, for a wide range of hydraulic parameters of practical significance, the SJ formula has substantial error. We derive an approximate analytical solution, which neglects the vertical component of flow velocity and introduces a correction factor to enforce mass conservation. Comparison with numerical simulations reveals that our solution is accurate in the parameter regimes for which the SJ formula is not and vice versa. The two solutions are complementary, covering the entire range of physically realizable parameters.

Transport Modelling of Multi-Phase Fluid Flow in Porous Media for Enhanced Oil Recovery

This article studies the combined effect of spatial heterogeneity and capillary pressure on the saturation of two fluids during the injection of immiscible nanoparticles. Various literature review exhibited that the nanoparticles are helpful in enhancing the oil recovery by varying several mechanisms, like wettability alteration, interfacial tension, disjoining pressure and mobility control. Multiphase modelling of fluids in porous media comprise balance equation formulation, and constitutive relations for both interphase mass transfer and pressure saturation curves. A classical equation of advection-dispersion is normally used to simulate the fluid flow in porous media, but this equation is unable to simulate nanoparticles flow due to the adsorption effect which happens. Several modifications on computational fluid dynamics (CFD) have been made to increase the number of unknown variables. The simulation results indicated the successful transportation of nanoparticles in two phase fluid flow in porous medium which helps in decreasing the wettability of rocks and hence increasing the oil recovery. The saturation, permeability and capillary pressure curves show that the wettability of the rocks increases with the increasing saturation of wetting phase (brine).

Workflow for Upscaling Wettability from the Nanoscale to Core Scale

Wettability is a key factor influencing multiphase flow in porous media. In addition to the average contact angle, the spatial distribution of contact angles throughout the porous medium is important, as it directly controls the connectivity of wetting and nonwetting phases. The controlling factors may not only relate to the surface chemistry of minerals but also to their texture, which implies that a length-scale range from nanometers to centimeters has to be considered. So far, an integrated workflow addressing wettability consistently through the different scales does not exist. In this study, we demonstrate that such a workflow is possible by combining microcomputed tomography (mu CT) imaging with atomic-force microscopy (AFM). We find that in a carbonate rock, consisting of 99.9% calcite with a dual-porosity structure, wettability is ultimately controlled by the surface texture of the mineral. Roughness and texture variation within the rock control the capillary pressure required for initializing proper crude oil-rock contacts that allow aging and subsequent wettability alteration. AFM enables us to characterize such surface-fluid interactions and to investigate the surface texture. In this study, we use AFM to image nanoscale fluid-configurations in 3D at connate water saturation and compare the fluid configuration with simulations on the rock surface, assuming different capillary pressures.

Numerical Simulation of Unstable Preferential Flow during Water Infiltration into Heterogeneous Dry Soil

Water infiltration and unsaturated flow through heterogeneous soil control the distribution of soil moisture in the vadose zone and the dynamics of groundwater recharge, providing the link between climate, biogeochemical soil processes and vegetation dynamics. Infiltration into dry soil is hydrodynamically unstable, leading to preferential flow through narrow wet regions (fingers). In this paper we use numerical simulation to study the interplay between fingering instabilities and soil heterogeneity during water infiltration. We consider soil with heterogeneous intrinsic permeability. Permeabilities are random, with point Gaussian statistics, and vary smoothly in space due to spatial correlation. The key research question is whether the presence of moderate or strong heterogeneity overwhelms the fingering instability, recovering the simple stable displacement patterns predicted by most simplified model of infiltration currently used in hydrological models from the Darcy to the basin scales. We perform detailed simulations of constant-rate infiltration into soils with isotropic and anisotropic intrinsic permeability fields. Our results demonstrate that soil heterogeneity does not suppress fingering instabilities, but it rather enhances its effect of preferential flow and channeling. Fingering patterns strongly depend on soil structure, in particular the correlation length and anisotropy of the permeability field. While the finger size and flow dynamics are only slightly controlled by correlation length in isotropic fields, layering leads to significant finger meandering and bulging, changing arrival times and wetting efficiencies. Fingering and soil heterogeneity need to be considered when upscaling the constitutive relationships of multiphase flow in porous media (relative permeability and water retention curve) from the finger to field and basin scales. While relative permeabilities remain unchanged upon upscaling for stable displacements, the inefficient wetting due to fingering leads to relative permeabilities at the field scale that are significantly different from those at the Darcy scale. These effective relative permeability functions also depend, although less strongly, on heterogeneity and soil structure.

An implicit local time-stepping method based on cell reordering for multiphase flow in porous media

We discuss how to introduce local time-step refinements in a sequential implicit method for multiphase flow in porous media. Our approach relies heavily on causality-based optimal ordering, which implies that cells can be ordered according to total fluxes after the pressure field has been computed, leaving the transport problem as a sequence of ordinary differential equations, which can be solved cell-by-cell or block-by-block. The method is suitable for arbitrary local time steps and grids, is mass-conservative, and reduces to the standard implicit upwind finite-volume method in the case of equal time steps in adjacent cells. The method is validated by a series of numerical simulations. We discuss various strategies for selecting local time steps and demonstrate the efficiency of the method and several of these strategies by through a series of numerical examples.