An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume averaging principles, where a unique set of partial differential equations is used to represent flow in both regions and scales. The crux of the proposed model is that it tends asymptotically towards the Navier-Stokes volume-of-fluid approach in solid-free regions and towards the multiphase Darcy equations in porous regions. Unlike existing multiscale multiphase solvers, it can match analytical predictions of capillary, relative permeability, and gravitational effects at both the pore and Darcy scales. Through its open-source implementation, hybridPorousInterFoam, the proposed approach marks the extension of computational fluid dynamics (CFD) simulation packages into porous multiscale, multiphase systems. The versatility of the solver is illustrated using applications to two-phase flow in a fractured porous matrix and wave interaction with a porous coastal barrier.
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise quantification of the permeability of a porous sample, a number of extensions to the lattice Boltzmann method are available which allow to study multiphase and multicomponent flows on a pore scale level. In this article we give an extensive overview on a number of these diffuse interface models and discuss their advantages and disadvantages. Furthermore, we shortly r…
Sub-resolution porosity (SRP) is an ubiquitous, yet often ignored, feature in Digital Rock Physics. It embodies the trade-off between image resolution and field-of-view, and it is a direct result of choosing an imaging resolution that is larger than the smallest pores in a heterogeneous rock sample. In this study, we investigate the impacts of SRP on multiphase flow in porous rocks. To do so, we use our newly developed Multiphase Micro-Continuum model to perform first-of-a-kind direct numerical simulations of two-phase flow in porous samples containing SRP. We show that SRP properties (porosit…
A two-phase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically compatible systems and on a model of nonlinear elastoplasticity combined with a two-phase compressible fluid flow model. The governing equations of the model include phase mass conservation laws, a total momentum conservation law, an equation for the relative velocities of the phases, an equation for mixture distortion, and a balance equation for porosity. They…
Dynamic multiphase flow triggers chaotic mixing in porous media
University of Oslo（奥斯陆大学）；Norwegian University of Science and Technology（挪威科技大学）；University of Copenhagen（哥本哈根大学）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Univ. Savoie Mont Blanc（萨瓦蒙布朗大学）；Univ. Gustave Eiffel（古斯塔夫·埃菲尔大学）；Université de Rennes（雷恩大学）
Porous asphalt (PA) is an open-graded porous material with a porosity of 20%, allowing fast drainage of rain and improving driving and acoustic conditions. However, the high porosity leads to significant contact with water resulting in a shorter life expectancy. To improve the durability and performance of PA, the distribution of water and its residence time have to be understood which entails capturing diverse multiphase phenomena. For these reasons, a numerical study is performed to analyze in detail the fluid transport mechanisms at play in PA, towards estimating the liquid distribution ins…
In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3D heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural networks, and is coupled with an efficient continuity-based smoother to predict flow responses that need spatial continuity. Furthermore, the transient regions are penalized to steer the training process such that the model can accurately capture flow in these regions. The model takes inputs including properties of porous media, fluid properties and well controls…
Learning and Inferring Multiphase Flow Dynamics in Porous Media using Scientific Machine Learning: Application to the "FluidFlower" CO2 Injection Experiment
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Massachusetts Institute of Technology（麻省理工学院）
Simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing partial-differential equations (PDEs) into algebraic systems via numerical methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint. Therefore, developing cost-effective, data-driven models can become a practical choice since deep learning ap…
Solute dispersion in magnetically influenced multiphase flow through a porous tube: axial transport and microrotational effects
Cooch Behar Panchanan Barma University（古奇比哈尔潘查南·巴尔马大学）；SRM Institute of Science and Technology（SRM科学技术研究所）；University of Galway（高威大学）；Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）
In reservoir simulation, solution of the coupled systems of nonlinear algebraic equations that are associated with fully-implicit (backward Euler) discretization is challenging. Having a robust and efficient nonlinear solver is necessary in order for reservoir simulation to serve as the primary tool for managing the recovery processes of large-scale reservoirs. Here, we develop a continuation method based on the use of a dissipation operator. We focus on nonlinear two-phase flow and transport in heterogeneous formations in the presence of viscous, gravitational, and capillary forces. The homot…
Efficient multiphysics models that can adapt to the varying complexity of physical processes in space and time are desirable for modeling fluid migration in the subsurface. Vertical equilibrium (VE) models are simplified mathematical models that are computationally efficient but rely on the assumption of instant gravity segregation of the two phases, which may not be valid at all times or at all locations in the domain. Here, we present a multiphysics model that couples a VE model to a full multidimensional model that has no reduction in dimensionality. We develop a criterion that determines s…
Direct pore scale simulations of two-fluid flow on digital rock images provide a promising tool to understand the role of surface wetting phenomena on flow and transport in geologic reservoirs. We present computational protocols that mimic conventional special core analysis laboratory (SCAL) experiments, which are implemented within the open source LBPM software package. Protocols are described to simulate unsteady displacement, steady-state flow at fixed saturation, and to mimic centrifuge experiments. These methods can be used to infer relative permeability and capillary curves, and otherwis…
Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operator
Khalifa University of Science and Technology（哈利法科技大学）；UAE University（阿联酋大学）；College of Petroleum Engineering and Geosciences, KFUPM（法赫德国王石油与矿业大学石油工程与地球科学学院）
In this study, we develop a probabilistic approach to map the parametric uncertainty to the output state uncertainty in first-order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two-phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from the incomplete description of either porosity field, injection flux, or both. The uncertainty in the total-velocity field leads to the spatiotemporal uncertainty in the saturation field. Given information about the spatial/temporal statis…
In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver, generally Newton(-Raphson). Strong nonlinearities can cause Newton iterations to converge very slowly. This frequently results in time step cuts, leading to computationally expensive simulations. Much literature has looked into how to improve the nonlinear solver through enhancements or safeguarding updates. In this work, we take a different approach; we aim to i…
Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations [Schmuck et al., Proc. R. Soc. A 468:3705-3724, 2012.], we rigorously derive an effective macroscopic phase field formulation under the assumption of periodic flow and a sufficiently large Péclet number. As for classical convection-diffusion problems, we obtain systematically diffusion-disp…
Pore-network modeling is a widely used predictive tool for pore-scale studies in various applications that deal with multiphase flow in porous media. Despite recent improvements to enable pore-network modeling on simplified pore geometry extracted from rock images and its computational efficiency compared to direct numerical simulation methods, there are still limitations to modeling a large representative pore-network for heterogeneous cores. These are due to the technical limits on sample size to discern void space during imaging and computational limits on pore-network extraction algorithms…
Numerical Simulation of Oscillating Multiphase Heat Transfer in Parallel plates using Pseudopotential Multiple-Relaxation-Time Lattice Boltzmann Method
Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) con…
The lattice Boltzmann method (LBM) is a popular numerical framework to investigate single and multiphase flow though porous media. For estimation of absolute permeability based on micro-tomographic images of the porous medium, the single-relaxation time (SRT) collision model is the most widely-used, although the multiple-relaxation-time (MRT) collision model also has recently acquired wider usage, especially for industrial applications. However, the SRT collision model and a sub-optimal choice of the MRT collision parameters can both lead to permeability predictions that depend on the relaxati…
