Accurately predicting the behaviour of multiphase flows is a problem of immense industrial and scientific interest. Modern computers can now study the dynamics in great detail and these simulations ...yield unprecedented insight. This book provides a comprehensive introduction to direct numerical simulations of multiphase flows for researchers and graduate students. After a brief overview of the context and history the authors review the governing equations. A particular emphasis is placed on the 'one-fluid' formulation where a single set of equations is used to describe the entire flow field and interface terms are included as singularity distributions. Several applications are discussed, showing how direct numerical simulations have helped researchers advance both our understanding and our ability to make predictions. The final chapter gives an overview of recent studies of flows with relatively complex physics, such as mass transfer and chemical reactions, solidification and boiling, and includes extensive references to current work.
Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this ...all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away.
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 mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO2 storage sites, where CO2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and CO2 saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.
•A workflow based on Gradient-based deep neural network (GDNN) emulates multiphase flow in porous media with high fidelity.•Differential operators derived from the governing PDEs are used as first principle prior knowledge to regularize the training of GDNN.•GDNN is further successfully extended to image-based approaches such as convolutional neural networks (CNN).
Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative ...to traditional simulators. Here we present U-FNO, a novel neural network architecture for solving multiphase flow problems with superior accuracy, speed, and data efficiency. U-FNO is designed based on the newly proposed Fourier neural operator (FNO), which has shown excellent performance in single-phase flows. We extend the FNO-based architecture to a highly complex CO2-water multiphase problem with wide ranges of permeability and porosity heterogeneity, anisotropy, reservoir conditions, injection configurations, flow rates, and multiphase flow properties. The U-FNO architecture is more accurate in gas saturation and pressure buildup predictions than the original FNO and a state-of-the-art convolutional neural network (CNN) benchmark. Meanwhile, it has superior data utilization efficiency, requiring only a third of the training data to achieve the equivalent accuracy as CNN. U-FNO provides superior performance in highly heterogeneous geological formations and critically important applications such as gas saturation and pressure buildup “fronts” determination. The trained model can serve as a general-purpose alternative to routine numerical simulations of 2D-radial CO2 injection problems with significant speed-ups than traditional simulators.
•U-FNO model for multiphase flow designed based on Fourier neural operator.•Data-efficient multiphase flow predictions for gas saturation and pressure buildup.•Results are significantly faster and more accurate than state-of-the-art CNNs.
A multiphase lattice Boltzmann flux solver (MLBFS) is proposed in this paper for incompressible multiphase flows with low- and large-density-ratios. In the solver, the flow variables at cell centers ...are given from the solution of macroscopic governing differential equations (Navier–Stokes equations recovered by multiphase lattice Boltzmann (LB) model) by the finite volume method. At each cell interface, the viscous and inviscid fluxes are evaluated simultaneously by local reconstruction of solution for the standard lattice Boltzmann equation (LBE). The forcing terms in the governing equations are directly treated by the finite volume discretization. The phase interfaces are captured by solving the phase-field Cahn–Hilliard equation with a fifth order upwind scheme. Unlike the conventional multiphase LB models, which restrict their applications on uniform grids with fixed time step, the MLBFS has the capability and advantage to simulate multiphase flows on non-uniform grids. The proposed solver is validated by several benchmark problems, such as two-phase co-current flow, Taylor–Couette flow in an annulus, Rayleigh–Taylor instability, and droplet splashing on a thin film at density ratio of 1000 with Reynolds numbers ranging from 20 to 1000. Numerical results show the reliability of the proposed solver for multiphase flows with high density ratio and high Reynolds number.
In this paper, an improved SPH model for multiphase flows with complex interfaces and large density differences is developed. The multiphase SPH model is based on the assumption of pressure ...continuity over the interfaces and avoids directly using the information of neighboring particles' densities or masses in solving governing equations. In order to improve computational accuracy and to obtain smooth pressure fields, a corrected density re-initialization is applied. A coupled dynamic solid boundary treatment (SBT) is implemented both to reduce numerical oscillations and to prevent unphysical particle penetration in the boundary area. The density correction and coupled dynamics SBT algorithms are modified to adapt to the density discontinuity on fluid interfaces in multiphase simulation. A cut-off value of the particle density is set to avoid negative pressure, which can lead to severe numerical difficulties and may even terminate the simulations. Three representative numerical examples, including a Rayleigh–Taylor instability test, a non-Boussinesq problem and a dam breaking simulation, are presented and compared with analytical results or experimental data. It is demonstrated that the present SPH model is capable of modeling complex multiphase flows with large interfacial deformations and density ratios.
Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the ...mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.
•A multiphase projection-based particle method for flows of large density ratios and discontinuous density fields.•A computational algorithm on the basis of optimized particle shifting is ...incorporated for interface stabilization.•Validations and comparisons are conducted through several multiphase benchmark tests.•An extended version of an iterative shifting scheme is implemented and tested.•The present study portrays the robustness of particle shifting concept for multiphase particle-based simulations.
A novel projection-based particle method is presented for simulation of multiphase flows characterized by large density ratios and discontinuous density fields at the phase interface. The method considers a multi-fluid continuous system and comprises of a specific computational algorithm utilizing the recently developed Optimized Particle Shifting (OPS 1) scheme to maintain the regularity of particles at the phase interface and free-surface. The method is founded on an improved version of Moving Particle Semi-implicit (MPS 2) as a projection-based particle method. A set of previously developed improved schemes are also adopted and hence the proposed method is referred to as improved MPS + OPS. Validations are made both qualitatively and quantitatively in terms of accuracy, energy conservation properties as well as convergence properties by consideration of several benchmark tests.
•Mesoscale structures in fluid-particle systems were reviewed.•Multiscale simulation methods for fluid-particle systems were reviewed.•Formation mechanism, experiment and simulation of mesoscale ...structures were summarized.•Measurement and simulation methods of porous particles or reactive particles were introduced.
This article reviews the general features of the multiscale structures in particle–fluid systems and the characterization, modeling, and simulation methods for these systems. The discussion focuses on the effects of mesoscale behavior, especially those present in process industries for materials and energy transformation and utilization. When there is substantial multiscale heterogeneity in these systems, local non-equilibrium and anisotropy generally lead to a lack of scale separation. Accurate and efficient simulation methods based on first principles and applied across different scales are highly desirable to reveal and quantify the complexities of these systems. Meanwhile, precisely designed experiments and exhaustive nonintrusive measurements are necessary to validate and expand the numerical findings. With this knowledge, rational mesoscale models can be established to provide multiscale simulation methods that do not need to fully reproduce the micro- and mesoscale details of the systems but can still take into account their effects on macroscales. Such multiscale methods are attractive for industrial applications but substantial effort in physical modeling and numerical implementation is still required before their widespread implementation.
► An enhanced stabilized Moving Particle Semi-implicit method is developed. ► A novel scheme is proposed for consistent modeling of density at a phase interface. ► The new scheme minimizes interface ...unphysical perturbations and density diffusions. ► The significance of a Taylor series consistent gradient model is highlighted. ► Detailed verifications are performed to show the enhancements and stabilizations.
The paper presents an enhanced stabilized MPS (Moving Particle Semi-implicit) method for simulation of multiphase flows characterized by high density ratios. The developed method benefits from four previously developed schemes 1 as well as a novel one proposed for accurate, consistent modeling of density at the phase interface. The new scheme can be considered as an extended version of a commonly applied density smoothening scheme and is shown to keep the sharpness of spatial density variations while enhancing the stability and performance of simulations. Further, the paper highlights the importance of applying a Taylor series consistent scheme for calculation of pressure gradient in multiphase MPS-based simulations. By presenting a simple perturbation analysis, it is shown that some commonly applied MPS-based pressure gradient models are prone to increase the level of unphysical perturbations at the phase interface leading to numerical instabilities. The original MPS gradient model with a Gradient Correction 1 is shown to provide stable and accurate results even in case of violent multiphase flows characterized by high density ratios.
