Multiphase Flow Problems Research Articles

CFD Study of Cuttings Transport through Vertical Wellbore

Cuttings transportation from the bit up the annulus to the surface is one the essentialfunctions that are performed by drilling fluid. Predication of drilling fluid efficiency totransport cuttings in the annulus is very complicated due to numerous parameters that haveaffected drilling operations. Computational Fluid Dynamics (CFD) is widely used as anumerical technique in handling complex multiphase flow problems in differentoperational conditions.The present work has taken the advancement of CFD to computationally analyse theinfluence of the effects of various parameters like drilling fluid rheology, flow rate, piperotation, cuttings density, shape, concentration and drilling fluid- cuttings particle couplingregimes on the cuttings transport in a vertical wellbore. The CFD simulation was carriedout by using transient solver of ANSYS-FLUENT CFD commercial code.The dense discrete phase model (DDPM) is suggested in this work to overcome themain shortcomings of Eulerian–Eulerian and CFD-DEM approaches in simulating drillingfluid-cuttings flow. Also, some of the experimental investigations were involved indetermining the fluid physical properties and essential input data to perform the CFDsimulations. Regarding the results validation and verification, well agreement has beenachieved between results obtained in this study with those reported in other studies

Numerical investigation of the effects of free surface on tip-leakage vortex cavitation behaviors over a NACA0009 hydrofoil

Tip-leakage vortex (TLV) cavitation is complex and challenging multiphase flow problem in propulsion equipment. In this paper, the large-eddy method and the Schnerr–Sauer cavitation model are combined to simulate a NACA0009 hydrofoil near the free surface. The numerical method used is validated by comparing the characteristics of TLV cavitation with available experimental data. The results show that the free surface affects the evolution of the cavitation and the characteristics of the hydrodynamic load. The lift and drag coefficient of the TLV hydrofoil decreases for the near free surface case, but the pulsation frequency of the lift coefficient increases. Meanwhile, the mechanism of the TLV near the free surface is found by comparing that case to a “no free surface” scenario. Moreover, an improved dynamic mode decomposition (DMD) method is used to investigate the unsteady cavitation flow characteristic of the TLV. The results show the main flow features of the TLV cavitation including the coherent structure and energy distribution are closely related to the existence of free surfaces by analyzing the first two modes based on the DMD method.

Generalized pressure-correction for viscous potential flow simulations of multiphase flows using boundary element method

A new formulation for correcting the pressure field in Viscous Potential Theory (VPT) is developed, generalizing previous Viscous Pressure Correction (VPC) methods to simulate multi-phase flows based on VPT. The latter theory is now applicable to a wider range of flow problems. Without limiting the general applicability of the formulation, the present work focuses on the dynamics of two-dimensional liquid blobs and liquid films in a void. The governing equations of the method are solved using the traditional Boundary Element Method together with fourth-order Runge-Kutta time-integration, thereby reducing the spatial dimension of the problem by one and increasing the computational efficiency dramatically as compared to general purpose solvers for interfacial flows. Verification and Validation of the new method and algorithm are carried out through comparison of the simulation results with those obtained from (semi-)analytical models, a general-purpose OpenFOAM solver with Volume-of-Fluid interface treatment, and a Smoothed-Particle Hydrodynamics solver. Several benchmark cases and a wide range of viscosities are considered. Significantly improved accuracy of the newly proposed method as compared to the original Viscous Pressure Correction of Viscous Potential Flow (VCVPF) approach is demonstrated for the case of a retracting free liquid film or ligament. In order to demonstrate the capacity of the present method and algorithm in handling complex multiphase flow problems and in providing physical insight into such phenomena, the disintegration mechanism of a strongly modulated discharging liquid sheet under the influence of gravity is analyzed.

A diffuse-interface method for reducing spurious pressure oscillations in multicomponent transcritical flow simulations

Spurious pressure oscillations are a numerical instability that is commonly observed in multiphase and multicomponent flow problems near the critical point. A diffuse-interface model has been created to simulate transcritical mixing in multispecies and multiphase systems where spurious pressure oscillations pose a serious challenge in achieving convergence. To reduce the spurious pressure oscillations, three methods have been proposed and implemented in the present paper: (1) artificially thickening the interface between different species, (2) reconstruction of the primitive variables in the characteristics space, and (3) developing a hybrid method (HY) that switches between quasi-conservative (QC) double-flux (DF) and the classical fully-conservative numerical procedures based on the changes in the effective specific heat ratio and the effective reference internal energy. The cases considered include (1) a transcritical shock tube problem between nitrogen and n-dodecane, (2) a near-critical shock-droplet interaction, and (3) the transcritical Spray A benchmark case of Engine Combustion Network (ECN) that represents the injection of n-dodecane into a high-pressure and high-temperature nitrogen environment. Characteristic-wise reconstruction of the primitive variables in our proposed fully-conservative method tends to reduce the spurious pressure oscillations compared to primitive-wise reconstruction including the reconstruction of the speed of sound. The HY model is found to effectively reduce the magnitude of the spurious pressure oscillations, the loss of energy conservation, and provides more accurate results for all tested cases. The artificial thickening of the interface between different species is found to reduce spurious pressure oscillations and reduce energy conservation loss when used in conjunction with a QC method (HY or DF).

Solving inverse problems using conditional invertible neural networks

Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex physical system of interest often expressed in the form of multiscale PDEs, the high-dimensionality of the spatial property of interest, and the incomplete and noisy nature of observations. To address these challenges, we develop a model that maps the given observations to the unknown input field in the form of a surrogate model. This inverse surrogate model will then allow us to estimate the unknown input field for any given sparse and noisy output observations. Here, the inverse mapping is limited to a broad prior distribution of the input field with which the surrogate model is trained. In this work, we construct a two- and three-dimensional inverse surrogate models consisting of an invertible and a conditional neural network trained in an end-to-end fashion with limited training data. The invertible network is developed using a flow-based generative model. The developed inverse surrogate model is then applied for an inversion task of a multiphase flow problem where given the pressure and saturation observations the aim is to recover a high-dimensional non-Gaussian log-permeability field where the two facies consist of heterogeneous log-permeability and varying length-scales. For both the two- and three-dimensional surrogate models, the predicted sample realizations of the non-Gaussian log-permeability field are diverse with the predictive mean being close to the ground truth even when the model is trained with limited data.

Comparative analysis of parallel algorithms for solving oil recovery problem using CUDA and OpenCL

‎In this paper the implementation of parallel algorithm of alternating direction implicit (ADI) method has been considered‎. ‎ADI parallel algorithm is used to solve a multiphase multicomponent fluid flow problem in porous media‎. ‎There are various technologies for implementing parallel algorithms on the CPU and GPU for solving hydrodynamic problems‎. ‎In this paper GPU-based (graphic processor unit) algorithm was used‎. ‎To implement the GPU-based parallel ADI method‎, ‎CUDA and OpenCL were used‎. ‎ADI is an iterative method used to solve matrix equations‎. ‎To solve the tridiagonal system of equations in ADI method‎, ‎the parallel version of cyclic reduction (CR) method was implemented‎. ‎The cyclic reduction is a method for solving linear equations by repeatedly splitting a problem as a Thomas method‎. ‎To implement of a sequential algorithm for solving the oil recovery problem‎, ‎the implicit Thomas method was used‎. ‎Thomas method or tridiagonal matrix algorithm is used to solve tridiagonal systems of equations‎. ‎To test parallel algorithms personal computer installed Nvidia RTX 2080 graphic card with 8 GB of video memory was used‎. ‎The computing results of parallel algorithms using CUDA and OpenCL were compared and analyzed‎. ‎The main purpose of this research work is a comparative analysis of the parallel algorithm computing results on different technologies‎, ‎in order to show the advantages and disadvantages each of CUDA and OpenCL for solving oil recovery problems‎.

An implicit bounding formulation for the volume fraction equation in multiphase flows

The solution of the volume fraction equations in multiphase flows has to satisfy geometric conservation, that is, the volume fraction fields at each control volume sum to 1. Enforcing this constraint on the volume fraction fields is critical for all multiphase flow applications especially for cases involving mass transfer. This article reviews some of the techniques used to enforce geometric conservation when solving the volume fraction equations for general multiphase flows, including free surface flows. An implicit method is then introduced and applied to a number of multiphase and free surface flow problems. It is compared to the current explicit approaches and its effectiveness in enforcing the geometric conservation demonstrated.

An extension of the multiple marker algorithm for study of phase separation problems at the mesoscale

Multiphase fluid flow is an active field of research in numerous branches of science and technology. An interesting subset of multiphase flow problems involves the dispersion of one phase into another in the form of many small bubbles or droplets, and their subsequent separation back into bulk phases after this has occurred. Phase dispersion may be a desirable effect, for example in the production of emulsions of otherwise immiscible liquids or to increase interfacial surface area for chemical reactions, or an undesirable one, for example in the intermixing of waste and product phases during processing or the generation of foams preventing gas-liquid decoupling. The present paper describes a computational fluid dynamics method based on the multiple marker front-capturing algorithm – itself an extension of the volume-of-fluids method for multiphase flow – which is capable of scaling to mesoscale systems involving thousands of droplets or bubbles. The method includes sub-grid models for solution of the Reynolds equation to account for thin film dynamics and rupture. The method is demonstrated with an implementation in the OpenFOAM® computational mechanics framework. Comparisons against empirical data are presented, together with a performance benchmarking study and example applications.

Numerical modeling of multiphase compressible flows with the presence of shock waves using an interface-sharpening five-equation model

An accurate shock- and interface-capturing method is introduced for simulations of compressible multiphase flows. First, an associated Godunov-type numerical scheme is established for a five-equation two-phase model obtained from a seven-equation model by assuming a single velocity and a single pressure between two phases. The computational finite-volume Riemann solver using the scheme and computing algorithms is presented. Next, an interface-sharpening technique (IST) is extended for the compressible two-phase model to improve numerical simulations and correct diffusion errors. The modified IST was applied as postprocessing to correct the numerical diffusion error in the solution of the discretization scheme while maintaining a sharp interface with a desired thickness after each time step. A mixture-consistent interface regularization approach of all conservative variables is combined with the IST to obtain consistent thermodynamic laws for the mixture, ensuring the consistency of the variables in the correction process. Several examples of fluid interface simulations including shock-tube, shock-bubble interactions, and underwater explosions were performed to demonstrate the accuracy and capability of the proposed method. Those compressible multiphase flow problems are complicated by the presence of both shock waves and the dynamics of interfaces. Comparisons of the numerical method with theoretical results and experimental data indicate that the present method can simulate interface dynamics with the presence of shock waves and large density differences.

Numerical simulation of Rayleigh-Bénard convection and three-phase Rayleigh-Taylor instability using a modified MPS method

The main objective of the current work is to enhance consistency and capabilities of Moving Particle Semi-implicit (MPS) method for simulating a wide range of free-surface flows and convection heat transfer. For this purpose, two novel high-order gradient and Laplacian operators are derived from the Taylor series expansion and are applied for the discretization of governing equations. Furthermore, the combination of the explicit Third-order TVD Runge-Kutta scheme and two-step projection algorithm is employed to approximate transient terms in the Navier-stokes and energy equations. To further improve the accuracy and performance of the method, a new kernel function is constructed by a combination of the Gaussian and cosine functions and then implemented for modeling the 1D Sod shock tube problem. Validation and verification of the proposed model are conducted through the simulations of several canonical test cases such as: dam break, rotation of a square patch of fluid, two-phase Rayleigh-Taylor instability, oscillating concentric circular drop and good agreement are achieved. The proposed model is then employed to simulate three-phase Rayleigh-Taylor instability and entropy generation due to natural convection heat transfer (Differentially Heated Cavity and Rayleigh-Bénard convection). The obtained results reveal that, the newly constructed kernel function provides more reliable results in comparison with two frequently used kernel functions namely; quartic spline and Wendland. Furthermore, it is found that, the enhanced MPS model is capable of handling multiphase flow problems with low and high density contrast.

Reservoir history matching by ensemble smoother with principle component and sensitivity analysis for heterogeneous formations

Ensemble-based data assimilation methods have been widely investigated and applied for inverse problems of fluid flow in porous media during the past decades. Among these methods, the ensemble Kalman filter and the ensemble smoother are probably the most popular in history-matching applications. For large-scale problems, the ensemble size is limited to the computational resources in running the forward simulation, and is usually much smaller than the total number of gridblocks. In this case, the ensemble forms a reduced-order subspace, and principle component analysis is suggested by retaining the leading eigenvectors after truncation.In this paper, we propose to improve the ensemble smoother by proper orthogonal decomposition with optimal parameter selection. The motivation behind this method is that the estimation would be more accurate if the subspace spanned by the ensemble favors the dominant components. Specifically, the principle component analysis is first applied to obtain the eigenvalues and orthogonal eigenvectors. Then, a number of eigenvectors are selected according to importance from sensitivity analysis, rather than the eigenvalues. Finally, the ensemble smoother is implemented using these eigenvectors.The proposed method is illustrated by a simple mathematical example, and tested in a 2D single-phase and a 3D multiphase flow problem. The numerical results show that the traditional ensemble smoother may provide poor results in some ill-posed inverse problems, because some important features are lost in the randomly generated realizations. The principle component analysis alleviates this issue by sorting the eigenvectors based on energy, but it may still produce unsatisfactory results. The combination of sensitivity analysis and principle component analysis provides more accurate matching and prediction than those obtained from the previous two methods. The local sensitivity analysis is preferred since it is much more efficient than the global sensitivity analysis, and its accuracy is validated in the case studies.

A new Simulation Model for Grate Firing Systems in OpenFOAM

A grate firing system can be seen as a multiphase flow problem. High volume fractions of solid fuel particles travel over the grate of a power plant, while heterogeneous reactions occure at the surface of the particles in combination with homogeneous combustion reactions inside the flue gas. Up to now, grate firing systems are still difficult to simulate with standard computational fluid dynamics (CFD). The movement of the solid particles inside the fuel bed and their heterogeneous reactions are difficult to combine with the homogeneous reactions of the gas phase species and the heat transfer. The emitted radiation from the gas has to be coupled with the heat balance inside the fuel bed.To solve this problem, we integrated a new library into a open source CFD code for coupling radiation models with the solids phase. We describe how to handle the workflow of the new library and present simulation results for two different furnace designs. An automatic mesh generator was developed. The work closes with simulation results for two different grate firing systems. Heterogeneous reactions and homogeneous reactions, as well as temperature fields inside the phase are presented. A validation of the simulations against measurement data is given.

Multi-phase fluid flow simulation by using peridynamic differential operator

The problems of multi-phase fluid flows are often encountered in engineering. In this study, a non-local numerical model of multi-phase fluid flows in the Lagrangian description is developed. Based on the peridynamic theory, a peridynamic differential operator is proposed which can convert any arbitrary order of differentials into their integral form without calculating the peridynamic parameters. Therefore, the Navier-Stokes equations including the surface tension forces are reformulated into their integral form. Subsequently, an updated Lagrangian algorithm for solving the multi-phase fluid flow problems is proposed. Besides, the particle shifting technology and moving least square algorithm are also adopted to avoid the possible tension instability. Finally, several benchmark multi-phase fluid flow problems such as two-phase hydrostatic problem, two-phase Poiseuille flow, and 2D square droplet deformation are solved to validate the proposed non-local model. It can be concluded from the current study that the peridynamic differential operator can be applied as an alternative method for multi-phase fluid flow simulation.

A mimetic method for polygons

A new method for mimetic interpolation on polygonal meshes is described. This new method is based on harmonic function interpolation. Explicit formulas for harmonic functions on general polygons do not exist, so truncated harmonic polynomial expansions are used for computational efficiency. We show that the naive harmonic polynomial expansion, is not stable for arbitrary polygons. However, higher level truncations of harmonic interpolations are stable and accurate. This new method is shown to be a direct extension of the lowest order Raviart-Thomas finite elements to polygons. This method is also a direct extension of the finite volume MAC method to polygons. The accuracy of the interpolation is shown to be first-order irrespective of the polynomial truncation level. However the accuracy of vector Laplace equation solutions using this inner product is shown to be second-order accurate, in keeping with other lowest order Mimetic methods. The versatility of this numerical method is demonstrated on a multiphase incompressible flow problem with a density jump of 1000, on a moving polygonal mesh.

Host-to-host airborne transmission as a multiphase flow problem for science-based social distance guidelines

The COVID-19 pandemic has strikingly demonstrated how important it is to develop fundamental knowledge related to the generation, transport and inhalation of pathogen-laden droplets and their subsequent possible fate as airborne particles, or aerosols, in the context of human to human transmission. It is also increasingly clear that airborne transmission is an important contributor to rapid spreading of the disease. In this paper, we discuss the processes of droplet generation by exhalation, their potential transformation into airborne particles by evaporation, transport over long distances by the exhaled puff and by ambient air turbulence, and their final inhalation by the receiving host as interconnected multiphase flow processes. A simple model for the time evolution of droplet/aerosol concentration is presented based on a theoretical analysis of the relevant physical processes. The modeling framework along with detailed experiments and simulations can be used to study a wide variety of scenarios involving breathing, talking, coughing and sneezing and in a number of environmental conditions, as humid or dry atmosphere, confined or open environment. Although a number of questions remain open on the physics of evaporation and coupling with persistence of the virus, it is clear that with a more reliable understanding of the underlying flow physics of virus transmission one can set the foundation for an improved methodology in designing case-specific social distancing and infection control guidelines.

Accelerated Multilevel Monte Carlo With Kernel‐Based Smoothing and Latinized Stratification

AbstractHeterogeneity and a paucity of measurements of key material properties undermine the veracity of quantitative predictions of subsurface flow and transport. For such model forecasts to be useful as a management tool, they must be accompanied by computationally expensive uncertainty quantification, which yields confidence intervals, probability of exceedance, and so forth. We design and implement novel multilevel Monte Carlo (MLMC) algorithms that accelerate estimation of the cumulative distribution functions (CDFs) of quantities of interest, for example, water breakthrough time or oil production rate. Compared to standard non‐smoothed MLMC, the new estimators achieve a significant variance reduction at each discretization level by smoothing the indicator function with a Gaussian kernel or replacing standard Monte Carlo (MC) with the recently developed hierarchical Latinized stratified sampling (HLSS). After validating the kernel‐smoothed MLMC and HLSS‐enhanced MLMC methods on a single‐phase flow test bed, we demonstrate that they are orders of magnitude faster than standard MC for estimating the CDF of breakthrough times in multiphase flow problems.

Numerical simulation of water entry of an inclined cylinder

Water entry of cylindrical structures is a complex multiphase flow problem involving a three-phase medium interaction that occurs instantaneously. It is a nonlinear and unsteady process, which the physical understanding of mechanism in the aspect of evolution of cavity dynamics and multiphase flow field is yet to be fully understood. In the present work, a three-dimensional numerical model of six degrees of freedom (DOF) based on the shear stress transport (SST) k−ω eddy viscosity model was established to capture the complicated characteristics of the vertical water entry of an inclined cylinder at various entry velocities. A volume of fluid method for tracking air-water interface and a combined dynamic fluid body interaction and overlapping grid technology were used to simulate the complex motion. The numerical model with laminar and turbulent model was verified against the published experimental data of cavity evolution and motion characteristics. A parametric study was conducted to study the translational and rotational characteristics of the structure due to the effect of water entry velocity. The investigation revealed the secondary closure phenomenon during the water entry. The asymmetrical multiphase flow field showed that its dynamic characteristics change with space and time under the effect of cavity evolution.

Multiscale model for flow and transport in CO2-enhanced coalbed methane recovery incorporating gas mixture adsorption effects

In this work we develop a multiscale model for flow and transport problem in CO2-enhanced coalbed methane recovery. The coalbed methane reservoir is characterized by two levels of porosity associated with nanopores in the matrix and cleat network. Mass conservation equations for fluid mixture (CH4 and CO2) in the matrix at the microscale are rigorously derived by using the formal homogenization technique taking into account the gas mixture adsorption in the nanopores. The Density Functional Theory (DFT) is used to compute the gas adsorption isotherms and the solvation force acting on the nanopore wall, showing a much more pronounced adsorption capacity of CO2 compared to CH4. The average transport equations in the matrix together with the multiphase flow problem in fracture network (gas mixture and water) are homogenized giving rise to a macroscopic model ruled by the effective conductivities, partition and transfer coefficients. The cleat permeability evolution due to deformation is taken into account through a three-scale poromechanical model reported in a previous work. Computational simulations illustrate the macroscopic laws underlying the gas pressure distributions, cleat closure phenomena and CH4 production curve enhanced by CO2 injection.

CFD Modeling of Hydrocyclones—A Study of Efficiency of Hydrodynamic Reservoirs

The dynamics of hydrocyclones is complex, because it is a multiphase flow problem that involves interaction between a discrete phase and multiple continuum phases. The performance of hydrocyclones is evaluated by using Computational Fluid Dynamics (CFD), and it is characterized by the pressure drop, split water ratio, and particle collection efficiency. In this paper, a computational model to improve and evaluate hydrocyclone performance is proposed. Four known computational turbulence models (renormalization group (RNG) k- ε , Reynolds stress model (RSM), and large-eddy simulation (LES)) are implemented, and the accuracy of each for predicting the hydrocyclone behavior is assessed. Four hydrocyclone configurations were analyzed using the RSM model. By analyzing the streamlines resulting from those simulations, it was found that the formation of some vortices and saddle points affect the separation efficiency. Furthermore, the effects of inlet width, cone length, and vortex finder diameter were found to be significant. The cut-size diameter was decreased by 33% compared to the Hsieh experimental hydrocyclone. An increase in the pressure drop leads to high values of cut-size and classification sharpness. If the pressure drop increases to twice its original value, the cut-size and the sharpness of classification are reduced to less than 63% and 55% of their initial values, respectively.

Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity

The multiphase flow model has been extensively used to describe complicated flow behaviors in subsurface formations, together with sophisticated reservoir models and well-defined fluid property. In this study, the fully implicit method, as one of most promising schemes for subsurface flow modeling, is employed to solve multiphase flow problems. In contrast to the conventional approach where mathematical models often include a pressure equation, the multiphase flow problems are modeled by up to three continuity equations so that mass conservation holds for all present phases. Another challenge that frequently shows up is the computed solution may sit outside its physically meaningful range, thereby leading to inaccurate predictions or even a failure of the simulation process. A simple remedy is to apply a cutting-off operation to the out-of-bound solution but such an action could ruin both local and global mass conservation. Instead, we replace the original model by a variational inequality formulation with box inequality constraints to protect the boundedness requirement on pressure and saturations from being violated. The variational inequality problem is then solved by a well-designed nonlinear solver consisting of the active-set reduced-space method and the nonlinear elimination preconditioning technique. A number of examples are presented to demonstrate that the proposed formulation is bound-preserving and mass-conservative for each of the present phases/components.