Multicomponent Flow Research Articles

On multicomponent gas diffusion and coupling concepts for porous media and free flow: a benchmark study

Multicomponent gas transport in porous media and at the interface between porous media and free flow occurs in a wide range of technical and environmental systems. Modeling tools are required for the quantitative description of such coupled environmental compartments. We present a benchmark study to compare different diffusion models as well as different coupling concepts employed for the description of multicomponent gas flow and transport at the porous medium/free-flow interface. The benchmark problems allowed us to compare two diffusion models (Fickian and Maxwell-Stefan formulations) for predicting the transport behavior of multicomponent mixtures in porous media and in presence of a free flow. The examples highlighted the importance of interaction between different diffusing components by applying the Maxwell-Stefan formulation, as well as the impact of the free flow velocity on gas migration at the interface under diffusion- and advection-dominated conditions. The problems were solved using two simulation tools, incorporating different coupling concepts to describe the physics of flow and transport processes. In COMSOL Multiphysics, we implemented a single-domain Brinkman approach, whereas in the DuMuX simulator we used a two-domain approach with the Navier-Stokes equation for the free flow and Darcy’s law for the porous medium. Also, the formulation of the Maxwell-Stefan equation for multicomponent transport was different between the two codes. Despite the different modeling concepts, mathematical descriptions and numerical schemes implemented in the two simulators, their outcomes demonstrate excellent agreement for all benchmark problems, as well as the capability to reproduce the results of previous modeling and experimental studies.

Investigation of CO2 and CH4 competitive adsorption during enhanced shale gas production

CO2–CH4 competitive adsorption during shale gas production is investigated through a replacement dynamics method at an isotherm temperature of 30 °C from 14.12 to 7.46 MP CH4 production experiments from pure CH4 (with no other gas injection), a mixture of CO2–CH4, and a mixture of N2–CH4 tests were conducted on a Silurian age Lower Jurassic whole shale sample. Gas production performances, pore size distribution, pressure, CO2/CH4 concentration ratio, and gas flow, are discussed to assess their impacts on CO2–CH4 competitive adsorption. Experimental results are validated by the Langmuir model of adsorption and model for multicomponent gas flow dynamics. At the initial stage of production when pressure is high, gas recovery is largely dependent on depressurization, while in the later stage as pressure decreases, competitive adsorption becomes significant. Observed dominances of bulk flow in larger pores (>10 nm) and surface diffusion in smaller pores (<10 nm), show gas recovering mechanism transforms from being largely dependent on reservoir depressurization to competitive adsorption as pressure decreases. Results from this study suggest that CO2–CH4 competitive adsorption is a dynamic process that changes with production conditions.

TOUGH-RFPA: Coupled thermal-hydraulic-mechanical Rock Failure Process Analysis with application to deep geothermal wells

This paper presents a coupled thermal-hydraulic-mechanical (THM) model for simulating failure processes in geological media. The coupling between stress/strain and heat transfer describing how thermal expansion affects stress is based on the theory of thermo-elasticity. Additionally, the coupling between stress/strain and fluid flow describing how pore-pressure affects stress is governed by Biot's consolidation theory. Stress/strain-dependent porosity/permeability/capillary-pressure defines the influence of stress on fluid flow and thermal fields. The THM model is implemented in the solver module that links the multiphase, multicomponent fluid flow simulator TOUGH2 with the geomechanical simulator RFPA (Rock Failure Process Analysis), which is based on the concept that heterogeneity leads to non-linearity and progressive failure behavior. Capability of TOUGH-RFPA simulator was verified by two benchmark problems related to hydraulic-mechanical and thermal-mechanical response in a hollow cylinder. Then the applicability of TOUGH-RFPA was demonstrated for modeling cooling-induced damage around a very deep geothermal well with mesoscopic heterogeneous properties, which showed complex damage evolution and fracturing during well cooling and fluid pressurization.

Operator-Based Linearization Approach for Modeling of Multiphase Flow with Buoyancy and Capillarity

SummaryNumerical simulation of coupled multiphase multicomponent flow and transport in porous media is a crucial tool for understanding and forecasting of complex industrial applications related to the subsurface. The discretized governing equations are highly nonlinear and usually need to be solved with Newton’s method, which corresponds with high computational cost and complexity. With the presence of capillary and gravity forces, the nonlinearity of the problem is amplified even further, which usually leads to a higher numerical cost. A recently proposed operator-based linearization (OBL) approach effectively improves the performance of complex physical modeling by transforming the discretized nonlinear conservation equations into a quasilinear form according to state-dependent operators. These operators are approximated by means of a discrete representation on a uniform mesh in physical parameter space. Continuous representation is achieved through the multilinear interpolation. This approach provides a unique framework for the multifidelity representation of physics in general-purpose simulation. The applicability of the OBL approach was demonstrated for various energy subsurface applications with multiphase flow of mass and heat in the presence of buoyancy and diffusive forces. In this work, the OBL approach is extended for multiphase multicomponent systems with capillarity. Through the comparisons with a legacy commercial simulator using a set of benchmark tests, we demonstrate that the extended OBL scheme significantly improves the computational efficiency with the controlled accuracy of approximation and converges to the results of the conventional continuous approach with an increased resolution of parametrization.

Reservoir Scale Porosity-Permeability Evolution in Sandstone Due to CO2 Geological Storage

CO2 injection into geological reservoirs is considered as a promising technology to improve oil recovery from oil reservoirs and to reduce greenhouse gas emissions. However, due to the density difference between the injected CO2 and formation brine, the injected CO2 tends to move vertically towards the surface. The risk of this vertical CO2 movement can be prevented by four different trapping mechanisms (i.e. structural, residual, dissolution, and mineral trapping). From the dissolution of CO2 in the aquifer brine, carbonic acid will be formed. Then, this carbonic acid will be reacted with rock minerals and resulted in mineral dissolution and precipitation. However, the effect of these mineral interactions on the porosity-permeability evolution during the CO2 storage process in the sandstone reservoir has not been addressed effectively. Thus, here, we developed a 3D reservoir simulation model to investigate the effect of mineral interactions on the reservoir porosity and permeability during CO2 injection and storage processes in a sandstone reservoir. The multicomponent, chemically reactive, non-isothermal and multiphase flow numerical simulation program TOUGHREACT has been used. The model length was 1000 m, model width was 1000 m and the model thickness was 1000 m (ranging from top depth of 1000 m and bottom depth of 2000 m) with a regularly spaced grid of 15 × 15 × 48 grid (10800 gridblocks). The developed reservoir simulation model consists of two main regions which are reservoir rock region (sandstone) and cap rock region (shale). The simulated sandstone formation consists of quartz, kaolinite, chlorite, and illite. Our results show that CO2 injection leads to significant mineral reactionس (dissolution and precipitation) in the sandstone reservoir. Furthermore, the results indicate that these mineral reactions lead to increase in the sandstone porosity and permeability during the storage period. Thus, we conclude that the mineral reactions (dissolution and precipitation) due to CO2 injection in the sandstone reservoir affect the sandstone porosity and permeability, and hence, affect the CO2 geological storage capacity.

Dual evolution mixed variational analysis of multiphase flow in the subsurface

Dual evolution mixed variational formulations of multiphase flow models in the subsurface are established and analyzed. Specifically, compositional multiphase flow of a triphasic water–oil–gas multicomponent flow is treated, with a dual Gibbs oil–gas mass transfer model. Qualitative analysis of the mixed variational models is performed applying composition duality principles and methods. For multiphysics as well as parallel computing, macro-hybrid variational reformulations are considered. Dual semi-implicit time-marching schemes are presented as semi-discrete approximations for the flow-transport variational models, as well as for a precondition augmented exactly penalized dual Gibbs optimality variational formulation, which are all implementable as parallel proximal penalty–duality algorithms. In this manner, bases for fully discrete non-conforming macro-hybrid mixed finite element numerical realizations are rendered.

Lattice Boltzmann multicomponent model for direct-writing printing

We introduce a mesoscale approach for the simulation of multicomponent flows to model the direct-writing printing process, along with the early stage of ink deposition. As an application scenario, alginate solutions at different concentrations are numerically investigated alongside processing parameters, such as apparent viscosity, extrusion rate, and print head velocity. The present approach offers useful insights on the ink rheological effects upon printed products, susceptible to geometric accuracy and shear stress, by manufacturing processes such as the direct-writing printing for complex photonic circuitry, bioscaffold fabrication, and tissue engineering.

Pore-scale investigation on reactive flow in porous media considering dissolution and precipitation by LBM

The reactive transport process in oil gas reservoirs is complicated due to the coupling between dissolution and precipitation. In the present study, based on lattice Boltzmann method, the coupled dissolution and precipitation process in randomly generated porous media by quartet structure generation is investigated at the scale of geological pores. The fluid velocity, temperature and concentration in porous media are solved by multicomponent flow lattice Boltzmann model, multicomponent thermal lattice Boltzmann model and mass transport lattice Boltzmann model, respectively. The solid phase is updated by volume of pixel method. The results show that the dissolution reaction rate has a positive impact on the consumption of reactants. For different precipitation reaction rates, there exists an optimal value resulting in abundant precipitate and sparse solid distribution. Reaction equilibrium constant affects reaction rates slightly but influence the solid morphology heavily. The coupled dissolution and precipitation process accelerates with the increase of Peclet number, but the precipitate produced increases with the decrease of Peclet number.

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).

A multiphase multicomponent flow and transport model for liquid aerosol filtration in coalescing fibrous filters

Pore-scale CFD simulations of liquid aerosol filtration in coalescing fibrous filters are currently limited by severe computational constraints. In this paper, we present a new multiphase multicomponent framework for modeling such dynamic filtration process at the Darcy-scale. Moving from the pore- to the Darcy-scale allows for significant reduction in computational efforts with limited repercussion on the representation of the filter geometry. In our model, two phases coexist within the filter, namely the injected oil-mist and the coalesced oil phase. The oil-mist phase consists of a mixture of a gas phase and oil droplets of different sizes. The governing equations are the standard ones of Darcy flow and transport in porous media, where the filtration processes, such as droplet capture and drainage, are accounted for through ad hoc mass exchange terms, which are coherent with the Jump & Channel model by Kampa et al. (2014). The equations are strongly non-linear and are solved through the IMplicit Pressure Explicit Saturation (IMPES) algorithm. Cell-centered finite volumes are used for discretization in space. The model is validated by replicating experiments of oil-mist filtration available in the literature for both wettable and non-wettable media, as well as for combinations of media with different wettability. Simulations are then performed for a variety of operational conditions, demonstrating both the accuracy and robustness of our implementation.

Hydro-mechanical-chemical modeling of sub-nanopore capillary-confinement on CO2-CCUS-EOR

Nanopore/subnanopore networks comprising tight reservoirs exhibit special behaviors in the storage and transport of capillary-confined fluids. We develop a hydro-mechanical-chemical model coupling the response of capillary-confined phase behavior, multicomponent flow, reservoir deformation and reaction-controlled porosity evolution to explore the effect of nanopore confinement on enhanced oil recovery and CO2 storage. The results reveal that confinement effects change both in chemical potential and isothermal compressibility of individual components and thus increases volume expansion for any given pressure drop. For constrained mixtures, the CO2 K-value (at fixed pressure) and the MMP(at fixed aperture) will shift to smaller than the bulk state. Moreover, capillary-confinement causes an increased production of heavier components when reservoir pressure is below MMP and a higher production of all components and a smaller reservoir inflation when reservoir pressure is higher than MMP - where miscibility dominates. Meanwhile, capillary-confinement causes a slight increase in CO2 retention rate in the calculation for two cases of native oils with contrasting light oil fractions but in identical reservoirs. Thus any production strategy for a combined CO2 capture and storage (CCS) operation needs to be formulated in full consideration of the rock and fluid properties for each potential site.

Phase-change lattice Boltzmann simulation of condensate falling and heat transfer on hybrid-wettability surface in the presence of non-condensable gas

• Condensate falling off hybrid-wettability surfaces is studied under non-condensable gas effect. • Pseudopotential MRT LB method is coupled with finite difference for phase-change multicomponent flow. • Droplet nucleation, growth and departure time prolong as non-condensable gas fraction increases. • Hydrophilic-superhydrophobic hybrid surface exhibits higher heat transfer performance. A hybrid phase-change lattice Boltzmann model is employed to investigate the condensate falling from subcooled surface in the presence of non-condensable gas. The effects of hydrophilic length ratio, the non-condensable gas fraction ( w NCG ) and the hybrid-wettability of the subcooled surface on condensate droplets dynamics and heat transfer characteristics are investigated systematically. It shows that the average heat flux at the subcooled surface first increases and then decreases with the increase of hydrophilic length ratio. Owing to the increased thermal resistance by the thicker non-condensable gas layer, the nucleation time, growth time as well as departure time of condensate droplets are prolonged as the non-condensable gas fraction increases. The nucleation time of w NCG = 0.4 is 1.5 times higher than that of w NCG = 0.1 , and the growth time and departure time of w NCG = 0.4 are 1.7 times higher than those of w NCG = 0.1 . As the surface wettability changes from hydrophilicity-superhydrophobicity ( θ y = 60 o - θ g = 150 o ) to hydrophilicity-more hydrophilicity ( θ y = 60 o - θ g = 30 o ), the condensation pattern transits from dropwise to filmwise mode. Moreover, the local heat flux at hydrophilic-superhydrophobic ( θ y = 60 o - θ g = 150 o ) and hydrophilic-hydrophobic ( θ y = 60 o - θ g = 105 o ) surface is obviously higher than that at hydrophilic-hydrophilic ( θ y = 60 o - θ g = 75 o ) and hydrophilic-more hydrophilic ( θ y = 60 o - θ g = 30 o ) surface. The present simulations clarify the mechanism of condensate droplets falling off subcooled surface with the existence of non-condensable gas and are conducive to the design of hybrid-wettability surfaces for condensation heat transfer enhancement, which is of great significance to energy resources conservation.

Improving ethylene oxide production inside microreactor by using ribbed wall

The current study presents a numerical simulation for multicomponent flow inside the Ethylene oxide microreactor channel. The catalyst surface is treated as a functional surface. The fluxes of each species are defined based on the Borman and Westerterp model. The Reynolds number in the study is below 250; therefore, the flow is laminar. The presence of V-shape ribs improves the process of ethylene oxide production inside the microreactor of ethylene oxide.

A consistent and conservative model and its scheme for N-phase-M-component incompressible flows

In the present work, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.

Simulation of Rayleigh Bubble Growth near a No-Slip Rigid Wall

In order to study the role of growing cavitation bubbles in the context of ultrasonic cleaning, we perform two-dimensional, axisymmetric Navier-Stokes simulation for compressible, multicomponent flow and examine the so-called Rayleigh growth of an air bubble (with initial radius 33 µm and pressure 10 MPa) near a rigid wall. The simulation suggests that strong shear stress, which is important in physical cleaning such as particle removal, appears as a result of the bubble-growth-induced shock passage. The parametric study with varying a standoff distance of the bubble to the wall shows that the wall shear stress linearly decreases against the standoff distance.

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.

Сравнение трех моделей течения и перемешивания модельных рабочих тел в смесительном элементе ЖРДМТ тягой 10…15 Н, основанных на решении осредненных по Рейнольдсу уравнений Навье — Стокса

The paper analyses the possibilities of using the ANSYS CFX hydrocode to simulate the flow and mixing of working bodies in the mixer and combustion chamber of a low-thrust liquid propellant rocket engine in the thrust range of 10 to 15 N. We built our models around solving Reynolds-averaged Navier — Stokes equations stated for three types of multiphase multicomponent incompressible fluid flow: a two-phase two-component two-velocity flow model; a two-phase two-component single-velocity flow model; a three-phase three-velocity flow model. We consider the advantages and disadvantages of each model. We compare our simulation results to the results of measurements conducted during hydraulic testing of mixers.

Efficient implementation of space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows

The present work is devoted to the study of efficient implementation of spacetime adaptive ADER finite element discontinuous Galerkin method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter scheme for simulation of non-stationary compressible multicomponent reactive flows. The multicomponent and reaction properties of the flow are considered in the form of convection-reaction equations. Therefore an effective scheme of splitting the original nonlinear system of algebraic equations of LST-DG predictor was developed to obtain an efficient iterative solution method. This approach is based on the use of the linearity property of the system of equations for the discrete spacetime solution for the system of convection equations, which makes it possible to pre-compute the inverse matrices, and allows the vectorized calculation of the transfer of individual components. The change in the concentrations of the components in the convection-reaction equations and the energy yield in the gas-dynamic equations due to the reactions are calculated using the global iterations. The iterative scheme for the original essentially nonlinear system of equations is split into a sequence of smaller systems. The approach is well applicable for the problems, especially in the case of a large number of components and reactions in the flow.

Numerical Simulation of Gas Mixtures Based on the Quasi-Gasdynamic Approach as Applied to the Interaction of a Shock Wave with a Gas Bubble

A new numerical algorithm for simulating transonic flows of nonreacting gas mixtures is proposed. The algorithm is based on the finite volume method as applied to regularized, or quasi-gasdynamic, equations. The equations describing multicomponent gas flows are derived phenomenologically using an existing regularized system for one-component gas and classical equations for gas mixtures. The numerical examples include the computation of the nonstationary interaction of gas flow with heavy and light gas bubbles.

A sustainable and scalable multicomponent continuous flow process to access fused imidazoheterocycle pharmacophores

A sustainable flow process has been established for the application of the Gröebke–Blackburn–Bienaymé reaction for access to high-value fused heteroaromatics.