Phase Flow Model Research Articles

Automatic differentiation using operator overloading (ADOO) for implicit resolution of hyperbolic single phase and two-phase flow models

Implicit time integration schemes are widely used in computational fluid dynamics to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit counterpart. The derivation of an implicit scheme is however a challenging and time-consuming task, increasing substantially with the model equations complexity since this method usually requires fairly accurate evaluation of the spatial scheme's matrix Jacobian. This article presents a flexible method to overcome the difficulties associated to the computation of the derivatives, based on the forward mode of automatic differentiation using operator overloading (ADOO). Flexibility and simplicity of the method are illustrated through implicit resolution of various flow models of increasing complexity such as the compressible Euler equations, a two-phase flow model in full equilibrium [28] and a symmetric variant [44] of the two-phase flow model of Baer and Nunziato [2] dealing with mixtures in total disequilibrium.

A relaxation scheme for a hyperbolic multiphase flow model

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

Hybrid mediated blood flow investigation for atherosclerotic bifurcated lesions with slip, convective and compliant wall impacts

ObjectiveThe present investigation is concerned with hybrid mediated blood flow model through atherosclerotic bifurcated artery with slip effects by considering the properties of compliant walls. Design/approachIn human body, the circulatory system is made up of a network of blood vessels that include the bifurcation therefore the influence of hybrid nanoparticles on parent artery with mild stenosis, at apex and in the region of daughter arteries (after being bifurcated) is observed. Blood streaming along the segment of vessel is considered to be Newtonian. The compliant nature of the atherosclerotic artery wall is also considered to create association with permeability aspects for the thickness of arterial wall. Property of heat transfer with convective impacts is taken into account to weaken the stenotic lesions. Through phase flow model approach, a mathematical model is develop with the phenomena of hybrid nanofluid. FindingsFor theoretical research of designed equations experimentally determined values of nanoparticles and base fluid are used. Further, flow configurations of hemodynamics are figure out to analyze the blood flow through bifurcated stenotic artery. The comparison in parent and daughter artery is plotted for velocity profile. These patterns provide us a graphical way to recognize the importance of theoretical assistance of this model to biomedical field. At the end, it is concluded from graphical results that slip to the boundary reduces the resistance to flow for atherosclerotic bifurcated artery. ConclusionsIn bifurcated artery, blood circulation is assumed due to difference of pressure between atherosclerotic and non-atherosclerotic portions. Slip impacts are more effective to reduce the hemodynamics effects of stenosis for bifurcated artery. Bifurcation angle reduces the shear stress for daughter artery whereas opposite behavior is observed for parent artery. Compliant wall parameters reduces the inner bolus size in stenotic region while number of bolus increases in bifurcated region. Reduction in the amplitude of shear stress for convective parameter is more prominent in the parent artery as compared to daughter artery.

Investigation of the synergy potential of oil and geothermal energy from a fluvial oil reservoir

Geothermal projects, as renewable energy projects, are not economically attractive in most places of the world at the current state of development; for this reason, subsidies are required by energy and environmental authorities in order to increase the interest in such projects. In this paper, we assess and model strategies for integration of geothermal energy with oil productions of the Moerkapelle oil field in the Netherlands. To do so, numerical simulations have been employed to analyse the feasibility of a fluvial oil reservoir for the synergy potential of oil and geothermal energy exploitation. In order to implement the simulation studies, single phase and two-phase non-isothermal fluid flow modelling are utilized for the geothermal well doublet system and for water flooding in an oil reservoir (including facies heterogeneity), respectively. A series of simulations have been conducted to investigate how hot water from a geothermal reservoir beneath a heavy oil reservoir in the fluvial sedimentary system of the West Netherlands Basin can be used for Thermal Enhanced Oil Recovery (TEOR) and geothermal energy production.This study finds that the high degree of heterogeneity in fluvial oil reservoirs could significantly affect oil recovery improvement and hence the synergy strategy. High values of a) Net to gross (N/G) b) Bottom Hole Pressure (BHP) and c) horizontal wellbore length are favourable for oil recovery. In contrast, wide horizontal wellbore spacing and high oil viscosity have an adverse effect on oil recovery enhancement. Furthermore, the results display that the enhanced oil production helps to reduce the required subsidy for a single doublet geothermal project up to 100%. Consequently, the extra amount of oil produced by utilising the geothermal energy, could make the geothermal business case independent and profitable.

RETRACTED: A new idea of Atangana-Baleanu time fractional derivatives to blood flow with magnetics particles in a circular cylinder: Two phase flow model

This study aims to examine the magnetohydrodynamic (MHD) effect on the blood flow of a Casson fluid in a vertical cylinder. Blood is taken as a non-Newtonian viscous fluid due to the viscosity which depends on the volume fraction of red blood cells. The effect of magnetic field on blood and particles velocities with temperature distribution has been studied. Using the definition of Atangana-Baleanu fractional derivatives, the classical model which governs the flow has been generalized and the exact solution of the problem has been obtained by applying the joint transformation of Laplace and Hankel. Effects of interesting embedded parameters on both velocities (blood velocity and particles velocity) have been examined and discussed graphically. Results showed that an increase in blood velocity or particle velocity is caused due to increase in Gr and λ, however, a reverse behavior is noticed for higher values of M. Rate of heat transfer at the plate surface is measured using Nusselt number relation. The results are computed and presented in a tabular form.

Integrated deterministic approaches for productivity index of reservoirs depleted by horizontal wells and undergone multiphase flow conditions

This paper introduces new integrated approaches for estimating pseudo-steady state productivity index (PI) and shape factor of oil and gas reservoirs drained by horizontal wells and dominated by multiphase flow conditions. These approaches couple PVT data, relative permeability curves, and pressure distribution models during pseudo-steady state flow (PSS). The objective is eliminating the uncertainties of applying single phase flow models and substantially comprising the realistic parameters that govern multiphase flow conditions. The importance of this study is represented by introducing the impact of multiphase flow (Gas, Oil, Water) to the productivity index and inflow performance relationship of reservoirs depleted by horizontal wellbores.This study is conducted throughout three tasks. The first includes reviewing currently used techniques for calculating pseudo-steady state PI and shape factor of bounded oil and gas reservoirs assuming single phase flow is the dominant flow pattern in the porous media. The second introduces new deterministic models for reservoir mobility and compressibility and new multiphase flow pressure function [f(P)mp]. While the third focuses on calculating PI and shape factor of reservoirs depleted by horizontal wellbores and predicting inflow performance relationship (IPR) considering multiphase flow conditions.The outcomes of this study can be summarized as: 1) Developing deterministic models by multi-regression analysis for reservoir mobility and compressibility using PVT data and relative permeability curves. 2) Generating multiphase flow reservoir pressure function [f(P)mp] that introduces the impact of multiphase flow conditions to PI model. 3) Applying the new approaches for calculating multiphase flow PI and shape factor and thereafter generating multiphase flow IPR. The study has pointed out: 1) The fact that the PI of constant Sandface flow rate is greater than constant wellbore pressure is confirmed for single and multiphase flow conditions. 2) PI and shape factor are time invariant at late production time and depends only on reservoir geometry and wellbore type. 3) PI of multiphase flow is less than the index of single phase flow while shape factor exhibits higher value for multiphase flow compared to the one for single phase flow. 4) Multiphase flow negatively changes the IPR either by increasing the pressure drop or by declining the flow rate. 5) Most of the deterministic models developed in this study show high accuracy (high R-squared value, R2≥90% ) for the changes in fluid properties with reservoir pressure.

CFD modelling of friction stir welding (FSW) process of AZ31 magnesium alloy using volume of fluid method

In this work, a validate couple-thermo flow model of the FSW process is generated using the CFD software FLUENT, with this model, then being developed to model the flash formation phenomena that occur during the FSW process using the volume of fluid method. From both models, pressure distribution on the tool surface was predicted at different radial positions. A comparison was made between single and multiple phase flow models. A significant reduction of the pressure values was seen when using a two-phase flow model. Volume fraction contour showed the changing in the metal phase when increased the welding time steps. A modelling procedure of this work is presented in details to utilize it in the further numerical investigation as a guide. This work could be used to afford more understanding of surface flash formation phenomena. Moreover, the outcome of this study can be a useful technique to aid the tool failure and increase the tool life during the FSW process.

Study of Hydraulic Disturbances From Single-Unit Load Rejection in a Pumped-Storage Hydropower Station With a Shared Water Delivery System

The transient characteristics of load rejection process in pumped-storage hydropower (PSH) stations have a close relation to the safety of electric power system and hydraulic facilities. A large portion of PSHs consist of multiple units sharing one tunnel (MUSOT). In this paper, a three-dimensional numerical simulation method for hydraulic disturbance caused by single unit load rejection transition process based on the volume of fluid (VOF) two phase flow model was proposed and a filed test was carried out in a PSH station with a two units sharing one tunnel (TUSOT) setting. The power output from the unit that operates in normal condition (UNC), the pressure fluctuations of the spiral casing inlet and tailrace tunnel outlet, the water level variation and flow pattern in surge tank were obtained through the numerical simulation and field test. The results showed that the highest and lowest water level in surge tank from the numerical method agreed well with the measured data obtained in the field test. The guide vanes closing law of the unit that runs in load rejection (ULR) mainly impacts on the variation of the above parameters. To reduce the influence of single-load load-rejection hydraulic disturbance, a more elaborate guide vanes adjustment scheme of the UNC should be proposed in the next step to avoid large short-time fluctuations in the power output and pressure.

Effect of vacuum deterioration on thermal performance of coaxial evacuated tube solar collector considering single and two phase flow modelling: A numerical study

Boiling and condensation play an important role in heat transfer in evacuated tube solar collectors (ETC), especially for low flow rates. Another factor that influences the efficiency of an ETC is deterioration of vacuum inside the ETC. The present study investigates numerically the effect of deteriorating vacuum during single and two phase flows inside an ETC to analyze its thermal performance. A steady-state one-dimensional model is developed which can simulate the steady-state thermal performance of the Evacuated tube solar collector (ETC) with single and two-phase flows under saturation conditions considering effects of vacuum deterioration to simulate a more real-life situation of solar collectors. The rise in pressure inside the ETC has a significant effect on the suppression of boiling and condensation due to rise in overall heat loss coefficient. The radiative, convective and conductive heat loss coefficients from the collector are studied for gradual pressure rise inside the ETC. The two phase model also indicates that if boiling starts inside the ETC in a particular inlet flow condition, consideration of two phase flow along with the effect of vacuum deterioration shows significant deviation of efficiency and temperature profile from those of single phase flow models and predicts more accurate results. Inducing of two-phase heat transfer in ETC, with all the fluid condensing again within the collector tube, will result in improved efficiency for that range of mass flow rates. It also helps in maintaining uniform temperature and equal heat gain throughout the collector absorber plate. The efficiency of the collector for higher inlet temperatures is seen to be effected more significantly by vacuum deterioration than at lower inlet temperatures in single phase flows. However, in two phase flows for a fixed saturation temperature of the fluid, vacuum deterioration has negligible effect on the efficiency at higher inlet temperatures (Tfi ≥ 85 °C).

A fully implicit finite volume scheme for single phase flow with reactive transport in porous media

Single phase flow and reactive transport modelling involve solving a highly nonlinear coupled system of partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. In this paper, we propose a fully implicit finite volume method using a direct substitution approach to improve the efficiency and the accuracy of numerical computations for such systems. The approach has been developed and implemented in the framework of the parallel open-source platform DuMuX. The object oriented code allows solving reactive transport problems considering different coupling approaches. A number of 2D and 3D numerical tests were performed for verifying and demonstrating the capability of the coupled fully implicit approach for single phase flow and reactive transport in porous media. Numerical results for the reactive transport benchmark of MoMaS and long-term fate of injected CO2 for geological storage including a comparison between the direct substitution approach and the sequential iterative approach are presented. Parallel scalability is investigated for simulations with different grid resolutions.

Numerical analysis of a two-phase flow discrete fracture matrix model

We present a new model for two phase Darcy flows in fractured media, in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain (matrix). Fractures can act as drains or as barriers, since pressure discontinuities at the matrix-fracture interfaces are permitted. Additionally, a layer of damaged rock at the matrix-fracture interfaces is accounted for. The numerical analysis is carried out in the general framework of the Gradient Discretisation Method. Compactness techniques are used to establish convergence results for a wide range of possible numerical schemes; the existence of a solution for the two phase flow model is obtained as a byproduct of the convergence analysis. A series of numerical experiments conclude the paper, with a study of the influence of the damaged layer on the numerical solution.

A Multiscale Approach Simulating Boiling in a Heated Pipe Including Flow Pattern Transition

The paper presents the extension of the GENeralized TwO Phase flow (GENTOP) model for phase transfer and discusses the submodels used. Boiling flow inside a wall heated vertical pipe is simulated by a multifield computational fluid dynamics (CFD) approach. Subcooled water enters the pipe from the lower end and heats up first in the near-wall region leading to the generation of small bubbles. Farther along the pipe, larger and larger bubbles are generated by coalescence and evaporation. This leads to transitions of the two-phase-flow patterns from bubbly to churn-turbulent and annular flow. The CFD simulation is based on the recently developed GENTOP concept. It is a multifield model using the Euler-Euler approach. It allows the consideration of different local flow morphologies including transitions between them. Small steam bubbles are handled as dispersed phases while the interface of large gas structures is statistically resolved. The GENTOP submodels and the wall boiling model need a constant improvement and separate, intensive validation effort using CFD-grade experiments.

Two Phase Flow Modeling and Characterization of Oxygen Bubbles in PEM Water Electrolysis Cells

The formation, growth, and stability of oxygen bubbles inside the porous transport layer (PTL) pores of a polymer electrolyte membrane water electrolysis (PEMWE) cell have been modeled. In a PEMWE cell, O2 bubbles form and grow inside the anode catalyst layer (ACL) and PTL pores. The most critical impact of the O2 bubbles on the overall performance is the screening of the ACL surface. Semi-empirical relations for the current density-surface coverage for gas evolving electrodes have previously been developed [1] and were used for our PEMWE modeling [2]. This screening effect has been evaluated as an overpotential term, and the results were used to predict the effects of the catalyst and PTL properties on the electrolysis cell performance. The fluctuations in the cell current density were used to identify different types of bubbles and their detachment frequency from the anode electrode. In this work, the anode catalyst surface has been described as a smooth, planar and horizontal plane. The PTL pores are described as identical straight hydrophilic cylinders with 1-mm height. Such a structure resembles tunable PTL structures such as those synthesized by Kang et al. [3]. Stable O2 bubble nuclei form mainly at the intersection of the anode catalyst layer and the PTL pore wall [3,4]. Our modeling results show the effects of three different types of bubbles in a PEMWE cell: i) nucleation-driven, ii) drag-driven, and iii) buoyancy-driven bubbles. Figure 1 shows the relative lifetime and overpotential effects of the O2 bubbles in a PEMWE with a PTL consisting of 11 μm dia. pores operated at a fixed temperature of 80°C and a balanced pressure of 1 bar [5]. Comparing the current density fluctuations in chronoamperometry experiments with the bubble detachment frequencies obtained through modeling provides a distribution of different types of bubbles in the electrolysis cell. These frequencies vary according to the PTL structure and the PEMWE cell operating conditions. Understanding of bubble growth and detachment mechanisms are of significant importance for reduction of mass transport-related losses and enhancement of PEMWE performance.

(Invited) Large Scale PEM Electrolysis Stack Development - the Megastack Project

In the MEGASTACK project, the existing PEM electrolyser stack designs of ITM power has been scaled up and combined with novel solutions to successfully achieve a MW-sized PEM stack design. Two-phase flow and structural mechanics modelling approach has been applied together with optimization of stack components such as MEAs, bipolar plates, current collectors and sealings. The development activities have focused on existing solutions, already proven in kW-sized electrolyser stacks, rather than aiming to use completely new, unproven concepts and materials. The two-phase flow model is based on the volume of fluid (VOF) model in ANSYS/Fluent 16.2 and implements sub-grid scale models for water electrolysis as a set of user-defined functions. These sub-grid scale models include, gas nucleation, gas-liquid mass transfer and bubble coalescence and breakup phenomena on subgrid length scales. Experiments using a transparent cell in combination with a high-speed digital camera as well as numerical image processing was used to quantify temporal and spatial gas distribution and flow velocities. The experimental results are compared to the two-phase flow model results and the validity and implications of the model are discussed. It is clear from both the modelling work and experimental results, that inlet and outlet manifolds, as well as the flow resulting from specific choices for current collector greatly impacts the water distribution of the electrolyser stack and therefore also on the gas distribution within the cell. The LCA compares in a life cycle (cradle-to-gate- plus use phase-) perspective the environmental aspects of the two design options by following practice guidance and required provisions developed by the FCH JU – a method that complies with the ISO 14040 and 14044 series. Results derived from the comparative LCA point towards an improved environmental performance of the new stack design demonstrated in the MEGASTACK project for all midpoint impact categories investigated in this study, i.e. for the abiotic depletion potential (ADP), global warming potential (GWP), acidification potential (AP), and eutrophication potential (EP). The lower environmental impacts resulting from the new stack design are linked to both increased current density that reduces the quantity of active materials required for a given hydrogen production capacity, and the reduction of material requirements through the improved stack design. Summary The FCH-JU project MEGASTACK has developed a PEM electrolyser stack design for MW-sized water electrolysers with the goal of significantly reducing the cost of large scale PEM electrolysers. This presentation will give a summary of the main achievements and results from the MEGASTACK project as well as a more detailed presentation of the results from two phase flow modelling of the liquid and gas transport in the anode flow field and results from a comparative life cycle analysis of the new stack.

Effect of pressurizing speed on filling behavior of gradual expansion structure in low pressure casting of ZL205A alloy

The mold filling behavior of gradual expansion structure in low pressure casting was studied by two phase flow model using the Volume of Fluid method, and was verified by water simulation with a Plexiglas mold. To get smooth mold filling process and provide a guide for the pressurizing speed design in the producing practice, the mathematical model with the pressurizing speed, expansion angle and height of the gradual expansion structure was established. For validation experiments, ZL205A alloy castings were produced under two different pressurizing speeds. Weibull probability plots were used to assess the fracture mechanisms under different pressurizing speeds. Mechanical properties of ZL205A alloy were applied to assess the entrainment of oxide film. The results show that the filling process of a gradual expansion structure in a low pressure casting can be divided into the spreading stage and filling stage by gate velocity. The gate velocity continues to increase in the gradual expansion structure, and increases with the increase of pressurizing speed or expansion angle. Under the effect of the falling fluid raised by the jet flow along the sidewall, the fluid velocity decreases in the jet zone from ingate to free surface. As such, oxide film entrainment does not occur when the gate velocity is greater than the critical velocity, andthe gate velocity no longer reflects the real state of the free surface. The scatter of the mechanical properties is strongly affected by the entrainment of oxide films.

Optimal system, invariant solutions and evolution of weak discontinuity for isentropic drift flux model

Inequivalent classes of similarity solutions for isentropic drift flux two phase flow model are obtained by using one dimensional optimal classifications. The optimality of this classification is shown in a constructive manner, i.e., by constructing various invariant functions including conditional and numerical invariants. Further, with the help of invariant solution, we discuss the evolution of weak discontinuity which displays the nature of the general solution.

Two Phase Flow Modeling and Characterization of Oxygen Bubbles in PEM Water Electrolysis Cells

The formation, growth, and stability of oxygen bubbles inside the porous transport layer (PTL) pores of a polymer electrolyte membrane water electrolysis (PEMWE) cell have been modeled. In a PEMWE cell, O2 bubbles form and grow inside the anode catalyst layer (ACL) and PTL pores. The most critical impact of the O2 bubbles on the overall performance is the screening of the ACL surface. Semi-empirical relations for the current density-surface coverage for gas evolving electrodes have previously been developed [1] and were used for our PEMWE modeling [2]. This screening effect has been evaluated as an overpotential term, and the results were used to predict the effects of the catalyst and PTL properties on the electrolysis cell performance. The fluctuations in the cell current density were used to identify different types of bubbles and their detachment frequency from the anode electrode. In this work, the anode catalyst surface has been described as a smooth, planar and horizontal plane. The PTL pores are described as identical straight hydrophilic cylinders with 1-mm height. Such a structure resembles tunable PTL structures such as those synthesized by Kang et al. [3]. Stable O2 bubble nuclei form mainly at the intersection of the anode catalyst layer and the PTL pore wall [3,4]. Our modeling results show the effects of three different types of bubbles in a PEMWE cell: i) nucleation-driven, ii) drag-driven, and iii) buoyancy-driven bubbles. Figure 1 shows the relative lifetime and overpotential effects of the O2 bubbles in a PEMWE with a PTL consisting of 11 μm dia. pores operated at a fixed temperature of 80°C and a balanced pressure of 1 bar [5]. Comparing the current density fluctuations in chronoamperometry experiments with the bubble detachment frequencies obtained through modeling provides a distribution of different types of bubbles in the electrolysis cell. These frequencies vary according to the PTL structure and the PEMWE cell operating conditions. Understanding of bubble growth and detachment mechanisms are of significant importance for reduction of mass transport-related losses and enhancement of PEMWE performance.

Temporal scale analysis of two phase flow in fractured well

Two phase flow between two fractures commonly exists around fractured wells. Due to the fracture network, the flow velocity is extremely variable in different regions and it can be described by the temporal scale analysis. The flow velocity also changes with time during the change in water saturation, but these changes cannot be captured by the conventional temporal scale analysis. The temporal scales are obtained based on a principal equation, so it is difficult to accurately estimate the formation properties and to determine the exploitation scheme. In this study, the two phase flow model between two fractures has been proposed for the temporal scale description.The impact of reservoir heterogeneity on the temporal scales is considered in the model. Due to the tortuous flow channel shape between the fractures, the flow pressure affects the fluid flow afterwards. This is explained by the time lag effect in the model. The temporal scales are obtained by using finite element method and Laplace transformation at all time points with these considerations. Moreover, the well is soaked intermittently. The soaking duration is chosen based on temporal scales, and then discussed in terms of efficiency and recovery factor.The results showed that the water saturation profile position is reflected by the temporal scales, the flow resistance and the flow velocity are represented by their zero status response contributions, while the initial flow pressure is described by their zero input contribution. The highest zero status response contribution is different for different properties. Moreover, the time lag effect promotes the initial pressure fluctuation, and also upscales the fluid flow in tortuous channels. Finally, the soaking duration is an approximation of the time required to reduce the fracture flow pressure.

Numerical assessment of two phase flow modeling using plunging jet configurations

This paper presents unsteady numerical simulation of air entrainment by water plunging jet using Volume of fluid model coupled to PLIC algorithm for phase interface reconstruction and Euler–Euler model considering continuous water phase and dispersed air phase.Plunging jet simulations aim to find out the ability of each model to reproduce air entrainment phenomenon. The investigation tackled the air plume depth, air entrainment rate and velocity profiles. Further simulations were performed to highlight the influence of the free jet length on the entrainment rate and plume development below the free surface.The results show good agreement with the available experimental data particularly velocity profiles in both radial and axial directions, plume shape and development along transient intervals. The initial impact is well reproduced referring to literature and bubbles penetration depth is comparable to the empirical correlations.It is noticed that further improvements are required for interfacial forces modeling in volume of fluid model to ensure good control of bubbles migration in the plume region.Entrainment rate discrepancies in Euler–Euler model are related to the lack of information about interface location due to averaging process; hence, an appropriate interface detection function is needed.

Modeling Mass Transfer in a Three-Phase Minireactor Filled with Trilobe Catalytic Extrudates in Series

The internal and external gas-liquid mass transfer limitations in a three phase spiral string bed mini-reactor are estimated, using as a model reaction the benzene hydrogenation over a commercial tri-lobe Ni/Al2O3 catalyst at elevated pressures and temperatures. A detailed two phase flow model incorporating liquid volatility, intrinsic catalytic reaction rates, gas-liquid mass transfer effects, liquid-solid mass transfer effects, internal mass transfer effects and wetting of the catalytic particles, was used for the simulation of the spiral string bed reactor performance. The benzene intrinsic reaction kinetics was estimated conducting benzene hydrogenation experiments over crushed catalyst particles. The gas-liquid mass transfer coefficient was estimated from the data of this study and the liquid-solid mass transfer effects were estimated from data of a previous communication. The proposed correlation for the prediction of gas-liquid mass transfer coefficients can describe the gas-liquid mass transfer li...