A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD

Novel reactors for multiphase processes

Process intensification tools, such as the capillary reactor, offer several benefits to the chemical process industries due to the well-defined high specific interfacial area available for heat and mass transfer, which increases the transfer rates, and due to low inventories, they also enhance the safety of the process. This has provided motivation to investigate three such tools, namely the capillary microreactor, spinning disc and rotating tube reactors, in this study.The gas-liquid slug flow capillary microreactor intensifies reactor performance through internal circulation caused by the shear between the continuous phase/wall surface and the slug axis, which enhances the diffusivity and consequently increases the reaction rates. However, integrating the complex hydrodynamics of this reactor with its chemical kinetics is a mathematically challenging task. Therefore, in this study, a simple-to-complex approach, using a set of state-of-the-art computational fluid dynamic tools, has been used. Firstly, simulations were performed without any chemical reaction to ascertain the extent of slug flow regime. The model also clearly captured the slug flow generation mechanism which can be used to structurally optimize the angle of entry in these reactors. Finally, the hydrodynamic model was also capable of estimating the pressure drop and slug lengths. After successfully simulating the hydrodynamics of the system, a reaction model was incorporated to study the chemical reaction kinetics. The results were compared with the published experimental work and were found to be in good agreement.The spinning disc reactor utilizes the centrifugal and shear forces to generate thin liquid films characterized with intense interfering waves. This enables a very high heat transfer coefficients to be realized between the disc and liquid, as well as very high mass transfer between the liquid and the bulk gas phase. The waves formed also produce an intense local mixing with very little back mixing. This makes a spinning disc reactor an ideal contactor for multiphase processes. The focus of this study has been to elucidate the hydrodynamic behaviour of the liquid film flow over the horizontal spinning disc. Investigations were also performed to elaborate the local and overall hydrodynamic characteristics of a fully developed spinning disc reactor. Simulation results showed a continuous linear liquid film on the horizontal spinning disc and intense mixing performance in the annulus of the reactor around the disc surface. Finally, the film thickness data from the simulations were compared with the limited amount of data available for this novel process.Rotating tube reactor also uses centrifugal forces to generate the liquid film and a high degree of mixing along with an improved control over the reactant retention times. In this work we have conducted a CFD analysis to understand the hydrodynamics of this new technology for future developments

A force-balanced control volume finite element method for multi-phase porous media flow modelling

A novel method for simulating multi-phase flow in porous media is presented. The approach is based on a control volume finite element mixed formulation and new force-balanced finite element pairs. The novelty of the method lies in: (a) permitting both continuous and discontinuous description of pressure and saturation between elements; (b) the use of arbitrarily high-order polynomial representation for pressure and velocity and (c) the use of high-order flux-limited methods in space and to time avoid introducing non-physical oscillations while achieving high-order accuracy where and when possible. The model is initially validated for two-phase flow. Results are in good agreement with analytically obtained solutions and experimental results. The potential of this method is demonstrated by simulating flow in a realistic geometry composed of highly permeable meandering channels

Balanced-force two-phase flow modelling on unstructured and adaptive meshes

Two-phase flows occur regularly in nature and industrial processes and their understanding is of significant interest in engineering research and development. Various numerical methods to predict two-phase phase flows have been developed as a result of extensive research efforts in past decades, however, most methods are limited to Cartesian meshes. A fully-coupled implicit numerical framework for two-phase flows on unstructured meshes is presented, solving the momentum equations and a specifically constructed continuity constraint in a single equation system. The continuity constraint, derived using a momentum interpolation method, satisfies continuity, provides a strong pressure-velocity coupling and ensures a discrete balance between pressure gradient and body forces. The numerical framework is not limited to specific density ratios or a particular interface topology and includes several novelties. A further step towards a more accurate prediction of two-phase flows on unstructured meshes is taken by proposing a new method to evaluate the interface curvature. The curvature estimates obtained with this new method are shown to be as good as or better than methods reported in literature, which are mostly limited to Cartesian meshes, and the accuracy on structured and unstructured meshes is shown to be comparable. Furthermore, lasting contributions are made towards the understanding of convolution methods for two-phase flow modelling and the underlying mechanisms of parasitic currents are studied in detailed. The mesh resolution is of particular importance for two-phase flows due to the inherent first-order accuracy of the interface position using interface capturing methods. A mesh adaption algorithm for tetrahedral meshes with application to two-phase flows and its implementation are presented. The algorithm is applied to study mesh resolution requirements at interfaces and force-balancing for surface-tension-dominated two-phase flows on adaptive meshes.Open Acces