Finite element analysis of non-isothermal multiphase porous media in dynamics

This work presents a mathematical and a numerical model for the analysis of the thermo-hydro-mechanical (THM) behavior of multiphase deformable porous materials in dynamics. The fully coupled governing equations are developed within the Hybrid Mixture Theory. To analyze the THM behavior of soil structures in the low frequency domain, e.g. under earthquake excitation, the u-p-T formulation is advocated by neglecting the relative acceleration of the fluids and their convective terms. The standard Bubnov-Galerkin method is applied to the governing equations for the spatial discretization, whereas the generalized Newmark scheme is used for the time discretization. The final non-linear and coupled system of algebraic equations is solved by the Newton method within the monolithic approach. The formulation and the implemented solution procedure are validated through the comparison with other finite element solutions or analytical solutions

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

Numerical modelling of thermo-hydromechanical (THM) in deforming porous media for subsurface systems

The study of multiphase flow and heat flow in partially saturated porous media is important in environmental geomechanics engineering because of its relevance to consolidation of porous media in unsaturated zone. A numerical model which describes the thermo-hydro-mechanical (THM) coupled problems in deformable porous material with two-phase flow has been developed. The relationships between capillary pressure, saturation of water and relative permeabilities of water and gas, proposed by Brooks and Corey was used. An extended study of the numerical model, based on the COMES-GEO code was conducted recently to solve unsaturated problems in local condition of Kg. Puteh wellfield, Kota Bharu. This site is a potential shallow aquifer which contribute to the largest groundwater supply in Kota Bharu, Kelantan. Some numerical investigation on the proposed formulation is discussed with illustrative example problems to demonstrate solution procedures and validating of the model

Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous finite volume element methods in combination with the optimise-then-discretise approach for the approximation of the optimal control problem, leading to nonsymmetric algebraic systems, and employing minimum regularity requirements. Estimates for the error (between a local reference solution of the infinite dimensional optimal control problem and its hybrid approximation) measured in suitable norms are derived, showing optimal orders of convergence

Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

© 2016 .A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach