Fluid flow and heat transfer in dual-scale porous media

Abstract

Porous media are omnipresent in various natural and engineered systems. The study of transport phenomena in porous media has attracted the attention of researchers from a wide variety of disciplines. In many applications such as hydrogeology, petroleum engineering and thermochemistry, porous media are encountered, in which heterogeneity exists at a multitude of length-scales. In solar thermochemical reactors, a promising approach to accomplish the thermochemical cycle is to form the reactive solid into a porous structure to promote efficient solid-gas reactions through a high specific surface area, while simultaneously achieving desired transport characteristics. Recently, in light of the apparent trade-offs between rapid reaction kinetics and efficient radiation absorption, reticulated porous ceramics (RPCs) featuring dual-scale porosity have been engineered. These structures are capable of combining the desired properties, namely uniform radiative absorption and high specific surface area. Therefore, investigations are required to understand and analyse different transport phenomena in such structures. This dissertation is motivated by the need for understanding and analysing transport phenomena dual-scale porous media appear and used in many applications such as hydrogeology, petroleum engineering, chemical reactors, and in particular, energy technologies in high-temperature thermochemistry. The main objective of this thesis is to theoretically formulate and numerically demonstrate the fluid flow and heat transfer phenomena in dual-scale porous media. The theoretical and numerical results are used to propose models in forms of effective flow and heat transfer coefficients. The models are capable of estimating the fluid flow and heat transfer phenomena taking place in dual-scale porous media with appropriate fidelity and lower computational cost. The physical understanding of the models of transport phenomena in dual-scale porous structures allows us to tailor and optimise the morphology to accomplish optimal transport characteristics for the desired applications. To determine the flow coefficients, numerical simulations are performed for the fluid flow in a dual-scale porous medium. Two numerical procedures are considered. Firstly, we perform direct pore-level simulations by solving the traditional mass and momentum conservation equations for a fluid flowing through the dual-scale porous structure. Secondly, numerical simulations are performed at the Darcy level. For this purpose, the permeability and Forchheimer coefficient of the small-scale pores are numerically determined. Then, they are implemented in Darcy-level simulations in which the volume-averaged and traditional conservation equations are solved for the small- and large-scale pores, respectively. The results of the two approaches are separately used to determine and compare the permeability and Forchheimer coefficient of the dual-scale porous media. To analyse the energy transport phenomena in dual-scale porous media, a mathematical model is developed by applying volume-averaging method to the convective-conductive energy conservation equation to derive the large-scale equations with effective coefficients. The closure problems are introduced along with the closure variables to establish the closed form of the two-equation model for heat transfer of dual-scale porous media. The closure problems are numerically solved for specific cases of dual-scale porous medium consisting of packed beds of porous spherical particles. The effective coefficients appearing in the two-equation model of heat transfer in dual-scale porous media are determined using the solution of the closure problems. The velocity field in the dual-scale porous structure is calculated using the solution of the fluid flow simulations in dual-scale porous medium. Finally, "numerical experiment" is performed to qualitatively and quantitatively analyse the accuracy of the up-scaled model. Show more