Pore-scale modelling of transport phenomena in homogeneous porous media

[摘要] ENGLISH ABSTRACT: The main purpose of this study is to develop deterministic, process-based models ofincompressible Newtonian flow and electrical c01iduction in homogeneous, anisotropicporous media.The foundation of the models is provided by the volume averaging theory which isused to obtain the macroscopic balance equations for momentum transport and electricalconduction. These volume averaged equations contain, amongst others, integralterms over the fluid-solid surface area where the integrands are related to the microscopicfluxes of the transport quantities. The closure modelling is conducted by employinga pore-scale model which requires explicit assumptions regarding the mean geometricproperties of the porous medium microstructure and accounts for the configuration ofthe fluid-solid surface area. The pore-scale model also provides an estimate of the microscopicflow paths. The average geometry of different anisotropic materials, namelytwo types of foamlike materials, granular porous media and fibre beds, is captured inrepresentative unit cells which form the core of the physical pore-scale model.This particular type of closure modelling further requires a direct transformation ofmicroscopic fluxes to the macroscopic level. It is indicated, in context of the volumeaveraging theory, that microscopic fluxes may be estimated by the respective macroscopicchannel average fluxes. The transformation of the microscopic flux to the channelaverage flux is accomplished through the flux related tortuosity tensor. New definitionsfor the tortuosity and lineality as second-order tensors are proposed for porous mediain general. Novel names, semantically in line with the respective physical meanings,are proposed for these quantities. It is shown that the definitions produce results whichconform with several other published results and are applicable to anisotropic media.Application of the modelling technique to Newtonian flow results in momentum transportequations valid for both the Darcy and Forchheimer flow regimes. The coefficientsappearing in these equations are expressed in terms of fluid properties and measurablegeometric features of the porous medium. The predictions of the anisotropic foamlikematerials are validated against experimental pressure gradient measurements for flowthrough a high porosity, anisotropic knitted wire mesh rolled up to form a cylindricalplug. The predictions compare reasonably well with the experimental results.The modelling approach is also applied to electrical conduction in anisotropic porousmedia saturated with an electrically conductive fluid. A macroscopic form of Ohm's lawis derived as well as deterministic expressions for the formation factor. The formationfactor predictions for isotropic porous media are compared to several experimental measurementsas well as to semi-empirical expressions. The predictions compare favourablyto the measurements.

[发布机构] Stellenbosch University