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Yes / A novel Lattice-Boltzmann model to simulate gas mixing in anaerobic digestion is developed and described. For the first time, Euler–Lagrange multiphase, non-Newtonian and turbulence modelling are applied jontly with a novel hybrid boundary condition. The model is validated in a laboratory-scale framework and flow patterns are assessed through Particle Imaging Velocimetry (PIV) and innovative Positron-Emission Particle Tracking (PEPT). The model is shown to reproduce the experimental flow patterns with fidelity in both qualitative and quantitative terms. The model opens up a new approach to computational modelling of the complex multiphase flow in anaerobic digesters and offers specific advantages, such as computational efficiency, over an analogous Euler-Lagrange finite-volume computational fluid dynamics approach. / UK EPSRC Grant (EP/R01485X/1, Computational Methods for Anaerobic Digestion Optimization, “CoMAnDO”). The numerical work was performed in the HPC Cirrus EPSRC Tier-2 National HPC Facility, Edinburgh, UK, under a UK EPSRC Tier-2 Research Allocation Panel (RAP) award.

A mathematical model is developed for quantification of aquifer deformation due to ground-water withdrawal and, with some modifications, is potentially applicable to petroleum reservoirs. A porous medium saturated with water is conceptually treated in the model as a nonlinearly viscous fluid continuum. The model employs a new three-dimensional extension, made in this thesis, of Helm's poroviscosity as a constitutive law governing the stress-strain relation of material deformation and Gersevanov's generalization of Darcy's law for fluid flow in porous media. Relative to the classical linear poroelasticity, the proposed model provides a more realistic tool, yet with greater simplicity, in modeling and prediction of aquifer movement. Based on laboratory consolidation tests conducted on clastic sedimentary materials, three phases of skeletal compaction are recognized. They are referred to as "instantaneous compression", "primary consolidation" and "secondary compression" according to Terzaghi and Biot's theory of poroelasticity. Among the three modes of consolidation, material behavior during the secondary compression phase has a nonlinear stress-strain relationship and is strongly time-dependent, exhibiting a phenomenon often known as "creep". In poroelasticity, the primary and secondary compressions have been conceptually considered as two separate physical processes that require two sets of material parameters to be evaluated. In contrast, the proposed poroviscosity model is a unified theory of time-dependent skeletal compression that realistically describes the physical phenomena of sediment compression as one single transient process. As a general model, two sets of governing equations are formulated for Cartesian and cylindrical coordinates, respectively, and allow for mechanical anisotropy and the assumption of principal hydraulic directions. Further simplifications of the governing equations are formulated by assuming mechanical isotropy, irrotational deformation and mechanical axisymmetry, which are more suitable for field applications. Incremental forms of the governing equations are also provided. / Ph. D.