Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

Steady-State Two-Phase Flow in Porous Media: Review of Progress in the Development of the

Scope of present article is to present the research efforts (implementing experimental study, theoretical analysis and modeling) taken towards the development of a complete theory for steady-state concurrent two-phase flow in porous media (the DeProF theory). The current state of progress is outlined and open problems are addressed. First attempts are traced back in the 1980s with the analysis, description and modeling of phenomena governing two-phase flow in pore scale. Appropriate simulators extending over hundreds and/or thousands of pores (network scale) were developed in the following decade (1990s); in parallel, extensive experimental research work identified three prototype/elementary flows comprising the average macroscopic flow, namely connected-oil pathway flow, ganglion dynamics and drop traffic flow and mapped their relative contribution to the macroscopic flow in terms of the process parameters. Efforts to provide a consistent physical rationale to explain the experimental observations, i.e. the map of prototype flow regimes, laid the grounds for developing the DeProF (Decomposition in Prototype Flows) theory. Amongst the main results/features of the DeProF theory was the identification of the actual operational and system parameters of the process and the introduction – according to ergodicity principles – of the domain of physically admissible internal flow arrangements of the average macroscopic flow. Use of the respective mechanistic model as a simulation tool (in the 2000s) revealed many characteristic properties of the sought process. Important is the existence of optimum operating conditions in the form of a smooth and continuous locus in the domain of the process operational parameters. This characteristic remained in latency within the relative permeability curves, until recently unveiled by the DeProF theory. Research efforts continue in the present (2010s) by elaborating appropriate physical considerations based on statistical thermodynamics and the introduction of the aSaPP (as Spontaneous as Physically Possible) concept that corroborates the correlation of the process efficiency to the multiplicity of the internal flow arrangements