Fluid flow, relative permeabilities and capillary pressure curves through heterogeneous porous media

• Published in: Applied Mathematical Modelling 2019-11, Vol.75, p.481-493
• Main Author: Pereira, G.G.
• Format: Article
• Language: English
• Subjects: Capillary flow; Capillary pressure; Digital imaging; Equilibrium flow; Fluid dynamics; Fluid flow; Fluids; Heterogeneity; Multiphase; Permeability; Porous media; Rocks
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.05.050

•Lattice Boltzmann (LB) model applied to multiphase, immiscible flow through real porous media (rocks).•Porous media have pores with heterogeneity in pore sizes, so that some pores cannot be fully resolved.•Model accounts for unresolved porosity by suitably modifying conventional LB.•Numerical results obtained for relative permeability and capillary pressures. There is a growing interest in fluid flow through rocks which show a large range, or heterogeneity, in pore sizes (from order tens of nanometres up to a hundred microns) which lead to small porosities and permeabilities. Digital imagery of these rocks yield under-resolved pore structures or a gray-scale sample. In this work we use the gray-scale lattice Boltzmann (LB) method to determine flow of two, immiscible fluids through such three-dimensional porous media. The method yields transient and equilibrium flow fields from which we determine relative permeability and capillary pressure curves. The method is applied to real digital rock data to extract flow properties through the sample. Both single phase and multiphase LB simulations are carried out. We find low permeabilities (of the order of milli-Darcy) together with large residual saturations (between 50–75%), indicative of a rock sample which has void regions remote from each other, i.e. either disconnected or connected by very narrow pore throats.