Phase connectivity in pore-scale networks and capillary entry conditions

Abstract

Quasi-static pore-network modelling is a numerical approach that estimates multi-phase flow properties, such as capillary pressure and relative permeability functions in representative digital models of permeable media, the pore-scale networks. The present dissertation introduces substantial improvements to the conventional workflow and methodology of modelling of immiscible capillary displacement in pore-scale networks. The most significant advancement of this research is the development of a novel algorithm, that introduces a highly efficient approach to interrogate the phase connectivity and execute its alteration following pore-scale displacements in simulation of two-phase drainage and imbibition processes. The main disadvantage of a conventional implementation of the phase connectivity algorithm is the poor scalability of simulation time with increasing model size due to the inefficiency of the phase connectivity interrogation. The proposed solution demonstrates a practical speed-up by at least two orders of magnitude compared to all other existing implementations. Application of our algorithm allows for routine simulation of large models, which may integrate multiple scales of heterogeneity and capture representative elementary volumes comprising millions of pores. Robust sensitivity studies become feasible to evaluate the impact of uncertainty in multi-phase flow behaviour. Additionally, this thesis proposes a new method for the numerically precise estimation of capillary entry conditions in pore throats of arbitrary geometry and wettability. The newly estimated results show a considerable deviation from standard approximations characterised by regular simple shapes. Results demonstrate that a major concern arises when an approximated shape requires averaging of non-uniform wettability distribution of the original shape.