Modelling the contact line dynamics of two-phase flows across surfaces of longitudinal multiple wettability sections in capillary channels for the characterisation of capillary filling processes

Abstract

In natural porous media, the wall of each induvial pore is commonly formed by chemically different materials to give various surface energies and wettability to fluids. In a two-phase capillary system with contrasting wet-surface sections along the capillary, when the interface between the invading and receding fluid moves cross each wet-surface interface, the dynamics of fluid-fluid-solid contact line is subject to a transition stage, in an accelerating (slip) or decelerating (stick) manner, due mainly to the transformation of surface, kinetic energy and viscous dissipation. Time and length durations of the slip-stick process are influenced by fluid properties, capillary geometry, and wettability as well as forces driving flow through imposed boundary conditions. The slip-stick process can have a strong impact on the dynamics of capillary filling process in individual capillaries and therefore subsequent selection of plausible pathways for a fluid to migrate through a pore system which is filled by another fluid. This impact is likely to be more severe in less-well connected pore systems with strong contrasts in surface wettability such as organic-rich shales and coals. However, the transitional dynamics of the contact line, the slip-stick process, is poorly understood in a parameter space of practical interest. This research fills this knowledge gap through a combined study of numerical modelling and analytical analysis. A two-phase multi-relaxation-time colour-gradient lattice-Boltzmann (LB) model is implemented for simulating contact line movement around wettability transitions in 2D. A 1D analytical model for homogenous-wet capillary filling, which considers the inertial effects of contrasting fluids, is employed to derive a dimensionless model for parameter groups and to perform dimensional analysis on energy and forces involved. The LB code is validated using this analytical model and is used to simulate capillary filling in 2D channels which contain two sections of different wetting surfaces along each channel, for a set of parameters, including respective velocity and pressure flow driven boundary conditions. The variation of the viscous dissipation generated by the slip-stick processes is analysed and it is found that the transient dynamics of the contact line coincides with the temporal variation of the viscous dissipation and that duration reflects the time the contact line requires to balance the change of surface energy arisen from the wettability change. The time and distance in which the transitional dynamics take place are evaluated under low capillary numbers over a wide range of fluid and capillary geometric parameters. Using the data obtained from this study, an empirical effective capillary filling model is developed. It is shown this model can be used to establish a simple rule-based criterion for determining whether an individual pore throat in a pore network is to be invaded or not under given boundary conditions during drainage and imbibition processes. Finally, using this criterion, the significant impact of multi-wet pore-throats on phase saturation in a simple pore system is demonstrated under quasi-static displacements.