Rink van Dijke

Criterion for three-fluid configurations including layers in pores with non-uniform wettability

Recently, a considerable effort has been made to determine the precise criteria for three-fluid configurations in pores of angular cross-sections, based on capillary entry pressures (van Dijke et al., J. Colloid Interface Sci. (2004) 184; van Dijke and Sorbie, Proc. CMWR XV, Chapel Hill (2004); Piri and Blunt, Phys. Rev. E, 70 (2004) 061603; Helland and Skjaeveland, Proc. 8th Int. Symposium on Reservoir Wettability, Houston (2004)). It has been shown that implementation of these criteria in pore network models may have a large effect on the simulation of three- phase displacements processes, such as NAPL migration in the unsaturated zone and gas injection for improved oil recovery. These configurations may contain thick conducting fluid layers, such as oil layers residing between gas in the centre and water in the corners of the pore, which significantly affect oil relative permeability. For pores of uniform, but arbitrary, wettability and in the absence of contact angle hysteresis a precise, thermodynamic, criterion for the existence of such layers has been established before. In this paper, we derive a similar criterion for pores of non-uniform wettability, a condition that commonly occurs when only parts of the pore walls are exposed to oil. Moreover, we show how this criterion depends on the different processes by which these layers form or collapse, such as gas invasion or oil extraction, as in each process different values of the various contact angles (advancing, receding or stationary) are involved. This criterion for formation and collapse of layers is consistent with the capillary entry conditions for the accompanying three-phase bulk phase displacements, which is essential for the accurate pore-scale modelling of three- phase flow.