A pore filling-based model to predict quasi-static displacement patterns in porous media with pore size gradient

Abstract

The displacement of immiscible fluids in porous media is common in many natural processes and engineering applications. Under quasi-static conditions, the displacement is affected by the geometry of the porous media and wetting condition. In an ordered porous medium, i.e., the pore size is maintained constant in the transverse direction and changes monotonously from the inlet to the outlet; previous works always focused on pore size gradient, but the role of wettability is not well-understood. Here, we investigate the pattern transition in ordered porous media with positive and negative pore size gradients under the wetting condition from imbibition to drainage. We first study the onsets of pore-filling events and then establish a link between these events and the local invasion morphologies at multiple pores under quasi-static conditions. We show that the burst and touch events, previously recognized to destabilize the displacement front, can cause a stable front in the negative and positive gradient porous media. We then link the local invasion morphologies to the displacement patterns, including the compact pattern, taper shape pattern, kite shape pattern, and single-fingering pattern. We propose a model to predict the transitions of these four patterns directly. The model prediction shows that the decreases in contact angles would destabilize the displacement front in the negative gradient porous media and stabilize the displacement front in the positive gradient porous media. We evaluate the predictive model using pore network simulations in this work and experiments in the literature, confirming that it can reasonably predict the pattern transition for immiscible displacements in ordered porous media under quasi-static conditions. Our work extends the classic phase diagram in ordered porous media and is of practical significance for multiphase flow control.