DataSheet1_A pore filling-based model to predict quasi-static displacement patterns in porous media with pore size gradient.DOCX

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.多孔介质内不混溶流体驱替现象广泛存在于诸多自然过程与工程应用场景中。在准静态（quasi-static）条件下，该驱替过程受多孔介质几何结构与润湿性（wetting condition）共同调控。针对有序多孔介质——即横向孔径保持恒定、且沿入口至出口方向单调变化的多孔介质——既往研究多聚焦于孔径梯度（pore size gradient）的影响，而润湿性的作用机制尚未得到充分阐明。本研究针对兼具正负孔径梯度的有序多孔介质，探究了自吸（imbibition）至排驱（drainage）润湿性条件下的驱替形貌转变规律。我们首先分析了孔隙充填事件的触发条件，随后建立了准静态条件下此类事件与多孔隙区域局部侵入形貌之间的关联。研究表明，此前被认为会破坏驱替前缘稳定性的突爆与接触事件，在负孔径梯度与正孔径梯度多孔介质中反而可促使驱替前缘趋于稳定。进一步将局部侵入形貌与四类驱替形貌关联，包括紧凑形貌、锥形形貌、风筝形形貌与单指状形貌，并提出了可直接预测这四类形貌转变的理论模型。模型预测结果显示，接触角的降低会使负孔径梯度多孔介质内的驱替前缘失稳，却能使正孔径梯度多孔介质内的驱替前缘趋于稳定。本研究通过孔隙网络模拟与文献中的实验数据对该预测模型进行了验证，证实其可合理预测准静态条件下有序多孔介质内不混溶流体驱替的形貌转变过程。本研究拓展了有序多孔介质内的经典相图，对多相流调控具有实际应用价值。