Packed beds are widely used to perform solid-catalyzed gas–liquid reactions, e.g., hydrodesulfurization, oxidation, and hydrogenation. The overall performance of packed beds is often governed by local liquid spreading. In the present work, the dynamics of liquid spreading through a randomly packed three-dimensional bed is investigated using particle-resolved volume-of-fluid simulations. The effect of particle surface-wettability ([Formula: see text]) at varying particle diameter ([Formula: see text]) on the relative contributions of forces governing the dynamics of liquid spreading is analyzed using the Ohnesorge ([Formula: see text]), Weber ([Formula: see text]), and [Formula: see text] (proposed in the present work) numbers. With the help of simulated liquid spreading and these numbers, we show that the contribution of inertial force is significant at the beginning of liquid spreading irrespective of [Formula: see text] as well as [Formula: see text] and promotes lateral liquid spreading ([Formula: see text] >1, [Formula: see text] >1). Once the dominance of inertial force diminishes, the capillary force leads to a substantial increase in the lateral spreading ([Formula: see text] > 1, [Formula: see text] < 1). In the final stages, the gravitational force dominates restricting the lateral liquid spreading ([Formula: see text] < 1). Furthermore, we have proposed a regime map constructed using [Formula: see text] and [Formula: see text], which provides a relationship between different forces and the resultant liquid spreading at breakthrough. We also show that the dominance of capillary force ([Formula: see text] >1, [Formula: see text] <1) results in the highest lateral spreading, whereas the flow dominated by inertial ([Formula: see text] >1, [Formula: see text] >1) and gravitational force ([Formula: see text] ≪ 1) leads to intermediate and least lateral liquid spreading, respectively.
Liquid spreading through a randomly packed particle-resolved bed influenced by capillary or inertial ( $AB_s \sim 1$ ), and gravitational force (moderately ( $AB_s \sim 0.1$ ) and strongly ( $AB_s \sim 0.01$ )) is investigated using the volume-of-fluid simulations. The relative contribution of governing forces at different stages of spreading is analysed using the time evolution of Weber ( $We_I$ ) and $AB_I$ numbers. We show that the dynamics of liquid spreading at $AB_s \sim 1$ is primarily governed by the inertial force in the beginning ( $AB_I > 1$ , $We_I > 1$ ) followed by the capillary force at $t/t^* \sim 1$ . This interplay of governing forces leads to inertia- and capillary-induced bubble entrapments at the void scale and promote lateral liquid spreading. When the $AB_s \sim 0.1$ , the $t/t^*$ for which the flow is governed by inertial ( $AB_I > 1$ , $We_I > 1$ ) and capillary forces ( $AB_I > 1$ , $We_I < 1$ ) decreases and the relative contribution of gravitational force is substantial at large $t/t^*$ ( $AB_I < 1$ ). This force balance leads to unified-void filling characterised by negligible bubble trapping and results in a decrease in the lateral spreading. Further decrease in the $AB_s$ to ${\sim } 0.01$ results in liquid spreading primarily governed by gravitational force ( $AB_I < 1$ ) with small contribution of inertial and capillary forces at the very beginning leading to trickling flow and a further decrease in lateral spreading. Finally, a regime map is proposed, which provides the relationship between different forces, void-scale events, and the resultant liquid spreading at $t/t^* \sim 1$ .
Two-phase flow through porous media is important to the development of secondary and tertiary oil recovery. In the present work, we have simulated oil recovery through a pore-resolved three-dimensional medium using volume-of-fluid method. The effects of wettability and interfacial tension (IFT) on two-phase flow mechanisms are investigated using pore-scale events, oil-phase morphology, forces acting on oil ganglia surfaces, and oil recovery curves, for Capillary numbers (Ca) in the range of 1.2 × 10−3 to 6 × 10−1. We found that the two-phase flow through oil-wet medium is governed by pore-by-pore filling mechanism dominated by the Haines-jumps. At low Ca values, a change in the wettability from oil- to neutrally wet resulted into the change of pore-by-pore filling mechanism to co-operative pore filling and as the medium wettability changes from the neutrally to the weakly water-wet, the corner flow events begin to emerge. At low Ca values, the invasion through weakly water-wet porous medium is dominated by co-operative filling and results into an increased oil recovery, whereas the two-phase flow through strongly water-wet medium is governed by corner flow events resulting in a low oil recovery. The corner flow events are found to be a function of not only the medium wettability, but also of Ca and are a characteristic of controlled imbibition. Further, we show that a substantial decrease in the IFT results in a fingerlike invasion at pore-scale, irrespective of the medium wettability. Finally, a two-phase flow regime map is proposed in terms of Ca and contact angle based on the two-phase interface morphology.
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