Direct numerical simulations of spontaneous imbibition at the pore-scale: impact of parasitic currents and dynamic capillary barriers

Abstract

Multiphase flows in large scale porous media applications depend on the cumulative collection of flow physics occurring within millions of interconnected pores. Even after several decades of research, many pore-scale flow phenomena lack profound understanding. Capillary driven spontaneous imbibition flows have attracted research interest in recent times due to their widespread occurrence in industrial and engineering applications. In this thesis, we investigate spontaneous imbibition flows at the pore-scale using direct numerical simulations (DNS). The volume of fluid (VOF) method is used to represent the twophase fluid system as a single mixture considering a volumetric colour function. The focus of this research work is to investigate pore body filling during imbibition. We identify scenarios where conventional quasi-static pore network models (PNM) fail to accurately predict the imbibition fronts due to the shortcomings in quantifying threshold pressures. In this regard, all the continuum scale numerical methods struggle to accurately approximate capillary forces. Hence, in the first part of this thesis, we provide a valuable dynamic benchmark case of spontaneous imbibition in a microchannel. In this benchmark study, we quantify parasitic currents, compare the accuracy and performance between various VOF formulations namely: the continuum surface force (CSF), the sharp surface force (SSF), the filtered surface force (FSF) and the piecewise linear interface calculation (PLIC). This benchmark study reveals that all formulations are within 10% accuracy compared to the analytical extended Lucas-Washburn solution. In the second part, we discuss the event of pore body filling during spontaneous imbibition and provide insight regarding the existence of dynamic capillary barriers that have been unidentified so far. We provide analytical expression to compute the critical contact angles for various pore geometries. The critical contact angles play a major role in foreseeing if capillary barriers exist for the considered contact angles of the fluid. Moreover, we provide a semi-analytical expression to determine the position of the capillary barrier zones. We show imbibition cases where the smaller pores are not favoured by the wetting phase to get imbibed - which contradict the flow behaviour of the conventional quasistatic PNM. In the third part, we provide another dynamic benchmark case of spontaneous imbibition in a pore singlet. We assess the accuracy of CSF, SSF and FSF formulations. We notice that CSF and SSF match the analytic solution, whereas smoothing the colour function and FSF result in erroneous flows. For this case, we find that an accurate representation of the interface curvature is important than to focus on eliminating parasitic currents. Then CSF and SSF are applied to investigate spontaneous imbibition in a 2D synthetic pore network. We observe that when capillary barriers exist, the invasion paths obtained through DNS would differ from the invasion paths that could be predicted by the conventional quasistatic PNM.