Development of truncated cone pore network model for two-phase flow simulation in porous media

Abstract

Understanding and predicting multiphase flow behaviors in a porous medium is an important issue in engineering fields. Among the available pore-scale modeling techniques, the pore network model (PNM) has been actively researched owing to its scalability and light computational effort. A ball-stick network has been widely used in many previous researches. Despite such advantages, the PNM has a limitation in that the pore geometry is overly simplified in a network, which often generates unreliable results. Therefore, in this study, the pore morphology is expressed using truncated cones, referred to as a truncated cone pore network model (TC PNM). First, the pore geometries of both Berea and Doddington sandstone were examined based on X-ray computed microtomography (X-ray CMT) images. It was found that the pore morphology was better expressed with groups of truncated cones rather than a consortium of balls and sticks. This indicates the possibility of using the truncated cone pore network model (TC PNM) to model the pore-scale morphology and multi-phase flow behaviors under such geometric conditions. Thus, an algorithm to extract a TC PNM was developed and applied to Berea and Doddington sandstone samples. In developing the TC PNM extraction, the concepts of the searching step and ball type were modified based on the maximum inscribed sphere (MIS) algorithm and the hierarchy system used in the maximal ball (MB) PNM algorithm. Thereafter, the Young-Laplace equation and Hagen-Poiseuille equation, modified for truncated cones, were incorporated into a dynamic multiphase flow PNM simulator. By conducting dynamic flow simulations, the displacement pattern, fluid saturation, and flow rate can be obtained over time, along with the macroscale parameters, such as the absolute permeability, capillary pressure curve, and relative permeability. For verification of the TC PNM, the TC pore networks extracted for the two sandstone samples were directly compared with X-ray CMT images and the pre-existing MB PNM. This confirmed that the TC network better reflects the actual pore geometry than the MB PNM. The multiphase flow simulation results from the TC pore networks were also verified against mercury intrusion porosimetry (MIP) experiment results, and compared with those of the MIS algorithm and the MB PNM. The non-wetting fluid invasion in a water-saturated porous medium was also examined using the three predictive methods, the TC PNM, MB PNM, and MIS algorithm. Among them, the capillary pressure curve and pore size distribution obtained from MIP were most similar to the TC PNM results. In particular, the pore size distribution defined and obtained through an MIP test was confirmed to be the most similar to the definition of nodes in the TC PNM. It was concluded that the developed TC PNM reflected the shape characteristics of pores in sandstone well, and provided reliable results on the transport characteristics and displacement patterns of multiphase fluid flows.