A new simulation model for multiphase flow in porous media

Oil production from petroleum reservoirs is accomplished as a result of its displacement from the reservoir pore spaces by either gas (solution gas or cap gas) and/or water. The natural drive mechanism present in a reservoir, and which is dominant during the primary stage of recovery, is relatively inefficient and often leaves an appreciable quantity of oil untapped. To increase recovery beyond the limits attainable by primary production, the natural energy in the reservoir is supplemented by the introduction of some form of artificial drive mechanism(s). The most basic methods of augmenting hydrocarbon recovery are those classified under secondary recovery schemes. These methods are targeted at sustaining production once well rates have declined during/after primary recovery. Typical examples of secondary recovery methods are waterflooding and natural gas injection. Usually, the selected secondary recovery method kicks off after primary recovery but, if deployed as a pressure maintenance scheme, could be conducted concurrently with primary recovery. Waterflooding is perhaps the most common secondary recovery method.;This study presents a novel mathematical model for investigating pore-level displacement processes in porous media. The flow medium considered in this work is a representative "physical model" made of parallel uniform circular capillary tubes assembled together to form a porous structure. Unlike earlier tube-bundle models which are composed of independent capillary tubes, the present model assumes that the tubes are separated by partitions that allow transfer flow from one tube to the other. In this way, at any perpendicular cross-section in the direction of flow, pressure is equilibrated; hence, fluid flow in any one tube is not independent of those in adjacent tubes. This is the concept of the interacting bundle of capillary tubes that was first introduced by Dong et. al (2005) for modelling immiscible displacement in porous media. This study also shows that predictions made from the interacting bundle of tubes are more representative of flow observations in real porous media than those furnished by the earlier non-interacting bundle of tubes.;The production methods highlighted above are immiscible displacement strategies. A displacing fluid (usually water or gas) is injected into the reservoir and forced to sweep through the portion of the reservoir lying between an injection well and a production well. As the injection fluid travels, it mobilizes and "pushes" any oil in its path to the production well. The success of these strategies significantly depends on the knowledge of the physics of multiphase flow in porous media. Traditional reservoir engineering models flow in porous media using Darcy's empirical transport rule. Darcy's law is a phenomenologically derived constitutive equation that describes flow in porous media from a macroscopic standpoint. It fails to account for microscopic fluid interactions and pore-level variations that play significant roles even in the macroscopic manifestation of multiphase flow.