Equivalent Radius for Well Inflow Calculations at Different Regimes in Reservoir Flow Simulations

A problem of well representation in numerical simulation of fluid flows in porous media is considered. When modelling hydrocarbon reservoirs, underground gas storages and other natural porous media, there’s a large typical difference in scales of wells (about 10 cm) and inter-well distances (from hundreds to thousands meters), so wells aren’t resolved on the grid as explicit boundaries in large-scale reservoir simulations. Instead, wells are represented by sources/sinks. The problem is that the average pressure in a grid block containing the well (well block pressure, WBP) isn’t equal to the well pressure (bottomhole pressure, BHP). D. Peaceman showed that WBP can be interpreted as the pressure at equivalent radius inside the well grid block. He derived the classical formula for the equivalent radius for steady-state (SS) Darcy flow. Though Peaceman showed it could be used for pseudo steady-state (PSS) flow as well, his derivation for PSS was not accurate. In this paper we compute the equivalent radius for PSS and boundary dominated (BD) regimes of Darcy flow and examine the impact of flow regime and distance to external boundary (or inter-well distance) on it. The results are important for accurate well representation in numerical flow simulations of underground reservoirs.