Crustal Reservoir Flow Simulation for Long-Range Spatially-Correlated Random Poroperm Media

Abstract

In interest of accurately modelling wellbore production in convective geothermal systems, we draw attention to two approaches to numerical simulation of crustal fluid flow. The historical ‘’strong’’ approach simulates the fluid mass conservation condition on a localised finite difference mesh approximation to poroelastic continua. The more flexible ‘’weak’’ approach globally enforces fluid mass conservation by in effect integrating over all numerical mesh cells. Strong formulation crustal flow simulation emerged from numerical simulations of mathematically tractable conductive heat flow in media typified by normally-distributed/spatially-uncorrelated thermal property distributions. Strong formulation numerical stability problems quickly intrude, however, when confronted with the lognormally-distributed/spatially-correlated crustal permeability distributions that pervade the ambient crust. Weak flow conservation solver formulations accurately handle abrupt wide-ranging crustal permeability spatial fluctuations arising from these crustal permeability structures. We use two Matlab-based weak formulation flow simulation schemes to model wellbore-centric production fluid connectivity within large-scale spatially erratic convective geothermal flow structures described by the empirical poroperm relation k(x,y,z) ~ exp(αφ(x,y,z)) acting over cm-to-km scale lengths. Through weak formulation reservoir flow modelling of convective geothermal systems, the advancing ability to support large-scale crustal flow structure models with multi-channel surface seismic data acquisition/processing can guide geothermal field exploration and developmental drilling via feedback loops between crustal flow imaging data and accurate wellbore production modelling data.