Fluid Flow and Heat Transport Computation for Power-Law Scaling Poroperm Media

Abstract

In applying Darcy’s law to fluid flow in geologic formations, it is generally assumed that flow variations average to an effectively constant formation flow property. This assumption is, however, fundamentally inaccurate for the ambient crust. Well-log, well-core, and well-flow empirics show that crustal flow spatial variations are systematically correlated from mm to km. Translating crustal flow spatial correlation empirics into numerical form for fluid flow/transport simulation requires computations to be performed on a single global mesh that supports long-range spatial correlation flow structures. Global meshes populated by spatially correlated stochastic poroperm distributions can be processed by 3D finite-element solvers. We model wellbore-logged Dm-scale temperature data due to heat advective flow into a well transecting small faults in a Hm-scale sandstone volume. Wellbore-centric thermal transport is described by Peclet number Pe ≡ a0φv0/D (a0 = wellbore radius, v0 = fluid velocity at a0, φ = mean crustal porosity, and D = rock-water thermal diffusivity). The modelling schema is (i) 3D global mesh for spatially correlated stochastic poropermeability; (ii) ambient percolation flow calibrated by well-core porosity-controlled permeability; (iii) advection via fault-like structures calibrated by well-log neutron porosity; (iv) flow Pe ~ 0.5 in ambient crust and Pe ~ 5 for fault-borne advection.