Flow Lognormality and Spatial Correlation in Crustal Reservoirs: III -- Nature Permeability Enhancment via Biot Fluid-Rock Coupling At All Scales

Abstract

Fluid-rock mechanical interaction is important to crustal processes, yet little is known of the in situ physics. Typically fluid-rock interaction is expressed by folding fluid pressure p into Hooke’s Law, sij = cijkm ekm + pdij. As generally conceived this relation treats rock as a material continuum with pore pressure smoothly distributed a uniform granular matrix with little scope for microscale rock fabric evolution coupled to in situ fluids. Recent years have revealed inhomogeneity aspects of crustal fluid-rock interaction, from microscopic grain-scale ~mm to megascopic reservoir-scale ~km. Micro-to-macro inhomogeneity rooted in the grain-scale properties of rock and clays allows in situ fluid pressure to vary in conjunction with grain-scale permeability fluctuations. Grain-scale inhomogeneity is seen in the empirical spatial fluctuation systematics relating the logarithm of permeability ? to clastic porosity d? ˜ ? df and clay void ratio e, d? ˜ ? de. These relations are evidence that in situ permeability increments occur most readily at sites with existing permeability and a predilection in rock for defects associated with locally high porosity, and in clay for locales in which small mobile clay particles do not choke flow channels. These empirics imply a natural/generic fluid-solid coupled feedback geomechanical interaction that can enhance permeability. To compute the fluid-solid interaction embodied d? ˜ ? df, we allow for inhomogeneity elastic properties the Biot (1941) 3D consolidation equilibrium condition in a saturated medium: e.g., for the x-component of displacement (u,v,w), equilibrium is expressed by G?^2u + G/(1–2?)ex = Px for uniform shear modulus G and Poisson’s ratio ?, total strain e, and fluid pressure P, with subscript x denoting partial differentiation ?/?x. Rendering Biot fluid-solid stress equilibrium in 2D plane-strain conditions for heterogeneous porosity f(x,y) and shear modulus G(f) gives x-component equilibrium G?^2u + G(1+?)/(1–?)ex = Px – 2Gx(ux/(1–?) + vy) – Gy(uy + vx). Enforcing the heterogeneous Biot solid-fluid stress relation on a numerically simulated 2D rock matrix with 1000x1000 node density characterising the porosity spatial fluctuation state f(x,y), we can simulate repeat application of pressure causing small random fluctuations to grow through the d? ˜ ? df feedback relation into the large-scale high-amplitude spatial fluctuation systematics characteristic of in situ field-scale flow systems.