PORE TOPOLOGY-BASED INTERPRETATIONS OF GAS PRODUCTION DECLINE CURVES

Production curves in unconventional shale plays show a sharp decline, with first-year declines in the Barnett Shale being on the order of 50 to 75%. A feature common to many production curves is a slope transition from a moderate decline (exponent around -0.5) to a much steeper decline within the first few months or years. This is conventionally interpreted as the transition from linear flow to boundary-dominated flow, but the physics often argues otherwise, and the exponents suggest alternative interpretations. In recent years the near-universal reliance on the empirical Arps equations has been challenged by (for example) power law exponential decline and modified hyperbolic decline equations, but these likewise often lack a theoretical basis.

The extremely low permeability of shale raises the possibility that the gas recovery is limited by topology (e.g., density of pore connections) rather than by geometry (e.g., pore size). Accordingly, we examine production decline curves from the perspective of percolation theory, which leads to alternative interpretations. Possibilities we examine include (1) accessible porosity and diffusion coefficient varying with distance from a fracture, resulting in anomalous diffusion; (2) a cross-over from invasion percolation to random percolation as the fracture network dewaters following hydraulic fracturing; and (3) a cross-over from 2D to 3D percolation behavior as the rock immediately adjacent to the fractures desorbs gas. Constraints imposed by the range of possible values of rock properties (e.g., porosity, fractal dimension) serve to eliminate some possibilities.