Efficient estimation of aquifer intrinsic permeability anisotropy using perturbation theory

Abstract

Inverse modeling of aquifer measurements aims at estimating the spatial distribution of rock properties that best fits the available measurements which, in turn, allows predicting water yields and pressures to an acceptable level of accuracy. Nonlinear automatic inverse methods require multiple solutions of the diffusion equation, also known as the groundwater flow equation. Although numerical solutions to the forward problems improve the understanding of complex groundwater flow systems, they are often computationally expensive, thereby rendering the inversion process inefficient. We introduce a gradient-based inversion algorithm that leverages perturbation theory to efficiently estimate the tensorial intrinsic permeability distribution of porous media from single-phase transient pressure measurements. With a maximum of two numerical simulations, the Joint Perturbation-Superposition (JPS) method allows one to compute flow-history-dependent Intrinsic permeability Sensitivity Functions (PSF) on the spatial-temporal domain. Regardless of the gradient-based iterative inversion technique, our method efficiently adapts the sensitivity functions yielded by perturbation theory to calculate the entries of the associated Jacobian matrix at every iteration. A two-dimensional synthetic model comprising multi-well conditions is examined for an anisotropic and spatially heterogeneous groundwater flow system. The perturbation method yields accurate and efficient parameter estimation by leveraging sensitivity functions for (1) the appropriate selection of input transient pressure measurements and (2) reducing the sequential calculation of Jacobian matrices. As a result, Monte Carlo uncertainties as low as <5% are obtained for the estimated tensorial intrinsic permeability distribution, with inversion times halved when compared to conventional techniques.