Sensitivity Study on Hydraulic Well Testing Inversion Using Simulated Annealing

Abstract

Cluster variable aperture (CVA) simulated annealing has been used as an inversion technique to construct fluid flow models of fractured formations based on transient pressure data from hydraulic tests. A two-dimensional fracture network system is represented as a filled regular lattice of fracture elements. The algorithm iteratively changes an aperture of cluster of fracture elements, which are chosen randomly from a list of discrete apertures, to improve the match to observed pressure transients. The size of the clusters is held constant throughout the iterations. Sensitivity studies using simple fracture models with eight wells show that, in general, it is necessary to conduct interference tests using at least three different wells as pumping well in order to reconstruct the fracture network with a transmissivity contrast of one order of magnitude, particularly when the cluster size is not known a priori. Because hydraulic inversion is inherently non-unique, it is important to utilize additional information. We investigated the relationship between the scale of heterogeneity and the optimum cluster size (and its shape) to enhance the reliability and convergence of the inversion. It appears that the cluster size corresponding to about 20 -40 % of the practical range of the spatial correlation is optimal. Inversion results of the Raymond test site data are also presented and the practical range of spatial correlation is evaluated to be 5 -10 m from the optimal .cluster size in the inversion.

Interpretation and inversion of low‐frequency head observations

“…All inverse methods require repeated solution of the forward problem in order to estimate model parameters which are compatible with a set of observations. This is true for both stochastic methods, such as simulated annealing [ Mauldon et al , 1993; Nakao et al , 2001] and Markov Chain Monte‐Carlo, as well as for deterministic methods such as the Gauss‐Newton technique [ Sun , 1994]. Even the more efficient methods, such as the adjoint state approach [ Sun , 1994], require repeated solution of the full transient flow problem.…”