Stochastic determination of well capture zones conditioned on regular grids of transmissivity measurements

Abstract

A stochastic approach is adopted for characterizing the uncertainty in time‐related well capture zones in heterogeneous formations. Transmissivity is modeled as a random space function, conditioned on regular grids of evenly distributed transmissivity measurements. Monte Carlo analysis is used to infer the probability distribution of the resulting stochastic capture zones. Three measures of conditioning performance are defined and evaluated for several combinations of conditioning density, transmissivity variance, and transmissivity integral scale. Furthermore, a connection is made with previous work on transport theory. Simulation results show that conditioning performance increases with an increasing conditioning density, an increasing transmissivity integral scale, and a decreasing transmissivity variance. However, there is a threshold combination of conditioning density and integral scale beyond which conditioning performance stagnates. The practical implications of the results in general and the threshold in particular are discussed.