Bayesian identification of the local transmissivity using time-drawdown data from pumping tests

Conventional pumping test analysis techniques focus mostly on estimating the effective transmissivity of the perturbed subsurface volume surrounding the extraction and observation wells, ignoring the existing local-scale heterogeneity. The purpose of this paper is to explore whether transient drawdown data derived from pumping tests can also be used to identify the statistical spatial structure of the local transmissivity field. The log-transmissivity is modeled as a multivariate random spatial function with stationary mean, and exponential semivariogram. Monte Carlo simulations are used to compute the transient drawdown for different values of the log-transmissivity variance and integral scale. On the basis of these simulations, a Bayesian procedure is developed to estimate the probability density functions of these two statistical parameters. The main benefit of using a Bayesian approach is that it readily accounts for the uncertainty of the estimated parameters. Application of the proposed procedure to simulated drawdown data shows that it is possible to characterize the local transmissivity from pumping test data and that the reliability of the estimates increases with an increase in the number of available tests.