Markov-chain Monte Carlo estimation of aquifer parameters, non-linear well losses, and probable costs of water extraction

Previous studies found that best-fit parameters from variable-rate pumping tests show very high correlation between both aquifer and non-linear head loss parameters. This correlation implies non-uniqueness of parameter sets and potentially similar non-uniqueness of predicted well behavior. The resulting uncertainty may lead to a wide range of potential future pumping costs, making it difficult to evaluate how up-front investments to improve well efficiency will ultimately influence overall costs. To address this and assess how filter-pack material affects predictive pumping costs, we implement (in Python) a Bayesian sampling of the posterior distribution of aquifer and non-linear well loss parameters using Markov-chain Monte Carlo (MCMC) methods. We also implement a novel discharge correction to account for wellbore storage that significantly changes efficiency estimation. These methods are needed to analyze a number of single-well step-drawdown tests from the city of Castle Rock, Colorado, including wells constructed with both sand and glass-bead filter packs. Some wells were constructed with the more expensive glass-bead filter packs with the intent of saving pumping costs due to higher well efficiency. The resulting parameter distributions are highly correlated and non-Gaussian. Forward simulations using an ensemble of these parameter sets, along with a cost function to predict future pumping costs weighed against initial capital costs, show that there were no statistically significant improvements to well efficiency by using glass bead filter packs. • Python freeware for Marquardt-Levenburg and Markov-Chain Monte Carlo analysis of step-drawdown tests. • Posterior probabilities of nonlinear head losses generated. • Probabilistic analysis of potential electric power saving from glass-bead (rather than gravel) filter pack. • Nonlinear head losses more closely associated with aquifer formation than filter pack material.