Using an Ensemble of Models to Design a Well Field Considering Regional Hydrologic Uncertainty

Abstract

Groundwater models are often developed as tools for environmental decision-making. However, sparse data availability can limit a model's utility by confounding attempts to select a single structural representation of a system or to find a unique and optimal set of model parameters. As a result, estimates of prediction uncertainty and the value of further data collection may be important results of a modeling effort. The Discrimination/Inference to Reduce Expected Cost Technique (DIRECT) is a new method for developing an ensemble of models that collectively define prediction uncertainty in a manner that supports risk-based decision making and monitoring network design optimization. We apply aspects of DIRECT to a modeling investigation of an aquifer system in Central Utah where a major Coalbed Methane gas field is located and a new approach for stimulating gas production is being explored. In the first stage of this study we develop an ensemble of regional MODFLOW models and calculate their relative likelihood using a set of observation data. These regional results and likelihoods are then transferred to a regional MT3D residence time model and to a local advective transport model to provide further information for the well design. A cost function is applied to the transport results to assess the relative expected costs of several proposed well field designs. The set of hydrologic results and associated likelihoods from the ensemble are combined into cost curves that allow for the selection of designs that minimize expected costs. These curves were found to be a useful tool for visualizing the ways that design decisions and hydrologic results interact to generate costs. Furthermore, these curves reveal ways in which uncertainty can add to the cost of implementing a design. A final analysis explored the cost of having uncertain model results by applying and manipulating synthetic likelihood distributions to the transport results. These results suggest the value that may be added by reducing uncertainty through data collection. Overall, the application of DIRECT was found to provide a rich set of information that is not available when ensemble methods and cost consideration are omitted from a modeling study.