Simplified groundwater flow modeling: An application of Kalman filter based identification

The need exists for methods to simplify groundwater contaminant transport models. Reduced-order models are needed in risk assessments for licensing and regulating long-term nuclear waste repositories. Such models will be used in Monte Carlo simulations to generate probabilities of nuclear waste migration in aquifers at candidate repository sites in the United States. In this feasibility study we focused on groundwater flow rather than contaminant transport because the flow problem is more simple. A pump-drawdown test is modeled with a reduced-order set of ordinary differential equations obtained by differencing the partial differential equation. We determined the accuracy of the reduced model by comparing it with the analytic solution for the drawdown test. We established an accuracy requirement of 2% error at the single observation well and found that a model with only 21 states satisfied that criterion. That model was used in an extended Kalman filter with synthesized measurement data from one observation well to identify transmissivity within 1% error and storage coefficient within 10% error. We used several statistical tests to assess the performance of the estimator/identifier and found it to be satisfactory for this application. This feasibility study highlighted problems known to others who have attempted to apply modern systems methods to hydrological problems and has led to related research studies at our laboratory.