Stochastic Subsurface Data Integration Assessing Aquifer Parameter and Boundary Condition Uncertainty

This research successfully extends a deterministic, physically-based inverse theory that is capable of simultaneous parameter and boundary condition estimation to uncertainty quantification in inverting steady-state groundwater flow in a two-dimensional aquifer with facies heterogeneity. Using facies and dynamic flow measurements sampled at wells as observations, a stochastic subsurface data integration technique is proposed: (1) Sequential Indicator Simulation integrates facies data by characterizing its geostatistical parameters (experimental directional variograms and sample facies proportions) to generate correlated facies models; (2) for each facies model, hydraulic conductivities and flow field (including the unknown boundary conditions) are estimated via a direct inversion method; (3) uncertainty in inversion, including both uncertainties of the estimated hydraulic conductivities and the flow field, is evaluated by assessing the inversion outcome for all facies models. To test the proposed integration technique, a reference forward model provides both facies characterization and dynamic measurements at increasing sampling densities (i.e., data quantity) and measurement errors (i.e., data quality). Via smoothing and grid coarsening, alternative hydraulic conductivity parameterization is also tested in inversion. Uncertainty in the estimated conductivities and boundary conditions is then quantified against the reference model to evaluate the quality of inversion. Results suggest that for the ranges of tested variation in data quantity, quality, and inverse conductivity parameterization, (1) data quantity has the strongest impact on both inversion accuracy and precision; (2) data quality influences inversion accuracy; (3) inverse parameterization has the weakest influence on inversion as long as the overall facies pattern is captured (i.e., sufficient data quantity). A balance can thus be achieved between parameterization, computational efficiency, and inversion performance. For Dongdong Wang Department of Geological Sciences, University of North Carolina, Chapel Hill, North Carolina, USA E-mail: [email protected] Ye Zhang 1000 University Ave., University of Wyoming, Laramie, Wyoming, USA E-mail: [email protected] 2 Dongdong Wang, Ye Zhang the heterogeneity pattern investigated herein, by defining an acceptable margin of uncertainty for either conductivity or flow field estimation, optimal well spacing in relation to the characteristic length of heterogeneity can be determined under unknown boundary conditions. Finally, inversion domain should be closely defined by the measurement locations in order to minimize extrapolation errors.