Analysis and Computational Mathematics Seminar
Hosted by the UW Math Department
Speaker: Ye Zhang
Title: Direct Method of Parameter Estimation for Steady State Flow in Heterogeneous Aquifers with Unknown Boundary Conditions
Date: Tuesday, Feb 26
Time: 4:10 - 5 pm
Location: Ross Hall 247
A new physics-based inversion method has been developed to simultaneously estimate steady-state hydraulic conductivities (K), source/sink strengths, state variables, and boundary condition (BC), for both confined and unconfined heterogeneous aquifers subject to natural or man-made recharge/discharge effect (e.g., well operations). Unlike the objective-function-based techniques, this method does not require forward flow simulations to assess data-model misfits, thus the knowledge of BC is not required. Instead, it directly incorporates noisy observed data (hydraulic heads, groundwater fluxes, or flow rates) at the measurement points in a single step, without solving a boundary value problem. The method is computationally very efficient. For problems where the underlying variations of the parameters (both hydraulic conductivities and source/sink strengths) are unknown, the method yields equivalent conductivities and average source/sink strengths. Given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently with linear or nonlinear optimization techniques. The solution is also stable when measurement errors are increased. The method has been successfully tested on two- and three-dimensional groundwater flow problems with regular and irregular geometries, different heterogeneity patterns, variances of heterogeneity, and error magnitudes. In all cases, parameters converge to the correct or expected values and are thus unique, based on which heads and flow fields are estimated directly via a set of analytical expressions. Accurate BCs are then inferred from these solutions. The inverse methods can also handle strongly heterogeneous systems. To date, the highest successfully inverted conductivity contrast is 100,000. Finally, to quantify estimation uncertainty, the method has been successfully integrated with geostatistics, whereas uncertainty in the static data (e.g., hydrofacies proportion, covariances, and correlation ranges) is propagated into the inversion outcomes --- a set of realizations of model parameters, flow fields, and BCs can be created. These realizations center on the ``true'' solution created from an underlying true model, while increased sampling (both of the static and dynamic data) leads to reduced spread in the estimated parameters, flow field, and BC. Future work will investigate highly parameterized inversion, transient effects, coupled flow with geomechanics, and multiphase flow.