Geostatistical solution to the inverse problem using surrogate functions for remediation of shallow aquifers
Creators: name: Bau, Domenico
name: Mayer, Alex
name: Bau, Domenico
Publisher: name: XVI International Conference on Computational Methods in Water Resources
Year: 2006

description: Pump-and-treat (PAT) techniques are often applied to the remediation of dissolved 
chemicals from shallow aquifers. A related management problem typically consists of 
the selection of the pumping strategy and the most appropriate treatment method, in 
order to minimize the total cleanup cost while meeting a set of technical, economic 
and social constraints. However, due to scarcity of information about the 
hydrogeological system, stochastic modeling approaches seem more appropriate. Of 
primary concern is the inherent spatial variability of hydraulic conductivity. In 
general, the implementation of a remediation strategy assessed based on uncertain 
hydrogeological parameters leads to a decision involving the risk of constraint 
violations. The decision-making process may then be formulated as a multiobjective 
optimization framework where the optimality of a pumping pattern is traded off 
against its reliability. Operations may be structured into a stochastic optimal 
control problem, in which the remediation strategy is sequentially updated based 
upon new measurements collected during the actual cleanup process. The procedure 
requires the implementation of an inverse simulation model to estimate the 
stochastic hydrogeological parameters based on a set of potential measurements. In 
this work, we follow a geostatistical conceptual model where the spatial 
distribution of hydraulic conductivity is represented as a realization of a log-
normally distributed stationary process, characterized by an exponential covariance
function. Using the maximum likelihood method, the parameter estimation problem is 
solved by determining the set of geostatistical parameters -- average, variance, 
and correlation scales. Available data may include direct measurements of hydraulic 
conductivity, water table elevation at a number of monitoring wells, and 
contaminant mass extracted from active remediation wells. A rigorous solution to 
this optimization problem would require a stochastic flow and transport model to be 
included in the optimization loop to calculate the expected values and the 
covariance matrix of the available measurements as functions of the decision 
variables. Because of the overwhelming computational effort involved, a surrogate 
model or response surface is introduced to approximate the objective function. The 
surrogate model is estimated using a multidimensional kriging interpolation over a 
set of data points or measurements obtained from a series of stochastic flow and 
transport simulations for pre-established combinations of the decision variables. 
Since the goodness of the solution is ultimately determined by the error of 
estimation of the objective function, which in turn depends on the number and the 
location of measurements, an optimal search procedure is used in order to optimize 
the pattern of data points. The method turns out to be computationally efficient 
and produces results that well approximate the actual geostatistical distribution of
hydraulic conductivity.