Conditional estimation of solute travel time in heterogeneous formations: Impact of transmissivity measurements

Solute transport through heterogeneous formations is modeled by the travel time approach, i.e., the time τ it takes a solute particle to travel from the source to a control plane. Due to uncertainty τ is a random variable characterized by its cumulative probability density function G(τ). This function is used by regulatory agencies in pollution site assessment. The main aim of the present study is to examine the impact of data, namely measured transmissivities, upon G(τ) and reduction of uncertainty. This is achieved for two‐dimensional steady flow of average uniform head gradient by using a Lagrangian approach developed in the past (Dagan, 1982, 1984, 1989; Rubin, 1990, 1991). The impact of data is seen in conditioning on measured values and in estimation of parameters characterizing flow and formation properties. The approach is illustrated by a simulation based on synthetic data. The results show how uncertainty is reduced by increasing the density of measurements for a control plane sufficiently far from the source.