EULERIAN-LAGRANGIAN ANALYSIS OF TRANSPORT CONDITIONED ON HYDRAULIC DATA .1. ANALYTICAL-NUMERICAL APPROACH

Recently, a unified Eulerian-Lagrangian theory has been developed by o ne of us for nonreactive solute transport in space-time nonstationary velocity fields. We describe a combined analytical-numerical method of solution based on this theory for the special case of steady state fl ow in a mildly fluctuating; statistically homogeneous, lognormal hydra ulic conductivity field. We take the unconditional mean velocity to be uniform but allow conditioning on measurements of log hydraulic condu ctivity (or transmissivity) and/or hydraulic head. This renders the ve locity field nonstationary. We solve the conditional transport problem analytically at early time and express it in pseudo-Fickian form at l ater time. The deterministic pseudo-Fickian equations involve a condit ional, space-time dependent dispersion tenser which we evaluate numeri cally along mean ''particle'' trajectories. These equations lend thems elves to accurate solution by standard Galerkin finite elements on a r elatively coarse grid. The final step is an explicit numerical computa tion of lower bounds on conditional concentration prediction variance- covariance (and coefficient of variation), travel time distribution, c umulative mass release across a ''compliance surface,'' the associated error, and plume spatial moments. Our method also allows quantificati on of the uncertainty in the original source location of any solute '' particle'' located anywhere in the field, at any time. This paper desc ribes the methodology and presents some unconditional results. Conditi oning and more advanced computations are presented in the subsequent p apers.