Impact of concentration measurements upon estimation of flow and transport parameters: The Lagrangian approach

Transport of a conservative solute takes place in a heterogeneous formation of spatially variable conductivity. The latter is modeled as a random space function of stationary lognormal distribution. As a result the velocity field and the concentration are also random. Assuming that measurements of concentration of an existing plume are available, the problem addressed here is to assess their effect upon identification of log conductivity and flow transport variables. The solution is sought in a Lagrangian framework in which transport is represented in terms of the random trajectories of particles originating from the initial plume. A concentration measurement is equivalent to the passage of a trajectory through the measurement point at a given time. The impact of measurements is achieved by conditioning any variable of interest on realizations for which at least one trajectory satisfies the requirement. It is shown that cokriging of concentration and another flow or transport variable leads to the correct conditioned mean of the latter. In contrast, the conditional variance based on cokriging is erroneous. The procedure is illustrated for two-dimensional flow under a few simplifying assumptions. The effect of a concentration measurement upon the expected value and variance of log transmissivity and plume centroid are examined in a few particular cases. The procedure may improve the solution of the inverse problem and the prediction of transport of existing plumes.