An asymptotic analysis for determining concentration uncertainty in aquifer transport

Transport of a conservative solute takes place by advection and by pore-scale dispersion in a formation of spatially variable logconductivity Y(x)=ln K(x). The latter is modeled as a normal stationary random space function, characterized by a few statistical parameters, like the mean , the variance (sigma)Y2, the horizontal and vertical integral scales Ih and Iv. The local solute concentration C(x,t), a random function of space and time, is characterized by its statistical moments, like, e.g. the mean and the standard deviation (sigma)C. A simplified analysis for determining the concentration uncertainty is proposed. The proposed methodology, valid for nonreactive solutes, is based on a few simplifications, the most important being: (i) large transverse dimensions of the injected plume compared to the logconductivity correlation lengths, (ii) mild heterogeneity of the hydraulic properties, which allows for the use of the first-order analysis, (iii) highly anisotropic formations, and (iv) mean uniform flow. The concentration uncertainty is represented through the coefficient of variation CVC=(sigma)C/ at the plume center, where the expected concentration is maximum. Results for CVC are illustrated as function of time and on two dimensionless parameters: (omega)=Iv2/(Ih(alpha)dT) and (lambda)=L1/(radical)(A11Ih)where L1 is the longitudinal dimension of the initial plume, A11 is the longitudinal macro dispersivity, and (alpha)dT is the local transverse dispersivity. Summary graphs lead to a quick and simple estimate of the time-dependent concentration uncertainty, as well as its peak and its setting time (i.e. the time needed to reach the peak coefficient of variation). The methodology and its results can be used to assess the concentration uncertainty at the plume center. The problem is quite important when dealing with contaminant prediction and risk analysis.