A simple closed-form solution for assessing concentration uncertainty

We propose closed-form approximate solutions for the moments of a nonreactive tracer that can be used in applications, such as risk analysis. This is in line with the tenet that analytical solutions provide useful information, with minimum cost, during initial site characterization efforts and can serve as a preliminary screening tool when used with prior knowledge. We show that with the help of a few assumptions, the first-order solutions of the concentration moments proposed by Fiori and Dagan (2000) can be further simplified to assume a form similar to well-known deterministic solutions, therefore facilitating their use in applications. A highly anisotropic formation is assumed, and we neglect the transverse components of the two-particle correlation trajectory. The proposed solution compares well with the work of Fiori and Dagan while presenting the same simplicity of use of existing solutions for homogeneous porous media.