A Stochastic Streamtube Model for NAPL Transport in Heterogeneous Media

Remediation schemes for contaminated sites are often evaluated to assess their potential for source zone reduction of mass, or treatment of the contaminant between the source and a control plane (CP) to achieve regulatory limits. In this study, we utilize a stochastic stream-tube model to explain the behavior of breakthrough curves (BTCs) across a CP. At the local-scale, mass dissolution at the source is combined with an advection model with first-order decay for the dissolved plume. Field-scale averaging is then employed to account for spatial variation in mass within the source zone, and variation in the velocity field. Under the assumption of instantaneous mass transfer from the source to the moving liquid, semi-analytical expressions for the BTC and temporal moments are developed, followed by derivation of expressions for effective velocity, dispersion, and degradation coefficients using the method of moments. Modified definitions of effective parameters are presented for degrading solutes to account for the normalization constant (zero-th moment) that keeps changing with time or distance to the CP. Implications of model results on estimating cleanup times and fulfillment of regulatory limits are discussed.