Stochastic Modelling of the Length of Steady Plumes Undergoing Bioremediation

The degradation of steady plumes is controlled by the interplay between large scale advection and transverse dispersion. Under the assumption of instantaneous reaction some analytical solutions for the concentration field can be derived. Modeling the hydraulic conductivity K as a random variable, the velocity V and concentration C fields are also random, and we aim at representing the concentration through its first two statistical moments, the mean and the variance. The solutions can be derived by employing the first-order analysis of transport, which is formally valid for low/medium heterogeneity. Hence, the probability density function (pdf) of the plume length can be evaluated. The pdf is function of a few relevant parameters, like e.g. the Peclet number, the anisotropy of the porous formation and the ratio between the initial concentrations of the electron donor and acceptor. The solution provides a simple tool to evaluate the longitudinal size of the plumes undergoing biodegradation, which can be used for a first screening of the contamination process.