STOCHASTIC MODELLING OF GROUNDWATER FLOW AND CONTAMINANT TRANSPORT

Abstract

The present study comprises development of a deterministic two-dimensional horizontal contaminant transport model and its subsequent application to a field problem treating transmissivity as a stochastic process. The model, invoking finite-difference (IADIE) based numerical solution of two coupled differential equations governing flow and solute transport in porous media, is capable of projecting the spatial distributions of piezometric head and solute concentration at advancing times. The field problem addressed in the study concerns with the disposal of ash slurry emanating from a thermal power plant on the upstream of a dyke. The head of the slurry causes entry, and subsequent lateral movement of the slurry into the groundwater system. The position of the slurry front (conceptualized as the contour of 50% concentration) and the corresponding state variables viz., contaminated areas at advancing times are simulated by invoking the deterministic transport model. The stochasticity of transmissivity considered in the present study renders the state variables (contaminated areas at advancing times) as random variables. The stochasticity is accounted for by Monte Carlo simulation that essentially involves generating several realizations of the transmissivity field, and computing corresponding realizations of the random state variables (contaminated areas at advancing times) through the deterministic model. The realizations of the state variables are further processed to arrive at discrete values of their probability distribution functions. Through a subjective inspection of the plots of the experimental probability distribution functions, log-normal distribution is tentatively fitted. The goodness of the fit is subsequently established through chi square test. The theoretical probability distribution functions so generated are employed to address the problem of arriving at safe slurry heads ensuring the restriction of the contaminated areas to permissible limits. The factor of safety in respect of the permissible limit on the contaminated area is correlated to the acceptable level of risk (probability of the contaminated area exceeding the corresponding permissible limit), coefficient of variation of transmissivity, and the time. The concept developed herein is illustrated invoking the data from a typical thermal power station.