We consider the effect of heterogeneity on estimation of the time that is necessary to reclaim an aquifer by means of a constant rate pumping well. We derive the predictor of resident time (rendered by its mean) together with the associated prediction error (rendered by its variance) for non reactive solute particles under mean radial flow conditions in a heterogeneous aquifer. The solutions are obtained numerically following a Monte Carlo procedure, and compared with a newly developed first-order analytical approach. The natural logarithm, Y, of aquifer transmissivity, T, is modelled as a statistically homogeneous Gaussian random field with a Gaussian spatial correlation function. The agreement between analytical and numerical solutions is very good for all the cases considered. We analyzed the effect on the travel time statistical moments of (i) distance from the injection point to the well, (ii) heterogeneity of the random field, (iii) domain size, in terms of correlation length of Y. One of the main results is that the mean travel time is always larger than the deterministic value obtained assuming a homogeneous media. Our analysis can be a useful tool in planning water resources protection strategies, since it would be possible to obtain an estimate of the maximum clean-up time, associated with a design probability, which would substitute the use of a single (underestimated) deterministic value.
Effect of heterogeneity on aquifer reclamation time
RIVA, MONICA;DE SIMONI, MICHELA;GUADAGNINI, ALBERTO;
2004-01-01
Abstract
We consider the effect of heterogeneity on estimation of the time that is necessary to reclaim an aquifer by means of a constant rate pumping well. We derive the predictor of resident time (rendered by its mean) together with the associated prediction error (rendered by its variance) for non reactive solute particles under mean radial flow conditions in a heterogeneous aquifer. The solutions are obtained numerically following a Monte Carlo procedure, and compared with a newly developed first-order analytical approach. The natural logarithm, Y, of aquifer transmissivity, T, is modelled as a statistically homogeneous Gaussian random field with a Gaussian spatial correlation function. The agreement between analytical and numerical solutions is very good for all the cases considered. We analyzed the effect on the travel time statistical moments of (i) distance from the injection point to the well, (ii) heterogeneity of the random field, (iii) domain size, in terms of correlation length of Y. One of the main results is that the mean travel time is always larger than the deterministic value obtained assuming a homogeneous media. Our analysis can be a useful tool in planning water resources protection strategies, since it would be possible to obtain an estimate of the maximum clean-up time, associated with a design probability, which would substitute the use of a single (underestimated) deterministic value.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
