In the past, the coastal leaky aquifer system, including two aquifers and an aquitard between them, was commonly assumed to be homogeneous and of infinite extent in the horizontal direction. The leaky aquifer system may however be heterogeneous and of finite extent due to variations in depositional and post depositional processes. In this paper, the leaky aquifer system is divided into several horizontal regions for the heterogeneous aquitard and underlying aquifer. A one-dimensional analytical model is developed for describing the head fluctuation in such a heterogeneous leaky aquifer system. The hydraulic head of the upper unconfined aquifer is assumed constant. It is found that both the length and location of the discontinuous aquitards presented in the coastal area have significant effects on the amplitude and phase shift of the head fluctuation in the lower aquifer. In addition, the influence of the formation heterogeneity on the spatial head distribution is also investigated.

This study proposes a new mathematical model for describing the drawdown distribution due to a constant rate pumping (CRP) in an unconfined aquifer considering the lagging theory. We introduce two lag times in Darcy's law and in turn in a free surface equation to reflect the effects of the capillary fringe and the capillary suction on the water table motion. The present free surface equation can reduce to those used in previous studies. The Laplace and Weber transform methods are used to derive the semianalytical solution to the model including the effect of wellbore storage. The algorithm of numerical Laplace inversion is applied to obtain the transient solution of the model. We find that the delay index, commonly used in the literature, is equivalent to the lag time associated with the effect of the capillary suction. The sensitivity analysis is performed to assess the drawdown behavior in response to the change in each aquifer parameter. The drawdown distributions predicted by the present solution agree fairly well to the field data taken from CRP tests at Cape Cod, Massachusetts; the Canadian Forces Base Borden, Ontario; and Saint Pardon de Conques, Gironde (France). The lag times determined by both CRP tests seem to decrease linearly with increasing distance on the logarithmic scale from the pumping well. The consideration of two lag times considerably improves the accuracy in estimated specific yields.