NUMERICAL MODELLING OF SEAWATER TRANSPORT IN COASTAL AQUIFERS

Abstract

An indiscriminate groundwater development in coastal aquifers may lead to severe consequences on account of seawater intrusion. Numerical modelling of the seawater transport in coastal aquifers can assist a groundwater manager in planning of a sustainable groundwater development as well as in evaluation of various salvage strategies. In the present study, a miscible transport numerical model has been developed for simulating two-dimensional (vertical plane) regional transient seawater transport in coastal aquifers. Modes of transport simulated by the model are advection and hydrodynamic dispersion. Advection is simulated by a variant form of the method of characteristics (originally proposed by Garder et al., 1964) and the hydrodynamic dispersion by finite differences. The initial distribution of seawater in the solution domain is simulated by placing moving packets with assigned volumes in that portion of the solution domain where seawater is initially present. The velocity distribution is obtained from the pressure distribution, which in turn is computed by solving the variablep density flow equation using the iterative alternating direction implicit explicit (IADIE) algorithm of finite differences. The movement of seawater due to advection is simulated by a stepwise tracking of these packets with a weighted average velocity computed by fourth-order Runge-Kutta algorithm. The initial and new positions of the tracked packets at respectively the beginning and end of" a time step along with their volumes, permit an estimation of advective flux during the i time step at the nodal points of a finite difference grid. The new positions also provide the nodal values of advective concentration at the end of the time step. Subsequently, the dispersive transport is added on by solving the transport equation by the IADIE algorithm of finite differences, treating the pre-computed advective transport as a source/sink term. Thus, a simultaneous occurrence of the advection and dispersion is simulated. This solution provides the total nodal concentrations at the end of the time step. The simulated dispersive transport during the time step is integrated with the moving packet system by changing the volumes of the moving packets. For this, first the dispersive flux at each nodal point is computed from the pre-computed total and advective concentrations. This flux is then distributed among the moving packets lying in the domain of the respective node, in proportion to their initial volumes. The above procedure repeated over the sequential time steps provides spatial distributions of the concentrations at various discrete times. In addition, the time-wise positions of the moving packets along with their volumes are also obtained. This permits a detailed mass balance of seawater including quantification of the circulation. The positions of the moving packets also assist in determining the path followed by the seawater within the domain. The proposed model has been validated by comparing the model simulated position of disperse interface (i.e., position of 0.5 isochlor) with the semianalytical and previously published numerical solutions of two test problems. The first test problem taken up in the study is Henry's problem (Henry, 1960; Cooper et ai, 1964). This problem pertains to seawater intrusion in a homogeneous, isotropic confined aquifer which is exposed to a seawater body on one side and receives a constant freshwater recharge from the other side. Assuming a constant hydrodynamic dispersion coefficient, Henry presented semi-analytical solutions for two cases corresponding to variations in freshwater recharge. The ii proposed model could attain steady state for both the cases. The simulated results are in general agreement with the corresponding Henry's semi-analytical solutions, although some differences are evident between the corresponding sets of solutions. For case two, which has been analysed by various researchers, the simulated results are in good agreement with previously reported numerical solutions, at both transient and steady states. Henry's problem was also simulated considering a velocity-dependent hydrodynamic dispersion coefficient. The model results are again in good agreement with previously reported numerical solutions. The second test problem originally considered by Huyakorn et al. (1987), addresses seawater intrusion in an anisotropic unconfined coastal aquifer, which receives both vertical and lateral recharge. At steady state, the model simulated results agree well with the reported numerical solutions. The model has been applied to the Biscayne aquifer near Miami, Florida, using field data reported by Kohout and Klein (1967). As a result of seawater intrusion this aquifer exhibits a wide transition zone. The model is employed to simulate the movement of the disperse interface in response to variations in freshwater recharge.