Study of flow and mass transport in multilayered aquifers using boundary integral method.

摘要

In recent years, the boundary integral element method (BIEM) has been widely used in the area of groundwater modeling. This method, which is based on Green's theorem, has a variety of advantages over domain methods. Earlier applications of the BIEM to multilayer aquifer problems were restricted to steady state flows. In these applications, layered aquifer systems were solved iteratively using Bessel function as the principal Green function. In this formulation the argument of the Bessel function is a function of hydraulic properties of the aquifer-aquitard system. Such an approach reduces the efficiency of the computations and yields less accurate numerical results due to the sensitivity of the Bessel function to its arguments, and other errors inherent in iterative procedures. Iterative methods are also usually slower than the direct solutions and are prone to errors due to their biased convergence criteria definitions.;In the study presented here a non-iterative boundary integral equation formulation (NIBIEM) for multilayer aquifer systems with or without a well network is developed. In this procedure the coefficients of the singular points associated with pumping or recharge wells are included in the analysis in an analytic sense. This improves the efficiency and the accuracy of the computation. The formulation presented is developed for three different phases of flow. These are steady state flow, unsteady state flow, and contaminant transport in multilayer aquifers. In steady state flow computations, formulation for two different approaches which utilize Bessel functions and natural log functions are given. The merits and demerits of each approach are discussed. Further, the direct discretized formulations of steady state and unsteady state are reduced to boundary only forms using the secondary reduction boundary element method (SR-BEM). Applications of the steady-state solution show that the natural-log approach yields a more accurate and efficient computation procedure. For unsteady flow problems, the unsteady flow equation for aquitards is solved analytically including the aquitard storage. This analytical solution is then coupled with a numerical algorithm for main aquifers yielding procedures for time dependent simulation of a multilayer aquifer system. The temporal terms in the unsteady flow equations are discretized using a finite difference formula. In the contaminant transport section, a quasi-three dimensional advection-diffusion equation is developed, which not only reduces the computational cost, but may be the only alternative solution in the sense of practical considerations. The diffusion equation for aquitards is also solved analytically and then coupled with the quasi-three dimensional advection-diffusion equation. Numerical examples are included to demonstrate the accuracy and efficiency of the proposed formulation in applications to classic multilayer aquifer problems.