COMPUTATION OF TYPE CURVES FOR FLOW TO PARTIALLY PENETRATING WELLS INWATER-TABLE AQUIFERS

Evaluation of Neuman's analytical solution for flow to a well in a hom ogeneous, anisotropic, water-table aquifer commonly requires large amo unts of computation time and can produce inaccurate results for select ed combinations of parameters. Large computation times occur because t he integrand of a semi-infinite integral involves the summation of an infinite series. Each term of the series requires evaluation of the ro ots of equations, and the series itself is sometimes slowly convergent . Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical integration. In this paper it is proposed to use a method of numerical inversion of the Laplace transfo rm solution, provided by Neuman, to overcome these difficulties. The s olution in Laplace space is simpler in form than the real-time solutio n; that is, the integrand of the semi-infinite integral does not invol ve an infinite series or the need to evaluate roots of equations. Beca use the integrand is evaluated rapidly, advanced methods of numerical integration can be used to improve accuracy with an overall reduction in computation time. The proposed method of computing type curves, for which a partially documented computer program (WTAQ1) was written, wa s found to reduce computation time by factors of 2 to 20 over the time needed to evaluate the closed-form, real-time solution.