METHOD FOR SEEKING SEMI-ANALYTICAL SOLUTIONS TO MULTI-SPECIES CONTAMINANT TRANSPORT EQUATIONS COUPLED WITH SEQUENTIAL FIRST-ORDER REACTIONS THROUGH SIMILARITY TRANSFORMATION OF CLEMENT AND A GENERALIZED INTEGRAL TRANSFORM TECHNIQUE

摘要

PURPOSE: A method for seeking semi-analytical solutions to a multi-species contaminant transport equation coupled with a first-order reaction network is provided to find semi-analytical solutions under the flow speed and the diffusion coefficient of groundwater varying in time and space and under the boundary condition varying in time.;CONSTITUTION: A method for seeking semi-analytical solutions to a dechlorination reaction equation coupled with sequential first-order reactions is characterized by obtaining new analytical solutions using similarity transformation approach of Clement et al. together with GITT(Generalized Integral Transform Technique). The method comprises the steps of: transforming concentrations of multi-species contaminants linearly combined with each other into independent concentrations of each single species through forward linear transformation; transforming governing equations of single species transport equations which are obtained through the forward linear transformation; transforming the initial condition and the boundary condition for the multi-species contaminant equation into the initial condition and the boundary condition for the single species transport equations based on the forward linear transformation; finding analytic solutions to the single species transport equations transformed through the forward linear transformation using GITT under the flow speed and the diffusion coefficient of groundwater which vary in space and time; and finding analytic solutions to the multi-species contaminant transport equation by transforming the solutions to the single species transport equations into the analytic solutions to the multi-species contaminant transport equation linearly combined with each other through backward linear transformation.;COPYRIGHT KIPO 2013;[Reference numerals] (AA) Forward linear transformation; (BB) Governing equation transformation by forward linear transformation; (CC) Initial and boundary condition transformation based on forward linear transformation; (DD) Find analytic solutions using GITT; (EE) Backward linear transformation