Inverse reactive transport simulator (INVERTS): an inverse model for contaminant transport with nonlinear adsorption and source terms

Abstract

A numerically based simulator was developed to assist in the interpretation of complex laboratory experiments examining transport processes of chemical and biological contaminants subject to nonlinear adsorption and/or source terms. The inversion is performed with any of three nonlinear regression methods, Marquardt–Levenberg, conjugate gradient, or quasi-Newton. The governing equations for the problem are solved by the method of finite-differences including any combination of three boundary conditions: 1) Dirichlet, 2) Neumann, and 3) Cauchy. The dispersive terms in the transport equations were solved using the second-order accurate in time and space Crank–Nicolson scheme, while the advective terms were handled using a third-order in time and space, total variation diminishing (TVD) scheme that damps spurious oscillations around sharp concentration fronts. The numerical algorithms were implemented in the computer code INVERTS, which runs on any standard personal computer. Apart from a comprehensive set of test problems, INVERTS was also used to model the elution of a nonradioactive tracer, ¹⁸⁵Re, in a pressurized unsaturated flow (PUF) experiment with a simulated waste glass for low-activity waste immobilization. Interpretation of the elution profile was best described with a nonlinear kinetic model for adsorption.