Laboratory longitudinal diffusion tests: 2. Parameter estimation by inverse analysis

This study focuses on the verification of test interpretations for different state analyses of diffusion experiments. Part 1 of this study identified that steady, quasi-steady and equilibrium state analyses for the through- and in-diffusion tests with solution reservoirs are generally feasible where the tracer is not highly sorptive. In Part 2 we investigate parameter identifiability in transient-state analysis of reservoir concentration variation using a numerical approach. For increased generality, the analytical models, objective functions and Jacobian matrix necessary for inverse analysis of transient-state data are reformulated using unified dimensionless parameters. In these dimensionless forms, the number of unknown parameters is reduced and a single dimensionless parameter represents the sorption property. The dimensionless objective functions are evaluated for individual test methods and parameter identifiability is discussed in relation to the sorption property. The effects of multiple minima and measurement error on parameter identifiability are also investigated. The main findings are that inverse problems for inlet and outlet reservoir concentration analyses are generally unstable and well-posed, respectively. Where the tracer is sorptive, the inverse problem for the inlet reservoir concentration analysis may have multiple minima. When insufficient measurement data is collected, multiple solutions may result and this should be taken into consideration when inversely analyzing data including that of inlet reservoir concentration. Verification of test interpretation by cross-checking different state analyses is feasible where the tracer is not highly sorptive. In an actual experiment, test interpretation validity is demonstrated through consistency between theory and practice for different state analyses.