On the Joint Estimation of External Mass Transfer and Diffusion Coefficients Using Optimal and Heuristic Experimental Designs

Abstract

Optimal experimental designs for maximum precision in the estimation of diffusivities (D) and mass transfer coefficients (Kc) for solute transport from/to a solid immersed in a fluid were determined. Diffusion in the solid was considered to lake place according to Fick's 2nd law. It was found that the optimal design was dependent on the Biol number. In the range of Biot numbers tested (0.1 lo 200). the firsl sampling time corresponded to values of fractional loss/uptake between 0.10 and 0.32. and the second sampling time corresponded to values of fractional loss/uptake between 0.67 and 0.82. Pseudo-experimental data were simulated by applying randomly generated errors following a normal distribution with 5% standard deviation to data calculated using given values of the model parameters, assuming both optimal and heuristic designs for which the sampling times corresponded to values of fractional loss/uptake from 0.30 to 0.95). The accuracy and precision of the estimates obtained by non-linear regression were compared Optimal designs were found to yield best results in terms of precision. It was concluded that the joint estimation of D and Kc should be avoided, particularly for very low Biot numbers, as even optimal designs are unable to yield good results; for largei Biot numbers die estimation of D was feasible, whereas the estimation of Kc was found to yield inaccurate values with large confidence intervals, in the whole range tested.