Stepwise algorithm for estimating intraparticle diffusivity by zero-length-column desorption experiments

There are two problems with intraparticle diffusivity estimation by Zero-length-column (ZLC) desorption experiment: 1) no viable algorithm for producing reliable accuracy estimation, and 2) difficulty in fitting short- and long-term ZLC data to the series solution. To tackle these problems, we propose replacing direct curve-fitting with an algebraic-equation solving followed by a single-parameter curve fitting. This stepwise algorithm uncouples parameters' estimation and facilitates the series-solution fitting. Moreover, the stepwise method can yield from one experimental run multiple parameter estimates, a set of estimates containing the information of random error distribution. This set of estimates provides a direct way of deriving statistics quantifying the parameter-estimation uncertainty, such as variance, standard deviation, confidence interval, etc. The new method was validated by using two independently reported ZLC data sets, and its idea is general and applies to other inverse problems of heat and mass transfer.