Sensitivity analysis of adsorption isotherms subject to measurement noise in the data
The analysis and design of many environmental and separation processes rely on the availability of accurate adsorption isotherms. These isotherms are estimated from measurements of the adsorption process variables. Unfortunately, these variables are usually contaminated with errors that affect the accuracy of their estimated parameters. Therefore, one objective of this work was to study the effect of measurement noise in the variables on the estimation accuracy of the Langmuir isotherm. In fact, Langmuir has three linearized forms, so it was sought to determine which out of these three forms would provide the most accurate estimated parameters. Another objective of this work was to estimate the isotherm parameters using the nonlinear Langmuir form using nonlinear optimization, and to compare the accuracy of the estimated parameters to the ones obtained using the most accurate linearized form. A third objective was to study the effect of measurement noise level on the accuracy of the Langmuir isotherm. As a result of this study, the following was found. One of the three linearized Langmuir forms provided the most accurate estimates. In fact, its accuracy was even comparable to that obtained by nonlinear optimization using the nonlinear isotherm. In addition, the estimation accuracy was more sensitive to the magnitude of the affinity constant than to the maximum amount of adsorbate in adsorbent; larger values of affinity constant result in higher estimation accuracy of both model parameters. Finally, it was confirmed that the higher the noise content in the variables, the larger the uncertainty of their estimation.