Reflecting the importance of adsorption as a major water purification method, the main objective of this research was to perform a sensitivity analysis on some of the common adsorption isotherms subject to measurement noise in data. Even though most of adsorption isotherms have been derived based on some theoretical assumptions about the adsorption mechanism, they involve model parameters that need to be estimated from experimental measurements of the process variables. Specifically, for the Langmuir isotherm, which can be linearized in three forms, it was sought to determine which of these three forms would give the highest accuracy of the adsorption model parameters – maximum amount of adsorbate per unit weight of the adsorbent and the constant related to the affinity between the adsorbent and adsorbate . Another objective was to estimate the adsorption parameters using the nonlinear Langmuir model, and to compare their accuracy to the ones estimated using the most accurate linear form. Furthermore, it was desired to examine the effect of noise magnitude on the estimation accuracy for the various Langmuir forms (linear or nonlinear) by varying the noise variance and the magnitude of the adsorption parameters themselves.

To achieve this aim, MATLAB programming software was used to simulate functions for the estimation of the Langmuir isotherm model parameters using its nonlinear and three linearized forms. These functions were used to determine the best form for the estimation of the model parameters from noisy measurements by adding noise to data – which were generated from a pre-defined model – and then comparing the estimated parameters with the given ones. Then, the same procedure was repeated for different levels of noise (different standard deviations) and using models with different given parameters to study the effect of noise magnitude and parameters' values on the estimation accuracy.

Finally, the results of this work could be summarized as follows: One of the linearized forms of Langmuir model showed normal distribution and provided most accurate estimation of both model parameters. In addition, it was shown that when the noise content (standard deviation) increased on the data, less accurate estimates were obtained for both adsorption parameters. Finally, 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. These results prove to be very significant practical outcome as it helps modeling adsorption processes designed by industries and other fields.