Novel mathematical modelling of Saudi Arabian natural diatomite clay

Background: Diatomite is a clay material and a mineral that contains high content of silica and alumina and additional element traces. The characteristics and properties of the Saudi Arabian natural diatomite clay were studied using temperature programmed desorption of pyrrole. The relation between the particular mathematical parameters and the diatomite clay was also investigated, with a mathematical modelling of pyrrole adsorption by means of a regression analysis. Methods: The Polanyi-Wigner equation was computed for the analysis of Saudi Arabian diatomite clay, using temperature programmed desorption (TPD) of pyrrole together with a regression analysis. The correlation and regression analyses were conducted according to the following variables; 1. Temperature versus WLD-Signal- to ascertain the temperature dependence of WLD Signal. 2. Time versus WLD- to determine the time dependence of WLD. 3. 1/Temperature versus lnk to establish both the temperature dependence of the reaction rates and the time dependence of the desorption of pyrrole. Results: The results revealed that a cubic polynomial is the most suitable for the interpretation of the TCD signal of Pyrrole adsorption at a variety of temperature ranges. The findings in this study have determined that Polanyi-Wigner equation for the analysis of natural Saudi Arabian diatomite clay was computed successfully. Conclusion: The proposed equation shown in the current paper serves as the best model in the analysis of natural Saudi Arabian clay in the improvement of accuracy and efficacy of the Pyrrole- TPD. The proposed equation also greatly assists in achieving accurate results when calculating the desorbed amount of pyrrole and as compared to the traditional method, helps set a clear direction and a feedback mechanism for researchers during the investigation of clay samples. Importantly, using the equation can help to develop pyrrole-TPD software which in turn may assist scientists to clearly determine directly desorbed pyrrole amount of the clay samples during the experimental process. The findings conclude that the usefulness of the pyrrole equation can, in future, contribute greatly to the development of TPD-pyrol instrument software. It will also provide better control and quality feedback to investigators in the process of experimental design and during the run in terms of the behavior of clays and their capacity for gas desorption.