(492a) Stochastic Modeling And Monte Carlo Simulation Of The Formation Of Activated Carbons

Activated carbons (ACs) are highly porous materials applied in the purification and separation of a variety of gaseous and liquid mixtures; they can also serve as catalysts or catalysis supports. The formation of ACs entails the modification of the original internal surfaces of carbonaceous substrates, e.g., coal or biomass, by resorting to various chemical or physical methods, thereby augmenting the carbonaceous substrates' adsorbing capacity. The process of AC formation tends to proceed randomly or stochastically, which is attributable to the discreteness and mesoscopic nature of the carbonaceous substrates whose characteristics vary incessantly with time as well as the random encounters between the activation agent and the carbon atoms on the carbonaceous substrates' internal surfaces. Hence, it is highly desirable that the formation of ACs from carbonaceous substrates be regarded as a stochastic process. Specifically, the process of AC formation is modeled as a pure-birth process with a linear intensity of transition. The resultant model gives rise to the process' master equation whose solution renders it possible to compute the mean and higher moments about the process' mean, e.g., the variance, which are collectively a manifestation of the process' inherent fluctuations. In addition, the master equation is simulated via the Monte Carlo method at the early stage of the process. The results of modeling and simulation are validated by comparing them with the available experimental data whenever possible.