Stochastic Modeling for the Formation of Activated Carbons: Nonlinear Approach
2011-08-03T00:00:00Z (GMT) by
Activated carbons (ACs) have been widely deployed in the purification of gases and liquids or the separation of their mixtures. The formation of ACs entails the modification of the original internal surfaces of carbonaceous substrates, for example, coal or biomass, which can be effected by a variety of chemical or physical methods, thereby augmenting the carbonaceous substrates’ adsorbing capacities. The formation of ACs tends to proceed randomly or stochastically in view of the discrete and mesoscopic nature of the carbonaceous substrates, as well as the random encounters between the activation agent and carbon on the carbonaceous substrates’ internal surfaces; in addition, the carbonaceous substrates’ internal surfaces exhibit an intricate morphology or structure. Naturally, these traits of the formation of ACs render the process to vary incessantly with time. Thus, it is highly desirable that the analysis, modeling, and simulation of the formation of ACs from carbonaceous substrates be performed in light of a stochastic paradigm. Herein, a stochastic model for the formation of ACs is formulated as a pure-death process based on a nonlinear intensity of transition. The model gives rise to the process’ nonlinear master equation whose solution is obtained by resorting to a rational approximation method, the system-size expansion. This solution renders it possible to compute the mean as well as higher moments about this mean, for example, variance or standard deviation, which reveal and quantify the process’ inherent fluctuations. The results of modeling are validated by comparing them with the available experimental data.