(695f) Markovian Analysis and Simulation of the Formation of Carbon Adsorbents: Non-Linear Modeling

Carbon adsorbents, such as activated carbons and carbon molecular sieves, have been widely known to be useful for gas separation, gas purification, catalysis, or as catalysts' supports. These carbon adsorbents are formed by modifying the internal surfaces of carbonaceous substrates, e.g., biomass, which can be effected by a variety of chemical and/or physical methods. The formation of carbon adsorbents proceeds randomly; this is mainly attributable to the discrete nature, mesoscopic sizes, and irregular shapes of the substrates being carbonized as well as to their intricate surface configuration. Moreover, any process of carbon-adsorbent formation may fluctuate incessantly with time. Hence, it is highly desirable that the formation of carbon adsorbents from carbonaceous substrates be regarded as a stochastic process. Specifically, the formation of carbon adsorbents is modeled as a pure-birth process, a subclass of Markovian processes, with its intensity of transition characterized by a non-linear rate law. The resultant model gives rise to the non-linear governing, i.e., master, equation of the process 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 of the process is simulated by the Monte Carlo method by resorting to the event-driven and time-driven approaches. The results of modeling and simulation are validated by comparing them with the available or simulated experimental data.