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Carbon adsorbents, namely, activated carbons and carbon molecular sieves, can be variously applied in the purification and separation of gaseous and liquid mixtures, e.g., in the separation of nitrogen or oxygen from air; often, carbon adsorbents also serve as catalysts or catalyst supports. The formation of carbon adsorbents entails the modification of the original internal surfaces of carbonaceous substrates by resorting to a variety of chemical or physical methods, thereby augmenting the carbonaceous substrates' adsorbing capacity. The formation of carbon adsorbents proceeds randomly, which is mainly attributable to the discrete nature, mesoscopic sizes, and irregular shapes of the substrates utilized as well as to their intricate internal surface configuration. Moreover, any process of carbon-adsorbent formation may fluctuate increasingly severely with time. It is desirable that such a process involving discrete and mesoscopic entities undergoing complex motion and behavior be explored by means of the statistical framework or a probabilistic paradigm. This work aims at probabilistic analysis, modeling, and simulation of the formation of carbon adsorbents on the basis of mechanistic rate expressions. Specifically, the current work has formulated a set of linear and non-linear models of varied complexity; derived the governing equations of the models formulated; obtained the analytical solutions of the governing equations whenever possible; simulated one of the models by the Monte Carlo method; and validated the results of solution and simulation in light of the available experimental data for carbon-adsorbent formation from carbonaceous substrates, e.g., biomass or coal, or simulated data obtained by sampling them from a probability distribution. It is expected that the results from this work will be useful in establishing manufacturing processes for carbon adsorbents. For instance, they can be adopted in planning bench-scale or pilot-scale experiments; preliminary design and economic analysis of production facilities; and devising the strategies for operating and controlling such facilities. |
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