First-passage processes applications

Passage time distributions and the mean first passage time provide a useful way for analyzing the time evolution of stochastic processes. An application to chemical reactions dominated by barrier crossing is given in Section 14.4.2 and Problem 14.3. 

We defer the proof to the appendix. The reason for presenting two methods for evaluating the mean first passage time is based on their diflierent scopes of applicability. If we were only interested in T, then equation (11.30) would be preferable because it requires less computation. However, we are limited to the first moment [8]. The advantage of the first approach is that we obtain any moment by one integration. Moreover, we have access to the time evolution of the escape process which allows for a more detailed analysis. 

The parallel-passage reactor was conceived and patented in the late 1960s [1-3] and saw its first application in the Shell flue gas desulfurization process in the early 1970s [4]. The lateral-flow reactor was conceived as a constructional modification of the PPR, and its first application was for NO removal from flue gas of a gas-fired furnace in the early 1990s [5]. 

The performance of the PPR for NOx removal by the Shell low-temperature NOx reduction has been investigated extensively [20]. In the first commercial application of the Shell process with parallel-passage reactors, flue gases of six ethylene cracker furnaces at Rheinische Olefin Werke at Wesseling, Germany, are treated in a PPR system with 120-m catalyst in total to reduce the nitrogen oxide emissions to about 40 ppm v. Since its successful start-up in April 1990, the unit has performed according to expectations... 

An RO membrane acts as a barrier to flow, allowing selective passage of a particular species (solvent) while other species (solutes) are retained partially or completely. Solute separation and permeate solvent (water in most cases) flux depend on the material selection, the preparation procedures, and the structure of the membrane barrier layer [5,15]. Cellulose acetate (CA) is the material for the first generation reverse osmosis membrane. The announcement of CA membranes for sea water desalination by Loeb and Sourirajan in 1960 triggered the applications of membrane separation processes in many industrial sectors. CA membranes are prepared by the dry-wet phase inversion technique. Another polymeric material for RO is aromatic polyamide [16]. 

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