Periodic operation rate model

The following will explain one way of essentially process intensification of trickle-bed reactors by periodic operation. The unsteady-state operation was considered as square waves cycling liquid flow rate at the reactor inlet. The hydrogenation of alpha-methylstyrene to cumene C6H5(CH3) = CH2(L) + H2(g) C6H5CH(CH3)2(l) over a palladium catalyst (0.7% Pd/y-Al203) was selected as a model reaction. Own experimental trickle-bed reactor investigations showed for this reaction system that the periodic variations of liquid flow rates by on/off... 

Figure 4-9 shows a plot of probability of failure in this situation. This can be compared with unavailability calculated with the constant restore rate model as a function of operating time. With the constant restore model, the unavailability reaches a steady state value. This value is clearly different from the result that would be obtained by averaging the unavailability calculated using a periodic restore period. 

Most previous theoretical studies of dynamic operating reactors used kinetic expressions obtained under steady-state operation. These models do not account for the detailed dynamics of the adsorption and desorption rate processes, and they may lead to erroneous predictions in periodic operation of the reactor. Thus, simulations of periodic processes may require use of kinetic models that are much more detailed than those used for predicting steady-state operation. These dynamic models also need to account for the rate of adsorption, desorption, and adsorption capacity of the catalyst. As mentioned above, the hot-temperature zone in a cooled RFR may exhibit complex dynamic features under... 

In theoretical studies Thullie and Renken [7] showed that operating under periodic variation of the inlet concentration leads to a considerable increase of the reactor performance exceeding the maximal performance obtainable under steady state conditions. The attainable enhancement under periodic operation depends on the sorption equilibrium constants and the sorption rates. Assuming instantaneous equilibrium on S2 and irreversible adsorption on S the model calculations lead to a maximal performance under periodic operation for cycle periods tqtproaching zero (tp- 0)... 

Briggs and Haldane [8] proposed a general mathematieal deseription of enzymatie kinetie reaetion. Their model is based on the assumption that after a short initial startup period, the eoneentration of the enzyme-substrate eomplex is in a pseudo-steady state (PSS). Eor a eonstant volume bateh reaetor operated at eonstant temperature T, and pH, the rate expressions and material balanees on S, E, ES, and P are... 

Suppose the flow rates entering and leaving a process are measured periodically. Determine the best value for stream A in kg/h for the process shown from the three hourly measurements indicated of B and C in Figure El.6, assuming steady-state operation at a fixed operating point. The process model is... 

In supervisory control, process and economic models of the plant are used to optimize the plant operation by maximizing daily profit, yields, or production rates. The computer program reviews operating conditions periodically, computes the new conditions that optimize a chosen objective function, and adjusts plant controller set points, thus implementing the new improved conditions. This scheme will obviously require a model of the plant, current information about operating conditions from the plant s control system, and finally, sophisticated optimization software. 

In a batch sedimentation experiment, the sediment builds up gradually and the solids which are deposited in the early stages are those which are subjected to the compressive forces for the longest period of time. In the continuous thickener, on the other hand, all of the particles are retained for the same length of time with fresh particles continuously being deposited at the top of the sediment and others being removed at the same rate in the underflow, with the inventory thus remaining constant. Residence time distributions are therefore not the same in batch and continuous systems. Therefore, the value of tR calculated from equation 5.59 will be subject to some inaccuracy because of the mismatch between the models for batch and continuous operation. 

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