Zero effluent operation times

The type of operation considered in the zero effluent methodology means that the amount of time points used for an operation has to increase. This is due to the fact that there is a processing step and a cleaning step associated with each batch of product. Normally two time points are used to describe a task in a unit. The first time point is used when the task commences in a unit and the second when the task terminates in a unit. In the type of operation considered in the zero effluent models, three time points are used. At the first time point the raw material processing task commences. The raw material processing step ends at the second time point, where the final product is removed and the cleaning operation commences. At the third time point the cleaning operation comes to an end and wastewater is produced. 

As the plant to be optimized considers a process operating at steady state, then the variation of the phase concentrations with time is zero. For this reason, the mathematical model that describes the plant is a set of ordinary differential equations, as the phase concentrations depend only on the module axial position. In the tanks, the concentrations are constant. The differential-algebraic nonlinear optimization (DNLP) problem PI to be solved includes the ordinary differential equations that represent the mass balances for the phases in the membrane module. The objective function to be maximized is the amount of metal processed FeC , where Fe is the effluent flow rate whose Cr(VI) concentration after dilution from wastewaters is C . The problem has the following form ... 

Extrapolation to Zero-time Kinetics. A striking feature of the alkylation experiments reported in this paper is the steady decline of the butene conversion with increasing time on stream (see Figure 2). Therefore, in order to study the kinetics of alkylation over a fresh catalyst, it is necessary to extrapolate the time-dependent data to zero-time. To facilitate extrapolation, several samples of the reactor effluent were gathered within the first 5 minutes of reactor operation. As can be seen from Figure 2, the rate of deactivation is quite high. Even under dilute 2-butene concentrations, the catalyst deactivates in a matter of minutes. In the remainder of this paper, only the initial (i.e. time zero) conversions will be presented and analyzed. The rate of catalyst deactivation and its relation to operating conditions will be examined in a future publication. 

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