Reactor, Heat and Mass Balance Considerations

In this section we develop a dynamic model from the same basis and assumptions as the steady-state model developed earlier. The model will include the necessarily unsteady-state dynamic terms, giving a set of initial value differential equations that describe the dynamic behavior of the system. Both the heat and coke capacitances are taken into consideration, while the vapor phase capacitances in both the dense and bubble phase are assumed negligible and therefore the corresponding mass-balance equations are assumed to be at pseudosteady state. This last assumption will be relaxed in the next subsection where the chemisorption capacities of gas oil and gasoline on the surface of the catalyst will be accounted for, albeit in a simple manner. In addition, the heat and mass capacities of the bubble phases are assumed to be negligible and thus the bubble phases of both the reactor and regenerator are assumed to be in a pseudosteady state. Based on these assumptions, the dynamics of the system are controlled by the thermal and coke dynamics in the dense phases of the reactor and of the regenerator. 

Effective axial transport properties can be determined using an adiabatic reactor. Steady state mass and heat balances result in second-order ordinary differential equations when the axial dispersion is taken into consideration, solutions of which can readily be obtained. Based on these solutions and temperature or concentration measurements, the effective transport properties can be calculated in a manner similar to the procedures used for the radial transport properties. As indicated earlier, a transient experiment can also be used for the determination. Here, experimental and analytical procedures are illustrated for the determination of the effective axial transport property for mass. An unsteady state mass balance for an adiabatic reactor can be written as ... 

The polymerization reactor is of the heat-balance type because of the change in the heat transfer characteristics of the reaction mass during the polymerization. As the viscosity increases, the rate of heat dissipation by mixing will generally decline, which must be taken into consideration in setting up the equipment and in taking the appropriate measurements. 

The optimization of an electrochemical reactor calls for a full description of the process to accomplish the specific objective of the mass and the energy balances together with heat transfer considerations and thermodynamic and enthalpy changes that are related to the unit cell and the whole stack [1,2]. A full description of the kinetics of both processes, the electric properties of the cell components, and the hydrodynamic aspects of the entire cell is also required. 

Keeping in mind these insights, we turn to a second application of the model, the estimation of the lifetime of a catalyst bed. This is an important consideration in the design of any reactor and is particularly critical in transportation applications where maintenance intervals must be well known. As an initial approach to developing metrics for this analysis we define Ae time in service or service life, at constant wall temperature, as the duration when the overall conversion in the reactor (for full power output) is greater than 85%. This conversion was chosen because it is close to the autothermal point of operation where the burning of unreacted methanol will just balance the endothermic heat of reaction. A reference catalyst mass was determined by requiring a methanol conversion of 85% at the wall temperature of 240"C for fresh catalyst. 

Heat exchange involves heat generation and transfer in and between elementary regions of a bioreactor and that of individual phases of a reactor (2). A rational start for these considerations is the general local heat balance, similar to that of mass transfer ... 

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