Coking mass-balance equation

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. 

The data in Fig. 5 also show that coke formation occurs rapidly at first and becomes increasingly slow as coke piles up. This behavior reflects the deactivating effect of coke on the coking reaction. Since the TEOM microbalance maintains temperature and the pressure time invariant, the mass balance equation for coke-on-catalyst can be described as [17] dC. 

It should be mentioned that the stoichiometric coefficient cancels out in this transformation to weight fractions. This equation, with the appropriate decay function can be solved numerically where the value of Ya is obtained from equation (3.5). Similarly the mass balance equation for the light gases plus coke lump can be written as ... 

The mass balance given in equation (1), was solved numerically with the following boundary condition at z=0, )>a=1, andyB=yc=yo=y =0, in order to calculate gas oil, gasoline, LPG, dry gas and coke yields for each feedstock.. 

Based on the kinetic parameters of the coke bum-off and the differential mass and heat balances for the gas and solid phase the regeneration process in an industrial fixed bed reactor was modeled. Thereby the four coupled diffential equations (eq. 6-9) were solved by the mathematical program PDEXPACK, developed at the Institute of Chemical Engineering, in Stuttgart (Germany). 

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