Heat Balance for the Reactor

Here we assume for simplicity that there is no change of phase in the reactor and moreover we use the average density p and the average specific heat Cp for the mixture in our model formulation. 

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Use Scalable Heat Transfer. The feed flow rate scales as S and a cold feed stream removes heat from the reaction in direct proportion to the flow rate. If the energy needed to heat the feed from to Tout can absorb the reaction exotherm, the heat balance for the reactor can be scaled indefinitely. Cooling costs may be an issue, but there are large-volume industrial processes that have Tin —40°C and Tout 200°C. Obviously, cold feed to a PFR will not work since the reaction will not start at low temperatures. Injection of cold reactants at intermediate points along the reactor is a possibility. In the limiting case of many injections, this will degrade reactor performance toward that of a CSTR. See Section 3.3 on transpired-wall reactors. 

Prepare a heat balance for the reactor (A) and quench column (B). 

The heat balance for the reactor contents assuming constant physical property values, is... 

Steady state results are consistent with a steady state heat balance for the reactor plant. 

The calculation of heat balance around the reactor is illustrated in Example 5-6. As shown, the unknown is the heat of reaction. It is calculated as the net heat from the heat balance divided by the feed flow in weight units. This approach to determining the heat of reaction is acceptable for unit monitoring. However, in designing a new cat cracker, a correlation is needed to calculate the heat of reaction. The heat of reaction is needed to specify other operating parameters, such... 

Heat balances for the several types of reactors are summarized in Tables 2.3-2.6. 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Leung s method is given in 6.3.2 below. The method.is an approximate solution to the differential mass and energy balances for the reactor during relief and takes account of both emptying via the relief system and the tempering effect of vapour production due to relief. The method makes use of adiabatic experimental data for the rate of heat release from the runaway reaction (see Annex 2). Nomenclature is given in Annex 10. 

The heat balance for a reactor has a form very similar to the general material balance, i.e. 

McGreavy and THORNTON(23) have developed an alternative approach to the problem of identifying such regions of unique and multiple solutions in packed bed reactors. Recognising that the resistance to heat transfer is probably due to a thin gas film surrounding the particle, but that the resistance to mass transfer is within the porous solid, they solved the mass and heat balance equations for a pellet with modified boundary conditions. Thus the heat balance for the pellet represented by equation 3.24 was replaced by ... 

Next we consider the heat balance for the cooling jacket in incremental form as depicted in Figure 7.2. Note first that ours is a case of cocurrent flow in the jacket and reactor. This simplifies the mathematical problem when compared with countercurrent cooling. Countercurrent cooling is physically more efficient, but it transforms the problem mathematically into a more demanding two point boundary value problem which we want to avoid here see problem 3 of the Exercises. 

The plots in Figures 7.8 and 7.9 make both Qer and Qeg infinite and therefore the dense phase and bubble phase conditions are identical and are equal to the output conditions of the reactor and the regenerator in this example. In case of finite exchange rates between the bubble and dense phases in reactor and regenerator, the output conditions from the reactor and the regenerator can be obtained by mass and heat balances for the concentration and the temperature of both phases and these expressions use the same symbols as before, but without the subscript D (used to signify the dense phase before). 

The condition for the practical implementation of such a feed control is the availability of a computer controlled feed system and of an on-line measurement of the accumulation. The later condition can be achieved either by an on-line measurement of the reactant concentration, using analytical methods or indirectly, by using a heat balance of the reactor. The amount of reactant fed to the reactor corresponds to a certain energy of reaction and can be compared to the heat removed from the reaction mass by the heat exchange system. For such a measurement, the required data are the mass flow rate of the cooling medium, its inlet temperature, and its outlet temperature. The feed profile can also be simplified into three constant feed rates, which approximate the ideal profile. This kind of semi-batch process shortens the time-cycle of the process and maintains safe conditions during the whole process time. This procedure was shown to work with different reaction schemes [16, 19, 20], as long as the fed compound B does not enter parallel reactions. 

The program numerically integrates the differential component and heat balances for the combined feed and recycle gas through the individual beds of both reactors accounting for the addition of cold quench gas between reactor beds and the recycling of fractionator bottoms to the second reactor inlet. 

The mass and heat balances for this reactor model are e.g. for consecutive reactions ... 

In a review article on oscillatory reactions (294), Sheintuch discusses the effect of introducing a heat balance for the catalyst rather than a mass balance for the reactor into the differential equation system for a surface reaction with oxidation/reduction cycles. Although the coverage equations alone can yield oscillatory behavior, as was the case for the models discussed in the previous section, Sheintuch s model is discussed in this section because introduction of the heat balance adds qualitatively new features. In this extended system complex, multiple peak behavior and quasiperiodicity was observed as shown in Fig. 8. Sheintuch also investigated the interaction of two oscillators. This work, however, will be treated in detail in Section V, were synchronization and chaos are discussed. 

In what follows we shall not be much concerned with variations in pressure, and so we will write the kinetic expressions as functions of temperature only, as in Eqs. (5) and (6). At constant pressure the energy balance for the reactor becomes an enthalpy balance and, if we write VQ t) for the rate of heat removal from the reactor, this becomes... 

We can obtain an additional equation for T iz), the coolant temperature, by making a heat balance over the reactor and cooling jacket as a whole between the inlet and the section through z. To do this, let denote the mass flow rate of the coolant per unit cross-sectional area of the reactor and Cpc the heat capacity per unit mass of the coolant. If is the cross-sectional... 

Description The DCC process overcame the limitations of conventional fluid catalytic cracking (FCC) processes. The propylene yield of DCC is 3-5 times that of conventional FCC processes. The processing scheme of DCC is similar to that of a conventional FCC unit consisting of reaction-regeneration, fractionation and gas concentration sections. The feedstock, dispersed with steam, is fed to the system and contacted with the hot regenerated catalyst either in a riser-plus fluidized dense-bed reactor (for DCC-I) or in a riser reactor (for DCC-II). The feed is catalytically cracked. Reactor effluent proceeds to the fractionation and gas concentration sections for stream separation and further recovery. The coke-deposited catalyst is stripped with steam and transferred to a regenerator where air is introduced and coke on the catalyst is removed by combustion. The hot regenerated catalyst is returned to the reactor at a controlled circulation rate to achieve the heat balance for the system. 

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). 

The equality in reactor behaviour of the stationary PFTR and unsteady BR, which was explained in Section 4.1.5, allows the direct formulation of the heat balance for the cooled BR. If the length of the PFTR is substituted by the characteristic reaction time for the batch process, and if the Stanton munber formulation is based on its general definition regarding the overall heat removal mechanism, the unsteady heat balance of the cooled BR is obtained. 

As already mentioned in the description of a fluid catalytic cracker the circulation rate of solids is determined by the heat balance between the reactor and the regenerator. Equating heat inputs and outputs over the reactor leads to the following ratio for the circulation rate between the reactor and the regenerator, m/kg/hr) and the gasoil feed rate,... 

A forced circulation, ambient pressure fused salt (flibe) intermediate heat transport loop carries the heat from the in-vessel intermediate heat exchanger (IHX) to the balance of plant (BOP). Figure XXIV-4 shows the overall heat flow for the reactor and BOP at full power of 400 MW(th). 

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