Adiabatic reaction, heat balance

Figure 6.4a shows the behavior of an endothermic reaction as a plot of equilibrium conversion against temperature. The plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as illustrated in Examples 6.1 and 6.2. If it is assumed that the reactor is operated adiabatically, a heat balance can be carried out to show the change in temperature with reaction conversion. If the mean molar heat capacity of the reactants and products are assumed constant, then for a given starting temperature for the reaction Ttn, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.4a. As the conversion increases, the temperature decreases because of the reaction endotherm. If the reaction could proceed as far as equilibrium, then it would reach the equilibrium temperature TE. Figure 6.4b shows how equilibrium conversion can be increased by dividing the reaction into stages and reheating the reactants...

A second order reaction is performed adiabatically in a CESTR. Use die data in Example 6-11 to plot bodi conversions for die mass and heat balance equations. The second order rate constant k is... 

It is obvious that reducing cr (i.e., increasing the dilution), results in a reduction in the adiabatic temperature rise and, thus, can help to keep the reaction temperature within acceptable constraints. The global heat balance over the system, with all heat generation terms included, is required to obtain the actual adiabatic temperature rise. From the safety perspective, the adiabatic temperature rise is a useful design parameter, although it must be emphasized that it shows only a maximum effect and not a rate. 

For a first order adiabatic reaction in a CSTR, the variation of concentration and temperature with time and in the steady state will be analyzed. Heat and material balances are based on the relation,... 

Under adiabatic conditions with external diffusion, temperature and concentration differences will develop between the bulk of the fluid and the surface of the catalyst. The rate of reaction is the rate of diffusion, r = kga(Cg-Cs) and the heat balance is... 

The composition of the gas produced is determined by the thermodynamic equilibrium of these reactions at the exit temperature, which is given by the adiabatic heat balance based on the composition and flow of the feed, steam and oxygen added to the reactor. 

The mass- and ener -balance equations must be solved numerically in the general situation where heat is transferred to or from walls. There are three terms on the right side of the energy equation, heat flow with reactants and products, reaction heat, and heat transfer through walls. Flowever, the adiabatic reactor is a special case where we need to solve only one equation for a single reaction. 

No simplifying assumptions are involved to this point in the derivation. Simplifying assumptions are involved to obtain the mass, m, at the point when the temperature begins to fall. The required relief flow rate can then be calculated on the basis that, at the maximum temperature, the heat released by the reaction is balanced by the heat removed by pressure relief. The method makes use of adiabatic experimental data, which can be obtained as described in Annex 2. 

If the reaction is carried out adiabatically (i.e. without heat transfer, so that Q = 0), the heat balance shows that the temperature at any stage in the reaction can be expressed in terms of the conversion only. This is because, however fast or slow the... 

For the purposes of this example we shall neglect the heat capacity of the reaction vessel. Since the anticipated temperature rise is small, the heat of reaction will be taken as independent of temperature. Because the heat capacity of the reactor is neglected, we may most conveniently take the adiabatic heat balance (equation 1.32) over the unit volume, i.e. I m3 of reaction mixture. Thus, integrating equation 1.32 with the temperature To when 0 ... 

In the previous article [1], for an adiabatic reaction the thermal balance equation led to an identity relation between consumption and reaction temperature. We now write the thermal balance equation with heat transfer ... 

Write the steady-state mass and heat balance equations for this system, assuming constant physical properties and constant heat of reaction. (Note Concentrate your modeling effort on the adiabatic nonisothermal reactor, and for the rest of the units, carry through a simple mass and heat balance in order to define the feed conditions for the reactor.)... 

Understanding the heat balance is essential when considering thermal process safety. This also applies to the industrial scale for reactors or storage units, as well as at laboratory scale for understanding the results of calorimetric experiments. In fact, the same heat balance terms will serve in both situations. For this reason, we first present the different terms of the heat balance of a reactor with a reacting system. This is followed by an often-used and simplified heat balance and finally we will study how reaction rate is affected by adiabatic conditions. 

Another important characteristic of a runaway reaction is the time a thermal explosion takes to develop under adiabatic conditions, or Time to Maximum Rate under adiabatic conditions (TMRai). To calculate this time, we consider the heat balance under adiabatic conditions for a zero-order reaction ... 

The adiabatic mode the reaction is performed without any exchange at all. This means the heat of reaction will be converted into a temperature increase. The temperature course can be calculated from the heat balance of the reactor ... 

Energy Balance. It was decided that a simple, fixed-bed, adiabatic reactor would be required In this process. Since the reactions Involved release considerable heat, this Influences the local temperature, which In turn Influences the reaction rates. An energy balance, or heat balance, having the following general form, was added along with the mass balance In all subsequent simulations ... 

Quite often, where the reaction is not highly exothermic or endothermic, a long, single bed is adequate. Because the reaction is adiabatic, there is a unique relationship between concentration and temperature for every reaction. In other words, two separate equations based on mass- and heat-balances are not required. For a reversible reaction of the type... 

The temperature reached in an adiabatic reactor is determined by a simple heat balance. For an exothermic reaction, the heat generation rate corresponding to conversion x is... 

A heat balance of an adiabatic reaction based on Equation 2 yields an expression of the form ... 

Under adiabatic conditions heat flows have to be modelled accordingly with respect to the mass balances. For exothermic reactions usually a stimulation of the chemical reaction is required due to the higher energy level at the beginning of the reaction. In general, the interactions between heat and mass balances are more difficult to model. More complicated cases occur when both conditions are mixed, i.e. under polytropic conditions. Here, solutions for heat and mass balances are hardly available analytically. Instead,... 

In mixing reactors, the heat balance is characterised by a temperature increase, due to the adiabatic heating of the reaction mixture, and the heat removal rate (without taking into account the boiling process) [4] ... 

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