Energy balances with heat exchange

ENTHALPY BALANCES IN HEAT EXCHANGERS. In heat exchangers there is no shaft work, and mechanical, potential, and kinetic energies are small in comparison with the other terms in the energy-balance equation. Thus, for one stream through the exchanger... 

Forms of Ihe energy balance for a CSTR with heat exchange... 

The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature), and enthalpy change of both streams are given in Table 6.1. 

The concept of an optimum reboiler or condenser AT relates to the fact that the value of energy changes with temperature. As the gap between supply and rejection widens, the real work in a distillation increases. The optimum AT is found by balancing this work penalty against the capital cost of bigger heat exchangers. 

With decreasing cell size, the temperature difference between the wall of the cell and the eatalyst partiele in the cell would decrease to zero. For sufficiently small cell dimensions, we may assume the two temperatures are the same. In this case, the heat conduction through the wall becomes dominant and affects the axial temperature profile. As the external heat exchange is absent and the outside of the reactor is normally insulated, the temperature profile is flat along the direction transverse to the reactant flow, and the conditions in all channels are identical to each other. The energy balance is... 

In order to assess the design of both the reactor and the heat exchanger required to control T, it is necessary to use the material balance and the energy balance, together with information on rate of reaction and rate of heat transfer, since there is an interaction between T and /A. In this section, we consider two cases of nonisothermal operation adiabatic (Q = 0) and nonadiabatic (Q = 0). 

Figure 9.11 Sketch of the energy balance equation showing the shift in adiabatic line caused by heat exchange with surroundings.

These configurations are essentially two reactors connected by the heat exchange area A, and we will consider this in more detail in a later chapter in connection with multiphase reactors. We do not need to write a species balance on the coolant, but the energy balance in the jacket or cooling coil is exactly the same as for the reactor except that we omit the reaction generation term. 

The obvious way to heat or cool a chemical reactor is by heat exchange through a wall, either by an external jacket or with a cooling or heating coil. As we discussed previously, the coolant energy balance must be solved along with the reactor energy balance to determine temperatures and heat loads. 

In real SOFC systems with the associated components like fans, heat exchangers, etc., it is necessary to consider the whole system, see Figure 2.11. The system is defined as a module consisting of SOFCs, which are connected electrically in parallel into stacks supplying a common burner with the depleted fuel. The energy balance of the stacks provides the necessary requirements for the excess air [2],... 

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. 

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