Sensible heat effects

All of the important heat effects are illnstratedby this relatively simple chemical-manu-factnring process. In contrast to sensible heat effects, which are characterized by temperatnre changes, the heat effects of chemical reaction, phase transition, and the formationand separation of solntions are determined from experimental measnrements made at constant temperatnre. In this chapter we apply thermodynamics to the evalnation of most of the heat effects that accompany physical and chemical operations. However, the heat effects of mixing processes, which depend on the thermodynamic properties of mixtnres, are treated in Chap. 12. 

Heat transfer to a system in which there are no phase transitions, no chemical reactions, and no changes m composition causes the temperatnre of the system to change. Onr purpose here is to develop relations between the quantity of heat transferred and the resnlting temperatnre change. 

When the system is a homogeneons substance of constant composition, the phase rule indicates that fixing the values of two intensive properties establishes its state. The molar or specific internal energy of a substance may therefore be expressed as a function of tuo 

Similarly, the molar or specific enthalpy may be expressed as a function of temperature 

two circumstances allow the final term to be set equal to zero  

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The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

It should be emphasized that the enthalpy change includes not only sensible heat effects but also a heat-of-reaction term and in some cases pressure effects. If there are multiple inlet and outlet streams, appropriate averaging techniques must be used to employ this equation. 

For reactors 2 and 3, there will not be any sensible heat effects. 

The internal energy changes (sensible-heat effects) can usually be neglected compared with the latent-heat effects. Thus a simple algebraic steadystate energy equation can be used... 

Molal heats of vaporization often differ substantially, as the few data of Table 13.4 suggest. When sensible heat effects are small, however, the condition of constant molal overflow still can be preserved by adjusting the molecular weight of one of the components, thus making it a pseudocomponent with the same... 

This solution, which corresponds to negligible sensible heat effects, can be used to start the numerical integration for any finite mi, since, in Eq. (99), Uy (0) = 0. The case mi = is well approximated, for example, by the melting of steel originally at room temperature. Here mi = 27, so that latent heat effects play a very small role. Some modification of the transformed variables is necessary to get the equations into convenient form for numerical integration. 

There are several other aspects about CSTRs with exothermic reactions that should be mentioned at this point. The first involves the temperature of the feed. The colder the feed, the less heat must be transferred from the reactor. So control would be expected to be improved. However, as we will see in Chapter 3, a cold feed can produce some interesting dynamics for instance, an increase in feed flowrate initially decreases reactor temperature because of the sensible-heat effect. But as the reactant concentration in the reactor increases, the temperature eventually increases. A reactor temperature runaway can result if the cold feed quenches the reaction and reactant concentration builds to a very high level before the reaction lights off. ... 

Because sensible heat effects are being neglected, the rate of latent heat release by the condensing vapor can be equated to heat transfer rate through the film to the wall, i.e., considering the control volume of length dx ... 

If the reactor is operated at isothermal conditions, then no sensible heat effects occur and Equation (9.3.9) becomes ... 

The energy balance for a CSTR can be derived from Equation (9.2.7) by again carrying out the reaction isothermally at the inlet temperature and then evaluating sensible heat effects at reactor outlet conditions, that is. 

Equation (11.7) is based on the assumption that the vapor enters the condenser as saturated vapor (no superheat) and the condensate leaves at condensing temperature without being further cooled. If either of these sensible-heat effects is important, it must be accounted for by an added term in the left-hand side of Eq. (11.7). For example, if the condensate leaves at a temperature 7 that... 

An estimation of the heat removed is complex since it not only involves latent heat of fusion, but sensible heat effects that may not be insignificant where large systems are involved. A further complication arises where natural convection in the water at the water ce interface occurs, i.e. modifying the simple conduction concept implied in Equation 9.5. 

Figure 5.2 gives the response of a one-CSTR process for step changes in feed rate from 100 to 150 lb-mo 1/hr and from 100 to 50 Ib-mol/hr for the system with k = 0.5 and 95 percent conversion. When feed rate is increased, the temperature in the reactor initially decreases. This is due to the sensible heat effect of the colder feed (70°F versus 140°F). After about five minutes, the temperature starts to increase because the concentration of reactant has increased, which increases the rate of reaction. The maximum temperature deviation is only 0.06°F, but it takes over five hours to return to the setpoint because of the slow change in reactor concentration and the large reset time. 

A two-stage evaporator is used to concentrate a brine solution of NaCl in water. Assume that the NaCl is completely nonvolatile. Steam is fed into the reboiler in stage 1 at a rate Vq (kg/hr). If we neglect sensible heat effects, this amount of steam will produce about the same amount of vapor in stage I V, kg/hr), and condensing V in a reboiler in stage 2 will produce about the same amount of vapor in stage 2 Vi, kg/hr). Thus, for a simplified model we will assume that 0=121= 2= V. Since NaCl is nonvolatile, these vapors are pure water. 

The solvents added to the system reduce the heat load of the reactor because energy is needed to increase the temperature of the solvent to the reactor conditions (sensible heat), yet no heat of polymerization is released by the solvent. This can be an effective measure to reduce heat load at the expense of reduced polymer productivity. When the reactor system operates at elevated temperatures, the additional solvent can pose a challenge to the heating system. Because of the sensible heat effect, some processes use chilling of the monomer, as long as the chilled temperature is not too low to freeze any component. 

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