Enthalpy balances general case

In the case of adiabatic rather than isothermal flashing, when the total enthalpy of the system rather than its temperature is specified, the equations associated with isothermal flash are solved jointly with an enthalpy-balance equation, treating the temperature as another variable. The general enthalpy balance is... 

Assumption 6 In the general case, we shall assume that there are no thermal effects and neglect the influence of the heat of adsorption on the band profile. In principle, heat or enthalpy balances for the mobile and stationary phases should be included in the system of equations, as discussed in Section 2.1.4. In practice, however, the temperature excursion associated with the migration of a band seems to be small and no detectable effect has been demonstrated [31]. Accordingly, we ignore the thermal effect in the rest of this book, except in Section 2.1.5. We assiune that the column is operated isothermally. A temperature gradient along the column would require appropriate adjustments in Eq. 2.2 to account for the variations of the isotherm and the kinetic parameters, of u, Di i, and, improbably, F with T, hence, in this case, z. 

However, the enthalpy balance of processes can be evaluated by solving Eqs. (4.26) and (4.27). The enthalpy balance is related to the heating and to the general reaction taking place in the system. In both cases, the initial and the final states of the system comprise the same number of elementary particles, hence the first term on the right-hand side of Eq. (4.27) is always canceled. When calculating the changes of enthalpy in the two types of processes, one can thus operate with relative enthalpy values, 7/rei(7 m)... 

In conclusion, the temperature profile in conventional distillation columns is the result of both phase equilibrium relations and enthalpy balances. In narrow-boiling mixtures, the phase equilibrium effect is generally more pronounced, while in wide-boiling mixtures, the enthalpy balances are more significant. The importance of the distinction between the two effects is twofold. First, different mathematical solution algorithms are better suited for each situation, as will be discussed in Chapter 13. Second, the understanding and prediction of column performance is enhanced when the two effects are recognized. Examples 7.1 and 7.2 illustrate the two cases. 

The McCabe-Thiele constructions described in Chapter 8 embody rather restrictive tenets. The assumptions of constant molal overflow in distillation and of interphase transfer of solute only in extraction seriously curtail the general utility of the method. Continued use of McCabe-Thiele procedures can be ascribed to the fact that (a) they often represent a fairly good engineering approximation and (b) sufficient thermodynamic data to justify a more accurate approach is often lacking. In the case of distillation, enthalpy-concentration data needed for making stage-to-stage enthalpy balances are often unavailable, while, in the Case of absorption or extraction, complete phase equilibrium data may not be at hand. 

Remark Complications can arise when stream j is a multiphase mixture. The energy (enthalpy) balance in terms of the specific enthalpies will anyway hold true, as well as the individual component balances, where yi is the mass fraction of C ( in the whole mixture. The case will, however, require again a special consideration. Generally, new variables, say pj will occur, where p is mass fraction of phase fin stream j, obeying... 

When calculating energy balance around a boiler it is important also to consider fuel and air inlet temperatures. In general fuel temperature can be neglected in boiler efficiency analysis, at least it is inside standard conditions. This temperature is more important for the performances of the fuel line and atomization process. The situation is different for inlet air its temperature can have an important impact on boiler efficiency due to the flow mass involved (compare Figure 34.4). In case the inlet air is preheated by exhaust smoke, the boiler efficiency expression doesn t change with respect to Equation 34.1. In case the air is preheated by an external source, sensible enthalpy of air has to be considered in both the denominator and the numerator. 

In industry many of the distillation processes involve the separation of more than two components. The general principles of design of multicomponent distillation towers are the same in many respects as those described for binary systems. There is one mass balance for each component in the multicomponent mixture. Enthalpy or heat balances are made which are similar to those for the binary case. Equilibrium data are used to calculate boiling points and dew points. The concepts of minimum reflux and total reflux as limiting cases are also used. 

In this case, we just sum up the enthalpies of the input streams and the output streams. If we have F input streams (and we use / as the counter for the input streams) and K output streams (we use k as the counter for output streams) with L components and N reactions, then we have the following most general heat balance equation ... 

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