Mass and Energy Transfer in Condensation

Typical composition and temperature profiles in condensation operations are shown in Figure 15.4. The analysis of mass and energy transfer in condensation that follows is an extension of the general analysis of simultaneous mass and energy transfer presented in Section 11.5. The additional complication here is that we must account for energy transfer (but not mass transfer) across the tube wall into the coolant. 

The purpose of this chapter is to present a general framework for dealing with the effect of mass transfer on heat transfer and the effect of heat transfer on mass transfer. Applications to distillation operations are included in this chapter mass and energy transfer in multicomponent condensation is considered in Chapter 15. 

In this chapter we have considered models of multicomponent condensation. In particular, we have considered various approaches to calculating the rates of mass and energy transfers in the vapor and condensate, respectively. Methods of solving the model equations have also been discussed. 

We will often be faced with the problem of determining the rates of mass and energy transfer across a phase boundary. It is these fluxes that appear in the equations that model processes, such as distillation, gas absorption, condensation, and so on. Here we present a summary of the relevant equations and suggest a procedure for determining the required fluxes. 

In most jacketed reactors or steam-heated reboilers the volume occupied by the steam is quite small compared to the volumetric flow rate of the steam vapor. Therefore the dymamic response of the jacket is usually very fast, and simple algebraic mass and energy balances can often be used. Steam flow rate is set equal to condensate flow rate, which is calculated by iteratively solving the heat-transfer relationship (Q = UA AT) and the valve flow equation for the pressure in the jacket and the condensate flow rate. 

The mass and energy balances constitute a linear set of constraints. The energy balances for the condensers state that all cooling required by a condenser of a particular column must be transferred either to a reboiler of another column in the same sequence or to a cold utility. Similarly, the energy balances for the reboilers state that all heating required by a condenser must be provided by either the condenser of another column in the same sequence or by the two available hot utilities. 

F. A. Williams, Condensed-Phase Mass and Energy Balances , chapter 3 of Heat Transfer in Fires Thermophysics, Social Aspects, Economic Impact, P. L. Blackshear, ed., Scripta Book Co., New York Wiley, 1974, 180-182. 

This suggests, that for the calculation of the heat and mass transfer, it would be sensible to subdivide the flow path into individual sections, and then solve the mass and energy balances for each section, taking the laws of heat and mass transfer into consideration. Calculations of this type for binary mixtures are only possible with the assistance of a computer. In the discussions presented here we want to limit ourselves to an explanation of the fundamental physical processes along with an illustration of the decisive balance equations. As the process of condensation in multicomponent mixtures with more than two components is similar to that in binary mixtures, we will limit ourselves to the consideration of binary mixtures. 

Perfectly isothermal systems are rare in chemical engineering practice and many processes, such as distillation, gas absorption, stripping, condensation, and evaporation, involve the simultaneous transfer of mass and energy across fluid-fluid interfaces. Representative temperature profiles in some nonisothermal processes are shown in Figure 11.1. The temperature profile also has a large influence in chemically reacting systems. For nonisothermal systems it is important to consider simultaneous heat transfer even though we are primarily interested in the mass transfer process. 

The operations considered in this chapter are concerned with the interphase transfer of mass and energy which result when a gas is brought into contact with a pure liquid in which it is essentially insoluble. The matter transferred between phases in such cases is the substance constituting the liquid phase, which either vaporizes or condenses. These operations are somewhat simpler—from the point of view of mass transfer—than absorption and stripping, for when the liquid contains only one component, there are no concentration gradients and no resistance to mass transfer in the liquid phase. On the other hand, both heat transfer and gas-phase mass transfer are important and must be considered simultaneously since they influence each other. 

At film condensation, the heat has to be transported through the film. If the film is laminar and the film surface is at thermodynamic equilibrium, then the heat is transferred by conduction. The transfer coefficient can be calculated, if the film thickness is known depending on the film length. In case of a laminar film the velocity profile is defined by an equihbrium between viscous and gravitational forces, see Chap. 3. Considering the conservation laws for mass and energy allows to derive the heat transfer coefficient on a theoretical basis. 

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