Heat Effects in Steady-Flow Processes

In a process design we are given values for the outputs from a process, and we must compute values for the process inputs. In the flash situation, we might know the product properties xp yp Nj, and N ) and we would compute the feed properties Tf, Pf, Zp and Nf) plus the heat duty Q. But note that in a process design the equations to be solved—phase equilibrium plus material and energy balances—are exactly the same as those to be solved in a process analysis. Moreover, the value of fhe number of variables needed to close each problem, is also the same. Analysis differs from design only in the identities of knowns and unknowns. 

Another type of design problem is optimization, in which we seek to adjust operating conditions to maximize or minimize an additional variable. For example, we might seek the feed composition that optimizes energy efficiency, where the efficiency is measured by the heat duty per mole of feed that is, we seek to minimize Q/Nf. In these kinds of problems, additional nonthermodynamic equations and models may be involved. Nevertheless, although numerical values for computed results could differ, the thermodynamic description would be unaltered. 

We now turn to processing situations in which heat effects are of primary importance examples include chemical reactors and separators that exploit phase partitioning. Thermodynamic analysis of these situations invoke the stuff equations in particular, steady-state heat effects are computed from (12.3.5). To obtain the partial molar enthalpies that appear in (12.3.5), we need enthalpies as functions of composition so in 12.4.1 we show how enthalpy-concentration diagrams can be constructed from volumetric equations of state applied to binary mixtures in phase equilibrium. Then we apply the energy balance (12.3.5) to multicomponent flash separators ( 12.4.2), binary absorbers ( 12.4.3), and chemical reactors ( 12.4.4). 

Before energy balances can be used in the analysis or design of multicomponent flow processes, we must have data or correlations for mixture enthalpies as functions of composition. Such correlations can be developed from models for volumetric equations of state or from models for g in the latter case, we would need a form for the temperature-dependence of the parameters in the g model. In this section we discuss how an equation of state can be used to compute an enthalpy-concentration diagram for a two-phase equilibrium situation such diagrams contribute to the analysis or design of distillation columns. 

To have a simple example, we consider an alkane(l) + aromatic(2) mixture, modeled by the Redlich-Kwong equation (8.2.1). Certain vapor-liquid phase diagrams for this mixture were displayed and discussed in 9.3. Here our objective is to compute residual enthalpies for vapor and liquid that coexist in equilibrium in particular, we want to construct an isothermal plot of vs. x and y. (We will call this an hxy diagram, even though it is that is actually plotted.) To do so, we set the temperature, pick a liquid composition Xp and then perform a bubble-P calculation to obtain values 

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We have used this chapter to illustrate how thermodynamics can contribute to the analysis and design of selected engineering processes. The applications considered here included calculations for phase equilibria, solubilities, heat effects in steady-flow processes, and the response of certain variables to changes of state. 

When we apply thermodynamics to industrial and research problems, we should draw fundamental ideas from Parts 1 and 11, devise an appropriate solution strategy, as in Chapter 10, and combine those with a computational technique, as in Chapter 11. Such a procedme provides values for measurables that can be used to interpret novel phenomena, to design new processes, and to improve existing processes. The procedure is illustrated in this chapter for several well-developed situations. They include conventional phase-equilibrium calculations for vapor-liquid, liquid-liquid, and solid-solid equilibria ( 12.1) solubility calculations for gases in liquids, solids in liquids, and solutes in near-critical solvents ( 12.2) independent variables in steady-flow processes ( 12.3) heat effects for flash separators, absorbers, and chemical rectors ( 12.4) and effects of changes of state on selected properties ( 12.5). 

You will be retrieving information on heats of formation from reference tables and data bases. The values in the tables have been reconciled from innumerable experiments. To determine the values of the standard heats (enthalpies) of forniation, the experimenter usually selects either a simple flow process without kinetic energy, potential energy, or work effects (a flow calorimeter), or a simple batch process (a bomb calorimeter), in which to conduct the reaction. Consider an experiment in a flow process under standard state conditions in which the experimental arrangement is such that the summation of sensible heat terms on the right-hand side of Eq. (4.33) is zero and no work is done. The steady-state (no accumulation term) version of Eq. (4.24a) for stoichiometric quantities of reactants and products reduces to... 

For certain products, skill is required to estimate a product s performance under steady-state heat-flow conditions, especially those made of RPs (Fig. 7-19). The method and repeatability of the processing technique can have a significant effect. In general, thermal conductivity is low for plastics and the plastic s structure does not alter its value significantly. To increase it the usual approach is to add metallic fillers, glass fibers, or electrically insulating fillers such as alumina. Foaming can be used to decrease thermal conductivity. 

The steady two-dimensional diabatic flow is described by the equations for mass, momentum and energy in conservation form (Schnerr and Dohrmann [7], Dohrmann [8]). Real gas effects are not yet included and inviscid fluids are assumed. Here the classical nucleation theory of Volmer [9] is used which gives a good qualitative representation of the behavior of condensing in the supersaturated state (Wegener [iO]). Oswatitsch [11] introduced this theory into the calculation of flow processes, a summary of all basic relationships for compressible flows with heat addition is given by Zierep [12]. To compute the nucleation rate J per unit time and volume, we take... 

The mechanisms of mass transport can be divided into convective and molecular flow processes. Convective flow is either forced flow, for example, in pipes and packed beds, or natural convection induced by temperature differences in a fluid. For diffusive flow we have to distinguish whether we have molecular diffusion in a free fluid phase or a more complicated effective diffusion in porous solids. Like heat transport, diffusion may be steady-state or transient. 

In order to identify EPHs of the cell or electrode reactions from the experimental information, there had been two principal approaches of treatments. One was based on the heat balance under the steady state or quasi-stationary conditions [6,11, 31]. This treatment considered all heat effects including the characteristic Peltier heat and the heat dissipation due to polarization or irreversibility of electrode processes such as the so-call heats of transfer of ions and electron, the Joule heat, the heat conductivity and the convection. Another was to apply the irreversible thermodynamics and the Onsager s reciprocal relations [8, 32, 33], on which the heat flux due to temperature gradient, the component fluxes due to concentration gradient and the electric current density due to potential gradient and some active components transfer are simply assumed to be directly proportional to these driving forces. Of course, there also were other methods, for instance, the numerical simulation with a finite element program for the complex heat and mass flow at the heated electrode was also used [34]. 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

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