Application of the Energy Balance

In writing Equation 5.7 we have used a reference temperature of 0°F for air. Note that Hj 2 s enthalpy per pound of dry air and includes the heat of the vapor associated with a pound of dry air. 

An energy balance for the water component alone gives 

The amount of makeup water that is needed to compensate for evaporation losses is 

By dividing Equation 5.9 by Lj and using Equation 5.10, we can rearrange our balance into a more generalized form  

If we then combine Equations 5.11 and 5.8, a general expression for makeup water requirements for any fixed set of conditions is obtained  

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The application of the energy balance equation to segment n, results similarly in the relationship... 

A typical piping application starts with a specified flow rate for a given fluid. The piping system is then designed with the necessary valves, fittings, etc. and should be sized for the most economical pipe size, as discussed in Chapter 7. Application of the energy balance (Bernoulli) equation to the entire system, from the upstream end (point 1) to the downstream end (point 2) determines the overall net driving force (DF) in the system required to overcome the frictional resistance ... 

Calculate the operating temperature in the reactor. Application of the energy balance shown above allows the reaction mass temperature to be calculated, since all quantities in the expression are known except T. Pertinent calculations and parameters are as follows ... 

Let us look now at some examples of applications of the energy balance for closed systems. Remember to follow the checklist presented in Chap. 2 in analyzing the problem. 

EXAMPLE 4.40 Application of the Energy Balance to a Process in which the Temperatures of the Entering and Exit Streams Differ... 

To express variations of the nsactor temperature, we apply the energy balance equation (first law of thermodynamics). Chapter 5 covers in detail the derivation and application of the energy balance equation in reactor design. The applications of the energy balance equation to ideal reactor configurations are covered in Chapters 5-9. 

Cooler/throttling/separator. The subsystem defined by the precooler, the throttling valve, and the separator exchanges no heat or work with the surroundings and it involves 3 streams (4,7, and 9) whose properties are known. The unknown flow rate x may be determined by application of the energy balance ... 

What is the plan In the following pages we manipulate Equation (11-9) in order to apply it to each of the reactor types we have been di.scussing batch. PER. PER, and CSTR. The end result of the application of the energy balance to each type of reactor is shown in Table 1 l-I. These equations can be used in Step 5 of the algorithm discussed in Example El 1-1. The equations in Table 11-1 relate temperature to conversion and to molar flow rates and to the system parameters, such as the overall heat-transfer coefficient and area. Ua, with the corresponding ambient temperature, Ta. and the heat of reaction,... 

Section 13.2 discusses the application of the energy balance to the operation of batch reactors and discusses reactor safety and the reasons for the explosion of an industrial batch reactor. 

With high concentrations, heat effects in the chromatographic column may be important. This would require the simultaneous application of an energy balance and the introduction of a term reflecting the influence of temperature on the adsorption equilibrium. 

The energy balance (3.301) is applicable for catalysis, adsorption, and ion exchange. More specifically, in catalysis, where the steady-state condition exists, frequently the accumulation term is zero. In contrast, adsorption and ion exchange operate under unsteady-state condition. The analysis of the energy balance equation for catalytic fixed beds is presented in detail in Section 5.3.4. 

Thermodynamic Governing Equations. Derivation of the expression for entropy production arising from mess transfer requires application of the fundamental balance equations. Potential and kinetic energy effects as well as momentum effects are neglected. With these assumptions the governing equations are given as follows ... 

Example 2 Application of total energy balance for the flow of an ideal gas. 

The infinite heat reservoir is an abstraction, often approximated in engineering applications by large bodies of air or water. Apply the closed-sy stemform of the energy balance [Eq. (2.3)] to such a reservoir, treating it as a constant-volume system. How is it that heat transfer to orfrom tire reservoir can be nonzero, yet the temperature of the reservoir remains constant ... 

As with the mass balance, it is useful to have a form of the energy balance applicable to a change from state 1 to state 2. This is easily obtained by integrating Eq. 3.1-4 over the time intervaUi to ti, the time required for the system to go from state 1 to state 2. 

Applications of the Mass and Energy Balances 81 and the difference form of the energy balance is... 

In this chapter we consider several practical applications of the energy and entropy balances that we have developed. These include the liquefaction of a gas. and the antilysis of cycles used to convert heat to work and to provide refrigeration and air conditioning. Finally, as engineers we have a social responsibility to consider safety as a paramount issue in anything we design or operate. Therefore, methods to estimate the energy that could be released in different types of nonchemical explosions are presented. 

Another interesting application of the multicomponent balance equations for reacting systems is in the estimation of the maTcimum work that can be obtained from an isothermal chemical reaction that occurs in a steady-state fuel cell or other work-producing device. The starting point here is the steady-state isothermal energy and... 

The application of the energy law to stationary flow processes often involves setting up enthalpy balance relations. 

The population balance approach to analysis of crystallizers was formalized and presented by Randolph and Larson (1971, 1988). The technique parallels other balance approaches such as material and energy balances, which are familiar to process engineers. The population balance is used to account for both the size (an attribute to be described later in this section) and number of particles. Therefore, before a discussion of the development and application of the population balance can be enjoined, it is necessary to consider size and size distributions of particles. 

For application of the steam balance in evaluating energy projects, the steam balance must have two features. One is the high precision, of course, and the other is that the steam balance must represent a good base case corresponding to the most common process operation to represent the true values of opportunities to be assessed. The above aspects will be further discussed in detail in the next chapters. 

Application of an energy balance to the system in Fig. 1 produces the following two differential equations, one for pressurizing gas and one for the container wall Pressurizing gas... 

The analysis of a regenerator is more complex than that of other heat exchangers because of the time and position dependence of its operating temperatures. Application of an energy balance to an element of regenerator length, dx, yields a set of differential equations which describe the heat... 

This section is concerned with the UA xtiT — Text) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then A xt refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T - Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is... 

Himmelbau (1995) or any of the general texts on material and energy balances listed at the end of Chapter 2. The Ponchon-Savarit graphical method used in the design of distillation columns, described in Volume 2, Chapter 11, is a further example of the application of the lever rule, and the use of enthalpy-concentration diagrams. 

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