Energy balance material

The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature), and enthalpy change of both streams are given in Table 6.1. 

The energy cost of the process can be set without having to design the heat exchanger network and utility system. These energy targets cam be calculated directly from the material and energy balance. Thus... 

In addition to being able to predict the energy costs of the heat exchanger network and utilities directly from the material and energy balance, it would be useful to be able to calculate the capital cost, if this is possible. The principal components that contribute to the capital cost of the heat exchanger network are... 

Let us take each of these components in turn and explore whether they can be accounted for from the material and energy balance without having to perform heat exchanger network design. 

Having explored the major degrees of freedom, the material and energy balance is now fixed, and hence the hot and cold streams which contribute to the heat exchanger network are firmly defined. The remaining task is to complete the design of the heat exchanger network. 

The scientific basis of extractive metallurgy is inorganic physical chemistry, mainly chemical thermodynamics and kinetics (see Thermodynamic properties). Metallurgical engineering reties on basic chemical engineering science, material and energy balances, and heat and mass transport. Metallurgical systems, however, are often complex. Scale-up from the bench to the commercial plant is more difficult than for other chemical processes. 

Total material, condensable component, and energy balances can be written for the entire column ... 

Most flow sheets have one or mote recycles, and trial-and-ettot becomes necessary for the calculation of material and energy balances. The calculations in a block sequential simulator ate repeated in this trial-and-ettot process. In the language of numerical analysis, this is known as convergence of the calculations. There ate mathematical techniques for speeding up this trial-and-ettot process, and special hypothetical calculation units called convergence, or recycle, units ate used in calculation flow diagrams that invoke special calculation routines. 

Equations-Oriented Simulators. In contrast to the sequential-modular simulators that handle the calculations of each unit operation as an iaput—output module, the equations-oriented simulators treat all the material and energy balance equations that arise ia all the unit operations of the process dow sheet as one set of simultaneous equations. In some cases, the physical properties estimation equations also are iacluded as additional equations ia this set of simultaneous equations. 

In the equation-oriented approach, the executive organizes the equations and controls a general-purpose equation solver. The equations for material and energy balances may be grouped separately from those for the calculation of physical properties or phase equiHbria, or as ia the design of some simulators, the distinction between these groups of equations may disappear completely. 

For many pieces of equipment, such as heat exchangers and distillation columns, stand-alone programs are available that calculate material and energy balances around that piece of equipment, size the equipment, and calculate or rate its performance. 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

Reconciled data must satisfy all material and energy balance constraints and those of rate equations for which coefficients and parameters are fully known. The mathematical process of reconciUation can be described schematically as in Figure 7. 

Overall Eactor Estimates. The next level of fixed capital estimate is based on a preliminary design that includes a flow sheet, material balances, energy balances, and enough equipment design to size all of the principal process equipment, including pumps and tanks. 

Utihty needs should be calculated direcdy from the process material and energy balances. Unit costs for the various utihties can be obtained from suppliers or purchasing agents. Although regional variations can be quite large, typical U.S. utihty costs in 1992 are tabulated in Table 3. 

When the basic physical laws are expressed in this form, the formulation is greatly facilitated. These expressions are quite often given the names, material balance, energy balance, and so forth. To be a little more specific, one could write the law of conservation of energy in the steady state as... 

Material and energy balances of a nonflow reactor are summarized in Table 7-5. Several catch operations are summarized in Fig. 7-5. 

TABLE 7-5 Material and Energy Balances of a Nonflow Reactor... 

Material and energy balances are based on the conservation law, Eq. (7-69). In the operation of liquid phase reactions at steady state, the input and output flow rates are constant so the holdup is fixed. The usual control of the discharge is on the liquid level in the tank. When the mixing is adequate, concentration and temperature are uniform, and the effluent has these same properties. The steady state material balance on a reacdant A is... 

Packed Red Reactors The commonest vessels are cylindrical. They will have gradients of composition and temperature in the radial and axial directions. The partial differential equations of the material and energy balances are summarized in Table 7-10. Example 4 of Modeling of Chemical Reactions in Sec. 23 is an apphcation of such equations. 

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