Complex system energy balance

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. 

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. 

This section discusses the principal causes of overpressure in refinery equipment and describes design procedures for minimizing the effects of these causes. Overpressure is the result of an unbalance or disruption of the normal flows of material and energy that cause material or energy, or both, to build up in some part of the system. Analysis of the causes and magnitudes of overpressure is, therefore a special and complex study of material and energy balances in a process system. 

In order to understand the stable states of complex systems, it is useful to imderstand how the system responds to external perturbations. Externally imposed changes in the energy balance of the planet are referred to as forcings,... 

Accordingly, serious commercially oriented attempts are currently being made to develop special gas-phase micro and mini reactors for reformer technology [91, 247-259], This is a complex task since the reaction step itself, hydrogen formation, covers several individual processes. Additionally, heat exchangers are required to optimize the energy balance and the use of liquid reactants demands micro evaporators [254, 260, 261], Moreover, further systems are required to reduce the CO content to a level that is no longer poisonous for a fuel cell. Overall, three to six micro-reactor components are typically needed to construct a complete, ready-to-use micro-reformer system. 

Energy balances are formulated by following the same set of guidelines as those given in Sec. 1.2.2 for mass balances. Energy balances are however considerably more complex, because of the many processes which cause temperature change in chemical systems. The treatment considered here is somewhat simplified, but is adequate to understand the non-isothermal simulation examples. The various texts cited in the reference section, provide additional advanced reading in this subject. 

Models for emulsion polymerization reactors vary greatly in their complexity. The level of sophistication needed depends upon the intended use of the model. One could distinguish between two levels of complexity. The first type of model simply involves reactor material and energy balances, and is used to predict the temperature, pressure and monomer concentrations in the reactor. Second level models cannot only predict the above quantities but also polymer properties such as particle size, molecular weight distribution (MWD) and branching frequency. In latex reactor systems, the level one balances are strongly coupled with the particle population balances, thereby making approximate level one models of limited value (1). 

Equation 1.5-1 used as a mass balance is normally applied to a chemical species. For a simple system (Section 1.4.4), only one equation is required, and it is a matter of convenience which substance is chosen. For a complex system, the maximum number of independent mass balance equations is equal to R, the number of chemical equations or noncomponent species. Here also it is largely a matter of convenience which species are chosen. Whether the system is simple or complex, there is usually only one energy balance. 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

For nonisothermal operation, the energy analysis, point (4) above, requires that the energy balance be developed for a complex system. The energy (enthalpy) balance previously developed for a BR, or CSTR, or PFR applies to a simple system (see equations 12.3-16,14.3-9, and 15.2-9). For a complex system, each reaction (i) in a specified network contributes to the energy balance (as (-AHRl)rt), and, thus, each must be accounted for in the equation. We illustrate this in the following example. 

The energy balance for this complex reaction in a PFR can be developed as a modification of the balance for a simple system, such as A +. . . -> products. In this latter case,... 

The type of behavior described here occurs in systems where the slope of the energy balance line, CpZ-Ai/ is small thus, large liberation of heat and pure reactants which leads to far from isothermal operations, van Heerden (1953, 1958) discusses and gives examples of this type of reacting system. In addition, though it is a much more complex situation, a gas flame illustrates well the... 

The solution of steady-state material and energy balances can be quite tedious, depending on the complexity of the process. Consequently, computers must be relied on heavily for more complex analysis. The following example illustrates a slightly more involved system than the one shown in Figure 3.3. As a refresher, the reader may try some of the study problems at the end of this chapter. More examples can be found in the literature [1-3]. 

In the present work we will deal with all the above problems and provide a unified framework to deal with the error correction for static or dynamic systems using multicomponent mass and energy balances. The topological character of the complex process is exploited for an easy classification of the measured and unmeasured variable independently of the linearity or nonlinearity of the balance equations. 

Due to its complexity (conversion and separation in the same unit) and because this system has been most widely studied experimentally, CMRs for dehydrogenation (or more generally for equilibrium-restricted reactions) have been the subject of modeling approaches [6, 54-59]. The modeling of CMRs requires mass and energy balances in both feed and permeate sides of the reactor (plug-flow behavior is always assumed) and appropriate boundary conditions. Generally these models fit the experimental data well. 

Equation 11.3-7 is simple in appearance, but its solution is still generally difficult to obtain. If, for example, the composition or temperature of the system contents varies with position in the system, it is difficult to express the total internal energy t/sys in terms of measurable quantities, and a similar problem occurs if phase changes or chemical reactions take place in the course of the process. To illustrate the solution of energy balance problems without becoming too involved in the thermodynamic complexities, we will impose the additional restrictions that follow. 

The present focus is on the gas-liquid flow riser. The model used is a complex nonlinear infinite-dimensional system accounting for momentum, mass and energy balances [3], and the measurements available include temperature and pressure at different locations along the riser. Since the problem being tackled is of distributed parameter nature, location where such measurements are taken, along with its type, is crucial for estimator performance. Moving horizon estimation (MHE) is well suited as it facilitates the sensor structure selection (both in a dynamic and static sense). MHE is proven to outperform... 

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