Isothermal systems optimization

The LDF model is a realistic representation of the system with a surface barrier. Otherwise, k can be treated as an apparent mass transfer coefficient irrespective of the true transport mechanism which can be directly used in the design and optimization of adsorbers. This concept has been successfully used to analyze column breakthrough data for practical non-isothermal systems [18-20]. It substantially... 

Given the reaction stoichiometry and rate laws for an isothermal system, a simple representation for targeting of reactor networks is the segregated-flow model (see, e.g., Zwietering, 1959). A schematic of this model is shown in Fig. 2. Here, we assume that only molecules of the same age, t, are perfectly mixed and that molecules of different ages mix only at the reactor exit. The performance of such a model is completely determined by the residence time distribution function,/(f). By finding the optimal/(f) for a specified reactor network objective, one can solve the synthesis problem in the absence of mixing. 

The adsorption equilibria measurements of N2 and CO2 on activated carbon were performed using a standard static gravimetric method. Further details of these measurements are reported elsewhere." " The Sips isotherm extended to multi-component adsorption was adopted to fit the experimental equilibrium data (Table 9.2). This model has the Langmuirian form applied to non-uniform surfaces and it has been extensively used to model gas adsorption on micro-porous adsorbents and PSA systems. Optimal parameters were found for the adsorption isotherm model, by fitting simultaneously all the data at multiple temperatures. A global isotherm was obtained for each species as illustrated in Figure 9.15." ... 

Figure 6 shows the temperature proflle that should be used with the initiator monomer system described in the caption to reduce the monomer concentration from 0.47 mol/L to 0.047 mol/L. The optimal nonisothermal policy consists of decreasing temperature from a temperature above the optimal isothermal temperature to one below it. The rate of polymerization could be increased, as expected, by an initially higher temperature, but the temperature must be decreased to avoid depletion of initiator and depolymerization. However, the amount of time saved by this policy does not seem to be significant in comparison to the isothermal policy for this case. 

The main difference between the chromatographic process carried out in the linear and the nonlinear range of the adsorption isotherm is the fact that in the latter case, due to the skewed shapes of the concentration profiles of the analytes involved, separation performance of a chromatographic system considerably drops, i.e., the number of theoretical plates (N) of a chromatographic system indisputably lowers. In these circumstances, all quantitative models, along with semiquantitative and nonquantitative rules, successfully applied to optimization of the linear adsorption TLC show a considerably worse applicability. 

A systematic, rational analysis of both isothermal and nonisothermal tubular systems in which two fluids are flowing must be carried out, if optimal design and economic operation of these pipeline devices is to be achieved. The design of all two-phase contactors must be based on a firm knowledge of two-phase hydrodynamics. In addition, a mathematical description is needed of the heat and mass transfer and of the chemical reaction occurring within a particular system. 

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. 

The following example illustrates a simple case of optimal operation of a multistage CSTR to minimize the total volume. We continue to assume a constant-density system with isothermal operation. 

To optimize a given preparative chromatographic process (highest productivity, lowest mobile phase consumption, and product dilution) the separation has to be performed with the highest product concentrations still compatible with the system. One immediate consequence of this is that each column has to be operated in the non-linear range of the adsorption isotherm. 

This chapter presents an introduction to the key issues of reactor-based and reactor-separator-recycle systems from the mixed-integer nonlinear optimization perspective. Section 10.1 introduces the reader to the synthesis problems of reactor-based systems and provides an outline of the research work for isothermal and nonisothermal operation. Further reading on this subject can be found in the suggested references and the recent review by Hildebrandt and Biegler (1994). 

Section 10.2 describes the MINLP approach of Kokossis and Floudas (1990) for the synthesis of isothermal reactor networks that may exhibit complex reaction mechanisms. Section 10.3 discusses the synthesis of reactor-separator-recycle systems through a mixed-integer nonlinear optimization approach proposed by Kokossis and Floudas (1991). The problem representations are presented and shown to include a very rich set of alternatives, and the mathematical models are presented for two illustrative examples. Further reading material in these topics can be found in the suggested references, while the work of Kokossis and Floudas (1994) presents a mixed-integer optimization approach for nonisothermal reactor networks. 

A. C. Kokossis and C. A. Floudas. Optimal synthesis of isothermal reactor-separator-recycle systems. Chem. Eng. Sci., 46 1361, 1991. 

The model is currently being refined to better allow for concentration related changes in the velocity of the shock waves, as well as improvements in modeling the density dependent parameters of the simulation. Work continues on the determination of adsorption and desorption isotherms for several ternary systems, as well as the thermal and mass transfer characteristics for the column and media being employed. Accurate determination of the model parameters will be required for optimization of the of the operational regime. 

Before each separation, process parameters have to be determined through a numerical simulation software. Knowing the size of the system and the adsorption isotherm of the components, the software is able to compute the optimal set of flowrates allowing to perform the separation. 

Water affects the reaction rate through its effect on reaction kinetics and protein hydration, which is required for optimal enzyme conformation and activity. Enzymes need a small amount of water to maintain their activity however, increasing the water content can decrease the reaction rate as a result of hydrophilic hin-drance/barrier to the hydrophobic substrate, or because of denaturation of the enzyme (189). These opposite effects result in an optimum water content for each enzyme. In SCFs, both the water content of the enzyme support and water solubilized in the supercritical phase determine the enzyme activity. Water content of the enzyme support is, in turn, determined by the distribution/partition of water between the enzyme and solvent, which can be estimated from water adsorption isotherms (141, 152). The solubility of water in the supercritical phase, operating conditions, and composition of the system (i.e., ethanol content) can affect the water distribution and, hence, determine the total amount of water that needs to be introduced into the system to attain the optimum water content of the support. The optimum water content of the enzyme is not affected by the reaction media, as demonstrated by Marty et al. (152), for esterification reaction using immobilized lipase in n-hexane and SCC02- Enzyme activity in different solvents should, thus, be compared at similar water content of the enzyme support. 

The application of the basic ideas to real combustion systems is then taken up in Chapters 6 and 7. In Chapter 6, experimental and modelling studies are described which link the mechanistic observations of Chapter 1 to combustion characteristics of fuels studied under laboratory conditions. The experimental emphasis is initially on global combustion phenomena - ignition and oscillatory cool-flames - for a range of hydrocarbons. Section 6.5 then addresses the distribution of products in hydrocarbon oxidation this discussion differs from that in Chapter 1 where the conditions were optimized to allow the investigation of specific reactions. The focus is now on studies of oxidation products over a range of isothermal and non-isothermal conditions, the interpretation of the results in terms of elementary reactions and the use of the experimental data as a detailed test of combustion models. The chapter provides an overview of the success of detailed models in describing combustion phenomena and combustion... 

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