Economic Model Identification

Batch crystallizers are often used in situations in which production quantities are small or special handling of the chemicals is required. In the manufacture of speciality chemicals, for example, it is economically beneficial to perform the crystallization stage in some optimal manner. In order to design an optimal control strategy to maximize crystallizer performance, a dynamic model that can accurately simulate crystallizer behavior is required. Unfortunately, the precise details of crystallization growth and nucleation rates are unknown. This lack of fundamental knowledge suggests that a reliable method of model identification is needed. 

For each policy specification, the technology matrix of the integrated industry model is transformed from the productive structure existing before the policy change to the productive structure existing after the policy change. This structural transformation is the master key to identifying the economic demands and supplies of the industries modeled. Identification is necessary to soundly estimate (1) the economic demands for crude oil, natural gas, coal, water, and capital (2) the economic costs of pollution control for major water and air pollutants and (3) the economic supplies of the endproducts in the model. 

No single method or algorithm of optimization exists that can be applied efficiently to all problems. The method chosen for any particular case will depend primarily on (1) the character of the objective function, (2) the nature of the constraints, and (3) the number of independent and dependent variables. Table 8-6 summarizes the six general steps for tne analysis and solution of optimization problems (Edgar, Himmelblau, and Lasdon, Optimization of Chemical Processes, 2d ed., McGraw-Hill, New York, 2001). You do not have to follow the cited order exactly, but you should cover all the steps at some level of detail. Shortcuts in the procedure are allowable, and the easy steps can be performed first. Steps 1,2, and 3 deal with the mathematical definition of the problem identification of variables, specification of the objective function, and statement of the constraints. If the process to be optimized is very complex, it may be necessary to reformulate the problem so that it can be solved with reasonable effort. Later in this section, we discuss the development of mathematical models for the process and the objective function (the economic model) in typical RTO applications. 

An economic model has been provided by die American Plastics Council [6] of the current and potential commercial infrastmcture that recovers value from a portion of the ten million vehicles disposed of annually in the United States. The model provides for identification of transactions, costs, values and other factors that strongly affect decisions regarding plastics disposal, and could serve as the basis for modelling the recovery of plastics from a range of industries producing large arisings. 

Today s end points considered include recycling of the plastic themselves feedstock recycling to reusable monomers, oils and gases conversion to energy (electricity and steam) and landfill disposal for material not suitable for more preferred alternatives. Study of the infrastructure, assisted by the economic model, assists identification of those costs that drive the choice of disposal, and provides additional information that will gradually divert an increasingly large amount of used plastic parts from landfill disposal to resource recovery. 

Al-Sharrah GK, Alatiqi I, Elkamel A (2003) Modeling and Identification of Economic Disturbances in the Planning of the Petrochemical Industry. Industrial Engineering Chemistry Research 42 4678-4688... 

Modeling and identification of economic disturbances in the planning of the petrochemical industry. Industrial Engineering Chemistry Research, 42, 4678. 

Figure 1 shows a computational framework, representing many years of Braun s research and development efforts in pyrolysis technology. Input to the system is a data base including pilot, commercial and literature sources. The data form the basis of a pyrolysis reactor model consistent with both theoretical and practical considerations. Modern computational techniques are used in the identification of model parameters. The model is then incorporated into a computer system capable of handling a wide range of industrial problems. Some of the applications are reactor design, economic and flexibility studies and process optimization and control. 

Added to this are the aesthetic issues of design, frequently requested as being better than or different from a particular product. A container should ultimately provide an economical basis for a balance between presentation, identification, protection and convenience. Models of new designs for bottles, closures, etc. can be produced either in wood or opaque or clear plastic, bearing in mind that a clear plastic model frequently looks better than the final glass bottle. 

Economics in process control, 3, 10-11, 15, 26, 532-34 Environmental regulations, 3 Equal-percentage valve, 254, 255 Equations of state, 57 Equilibria, 56, 78 chemical, 56 phase, 56-57, 71, 75, 78 Error criteria (see Time integral criteria) Euler s identities, 131-32, 149 Experimental modeling, 45, 656 frequency response techniques, 668 process identification, 657-62 time constant determination, 228, 232 Exponential function, 130 approximations, 215-16 Laplace transform, 130 z-transform, 592... 

Trying to set up a physicochemically exact kinetic model for all simultaneously proceeding reactions with identification of all parameters would be a task so extremely time-consuming tiiat it could not be justified economically. Even modem computer programs, which use non-linear optimization techniques for the parameter adjustment in complex models, require an amount of analytical information on all substances participating in the process which is not to be underestimated [46]. 

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