Kinetic modeling, process optimization

Kasiri S, Ulrich A, Prasad V Kinetic modeling and optimization of carbon dioxide fixation using microalgae cultivated in oil-sands process water, Chem EngSci 137 697—711,2015. 

Minimizing the cycle time in filament wound composites can be critical to the economic success of the process. The process parameters that influence the cycle time are winding speed, molding temperature and polymer formulation. To optimize the process, a finite element analysis (FEA) was used to characterize the effect of each process parameter on the cycle time. The FEA simultaneously solved equations of mass and energy which were coupled through the temperature and conversion dependent reaction rate. The rate expression accounting for polymer cure rate was derived from a mechanistic kinetic model. 

Overall, catalytic processes in industry are more commonly described by simple power rate law kinetics, as discussed in Chapter 2. However, power rate laws are simply a parameterization of experimental data and provide little insight into the underlying processes. A micro-kinetic model may be less accurate as a description, but it enables the researcher to focus on those steps in the reaction that are critical for process optimization. 

The kinetics of the ammonia synthesis have been discussed as an example of micro-kinetic modeling in Chapter 7. Here we present a brief description of the process, concentrating on how process variables are related to the microscopic details and the optimization of the synthesis. 

Most accidents in the chemical and related industries occur in batch processing. Therefore, in Chapter 5 much attention is paid to theoretical analysis and experimental techniques for assessing hazards when scaling up a process. Reaction calorimetry, which has become a routine technique to scale up chemical reactors safely, is discussed in much detail. This technique has been proven to be very successful also in the identification of kinetic models suitable for reactor optimization and scale-up. 

Kinetic models developed for reactor scale-up are also suitable for reactor optimization. The development of detailed kinetic models accounting for all factors influencing process rates is a time-consuming task. Therefore, more empirical simplified models are often used for simulation and optimization of existing reactors. 

Based on the experimental data kinetic parameters (reaction orders, activation energies, and preexponential factors) as well as heats of reaction can be estimated. As the kinetic models might not be strictly related to the true reaction mechanism, an optimum found will probably not be the same as the real optimum. Therefore, an iterative procedure, i.e. optimization-model updating-optimization, is used, which lets us approach the real process optimum reasonably well. To provide the initial set of data, two-level factorial design can be used. 

Timm, Gilbert, Ko, and Simmons O) presented a dynamic model for an isothermal, continuous, well-mixed polystyrene reactor. This model was in turn based upon the kinetic model developed by Timm and co-workers (2-4) based on steady state data. The process was simulated using the model and a simple steady state optimization and decoupling algorithm was tested. The results showed that steady state decoupling was adequate for molecular weight control, but not for the control of production rate. In the latter case the transient fluctuations were excessive. 

The detailed kinetic description of a chemical process is a primary feature for both the industrial practice and the comprehension of the reaction mechanism. The development of a kinetic model able to predict at the same time the reactants conversion and the products distribution (i.e., a detailed kinetic model) is a prerequisite for the design, optimization, and simulation of the industrial process. Also, the detailed description of process kinetics allows the ex post evaluation of the goodness of the mechanistic scheme on the basis of which the model itself is developed, making possible the collection of further insight in the chemistry of the process. 

Finally, we should mention that in addition to solving an optimization problem with the aid of a process simulator, you frequently need to find the sensitivity of the variables and functions at the optimal solution to changes in fixed parameters, such as thermodynamic, transport and kinetic coefficients, and changes in variables such as feed rates, and in costs and prices used in the objective function. Fiacco in 1976 showed how to develop the sensitivity relations based on the Kuhn-Tucker conditions (refer to Chapter 8). For optimization using equation-based simulators, the sensitivity coefficients such as (dhi/dxi) and (dxi/dxj) can be obtained directly from the equations in the process model. For optimization based on modular process simulators, refer to Section 15.3. In general, sensitivity analysis relies on linearization of functions, and the sensitivity coefficients may not be valid for large changes in parameters or variables from the optimal solution. 

E. James Davis, Microchemical Engineering The Physics and Chemistry of the Microparticle Selim M. Senkan, Detailed Chemical Kinetic Modeling Chemical Reaction Engineering of the Future Lorenz T. Biegler, Optimization Strategies for Complex Process Models... 

Duesterberg CK, Waite TD (2006) Process Optimization of Fenton Oxidation Using Kinetic Modeling. Environ Sci Technol 40 4189... 

The development and application of a rigorous model for a chemically reactive system typically involves four steps (1) development of a thermodynamic model to describe the physical and chemical equilibrium (2) adoption and use of a modeling framework to describe the mass transfer and chemical reactions (3) parameterization of the mass-transfer and kinetic models based upon laboratory, pilot-plant, or commercial-plant data and (4) use of the integrated model to optimize the process and perform equipment design. 

The thermal and kinetic models discussed above are the basis for determining the processing conditions for reactive processing by ionic polymerization,29 addition polymerization, vulcanization of rubbers and radical polymerization, although in the latter case additional assumptions of a constant initiation rate and a quasi-stationary concentration of radicals are made.89 These models can also be used to solve optimization problems to improve the performance and properties of end-products. 

The reaction and separation synthesis approach of Section 5 has been adopted to the problem of activated sludge process design (83). The conventional designs as well as all novel schemes for combined oxidation/denitrification of wastewater are explored. The process is optimized using a novel methodology for optimal reaction/separation network synthesis, supplied with a comprehensive kinetic model (84). The activated sludge process is synthesized using the systematic... 

If the behaviour of complex chemical (in our case catalytic) reactions is known, it will be clear in what way these reactions can be carried out under optimal conditions. The results of studying kinetic models must be used as a basis for the mathematical modelling of chemical reactors to perform processes with probable non trivial kinetic behaviour. It is real systems that can appear to show such behaviour first far from equilibrium, second nonlinear, and third multi dimensional. One can hardly believe that their associated difficulties will be overcome completely, but it is necessary to approach an effective theory accounting for several important problems and first of all provide fundamentals to interpret the dependence between the type of observed kinetic relationships and the mechanism structure. 

The simulation program has been extensively used for process optimization studies as it permits accurate prediction of isomer distribution and heat release. It offers theoretical explanations for isomer control practices arrived at through several years of plant operating experience. The model was used in designing laboratory experiments to study mass transfer under various process conditions and reactor configuration. Since mass transfer and chemical kinetics are simultaneously important in this process, a model is necessary to "filter out" the kinetics effects for mass transfer correlations. The results of our laboratory studies will be presented in future papers. 

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