Large kinetic simulations, solving

III. Efficiently and Accurately Solving Large Kinetic Simulations... 

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. 

In this case study we will model, simulate and design an industrial-scale BioDeNOx process. Rigorous rate-based models of the absorption and reaction units will be presented, taking into account the kinetics of chemical and biochemical reactions, as well as the rate of gas-liquid mass transfer. After transformation in dimensionless form, the mathematical model will be solved numerically. Because of the steep profiles around the gas/liquid interface and of the relatively large number of chemical species involved, the numerical solution is computationally expensive. For this reason we will derive a simplified model, which will be used to size the units. Critical design and operating parameters will be identified... 

Studies of proteinase activities comprise some of the most important current research efforts in the field of theoretical enzyme mechanisms. Results from crystallography and kinetics in the 70 s and 80 s paved the way for such theoretical studies, mainly of the serine proteinase family. Such studies are extending nowadays, as more structures of proteinases are solved with high resolution and more detailed kinetic studies are conducted. But, while earlier structural results were available for the native structures alone, recent crystallographic evidence is available for complexes with peptide analogs, with intermediate analogs and with mutant enzymes. When these structural studies are coupled with results of kinetic research, a large database is formed for the theoretician to consider as a basis for construction, simulation and analysis by computer models. 

Molecular dynamics (MD) is the most widely used computational method to study the kinetic and thermodynamic properties of atomic and molecular systems.These properties are obtained by solving the microscopic equations of motion (Eq. [1]) for the system under consideration. The multiple time-step algorithms discussed earlier have extended the time scale that can be reached, but, the gain is still insufficient for the study of many processes for many systems, such as biomolecules, this simulation time is inadequate to study large conformational changes or to study rare but important events as examples. 

It has been shown that various small scale models consisting of idealized reactor types can be used to simulate large scale fermentation processes, with respect to dissolved oxygen inhomogeneities. The reaction kinetic expressions, material balances on substrates, and products have to be formulated and solved in the context of the combined model network. The choice of the model configuration depends on (1) the system that has to be simulated, (2) knowledge of the hydrodynamics of the system, and (3) the equipment available and financial resources. 

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