Kinetics hierarchical approach

The reactor/separation/recycle level allows plantwide control issues to be included in the hierarchical approach at an early level of design. In most cases, the Separation is considered as a black-box for which targets are set, for example as species recovery or product purities. A stoichiometric or a kinetic reactor can be used. In the first case, plantwide control structures can only be proposed, while in the second case these can be also evaluated. 

The detailed reaction mechanism proposed by Yetter [26] and augmented by Lin and co-workers [4] is employed to treat the gas-phase chemical kinetics. The model is developed based on a hierarchical approach for collecting kinetic... 

The chemical reactor has a determinant role on both the material balance and the structure of the whole flowsheet. It is important to stress that the downstream levels in the Hierarchical Approach, as the separation system and heat integration, depend entirely on the composition of the reactor exit stream. However, a comprehensive kinetic model of the reaction network is hardly available at an early conceptual stage. To overcome this shortcoming, in a first attempt we may neglect the interaction between the reactor and the rest of the process, and use an analysis based on stoichiometry. A reliable quantitative relationship between the input and the output molar flow rates of components would be sufficient. This information is usually available from laboratory studies on chemistry. Kinetics requires much more effort, which may be justified only after proving that the process is feasible. Note that the detailed description of stoichiometry, taking into account the formation of sub-products and impurities is not a trivial task. The effort is necessary, because otherwise the separation system will be largely underestimated. 

The first application of hierarchical SA for parameter estimation included refinement of the pre-exponentials in a surface kinetics mechanism of CO oxidation on Pt (a lattice KMC model with parameters) (Raimondeau et al., 2003). A second example entailed parameter estimation of a dual site 3D lattice KMC model for the benzene/faujasite zeolite system where benzene-benzene interactions, equilibrium constants for adsorption/desorption of benzene on different types of sites, and diffusion parameters of benzene (a total of 15 parameters) were determined (Snyder and Vlachos, 2004). While this approach appears promising, the development of accurate but inexpensive surfaces (reduced models) deserves further attention to fully understand its success and limitation. 

The potentiality of hierarchical stratification of complex reactive systems, according to the characteristic times of the involved processes, makes it difficult to use direcdy thermodynamic tools as well as to apply the con cept of stability to very compHcated (in particular, biological) systems. The statistical approach to describe the behavior of a system that contains a large number of particles takes into account the instabihty of mechanical trajectories of individual particles. Indeed, any infinitesimally small distur bances in the particles motion can make it impossible to determine from the starting conditions the trajectory of even one particle s motion. As a result, a global instabihty of mechanical states of individual particles is observed, the system becomes statistical as a whole, and the trajectories of individual particles are no longer predictable. At the same time, the states that correspond to stable solutions of any dynamic (kinetic) problem can only be observed in real systems. In terms of a statistical approach, the dynamic solution of a particular initial state of an ensemble of particles is a fluctuation, while the evolution of instabihty upon destruction of this solution is a relaxation of this fluctuation. 

When the coordination bonds that hold these assemblies together are both stable and inert, their formation from the components occurs under kinetic rather than thermodynamic control and it is thus disputable if they can be truly defined as supramolecular systems. On the other hand, owing to their kinetic stability, some of these species can be further exploited as building blocks in the construction of higher order architectures through a hierarchical self-assembly approach (see for example the molecular sandwiches 13-15). Through this modular approach, multichromophore systems become easily accessible on demand, with a limited synthetic effort. 

The general approach followed to obtain the dilfusivity, based on atomistic TST-based determination of rate constants for individual jumps executed by the penetrant in the polymer matrix and subsequent use of these rate constants within a kinetic MC simulation to track displacement at long times, is another good example of hierarchical modeling. 

---