Mixing process dynamic model

In a continuous-flow chemical reactor, the concern is not only with probabilistic transitions among chemical species but also with probabilistic liansitions of each chemical species between the interior and exterior of the reactor. Pippel and Philipp [8] used Markov chains for simulating the dynamics of a chemical system. In their approach, the kinetics of a chemical reaction are treated deterministically and the flow through the system are treated stochastically by means of a Markov chain. Shinnar et al. [9] superimposed the kinetics of the first order chemical reactions on a stochastically modeled mixing process to characterize the performance of a continuous-flow reactor and compared it with that of the corresponding batch reactor. Most stochastic approaches to analysis and modeling of chemical reactions in a flow system have combined deterministic chemical kinetics and stochastic flows. 

Computational fluid dynamics (CFD) is now quite well established as a tool for modeling mixing processes with single-phase systems, but its success in predicting multiphase coalescing or dispersing flows has hitherto been limited. A brief overview in the context of the modeling of gas-liquid systems has been included in Section 11-3.1. 

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. 

A dynamic spatial conceptual model which illustrates the evolution of the various sub-groups of water as a function of the flushing and mixing processes is suggested in Fig. 4. 

A.G. Murray, G.A. Jackson (1993). Viral dynamics II A model of the interaction of ultraviolet light and mixing processes on virus survival in seawater. Mar. Ecol. Prog. Ser., 102,105-114. 

Automatic control of purities is difficult due to the long time delays and the complex dynamics that are described by nonlinear distributed parameter models and switching of the inputs, leading to mixed discrete and continuous dynamics, small operating windows, and a pronouncedly nonlinear response of the purities to input variations. Because of the complex nonlinear dynamics of SMB processes, their automatic control has attracted the interest of many academic research groups and many different control schemes have been proposed however, few of them have been tested in experimental work for real plants with limited sensor information. 

As follows from the previous chapters, a complex interface Metal/MIEC/Electrolyte (MIEC = mixed ion-electron conductor) appears in many processes related to the electrochemistry of polyvalent metals. The model of MIEC in terms of the concept of polyfunctional conductor (PFC) can be a useful approach to deal with the mechanisms of the processes in such systems. The qualitative classification of EPS has been given based on this approach. Further on, we are going to demonstrate that this concept is useful for quantitative (or at least, semi-quantitative) modelling of macrokinetics (dynamics) of the processes in highly non-equilibrium systems. Before doing this, it is worthwhile to outline some basic ideas related to the MIEC. These considerations will also show some restrictions and approximations that are commonly applied in electrochemical practice and which are no longer valid in such kind of systems. 

Dynamic models are based on a causal analysis of the processes governing the fluxes of matter and substances. If dynamic models are to be used in practice, e.g., to quantify fluxes of energy or contaminants in lakes, the rates that govern the transport between the various compartments in the lake ecosystem have to be known, simulated or estimated. Here, a new mixed dynamic model (Hakanson 1991 Hakanson and Peters 1995) will be introduced as a tool to discuss important... 

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