Dynamical systems Quasi-Steady State Approximation

The first two sections of Chapter 5 give a practical introduction to dynamic models and their numerical solution. In addition to some classical methods, an efficient procedure is presented for solving systems of stiff differential equations frequently encountered in chemistry and biology. Sensitivity analysis of dynamic models and their reduction based on quasy-steady-state approximation are discussed. The second central problem of this chapter is estimating parameters in ordinary differential equations. An efficient short-cut method designed specifically for PC s is presented and applied to parameter estimation, numerical deconvolution and input determination. Application examples concern enzyme kinetics and pharmacokinetic compartmental modelling. 

Quasi-steady-state periodic regime (T Tj. The input variable varies rather slowly compared to the dynamics of the system, and the system follows the input variable almost exactly. The time-averaged performance of the reactor is calculated applying the quasi-steady-state approximation to the state of the system and averaging out the resulting performances at any time. 

The quasi-steady-state approximation (QSSA) is commonly made for the moments of living polymer chains since, for most practical situations, an equilibrium is achieved instantaneously between chain initiation and chain transfer, fc,C [M] = ( cpR + daclMo- This equilibrium results from the fast dynamics of the initiation and transfer reactions compared to that of the overall polymerization rate. In this case, an even simpler system of equations is obtained than the one listed in Table 2.6. 

Many HVAC system engineering problems focus on the operation and the control of the system. In many cases, the optimization of the system s control and operation is the objective of the simulation. Therefore, the appropriate modeling of the controllers and the selected control strategies are of crucial importance in the simulation. Once the system is correctly set up, the use of simulation tools is very helpful when dealing with such problems. Dynamic system operation is often approximated by series of quasi-steady-state operating conditions, provided that the time step of the simulation is large compared to the dynamic response time of the HVAC equipment. However, for dynamic systems and plant simulation and, most important, for the realistic simulation... 

The second approach to speeding up the SSA involves separating the system into slow and fast subsets of reactions. In these methods, analytical or numerical approximations to the dynamics of the fast subset are computed while the slow subset is stochastically simulated. In one of the first such methods, Rao and Arkin (see Further reading) applied a quasi-steady-state assumption to the fast reactions and treated the remaining slow reactions as stochastic events. 

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