Steady and Dynamic Behavioral Analysis

The sixth design space of the multiechelon approach (c/. chapter 4) in reactive distillation is the focus of this chapter. After having defined the spatial and control structmes the process behavior in steady-state and dynamic domains are now addressed. The input and output information flow at this design space is detailed on table 7.1. 

Design specifications Design/operational variables Domain knowledge 

The analysis of steady-state behavior allows the designer to explore the effect of kinetics, gas/liquid mass transfer and hydrodynamics and the steady-states of the unit. On the other hand, dynamic simulations are carried out to check the robustness of the design, in terms of the ability of maintain product purities and conversion in desired range 

This chapter addresses those two aspects of process behavior steady-state and dynamic operation. In the first case, a reactive flash with a rather ideal exothermic isomerization reaction is considered. This simplified system is selected to accoimt exclusively on the effect of phenomena interaction on the occurrence of input and output multiphcity. Therefore, any effect related to unit configuration is considered outside the scope of the analysis. 

The second part of this chapter deals with the dynamic behavior of a full RD column, with special focus on the synthesis of MTBE. Although the design of the control structure is rather conventional (SISO and PI controllers), it is regarded as reference case for the new developments to be introduced in chapter 8. 

---

Steady and Dynamic Behavioral Analysis 7.2 Steady-State Behavior 7.2.1 Introduction... 

Steady and Dynamic Behavioral Analysis sibility boundaries. 

Answer. Improved residue curve mapping technique, multilevel modeling approach, dynamic optimization of spatial and control structures, steady-state and dynamic behavior analysis, generic lumped reactive distillation volume element, multiobjective optimization criteria. 

The empty-site requirement in Eq. (28) can be physically interpreted in one of two different ways either the adsorbed A and B have to rearrange prior to reaction, or they are bound to more than one adsorption site. For the latter case, the intermediate concentration is low, thus allowing a pseudo-steady-state assumption. Through the application of bifurcation analysis and catastrophe theory this model was found to predict a very rich bifurcation and dynamic behavior. For certain parameter values, sub- and supercritical Hopf bifurcations as well as homoclinic bifurcations were discovered with this simple model. The oscillation cycle predicted by such a model is sketched in Fig. 6c. This model was also used to analyze how white noise would affect the behavior of an oscillatory reaction system... 

Analysis of steady state and dynamic behavior. J. Biol. Chem. 267, 22926-22933. 

The steady-state and dynamic behavior in RD are addressed in this chapter. Fundamental understanding of multiplicity in a reactive flash is provided. Moreover, the domain knowledge is extended by dynamic analysis, whose tasks include model development, control structure selection, controller tuning and simulation of closed loop dynamics. The output of this section serves as reference case to be compared with that of the life-span inspired design methodology (c/. section 1.4). The material presented in this chapter answers partially Question 6. 

For the middle line R(y) with fixed slope equal to b and horizontal axis intercept equal to a in Figure 4 (A-2), there are maximally three steady states yi, j/2 and 2/3. Stability information of the three steady states and a qualitative analysis of the dynamic behavior of the system can be obtained from the static diagram. The steady-state temperatures 2/1, 2/2 and 2/3 correspond to points where the heat generation and heat removal are equal. That is the defining property of a steady state. 

The model optimized based on steady-state analysis allows for a dynamic real-time simulation of the entire absorption process. Because dynamic behavior is determined mainly by process hydraulics, it is necessary to consider those elements of the column periphery that lead to larger time constants than the column itself. Therefore, major elements of the column periphery, such as distributors, stirred tanks, and pipelines, have been additionally implemented into the dynamic model. 

Whereas the operation of batch reactors is intrinsically unsteady, the continuous reactors, as any open system, allow for at least one reacting steady-state. Thus, the control problem consists in approaching the design steady-state with a proper startup procedure and in maintaining it, irrespective of the unavoidable changes in the operating conditions (typically, flow rate and composition of the feed streams) and/or of the possible failures of the control devices. When the reaction scheme is complex enough, the continuous reactors behave as a nonlinear dynamic system and show a complex dynamic behavior. In particular, the steady-state operation can be hindered by limit cycles, which can result in a marked decrease of the reactor performance. The analysis of the above problem is outside the purpose of the present text ... 

The results above indicate clearly that the presence of flow rates of different magnitudes (a steady-state design feature of many process systems) impacts upon the dynamic behavior of the process. In what follows, we further our analysis by emphasizing the implications of steady-state design on the selection of control structures and the synthesis of well-conditioned controllers for the class of processes considered. 

The effect of the structure of the polymer backbone on photo-orientation can be seen from the dynamic behavior as well as from the steady-state values of the photoinduced anisotropy in all azo-PURs. The photo-orientation dynamics of PUR-2 resemble but also contrast with those of PUR-1. In PUR-2, AbSi exceeds AbsQ, but not quite, as is the case for PUR-1, and the photostationary-state anisotropy is smaller than that of PUR-1, as can be seen in Figure 4.20. PUR-1 and PUR-2 exhibit exactly the same extinction coefficient at the analysis wavelength because they have the same azo chromophore furthermore, the rate of the cis- trans thermal isomerization is nearly the same in both polymers. The seemingly small difference into the... 

The dynamic behavior of the FCS is firstly verified starting from the analysis of the energy lost during the start-up phases, evaluating the performance as function of acceleration rates [2]. In particular, warm-up tests are performed starting from two different initial stack temperatures, 15 and 30°C. For each one of these temperatures, two accelerations of 20 and 200 Ws are used up to the stack power of 1200 W. At the end of each acceleration phase, a steady-state operation follows until the stack temperature reaches the value of 45°C. 

---