Dynamic energy recycle

To proceed with the analysis, we note that the structure of the process in Figure 7.1 is very similar to that of the processes with significant energy recycle considered in the previous chapter (Figure 6.1), with the obvious and necessary distinction that in the present case Q n Qout. Thus, using Assumptions 6.1-6.3, the dynamic behavior of the process in Figure 7.1 can be modeled by a system of equations of the type (6.10), that is... 

Jogwar, S. S., Baldea, M., and Daoutidis, P. (2009). Dynamics and control of process networks with large energy recycle. Ind. Eng. Chem. Res., 48, 6087-6097. 

In Chapter 2 (Section 2.9.2) the steady-state design of a reactor-stripper process was studied. Now we investigate the dynamic controllability of this process. The dynamic model of the reactor is the same as Eqs. (3.9)—(3.11) except there is a second stream entering the reactor, the recycle stream D (kmol/s) from the column with composition. Vj) (mole fraction A). The reactor effluent is F (kmol/s) with composition z (mole fraction A). The reactor component and energy balances are ... 

The arguments presented above indicate that the large recycle and coolant flow rates wr and uq are the only manipulated inputs available in the fast time scale, and should be used to control the process temperatures. Likewise, the dynamics of the material-balance variables in the slow time scale are affected only by the small feed and effluent flow rates uq and up, which are thus the manipulated inputs that must be used to tackle control objectives involving the material balance. 6sp, the setpoints of the temperature controllers in the fast time scale, are also available as manipulated inputs in the slow time scale, a choice that leads to cascaded control configurations between the energy- and material-balance controllers. 

In this chapter we have applied the plantwide control design procedure to the HDA process. The HDA process is typical of many chemical process with many chemical components, many unit operations, several recycle streams, and energy integration. The steady-state design of the HDA process has been extensively studied in the literature, but no quantitative study of its dynamics and control has been reported. 

Plantwide control problems arise in the context of plants with recycles of mass and energy. Positive feedback effects complicate the dynamics because of interactions and non-linear phenomena, as multiple steady states and chaotic behaviour. 

The above simple analysis highlights an important issue in process dynamics the influence of positive and negative feedback on system s stability. Instability can occur in recycle systems due to positive feedback when the gain is larger than unity. We may give as example the recycle of energy developed by an exothermal reaction in an adiabatic PFR for feed preheating. Instability may occur because of the exponential increase in reaction rate with the temperature when this cannot be properly controlled (Bildea Dimian, 1998). Another example is the recycle of impurities in a plant with recycles, whose inventory cannot be kept at equilibrium by the separation system (Dimian et al., 2000). 

The recycle of mass and energy have important effects on the dynamics and control of complex plants. Positive feedback increases the time constant of units placed in recycle, the effect depending on the recycle gain. Larger gains can lead even to unstable behaviour. On the contrary, negative feedback has always a stabilising effect. 

Use the remaining control valves for either steady-state optimization (minimize energy, maximize yield, etc.) or to improve dynamic controllability. A common example is controlling purities of recycle streams. Even though these streams... 

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