Comparison of EQ and NEQ Models

Applications of the EQ and NEQ models to RD were reviewed by Taylor and Krishna [1], Most papers do not compare the two models directly (or even indirectly). Here, we wish to highlight a few studies that reveal the differences between these fundamentally different types of model.

Kreul et al. [16] used an NEQ model of homogeneous RD and, via a series of case studies, studied the importance of various model simplifications. They found little difference between the full MS description of multi-component mass transfer and a much simpler effective diffusivity models. However, they also conclude that there can be significant differences between EQ and NEQ models, and that the additional effort of the more complicated NEQ approach is justified.

Baur et al. [17] have compared the EQ and the NEQ models for the MTBE process. They underlined some counter-intuitive features of RD processes. For example, for a methanol feed location yielding a low-conversion steady state, the introduction of mass-transfer resistance (i. e., use of the NEQ model), leads to a conversion higher than that predicted by the EQ model). The introduction of a mass-transfer resistance alleviates a 'bad situation' and has the effect of improving conversion.

Lee and Dudukovic [18] described an NEQ model for homogeneous RD in tray columns. The Maxwell-Stefan equations are used to describe interphase transport, with the AIChE correlations used for the binary (Maxwell-Stefan) mass-transfer coefficients. Newton's method and homotopy continuation are used to solve the model equations. Close agreement between the predictions of EQ and NEQ models were found only when the tray efficiency could correctly be predicted for the EQ model. In a subsequent paper Lee and Dudukovic [19] presented a dynamic NEQ model of RD in tray columns. The DAE equations were solved by use of an implicit Euler method combined with homotopy continuation. Murphree efficiencies calculated from the results of an NEQ simulation of the production of ethyl acetate were not constant with time.

Sundmacher et al. [20] used both EQ stage (with Murphree efficiency) and NEQ models to simulate the MTBE and TAME processes. The reactions were handled using both quasi-homogeneous and heterogeneous methods. Simulation results were compared to experimental data obtained in two laboratory-scale columns. A detailed NEQ model was needed to describe the TAME process, but both NEQ and the EQ stage (with an efficiency of 0.8) model could adequately represent the MTBE process.

Multiple steady states (MSS) in conventional distillation have been known from simulation and theoretical studies dating back to the 1970s and has been a topic of considerable interest in the distillation community. Taylor and Krishna [1] cite the papers highlighting MSS in RD. We single out just a few of these papers for mention here.

Mohl et al. [21, 22] implemented a dynamic EQ model (with Murphree type efficiencies) in the DIVA simulator and carried out a numerical bifurcation and stability analysis on the MTBE and TAME processes. They also show that the window of opportunity for MSS to actually occur in the MTBE process is quite small. For the TAME process MSS occur in the kinetic regime and vanish when chemical equilibrium prevails. The window of opportunity for MSS in the TAME process is larger than for the MTBE process.

Experimental confirmation of MSS in RD was provided by Thiel et al. [23] and by Rapmund et al. [24]. Mohl et al. [1] used a pilot scale column to produce MTBE and TAME. MSS were found experimentally when the column was used to produce TAME, but not in the MTBE process. The measured steady state temperature profiles for the low and high steady states for the TAME process are shown in

Fig. 9.10a. For a column operating at the low steady state, a pulse injection of pure TAME for a short period resulted in a shift from the low to the higher steady state (Fig. 9.10b).

The MSS observed in these experiments can be reproduced using the NEQ model in which the reaction is treated as pseudo-homogeneous and the Wilson model is used to describe the liquid phase non-ideality. A reasonable match of the column temperature profiles also is shown in Fig. 9.10a; these profiles are

Fig. 9.10a. For a column operating at the low steady state, a pulse injection of pure TAME for a short period resulted in a shift from the low to the higher steady state (Fig. 9.10b).

The MSS observed in these experiments can be reproduced using the NEQ model in which the reaction is treated as pseudo-homogeneous and the Wilson model is used to describe the liquid phase non-ideality. A reasonable match of the column temperature profiles also is shown in Fig. 9.10a; these profiles are

Fig. 9.10 a) Multiple steady states in TAME during the period 860-920 min. The column synthesis. Experimental data on low- and high- shifts from a low steady-state to the higher one. conversion steady states. b) Response ofTAME Measurements of Mohl et al. [25] column to injection of pure TAME in the feed

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