Steady State Solution of the Dynamic Model

The global system of DAEs for the simplified dynamic model of the 10 stage reactive distillation column (Figure 3.1) comprises 568 algebraic variables and 505 linear and nonlinear equations. By comparison, the full steady state model (with five components but excluding equations for dynamics, stage-to-stage pressure drops, etc.) contained 578 variables and 504 equations.

The feed conditions and column configuration that was specified in Chapter 3 for steady state simulations (see Table 3.4) were used again here. The results obtained from the simplified dynamic model (which includes several simplifying assumptions) are compared with the previous results from the full steady state model in Table 7.1. The two sets of results are almost identical and validate the use of simplifying assumptions in the dynamic model. Probably the most significant shortcomings of the dynamic model is its inability to estimate the extent of DIB formation or identity transient effects on the side-reaction rate. However, the model remains valid for most simulation studies and could be readily extended to model the side-reaction but only with a penalty to the ratio of real time to simulation time.

Table 7.1 - Comparison of Steady State and Dynamic Model Simulation Outputs


Steady State Model

Dynamic Model

Condenser Temperature (°C)



Reaction Zone Temperatures (°C)



Reboiler Temperature (°C)



Isobutene Conversion (mol%)



Bottoms Composition (wt%)

96.5% ETBE, 2.7% ethanol, 0.7% butenes, 0.04% DIB

96.6% ETBE, 2.6% ethanol, 0.8% butenes

Distillate Composition (wt%)

97.7% n-butenes, 1.6% isobutene, 0.7% ethanol

97.8% n-butenes, 1.5% isobutene, 0.7% ethanol

Condenser Duty (kW)



Reboiler Duty (kW)



Reaction Rates (mol/min)

0.18 (stage 3), 0.19 (stage 4), 0.11 (stage 5)

0.17 (stage 3), 0.18 (stage 4), 0.13 (stage 5)

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