Component mass balance:
—jt— = Lj-ixj-u +vj+iyj+u+Fxfi-Vjyji-Ljxß-L/xß +rPH j
Barolo et al. (1998) developed a mathematical model of a pilot-plant MVC column. The model was validated using experimental data on a highly non-ideal mixture (ethanol-water). The pilot plant and some of the operating constraints are described in Table 4.13. The column is equipped with a steam-heated thermosiphon reboiler, and a water-cooled total condenser (with subcooling of the condensate). Electro-pneumatic valves are installed in the process and steam lines. All flows are measured on a volumetric basis; the steam flow measurement is pressure- and temperature-compensated, so that a mass flow measurement is available indirectly. Temperature measurements from several trays along the column are also available. The plant is interfaced to a personal computer, which performs data acquisition and logging, control routine calculation, and direct valve manipulation.
The model consists of dynamic mass and algebraic energy balances (the model type is somewhat in between type III and IV). Internal plates, condenser, reboiler, middle vessel are assumed to be well mixed. A linear pressure profile is also assumed. The internal liquid flows are calculated using the Francis Weir formula. The start-up period i.e. the filling of the condenser hold up tank and of the internal plates (from top to bottom) is also modelled. The integration of the differential equations is performed using Runge-Kutta-Fehlberg algorithm.
Table 4.13. Column Configuration and Operating Constraints
Total number of plates = 30
Plate type = Sieve. Column diameter = 0.3 m, Column height = 9.9 m.
Reboiler type = Vertical steam-heated thermosiphon
Maximum reboiler capacity = 90 L
Condenser type = Horizontal water-cooled shell-and-tube
Reflux drum capacity = 40 L (open to atmosphere)
Maximum capacity of the middle vessel = 500 L_
Subcooled reflux to maintain low ethanol vapour pressure
Subcooled liquid from tray to middle vessel_
Three parameters were identified and adjusted to validate the model against the experiments. The parameters are: the heat losses, the nominal tray holdup and the Murphree tray efficiency (EM). Figure 4.16 shows how EM is adjusted to match the dynamic model prediction and experimental temperature profile measured on Plate #12. Figure 4.17 shows the comparison between the experimental and model prediction of ethanol composition in the reflux drum, middle vessel and in the bottom of the column. Figures 4.16-17 show a good match between the model prediction and experiments.
Using the model, Barolo et al. (1998) further studied the dynamic behaviour of the column and interactions of different design and operating parameters on the column operability and productivity were established. See the original reference for further details. The optimisation study carried out by Greaves et al (2003) using a Neural Network based dynamic model is presented in Chapter 12.
Figure 4.16. Adjustment of Murphree Tray Efficiency. Dotted line: Experiment. Full lines: Model Predictions. [Barolo et al„ 1998]a time (min)
Figure 4.16. Adjustment of Murphree Tray Efficiency. Dotted line: Experiment. Full lines: Model Predictions. [Barolo et al„ 1998]a
Using the model type III but with chemical reaction Mujtaba and Macchietto (1994) considered simulation of simultaneous chemical reaction and distillation in an MVC column, with the following reversible reaction scheme.
The reaction products are C (main product) and D, the latter being the most volatile component and C being the least volatile component in the reaction mixture. Separation of the product by distillation permits increasing conversion, while at the same time yielding the product in concentrated form.
The input data defining the column configurations, feed, feed composition, column holdup, etc. are given in Table 4.14. The reaction is modelled by simple rate equations (Table 4.14). The feed tank location was Nf = l (stages numbered from the top down). The given batch time is 12 hrs. Conversion to product C was 70%.
Also 1.52 kmol of product C with an accumulated composition of 0.70 molefraction was obtained in the distillate tank. Figure 4.18 shows the accumulated distillate, feed tank and bottom product composition profiles for the operation and Figure 4.19 shows the holdup profiles in the distillate accumulator, feed tank and bottom product accumulator.
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