Distillation - Modelling, Simulation and Optimization

product. The equipment used to carry out the distillation process is the distillation columns or the distillation pilot plants, as shown in Figure 1.

dxi

DOI: http://dx.doi.org/10.5772/intechopen.83479

the light component balance in each element of the column. For the condenser, numbered as plate 1, Eq. (2) shows:

dx<sup>1</sup>

dt <sup>¼</sup> V yiþ<sup>1</sup> � yi

dt <sup>¼</sup> V xn � yn

where D is the distilled product and n is the total number of plates.

The state-space dynamics of the distillation column, considering as states the light component composition in all the plates and as control inputs to the heating

1

CCCCCCA

V · G xð Þ <sup>i</sup>α<sup>i</sup> Mi

⋮

� <sup>V</sup> · G xð Þ� <sup>n</sup>�<sup>1</sup> <sup>α</sup><sup>n</sup>�<sup>1</sup> <sup>L</sup> Mn�<sup>1</sup>

> L Mn

� <sup>V</sup> · G xð Þ� <sup>i</sup>þ<sup>1</sup>α<sup>i</sup>þ<sup>1</sup> <sup>L</sup> Mi

<sup>þ</sup> <sup>B</sup> Rf

⋯ 0 0

⋯ 0 0

⋮

1

CCCCCCCCCCCCCCCCA

V · G xð Þ <sup>n</sup> α<sup>n</sup> Mn�<sup>1</sup>

> � L Mn

Qb � � (5)

x1 x2 ⋮ xn�<sup>1</sup> xn

0

BBBBBB@

dxi

For the boiler, numbered as plate 1, Eq. (4) shows:

dxn

power, Qf , and the reflux, Rf , is expressed in Eq. (5):

where A and B matrixes are defined by

L Mi

⋯

⋯

⋯

A ¼

13

⋮

BBBBBBBBBBBBBBBB@

0

⋮

0

0

0

0

x\_ ¼ A

� ð Þ <sup>V</sup> <sup>þ</sup> <sup>D</sup> Mi

2.1.1 Distillation column state-space model

where i ¼ 2, 3…n � 1.

plate i.

dt <sup>¼</sup> V yiþ<sup>1</sup> � yi

� � <sup>þ</sup> L xð Þ <sup>i</sup>�<sup>1</sup> � xi Mi

where V is the vapor molar flow, L is the liquid molar flow, M is the retained mass, xi is the liquid composition in plate i, and yi is the vapor composition in

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation…

The dynamic representation of a distillation column is based on submodels of

dt <sup>¼</sup> Vyiþ<sup>1</sup> � Lxi�<sup>1</sup> � Dx M<sup>1</sup>

For the intermediate plates of the body of the distillation column, Eq. (3) shows:

� � <sup>þ</sup> L xð Þ <sup>i</sup>�<sup>1</sup> � xi Mi

� � <sup>þ</sup> L xð Þ <sup>n</sup>�<sup>1</sup> � xn Mn

(1)

(2)

(3)

(4)

A distillation column is composed by a boiler that provides the heat necessary to evaporate the mixture to be distilled; the body of the column is formed by n 2 plates, where a partial separation of the mixture is performed due to the phase equilibrium and a condenser that provides the necessary cooling to convert the distilled product to liquid [11].

Due to the high cost of the distillation columns and the amount of energy required in a distillation process, it is necessary to design adequate control strategies to monitor the main process variables and detect sensor and actuator faults to improve the quality of the distilled product and the safety of the process and the user.
