2.1 Binary distillation column nonlinear model

The mathematical model of a distillation column consists of a set of differential equations that represent the dynamics of each plate of the column. Usually, the model of a distillation column is based on the balance of the light component in all the plates [10]. The model of a distillation column that considers a binary mixture as well as constant vapor and liquid flows through all columns is shown in Eq. (1):

Figure 1. Distillation column.

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation… DOI: http://dx.doi.org/10.5772/intechopen.83479

$$\frac{d\mathbf{x}\_i}{dt} = \frac{V(\mathbf{y}\_{i+1} - \mathbf{y}\_i) + L(\mathbf{x}\_{i-1} - \mathbf{x}\_i)}{M\_i} \tag{1}$$

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 plate i.

The dynamic representation of a distillation column is based on submodels of the light component balance in each element of the column.

For the condenser, numbered as plate 1, Eq. (2) shows:

$$\frac{d\mathbf{x}\_1}{dt} = \frac{V\mathbf{y}\_{i+1} - L\mathbf{x}\_{i-1} - D\mathbf{x}}{M\_1} \tag{2}$$

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

$$\frac{d\mathbf{x}\_i}{dt} = \frac{V(\mathbf{y}\_{i+1} - \mathbf{y}\_i) + L(\mathbf{x}\_{i-1} - \mathbf{x}\_i)}{M\_i} \tag{3}$$

where i ¼ 2, 3…n � 1.

product. The equipment used to carry out the distillation process is the distillation

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 mathematical model of a distillation column consists of a set of differential equations that represent the dynamics of each plate of the column. Usually, the model of a distillation column is based on the balance of the light component in all the plates [10]. The model of a distillation column that considers a binary mixture as well as constant vapor and liquid flows through all

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

columns or the distillation pilot plants, as shown in Figure 1.

Distillation - Modelling, Simulation and Optimization

2.1 Binary distillation column nonlinear model

distilled product to liquid [11].

columns is shown in Eq. (1):

the user.

Figure 1. Distillation column.

12

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

$$\frac{d\mathbf{x}\_n}{dt} = \frac{V\left(\mathbf{x}\_n - \boldsymbol{\chi}\_n\right) + L\left(\boldsymbol{\chi}\_{n-1} - \boldsymbol{\chi}\_n\right)}{M\_n} \tag{4}$$

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