**1. Introduction**

Distillation is a process that separates two or more components into an overhead distillate and a bottoms product. The bottoms product is almost exclusively liquid, while the distillate may be liquid or a vapor or both.

The separation process requires three things. Firstly, a second phase must be formed so that both liquid and vapor phases are present and can contact each other on each stage within a separation column. Secondly, the components have different volatilities so that they will partition between the two phases to a different extent. Lastly, the two phases can be separated by gravity or other mechanical means.

Calculation of the distillation column in this chapter is based on a real petroleum project to build a gas processing plant to raise the utility value of condensate. The nominal capacity of the plant is 130,000 tons of raw condensate per year based on 24 operating hours per day and 350 working days per year. The quality of the output products is the purity of the distillate, *xD*, higher than or equal to 98% and the impurity of the bottoms, *xB*, may be less/equal than 2%. The basic feed stock data and its actual compositions are based on the other literature (PetroVietnam Gas Company,1999).

The distillation column contains one feed component, *<sup>F</sup> x* . The product stream exiting the top has a composition of *xD* of the light component. The product stream leaving the bottom contains a composition of *Bx* of the light component. The column is broken in two sections. The top section is referred to as the rectifying section. The bottom section is known as the stripping section as shown in Figure 1.1.

The top product stream passes through a total condenser. This effectively condenses all of the vapor distillate to liquid. The bottom product stream uses a partial re-boiler. This allows for the input of energy into the column. Distillation of condensate (or natural gasoline) is cutting off light components as propane and butane to ensure the saturated vapor pressure and volatility of the final product.

The goals of this chapter are twofold: first, to present a theoretical calculation procedure of a condensate column for simulation and analysis as an initial step of a project feasibility study, and second, for the controller design: a reduced-order linear model is derived such that it best reflects the dynamics of the distillation process and used as the reference model

Modeling and Control Simulation for a Condensate Distillation Column 5

b. *Fractionation:* Increasing the reflux ratio (or boil-up rate) will reduce the impurities in

Feed split usually has a much stronger effect on product compositions than does fractionation. One of the important consequences of the overwhelming effect of feed split is that it is usually impossible to control any composition (or temperature) in a column if the feed split is fixed (i.e. the distillate or the bottoms product flows are held constant). Any small changes in feed rate or feed composition will drastically affect the compositions of both products, and will not be possible to change fractionation enough to counter this effect.

The degrees of freedom of a process system are the independent variables that must be specified in order to define the process completely. Consequently, the desired control of a process will be achieved when and only when all degrees of freedom have been specified. The mathematical approach to determine the degrees of freedom of any process (George, S., 1986) is to sum up all the variables and subtract the number of independent equations. However, there is a much easier approach developed by Waller, V. (1992): There are five control valves as shown in Figure 1.2, one on each of the following streams: distillate, reflux, coolant, bottoms and heating medium. The feed stream is considered being set by the upstream process. So this column has five degrees of freedom. Inventories in any process must be always controlled. Inventory loops involve liquid levels and pressures. This means that the liquid level in the reflux drum, the liquid level in the column base, and the column

If we subtract the three variables that must be controlled from five, we end up with two degrees of freedom. Thus, there are two and only two additional variables that can (and must) be controlled in the distillation column. Notice that we have made no assumptions about the number or type of chemical components being distilled. Therefore a simple, ideal, binary system has two degrees of freedom; a complex, multi-component system also has

both distillate and the bottoms product.

**2.1.2 Degrees of freedom of the distillation process** 

pressure must be controlled.

two degrees of freedom.

Fig. 2.1. Control Valves Location

#### Fig. 1.1. Distillation Flow-sheet

for a model-reference adaptive control (MRAC) system to verify the ability of a conventional adaptive controller for a distillation process dealing with the disturbance and the plantmodel mismatch as the influence of the feed disturbances.

In this study, the system identification is not employed since experiments requiring a real distillation column is still not implemented. So that a process model based on experimentation on a real process cannot be done. A mathematical modeling based on physical laws is performed instead. Further, the MRAC controller model is not suitable for handling the process constraints on inputs and outputs as discussed in other literature (Marie, E. *et al*., 2008) for a coordinator model predictive control (MPC). In this chapter, the calculations and simulations are implemented by using MATLAB (version 7.0) software package.

### **2. Process data calculation**

#### **2.1 Methods of distillation column control**

#### **2.1.1 Fundamental variables for composition control**

The purity of distillate or the bottoms product is affected by two fundamental variables: feed split (or cutting point) and fractionation. The feed split variable refers to the fraction of the feed that is taken overhead or out the bottom. The fractionation variable refers to the energy that is put into the column to accomplish the separation. Both of these fundamental variables affect both product compositions but in different ways and with different sensitivities.

a. *Feed Split*: Taking more distillate tends to decrease the purity of the distillate and increase the purity of the bottoms. Taking more bottoms tends to increase distillate purity and decrease bottoms product purity.

for a model-reference adaptive control (MRAC) system to verify the ability of a conventional adaptive controller for a distillation process dealing with the disturbance and the plant-

In this study, the system identification is not employed since experiments requiring a real distillation column is still not implemented. So that a process model based on experimentation on a real process cannot be done. A mathematical modeling based on physical laws is performed instead. Further, the MRAC controller model is not suitable for handling the process constraints on inputs and outputs as discussed in other literature (Marie, E. *et al*., 2008) for a coordinator model predictive control (MPC). In this chapter, the calculations and

The purity of distillate or the bottoms product is affected by two fundamental variables: feed split (or cutting point) and fractionation. The feed split variable refers to the fraction of the feed that is taken overhead or out the bottom. The fractionation variable refers to the energy that is put into the column to accomplish the separation. Both of these fundamental variables affect

a. *Feed Split*: Taking more distillate tends to decrease the purity of the distillate and increase the purity of the bottoms. Taking more bottoms tends to increase distillate

simulations are implemented by using MATLAB (version 7.0) software package.

both product compositions but in different ways and with different sensitivities.

Fig. 1.1. Distillation Flow-sheet

**2. Process data calculation** 

**2.1 Methods of distillation column control** 

**2.1.1 Fundamental variables for composition control** 

purity and decrease bottoms product purity.

model mismatch as the influence of the feed disturbances.

b. *Fractionation:* Increasing the reflux ratio (or boil-up rate) will reduce the impurities in both distillate and the bottoms product.

Feed split usually has a much stronger effect on product compositions than does fractionation. One of the important consequences of the overwhelming effect of feed split is that it is usually impossible to control any composition (or temperature) in a column if the feed split is fixed (i.e. the distillate or the bottoms product flows are held constant). Any small changes in feed rate or feed composition will drastically affect the compositions of both products, and will not be possible to change fractionation enough to counter this effect.

#### **2.1.2 Degrees of freedom of the distillation process**

The degrees of freedom of a process system are the independent variables that must be specified in order to define the process completely. Consequently, the desired control of a process will be achieved when and only when all degrees of freedom have been specified. The mathematical approach to determine the degrees of freedom of any process (George, S., 1986) is to sum up all the variables and subtract the number of independent equations. However, there is a much easier approach developed by Waller, V. (1992): There are five control valves as shown in Figure 1.2, one on each of the following streams: distillate, reflux, coolant, bottoms and heating medium. The feed stream is considered being set by the upstream process. So this column has five degrees of freedom. Inventories in any process must be always controlled. Inventory loops involve liquid levels and pressures. This means that the liquid level in the reflux drum, the liquid level in the column base, and the column pressure must be controlled.

If we subtract the three variables that must be controlled from five, we end up with two degrees of freedom. Thus, there are two and only two additional variables that can (and must) be controlled in the distillation column. Notice that we have made no assumptions about the number or type of chemical components being distilled. Therefore a simple, ideal, binary system has two degrees of freedom; a complex, multi-component system also has two degrees of freedom.

Fig. 2.1. Control Valves Location

Modeling and Control Simulation for a Condensate Distillation Column 7

The actual composition of the raw condensate for the gas processing plant is always fluctuates around the average composition as shown in the Table 2.2. The distillation data

Component Mole %

0.00 19.00 26.65 20.95 10.05 7.26 3.23 1.21 0.00 0.00 1.94 2.02 1.61 2.02 1.61 0.00 0.00 0.00 0.00

Propane Normal Butane Iso-butane Iso-pentane Normal Pentane

Hexane Heptane Octane Nonane

Benzene Toluen O-xylene E-benzen 124-Mbenzen

Table 2.2. Compositions of raw condensate

the range as shown in the Table 2.4.

 

*y x K y K*

*i i i*

*x*

*j*

*j j*

*Relative volatility:* 

*ij*

Normal Decane n-C11H24 n-C12H26 Cyclopentane Methylclopentane

The feed is considered as a pseudo *binary mixture* of Ligas (iso-butane, n-butane and propane) and Naphthas (iso-pentane, n-pentane, and heavier components). The column is designed with *N*=14 trays. The model is simplified by lumping some components together (pseudocomponents) and modeling of the column dynamics is based on these pseudocomponents only (Kehlen, H. & Ratzsch, M., 1987). Depending on the feed composition fluctuation, the properties of pseudo components are allowed to change within

Relative volatility is a measure of the differences in volatility between two components, and hence their boiling points. It indicates how easy or difficult a particular separation will be.

> mole fraction of component i in the vapor mole fraction of component i in the liquid

*x*

The relative volatility of component *i* with respect to component *j* is defined as:

where

*i i y*

for given raw condensate are shown in the Table 2.3.

#### **2.1.3 Control structure**

The manipulated variables and controlled variables of a distillation column are displayed in the Table 2.1 and in the Figure 2.1.


Table 2.1. Manipulated variables and controlled variables of a distillation column

Selecting a control structure is a complex problem with many facets. It requires looking at the column control problem from several perspectives:


#### **2.1.4 Energy balance control structure (L-V)**

The *L-V* control structure, which is called energy balance structure, can be viewed as the *standard control structure* for dual composition control of distillation. In this control structure, the reflux flow rate *L* and the boil-up flow rate *V* are used to control the "primary" outputs associated with the product specifications. The liquid holdups in the drum and in the column base (the "secondary" outputs) are usually controlled by distillate flow rate *D* and the bottoms flow rate *B*.

### **2.1.5 Material balance control structure (D-V) and (L-B)**

Two other frequently used control structures are the material balance structures (*D-V*) and (*L-B*). The (*D-V*) structure seems very similar to the (*L-V*) structure. The only difference between the (*L-V*) and the (*D-V*) structures is that the roles of *L* and *D* are switched.

#### **2.2 Distillation process calculation**

#### **2.2.1 Preparation for initial data**

The plant nominal capacity is 130,000 tons of raw condensate per year based on 24 operating hours per day and 350 working days per year. The plant equipment is specified with a design margin of 10% above the nominal capacity and turndown ratio of 50%. Hence, the raw condensate *feed rate* for the plant is determined as follows:

$$\text{Feed} = \frac{130,000 \text{ tons}}{\text{(24 h)} \times \text{(350 working days)}} = 15.47619 \text{ tons / hour} \tag{2.1}$$

The actual composition of the raw condensate for the gas processing plant is always fluctuates around the average composition as shown in the Table 2.2. The distillation data for given raw condensate are shown in the Table 2.3.


Table 2.2. Compositions of raw condensate

The feed is considered as a pseudo *binary mixture* of Ligas (iso-butane, n-butane and propane) and Naphthas (iso-pentane, n-pentane, and heavier components). The column is designed with *N*=14 trays. The model is simplified by lumping some components together (pseudocomponents) and modeling of the column dynamics is based on these pseudocomponents only (Kehlen, H. & Ratzsch, M., 1987). Depending on the feed composition fluctuation, the properties of pseudo components are allowed to change within the range as shown in the Table 2.4.

#### *Relative volatility:*

6 Distillation – Advances from Modeling to Applications

The manipulated variables and controlled variables of a distillation column are displayed in

 Controlled variables Manipulated variables Control valve 1 Column pressure Condenser duty Coolant flow *V*1 2 Concentration (temperature) of distillate Reflux flow rate Reflux flow *V*2 3 Liquid level in the reflux drum Distillate flow rate Distillate flow *V*3 4 Concentration (temperature) of bottoms Re-boiler duty Heat flow *V*4 5 Liquid level in the column base Bottoms flow rate Bottom flow *V*5

Table 2.1. Manipulated variables and controlled variables of a distillation column

 Local perspective considering the steady state characteristics of the column. Local perspective considering the dynamic characteristics of the column.

the column control problem from several perspectives:

**2.1.4 Energy balance control structure (L-V)** 

**2.1.5 Material balance control structure (D-V) and (L-B)** 

raw condensate *feed rate* for the plant is determined as follows:

Selecting a control structure is a complex problem with many facets. It requires looking at

Global perspective considering the interaction of the column with other unit operations

The *L-V* control structure, which is called energy balance structure, can be viewed as the *standard control structure* for dual composition control of distillation. In this control structure, the reflux flow rate *L* and the boil-up flow rate *V* are used to control the "primary" outputs associated with the product specifications. The liquid holdups in the drum and in the column base (the "secondary" outputs) are usually controlled by distillate flow rate *D* and

Two other frequently used control structures are the material balance structures (*D-V*) and (*L-B*). The (*D-V*) structure seems very similar to the (*L-V*) structure. The only difference

The plant nominal capacity is 130,000 tons of raw condensate per year based on 24 operating hours per day and 350 working days per year. The plant equipment is specified with a design margin of 10% above the nominal capacity and turndown ratio of 50%. Hence, the

> 130,000 15.47619 / (24 ) x (350 ) *tons Feed tons hour*

*h working days* (2.1)

between the (*L-V*) and the (*D-V*) structures is that the roles of *L* and *D* are switched.

**2.1.3 Control structure** 

in the plant.

the bottoms flow rate *B*.

**2.2 Distillation process calculation 2.2.1 Preparation for initial data** 

the Table 2.1 and in the Figure 2.1.

Relative volatility is a measure of the differences in volatility between two components, and hence their boiling points. It indicates how easy or difficult a particular separation will be. The relative volatility of component *i* with respect to component *j* is defined as:

$$\mathbf{x}\_{ij} = \frac{\begin{vmatrix} \underline{y}\_i \\ \underline{x}\_i \end{vmatrix}}{\begin{bmatrix} \underline{y}\_j \\ \underline{x}\_j \end{bmatrix}} = \frac{K\_i}{K\_j} \text{ where } \begin{cases} y\_i = \text{mole fraction of component i in the vapor} \\ \mathbf{x}\_i = \text{mole fraction of component i in the liquid} \end{cases}$$

Modeling and Control Simulation for a Condensate Distillation Column 9

The EFV curve is converted from the TBP data according to (Luyben, W., 1990). The initial

50%( ) 58.42 *TBP t* °C

*t*(30% 10%)( ) *TBP* 35.99 24.67 11.32 °C

Repeating the above procedure for all TBP data, the EFV (1 atm) data are determined. Then convert the EFV (1 atm) data into the EFV (4.6 atm) data by using Cox chart. The results are

The column is designed with 14 trays, and the pressure drop across each tray is 80 kPa. Thus

TBP EFV (1 atm) EFV (4.6 atm)

t °C t t t °C t °C

I.B.P. -1.44 41.62 93 1.2 1.5

<sup>5</sup>10.56 43.12 95

<sup>10</sup>24.67 47.12 102

<sup>20</sup>31.58 50.12 106

<sup>30</sup>35.99 52.62 110

<sup>40</sup>43.93 57.62 116

<sup>50</sup>58.42 63.62 125

<sup>60</sup>69.51 69.12 132

<sup>70</sup>75.91 75.62 141

<sup>80</sup>98.63 83.12 150

115.54 90.12 158

the pressures at feed section and top section are 4.6 atm and 4 atm respectively.

14.11 4

6.91 3

4.41 2.5

7.95 5

14.48 6

11.09 5.5

6.4 6.5

22.72 7.5

16.91 7

Table 2.5. Correlation between TBP and EFV of raw condensate

*Correlation between TBP and Equilibrium Flash Vaporization (EFV):* 

Consulting TBP-EFV correlation chart, we obtain 50%( ) 5.2 *EFV TBP t* °C

Therefore: *t*50%( ) *EFV* 58.42 5.2 63.62 °C

% vol.

shown in the Table 2.5.

*Operating pressure:* 

data are:


Table 2.3. Distillation data


Table 2.4. Properties of the pseudo components

Checking the data in the handbook (Perry, R. & Green, D., 1984) for the operating range of temperature and pressure, the relative volatility is calculated as: 5.68 .

*Correlation between TBP and Equilibrium Flash Vaporization (EFV):* 

The EFV curve is converted from the TBP data according to (Luyben, W., 1990). The initial data are:

$$t\_{\text{50\%}(TBP)} = 58.42 \, ^\circ \text{C}$$

$$t\_{(30\,\%-10\,\%)(TBP)} = 35.99 - 24.67 = 11.32 \,\text{°C}$$

Consulting TBP-EFV correlation chart, we obtain 50%( ) 5.2 *EFV TBP t* °C

Therefore: *t*50%( ) *EFV* 58.42 5.2 63.62 °C

Repeating the above procedure for all TBP data, the EFV (1 atm) data are determined. Then convert the EFV (1 atm) data into the EFV (4.6 atm) data by using Cox chart. The results are shown in the Table 2.5.

#### *Operating pressure:*

8 Distillation – Advances from Modeling to Applications


Properties Ligas Naphthas Molar weight 54.4-55.6 84.1-86.3 Liquid density (kg/m3) 570-575 725-735 Feed composition (vol %) 38-42 58-62

Checking the data in the handbook (Perry, R. & Green, D., 1984) for the operating range of

5.68 .

TBP (°C) ASTM (°C)

31.22 31.63 32.94 35.33 37.72 40.29 45.29 47.32 47.84 48.35 48.86 49.89 51.09 52.92 55.83 59.64 65.19 70.38 72.55 73.34 76.68 84.11 94.20 95.91 109.54 118.90 124.24 131.05 140.20 146.78 156.75

Cut point (%) Testing methods

0.00 1.00 2.00 3.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 75.00 80.00 85.00 90.00 92.50 95.00 96.50 98.00 99.00 100.00

Table 2.3. Distillation data

Table 2.4. Properties of the pseudo components

temperature and pressure, the relative volatility is calculated as:

The column is designed with 14 trays, and the pressure drop across each tray is 80 kPa. Thus the pressures at feed section and top section are 4.6 atm and 4 atm respectively.


Table 2.5. Correlation between TBP and EFV of raw condensate

Modeling and Control Simulation for a Condensate Distillation Column 11

Liquid flow rate m3/h

fraction 38 10.1923 0.577 5.8810 *L*F 58 12.3639 0.726 8.9762 *V*f -28 -7.2464 0.598 -4.3333 *L*f 32 8.0527 0.615 4.9524 *B* 62 13.1984 0.727 9.5952

The column base pressure is approximately the pressure at the feed section because pressure drop across this section is negligible. Consulting the EFV curve of stripping section and the Cox chart, the equilibrium temperature at this section is 144 °C. The re-boiler duty is equal to heat input in order to generate boil-up of stripping section an increment of 144-118=26 °C. The material and energy balances for stripping section is displayed in the Table 2.7 and with

The re-boiler duty must be supplied: <sup>3</sup> 6283.535 3983.575 2299.96 \* 10 *QB* (kJ/h).

INLET ton/h kcal/kg kcal/h.103 kJ/h.103 *L*F 8.9762 68 610.3816 2553.837 *L*f 4.9524 69 341.7156 1429.738 Total 13.9286 952.0972 3983.575 OUTLET ton/h kcal/kg kcal/h.103 kJ/h.103 *V*f 4.3333 165 714.9945 2991.537 *B* 9.5952 82 786.8064 3291.998 Total 13.9285 1501.801 6283.535

The overhead vapor flow, which includes *VF* from feed section and *Vf* from stripping section, passes through the condenser (to remove heat) and then enter into the reflux drum. There exists two equilibrium phases: liquid (butane as major amount) and vapor (butane vapor, uncondensed gas – dry gas: *C*1, *C*2, e.g.). The liquid from the reflux drum is partly pumped back into the top tray as reflux flow *L* and partly removed as distillate flow *D*. The top pressure is 4 atm due to pressure drop across the rectifying section. The dew point of distillate is correspondingly the point 100% of the EFV curve of rectifying section. Also

consulting the Cox chart, the top section temperature is determined as 46 °C.

*V*F 42 10.9983 0.591 6.5000 *V*f 28 7.2464 0.598 4.3333 *L*f -32 -8.0527 0.615 -4.9524

Liquid density ton/ m3

Mass flow rate ton/h

Stream Volume fraction

Table 2.6. Material Balances for the Feed Section

Table 2.7. Material and Energy Balances for Stripping Section

**2.2.4 Calculation for rectifying section** 

Total light

one *calTC =* 4.184 J*.*

% vol

#### **2.2.2 Calculation for feed section**

The feed is in liquid-gas equilibrium with gas percentage of 38% volume. However it is usual to deeply cut 4% of the unexpected heavy components, which will be condensed and refluxed to the columnmore bottom. Thus there are two equilibrium phase flows: vapor *VF*=38+4=42% and liquid *LF*=100-42=58%.

#### *Operating temperature:*

Consulting the EFV curve (4.6 atm) of feed section, the required feed temperature is 118 0C corresponding to 42% volume point.

The phase equilibrium is shown in the Figure 2.2.

Fig. 2.2. The Equilibrium phase flows at the feed section

Where, *VF*: Vapor phase rate in the feed flow; *LF*: Liquid phase rate in the feed flow; *Vf*: Vapor flow arising from the stripping section; *Lf*: Internal reflux descending across the feed section.

The heavy fraction flow *Lf* dissolved an amount of light components is descending to the column bottom. These undesirable light components shall be caught by the vapor flow *Vf* arising to the top column. *Vf*, which can be calculated by empirical method, is equal to 28% vol. The bottoms product flow *B* is determined by yield curve as 62% vol. Hence, the internal reflux across the feed section can be computed as: *L BL V f Ff* =62+28=32%*vol*.

Material balances for the feed section is shown in the Table 2.6. The calculation based on the raw condensate *feed rate* for the plant: 15.4762 tons/hour.

#### **2.2.3 Calculation for stripping section**

In the stripping section, liquid flows, which are descending from the feed section, include the equilibrium phase flow *LF*, and the internal reflux flow *Lf*. They are contacting with the arising vapor flow *Vf* for heat transfer and mass transfer. This process is accomplished with the aid of heat flow supplied by the re-boiler.

Main parameters to be determined are the bottoms product temperature and the re-boiler duty *QB*.

The feed is in liquid-gas equilibrium with gas percentage of 38% volume. However it is usual to deeply cut 4% of the unexpected heavy components, which will be condensed and refluxed to the columnmore bottom. Thus there are two equilibrium phase flows: vapor

Consulting the EFV curve (4.6 atm) of feed section, the required feed temperature is 118 0C

Where, *VF*: Vapor phase rate in the feed flow; *LF*: Liquid phase rate in the feed flow; *Vf*: Vapor flow arising from the stripping section; *Lf*: Internal reflux descending across the feed section. The heavy fraction flow *Lf* dissolved an amount of light components is descending to the column bottom. These undesirable light components shall be caught by the vapor flow *Vf* arising to the top column. *Vf*, which can be calculated by empirical method, is equal to 28% vol. The bottoms product flow *B* is determined by yield curve as 62% vol. Hence, the internal reflux across the feed section can be computed as: *L BL V f Ff* =62+28=32%*vol*. Material balances for the feed section is shown in the Table 2.6. The calculation based on the

In the stripping section, liquid flows, which are descending from the feed section, include the equilibrium phase flow *LF*, and the internal reflux flow *Lf*. They are contacting with the arising vapor flow *Vf* for heat transfer and mass transfer. This process is accomplished with

Main parameters to be determined are the bottoms product temperature and the re-boiler

**2.2.2 Calculation for feed section** 

*Operating temperature:* 

*VF*=38+4=42% and liquid *LF*=100-42=58%.

The phase equilibrium is shown in the Figure 2.2.

Fig. 2.2. The Equilibrium phase flows at the feed section

raw condensate *feed rate* for the plant: 15.4762 tons/hour.

**2.2.3 Calculation for stripping section** 

the aid of heat flow supplied by the re-boiler.

duty *QB*.

corresponding to 42% volume point.


Table 2.6. Material Balances for the Feed Section

The column base pressure is approximately the pressure at the feed section because pressure drop across this section is negligible. Consulting the EFV curve of stripping section and the Cox chart, the equilibrium temperature at this section is 144 °C. The re-boiler duty is equal to heat input in order to generate boil-up of stripping section an increment of 144-118=26 °C.

The material and energy balances for stripping section is displayed in the Table 2.7 and with one *calTC =* 4.184 J*.*

The re-boiler duty must be supplied: <sup>3</sup> 6283.535 3983.575 2299.96 \* 10 *QB* (kJ/h).


Table 2.7. Material and Energy Balances for Stripping Section

#### **2.2.4 Calculation for rectifying section**

The overhead vapor flow, which includes *VF* from feed section and *Vf* from stripping section, passes through the condenser (to remove heat) and then enter into the reflux drum. There exists two equilibrium phases: liquid (butane as major amount) and vapor (butane vapor, uncondensed gas – dry gas: *C*1, *C*2, e.g.). The liquid from the reflux drum is partly pumped back into the top tray as reflux flow *L* and partly removed as distillate flow *D*. The top pressure is 4 atm due to pressure drop across the rectifying section. The dew point of distillate is correspondingly the point 100% of the EFV curve of rectifying section. Also consulting the Cox chart, the top section temperature is determined as 46 °C.

Modeling and Control Simulation for a Condensate Distillation Column 13

Major design parameters to determine the liquid holdup on a tray, column base and reflux drum are calculated mainly based on other literature (Joshi, M., 1979; Wanrren, L. *et al*.,

(0.80 0.85)

The height of the column is calculated on distance of trays. The distance is selected on basis

2 4( ) *NB k B*

*H D <sup>d</sup> <sup>M</sup>*

bottom product (kg/kmole); *Bd* : density of the bottom product (kg/m3). Then,

 <sup>2</sup> 0.95

*Td* : the mean density of the liquid holdup on a tray (kg/m3). Then,

*D*

*h D <sup>d</sup> <sup>M</sup>*

*L G <sup>n</sup>*

*<sup>G</sup>* : density of vapor phase; *C*: correction factor depending flow rates of two-

 <sup>4</sup> 3600 *<sup>m</sup> <sup>k</sup>*

*B*

*MW*

where: *HNB* : normal liquid level in the column base (m); ( ) *MW <sup>B</sup>* : molar weight of the

<sup>2</sup> 3.14(1.4)(1.75) 726.5 31.11 4 78.6 *MB* (kmole).

> 4 () *T k T*

<sup>2</sup> 0.95(3.14)(0.28)(1.75) 680

 5( ) 60 *f f*

*L D*

clear liquid on a tray (m); ( ) *MW <sup>T</sup>* : molar weight of the liquid holdup on a tray (kg/kmole);

4 75 *M* =5.80 kmole.

The holdup in the reflux drum: Liquid holdup *MD* is equal to the quantity of distillate

drum; *Lf* : the reflux flow rate – (4952.4 kg/h)/(60.1 mole weight) = 82.4 kmole/h; *Vf* : the distillate flow rate – (4333.3 kg/h)/(58.2 mole weight) = 74.46 kmole/h. Then,

*T*

*C* (m/s), where:

*f*

*<sup>V</sup> <sup>D</sup>* (m), where, *Vm* : the mean flow of

*MW* (kmole), where, *Th* : average depth of

*M* (kmole), where, *MD* : holdup in the reflux

(kmole) (2.2)

*<sup>L</sup> <sup>P</sup> G* *<sup>G</sup>*

*<sup>n</sup>* for paraffinic vapor. The diameter of

*L*

*<sup>L</sup>* : density of

. The actual

*G*

**2.2.6 Liquid holdup** 

liquid phase;

velocity

2005; & Wuithier, P., 1972):

The holdup on each tray:

contained in the reflux drum,

 5(82.4 74.46) 13.07 60

*MD* (kmole).

Velocity of vapor phase arising in the column:

is normally selected that

the column is calculated with the formula:

vapor in the column. Result: 1.75 *Dk* (m).

phase flows, obtained from the empirical chart ,*C P f f* with

of the column diameter. The holdup in the column base is determined as:

*B*


The equilibrium phase flows at the rectifying sections are displayed in the Table 2.8.

Table 2.8. Material and Energy Balances for Rectifying Section

Calculate the internal reflux flow *L*0: Energy balance, INLET=OUTLET:

 0 0 0 0 5212.553 100.416 2718.326 405.848 8.166 (ton/h) Total light fraction + L 14.047 (ton/h) *L L L*

Calculate the external reflux flow *L*: Enthalpy data of reflux flow *L* looked up the experimental chart for petroleum enthalpy are corresponding to the liquid state of 40 °C (liquid inlet at the top tray) and the vapor state of 46 °C (vapor outlet at the column top).

*L* inlet at 40 °C: *H* liquid(inlet) = 22 kcal/kg; *L* outlet at 46 °C: *H* vapor(outlet) = 106 kcal/kg. Then,

<sup>0</sup> *H L HL L L* <sup>0</sup> (115 24)(8.166) (106 22) 8.847 (ton/h) *L L* .

#### **2.2.5 Latent heat and boil-up flow rate**

The heat input of *Q*B (re-boiler duty) to the reboiler is to increase the temperature of stripping section and to generate boil-up *V*0 as (Franks, R., 1972): <sup>0</sup> ( ) *Q Bc t t B BB F <sup>V</sup>* , where, *Q*B: re-boiler duty – 2299.96\*103 (kJ/h); *B*: flow rate of bottom product – 9595.2 (kg/h); *c*B: specific heat capacity – 85 (kJ/kg. °C); *t*F: inlet temperature – 118 (°C, the feed temperature); *t*B: outlet temperature – 144 °C; : the latent heat or heat of vaporization.

The latent heat at any temperature is described in terms of the latent heat at the normal boiling point (Nelson, W., 1985): *<sup>B</sup> B T <sup>T</sup>* (kJ/kg), where, : latent heat at absolute temperature *T* (kJ/kg); *<sup>B</sup>* : latent heat at absolute normal boiling point *T*B (kJ/kg); : correction factor obtained from the empirical chart. The result: =8500 (kJ/kg); *V*0=4540.42 (kg/h) or 77.67 (kmole/h); *V*f=4333.3 (kg/h) or 74.13 (kmole/h). The average vapor flow rate is rising in the stripping section <sup>0</sup> 77.67 74.13 2 2 *V Vf <sup>V</sup>* =75.9 (kmole/h).

#### **2.2.6 Liquid holdup**

12 Distillation – Advances from Modeling to Applications

INLET

*V*F+*V*f 10.8333 115 1245.83 5212.553 *L*<sup>0</sup> *L*0 24 24x*L*0 100.416x*L*<sup>0</sup> *Total 10.8333+ L0 1245.83+24*x*L0 5212.553+100.416\*L0*

OUTLET

*Total light fraction+L*0 5.8810*+L*0 97 570.457*+97*x*L*0 2386.792+405.848x*L*<sup>0</sup> *L*f 4.9524 16 79.2384 331.533 *Total 10.8334+L0 649.695+97*x*L0 2718.326+405.848*x*L0*

0 0 0 0

5212.553 100.416 2718.326 405.848 8.166 (ton/h) Total light fraction + L 14.047 (ton/h) *L L L*

Calculate the external reflux flow *L*: Enthalpy data of reflux flow *L* looked up the experimental chart for petroleum enthalpy are corresponding to the liquid state of 40 °C (liquid inlet at the top tray) and the vapor state of 46 °C (vapor outlet at the column top).

*L* inlet at 40 °C: *H* liquid(inlet) = 22 kcal/kg; *L* outlet at 46 °C: *H* vapor(outlet) = 106 kcal/kg. Then,

<sup>0</sup> *H L HL L L* <sup>0</sup> (115 24)(8.166) (106 22) 8.847 (ton/h) *L L* .

The heat input of *Q*B (re-boiler duty) to the reboiler is to increase the temperature of

where, *Q*B: re-boiler duty – 2299.96\*103 (kJ/h); *B*: flow rate of bottom product – 9595.2 (kg/h); *c*B: specific heat capacity – 85 (kJ/kg. °C); *t*F: inlet temperature – 118 (°C, the feed

The latent heat at any temperature is described in terms of the latent heat at the normal

(kg/h) or 77.67 (kmole/h); *V*f=4333.3 (kg/h) or 74.13 (kmole/h). The average vapor flow

*<sup>T</sup>* (kJ/kg), where,

 <sup>0</sup> 77.67 74.13 2 2

*B T*

:

: latent heat at absolute

=8500 (kJ/kg); *V*0=4540.42

: the latent heat or heat of vaporization.

*<sup>B</sup>* : latent heat at absolute normal boiling point *T*B (kJ/kg);

*V Vf <sup>V</sup>* =75.9 (kmole/h).

 <sup>0</sup> ( ) *Q Bc t t B BB F <sup>V</sup>* ,

Table 2.8. Material and Energy Balances for Rectifying Section

**2.2.5 Latent heat and boil-up flow rate** 

temperature); *t*B: outlet temperature – 144 °C;

boiling point (Nelson, W., 1985):

rate is rising in the stripping section

temperature *T* (kJ/kg);

Calculate the internal reflux flow *L*0: Energy balance, INLET=OUTLET:

stripping section and to generate boil-up *V*0 as (Franks, R., 1972):

 *<sup>B</sup>*

correction factor obtained from the empirical chart. The result:

*ton/h kcal/kg kcal/h.103 kJ/h.103*

*ton/h kcal/kg kcal/h.103 kJ/h.103*

The equilibrium phase flows at the rectifying sections are displayed in the Table 2.8.

Major design parameters to determine the liquid holdup on a tray, column base and reflux drum are calculated mainly based on other literature (Joshi, M., 1979; Wanrren, L. *et al*., 2005; & Wuithier, P., 1972):

Velocity of vapor phase arising in the column: *L G <sup>n</sup> G C* (m/s), where: *<sup>L</sup>* : density of liquid phase; *<sup>G</sup>* : density of vapor phase; *C*: correction factor depending flow rates of twophase flows, obtained from the empirical chart ,*C P f f* with *<sup>G</sup> f L <sup>L</sup> <sup>P</sup> G* . The actual velocity is normally selected that (0.80 0.85)*<sup>n</sup>* for paraffinic vapor. The diameter of the column is calculated with the formula: <sup>4</sup> 3600 *<sup>m</sup> <sup>k</sup> <sup>V</sup> <sup>D</sup>* (m), where, *Vm* : the mean flow of vapor in the column. Result: 1.75 *Dk* (m).

The height of the column is calculated on distance of trays. The distance is selected on basis of the column diameter. The holdup in the column base is determined as:

$$M\_B = \frac{\pi H\_{NB} D\_k^2}{4} \frac{d\_B}{\text{(MWV)}\_B} \text{ (kmole)}\tag{2.2}$$

where: *HNB* : normal liquid level in the column base (m); ( ) *MW <sup>B</sup>* : molar weight of the bottom product (kg/kmole); *Bd* : density of the bottom product (kg/m3). Then,

$$\implies M\_B = \frac{3.14(1.4)(1.75)^2}{4} \frac{726.5}{78.6} = 31.11 \text{ (kmole)}.$$

The holdup on each tray: <sup>2</sup> 0.95 4 () *T k T T h D <sup>d</sup> <sup>M</sup> MW* (kmole), where, *Th* : average depth of clear liquid on a tray (m); ( ) *MW <sup>T</sup>* : molar weight of the liquid holdup on a tray (kg/kmole); *Td* : the mean density of the liquid holdup on a tray (kg/m3). Then,

$$\implies M = \frac{0.95(3.14)(0.28)(1.75)^2}{4} \frac{680}{75} = 5.80 \text{ kmole.}$$

The holdup in the reflux drum: Liquid holdup *MD* is equal to the quantity of distillate contained in the reflux drum, 5( ) 60 *f f D L D M* (kmole), where, *MD* : holdup in the reflux drum; *Lf* : the reflux flow rate – (4952.4 kg/h)/(60.1 mole weight) = 82.4 kmole/h; *Vf* : the distillate flow rate – (4333.3 kg/h)/(58.2 mole weight) = 74.46 kmole/h. Then, 5(82.4 74.46) 13.07 60 *MD* (kmole).

Modeling and Control Simulation for a Condensate Distillation Column 15

 11 11 1 1 ( ) *nn nn n n n <sup>n</sup> n n*

where, n: tray *n*th; *V*: vapor flow; *L*: liquid flow; *x*: liquid concentration of light component; *y*: vapor concentration of light component; *h*: enthalpy for liquid; *H*: enthalpy for vapor.

1 1

*Fc L x V y L x V y dt dx L x V y L V x Vy x*

*n n n n n n n n nn n n*

11 11

 

*F nn nn n n n <sup>n</sup> n n*

*hF h L H V L V h <sup>V</sup> H h*

11 11 1 1

*f n n n n nn nn*

*hF h L H V hL HV*

11 11

*f f f f f ff ff*

*dt M*

11 11 1 1

*FL V L V*

*f f ff*

*dt* (3.7)

( )()

( )

**3.2 Equations for the feed tray: (Stage n=***f***) (See Figure 3.2)** 

( )*<sup>f</sup>*

*d M*

( )

*dMx*

( )

*dt*

*dMh*

*f f*

*f f*

Total mass balance:

Component balance:

Energy balance:

Fig. 3.2. Feed Section

*H h* (3.6)

(3.8)

(3.9)

*hL HV L V h <sup>V</sup>*
