Assignment 4: Chemical Engineering Design at Alma Mater University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

ASSIGNMENT 4 Tray Column Design

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

Index

Flow Specification. 3 Input Data 3 Unit Operation 3 Equilibrium Data 4 Material Balance and Operative Condition 6 Operating Lines 7 q-line Calculation 7 Minimum Reflux Ratio 8 Internal Flowrate 9 Actual Operating Lines 9 McCabe & Thiele 10 Check on Material Balance 11 Energy Balance and Reboiler Choice 11 Design points 12 Fluid Properties 12 Design of the equipment 13 Material Selection 13 Selection of flow pattern 14 Tray Spacing 15 Flooding Velocity 15 Check for excessive entrainment 16 Tray Design 18 Checks on the initial assumptions 18 Diameter and Flow Pattern Check. 19 Evaluation of Weir Length 19 Weeping Check 20 Pressure Drops 21 Downcomer flooding check 22 Residence Time Check 22 Overall Column Efficiency 23 Nozzle Sizing 25 Column Height Calculation 26 Overall Pressure Drop 26 References 27 Datasheet and Sketch 29

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

Flow Specification

Input Data

This assignment requires the design of a tray column for distillation of Chloroform and Methanol. The concentrations and operating conditions are provided in the following table:

TABLE 1 - INPUT DATA Compound A Chloroform - Compound B Methanol Feed Flowrate 21000 kg/h Feed Composition in A 28 % Feed Temperature 55 Top Composition 48 % Bottom Composition 0.9 % Operating Pressure 2 bara -

Unit Operation

The assumption made before starting the design are resumed in the following table:

TABLE 2 - ASSUMPTION

1. Saturated liquid at the bubble point condition
2. Constant pressure in the column for the equilibrium calculation (neglecting pressure drops)
3. Reflux ratio 1.5 times the minimum reflux ratio
4. McCabe - Thiele method was used
5. Total condenser should be used

This section aims to determine the molar flow rate and mole fraction of each component in the inlet and outlet streams, by using mass balance and McCabe & Thiele 1 method. The latter has some assumptions which are reported below:

TABLE 3 - MCCABE & THIELE ASSUMPTION

1. No heat losses along the column
2. Constant heat of vaporization
3. Heat of mixing negligible

Molecular weights of inlet and outlet streams were calculated by means of arithmetic average using the composition indicated in the input data. Results are provided below:

MWstream = MWa . Xa + MWb . Xb

TABLE 4 - MOLECULAR WEIGHTS 2 OF PURE SUBSTANCES Chloroform 119.38 kg/kmol Methanol 32.04 kg/kmol

1 Coulson & Richardson, Chemical Engineering, Vol 2, p. 566 2 Aspen HYSYS

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

TABLE 5 - COMPOSITION OF INLET AND OUTLET STREAMS Compound Bottom Feed Top Chloroform 0.09 0.28 0.48 Methanol 0.91 0.72 0.52

TABLE 6 - MOLECULAR WEIGHTS OF STREAMS Compound Bottom [kg/kmol] Feed [kg/kmol] Top [kg/kmol] Average Molecular Weight 39.9 56.5 73.96

Equilibrium Data

The equilibrium data for the binary mixture is provided by the assignment and it can be found in the following table:

TABLE 7 - EQUILIBRIUM DATA Component A Chloroform Component B Methanol Total pressure (kPa) 200 Temperature °C Mole fraction A in xA yA 82.82 0 0 82.20 0.015 0.035 81.59 0.030 0.070 80.98 0.047 0.103 80.38 0.064 0.136 79.78 0.081 0.169 79.19 0.100 0.200 78.62 0.119 0.231 78.05 0.139 0.261 77.51 0.160 0.290 76.98 0.182 0.318 76.47 0.205 0.345 75.99 0.228 0.372 75.53 0.253 0.397 75.10 0.279 0.421 74.71 0.306 0.444 74.35 0.334 0.466 74.03 0.364 0.486 73.75 0.394 0.506 73.51 0.426 0.524 73.31 0.458 0.542 73.16 0.492 0.558 73.05 0.527 0.573 72.98 0.563 0.587 72.97 0.599 0.601 72.97 0.637 0.613 73.04 0.674 0.626 73.14 0.712 0.638 73.30 0.749 0.651 73.53 0.785 0.665 73.85 0.820 0.680 74.28 0.851 0.699 74.85 0.879 0.721 75.56 0.904 0.746 76.42 0.926 0.774 77.41 0.944 0.806 78.51 0.959 0.841 79.69 0.972 0.878 80.93 0.983 0.917 82.22 0.992 0.958 83.53 1 1

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

FIGURE 1 - EQUILIBRIUM PLOT Equilibrium Curve 1.00 0.90 0.80 0.70 0.60 ya [-] 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 xa [-]

FIGURE 2 - TXY PLOT 84 TXY (P = 2 bar) Chloroform / Methanol 82 80 T[ºC] 78 - Bubble 76 - Dew 74 72 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 x [-]

Since in the equilibrium plot there is an intersection between the equilibrium curve and bisector, an azeotrope point exists. But it is not of major importance since the outlet composition is below the intersection point and therefore, we can handle the problem as a normal distillation problem.

By using the TXY diagram it is possible to determine which component is more volatile. Additionally, since there is an azeotrope point, to estimate the saturated temperature, it should be considered the composition of azeotrope, not the pure A component. TSAT Methanol = 82.82 ℃ > TSAT Azeotrope Point, Chloroform = 72.97 ℃ The more volatile component is Chloroform.

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

Regarding the state of the feed, by using the inlet composition it is possible to estimate the Bubble and Dew temperatures:

TABLE 8 - FEED TEMPERATURES Feed Temperature [°C] Bubble Temperature Feed [°C] Dew Temperature Feed [°C] 55 75.24 77.68

Material Balance and Operative Condition

TABLE 9 - COMPOSITION XB [-] ZF [-] XD [-] 0.09 0.28 0.48

By means of material balance it is possible to estimate the outlet streams flowrate:

EQUATION 1 - MATERIAL BALANCE kg F : 21000- 56.5 ℎ = 371.7 kmol ℎ { { (37 kmol ℎ 371.7 · 0.28 = D · 0.48 + B · 0.09 → D = 181.1 B =190.6 ℎ kmol ℎ As it was said before, the outlet streams leave the column in saturated liquid condition. The outlet temperatures were obtained by using Aspen HYSYS.

TABLE 10 - MATERIAL BALANCE Feed [kmol/h] Distillate [kmol/h] Bottom [kmol/h] 371.7 181.1 190.6

TABLE 11 - OUTLET STREAMS TEMPERATURE Distillate Product Temperature [°C] Bottom Product Temperature [°C] 73.60 80.20

kg kmol kmol ℎ = D + B kmol F = D+B F . ZF = D . Xp + B . XB →

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

Operating Lines

Distillation column can be divided into two sections: Rectifying and Stripping sections. By writing material balances at top and bottom of the column it is possible to derive the following equations. VI I D Ln+1 Xd n+1 C F Xf Lm+1 m+1 Vm-+ m EQUATION 2 - RECTIFYING LINE Vn = Ln+1 + D (Vn . Vn = Ln+1 . Xn+1 + D . XD Vn = n + 1 . xn +1 + V . XD EQUATION 3 - STRIPPING LINE Vm = Lm+1 - W (Vm Vm = Lm+1 . Xm+1 - W . Xw Lm+1 Vm = V Xm + 1 - Vp . Xw These two equations are the equations of the II W operating lines. In order to calculate the change in Xw composition from one plate to the next, the equilibrium data are used to find the composition of the vapor above the liquid, and the enrichment line to calculate the composition of the liquid on the next plate. Note that in the figure above, the bottom composition is indicated as Xw, but in the assignment it will be treated as XB.

q-line Calculation

To obtain a relation between the internal flowrate it is necessary to calculate the parameters q in advance. Based on McCabe & Thiele method, q is defined as it follows:

EQUATION 4 - Q-LINE CALCULATION heat to vaporize 1 mol of feed q =- molar latent heat of the feed The parameter q represents the mole fraction of liquid in the feed, and since the feed is entering the column with a temperature lower than its bubble point, it was expected to have a subcooled feed, thus q>1. HSV - HF q - HSV - HSL A(TF,Dew) + CPL,2(TF,Dew - TF,Bubble) CPL,1 was calculated at average between Dew and Feed temperature, while CpL,2 was calculated at average between Dew and Bubble feed temperature.

TABLE 12 - FEED PROPERTIES3 TF [ºC] TF,Dew [ºC] TF,Bubble TAVG1 [°C] TAVG2 λ (TF, Dew) [kJ/kmol] CPL,1 @(TAVG1) [kJ/kmol ºC] CPL,2 @(TAVG2) [kJ/kmol ºC] 55 77.68 75.24 66.34 76.46 3.61 · 104 118.3 120.3 2(TF,Dew) + CPL,1(TF,Dew -TF) 3 Collected on Aspen HYSYS

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

3.61 . 104 kmol kJ + 118.3 kJ kmol · ℃ . (77.68 - 55)℃ 1.065 > 1 q = 3.61 · 104 k] kmol + 120.3 k] kmol . ºC. (77.68 - 75.24)℃ Once the parameter q was calculated, it is possible to write the equation of the q-line:

EQUATION 5 - Q-LINE EQUATION y = 9 . x- q-1 ZF q-1 1.065 1.065 - 1 · x 1.065 - 1 0.28 = 16.38 . x - 4.31

Minimum Reflux Ratio

In order to estimate the minimum reflux ratio, it is necessary to identify the intersection point between the q-line and the equilibrium curve and see what the value of y is, while x goes to zero. The value of the intersection was obtained by using Matlab, interpolating the point.

FIGURE 3 - MINIMUM REFLUX RATIO McCabe & Thiele 0.6 0.5 0.4 - - Equilibrium y* ya [-] 0.3 - q-line - xB 0.2 -XD 0.1 -ZF 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Xa [-] The plot display is limited to the points (0.6,0.6) due to the presence of the azeotrope. y* = 0.343

EQUATION 6 - MINIMUM REFLUX RATIO Rmin = XD - 1 = 0.343 0.48 - 1 = 0.4 R4 = 1.5 . Rmin = 1.5 . 0.4 = 0.6

4 From the assignment it was suggested to calculate reflux ratio as 1.5 times the minimum

8 Bisector

Alma Mater - University of Bologna

Sustainable Technologies and Biotechnologies for Energy and Materials (STEM)

Chemical Engineering Equipment Design - A.Y. 2023 - 2024

Internal Flowrate

The flowrate of liquid and gas that are inside the column can now be calculated by using the results of the previous section:

Liquid Flowrate Rectifiyng Section -> L = R . D Vapor Flowrate Rectifiyng Section -> V = L + D Liquid Flowrate Stripping Section -> L = L + F . q Vapor Flowrate Stripping Section -> V = V - F . (1 - q)

TABLE 13 - INTERNAL FLOWRATE Rectifying Section Stripping Section Liquid [kmol/h] Vapor [kmol/h] Liquid [kmol/h] Vapor [kmol/h] L V L V 108.6 289.6 504.5 313.7

Actual Operating Lines

Since the current reflux ratio and internal flowrates were known, it is possible to calculate and plot the actual operating lines, by using the correlation derived in the section Operating Lines.

EQUATION 7 - ACTUAL RECTIFYING LINE L V ·x+D·xp=10 108.6 289.6 kmol kmol h h 181.1 .X+ 289.6 kmol h · 0.48 = 0.375 . x + 0.3

EQUATION 8 - ACTUAL STRIPPING LINE L Vm = x- xB= B 504.5 313.7 kmol h h x - 190.6 313.7 kmol h h 0.09 = 1.606 · x - 0.054

FIGURE 4 - RECTIFYING AND STRIPPING LINES McCabe & Thiele 0.6 0.5 -Equilibrium 0.4 Bisector q-line ya [-] 0.3 xB - XD 0.2 - ZF Rectifying 0.1 - Stripping 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Xa [-]

9 kmol kmol kmol