CHAPTER 5.T-102(5.4)

5-103

5.4 DISTILLATION COLUMN (T-102)

5.4.1 INTRODUCTION

In this process, acetylated castor oil (ACO) which is also known as palmatic acid or

hexadecanoic acid (C15H31COOH), undergoes thermal cracking to produce 1-tetradecene

(C14H28), which is referred to as drying oil (DO); and acetic acid (CH3COOH). However, there

is an undesired reaction that produces 1-octacosene (C28H56), which is referred as gum, from

the drying oil dimers. The chemical reactions and reaction kinetics for the thermal cracking

process are as follows (Grummit & Fleming, 1945):

Chemical Reactions

DO acid acetic ACO

)()()( 281431

3115 lHCgCOOHCHlCOOHHCk

(5.4.1)

gum DO

)()(2 562828142 sHClHC k

(5.4.2)

There are two chemical reactions that occur in the thermal cracking of ACO. The first

(equation 5.4.1) is the main reaction where 1 mole of ACO (palmatic acid) reacts under high

temperature to produce 1 mole each of Acetic Acid & Drying Oil (1-tetradecene). The second

reaction (equation 5.4.2) is an undesired side reaction that produces 1 mole of Gum (1-

octacosene) from 2 moles of Drying oil (DO).

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5.4.1.1 Process Description

Figure 5.4.1 shows the process flow diagram for this plant. This process begins with

the raw material, ACO, being fed from a holding tank where it is mixed with recycled ACO.

The mixed feed would then heated to reaction temperature. Since the reaction occurs at high

temperatures, there is no need for a catalyst. The heated feed then flows into a plug flow

reactor. The reactor is simply a vessel to promote radial mixing. Then, process fluid is feed to

the distillation column (T-101) to separate the gum from the product. Another stream from

first distillation column (T-101) is fed to a distillation column (T-102) where the ACO is

separated and recycled. The non-recycled stream again goes through another distillation

column (T-103) where the DO is purified from the acetic acid. The contents of Streams 18

(acetic acid) and 19 (DO) are cooled and sent to storage. Drying oil (DO) is the main product

for sale, while the acetic acid is sold as a by-product (Grummit & Fleming, 1945).

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5.4.1.2 Process Flow Diagram

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5.4.2 OBJECTIVE OF THE DESIGN

The objective of this chapter is to determine detail design parameter for distillation

column T-102. The purpose of this distillation column is to separate the recycled stream

(Stream 16), which consists of hexadecanoic acid (ACO) and tetradecene (DO), from stream

14. Hexadecanoic acid and tetradecene are then recycled back to the reactor to obtain

higher conversion in reactor 101 and 102. The non-recycled stream again goes through

another distillation column (T-103) where the DO is purified from the acetic acid.

5.4.3 CHEMICAL DESIGN PROCESS FOR DISTILLATION COLUMN (T-102)

Distillation is by far the most important separation process in the petroleum and

chemical industries. It is the separation of key components in a mixture by the difference in

their relative volatility or boiling points. In most cases, distillation is the most economical

separating method for liquid mixtures (Sinnott, 2005). In this process, the feed in stream 10

contains more than two components which are hexadecanoic acid, tetradecene, acetic acid

and octacosene. It is commonly referred to as multi-component distillation. Figure 5.4.2

below shows the schematic diagram of the distillation column unit (T-102).

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Figure 5.4.2: Distillation column (T-102)

Component Flowrate (kmol/hr)

Mole Fraction

ACO 0.2653 0.00215

DO 61.4943 0.49889

AA 61.5026 0.49896

Gum 0.0001 0.00000


Mole Fraction

ACO 191.4709 0.60744

DO 61.6862 0.19570

AA 61.5026 0.19512

Gum 0.5521 0.00175


Mole Fraction

ACO 191.2056 0.99612

DO 0.19197 0.00100

AA 0.0000 0.00000

Gum 0.5520 0.00288

T-102

(S10)

315.21 kmol/hr

(S12)

123.26 kmol/hr

(S13)

191.95 kmol/hr

T = 125.5 oC

P = 13 kPa

T = 82.8 oC

P = 11 kPa

T =268.1 oC

P = 12 kPa

Where

ACO = hexadecanoic Acid

DO = Tetradecene

AA = Acetic Acid

Gum = Octacosene

5-108

5.4.4 FLOWCHART FOR CHEMICAL DESIGN

NO

YES

5-109

Figure 5.4.3: Algorithm for distillation column design

5-110

5.4.5 THEORETICAL BACKGROUND

5.4.5.1 Activity coefficients (Non-ideal Content)

The activity coefficient is a unitless thermodynamic function. If γk = 1 (an ideal

solution), the activity of component k is equal to its mole fraction and the behavior of k, from

the point of view of its chemical potential, is completely determined by its composition. If γk>

1 (a nonideal solution where the component k is said to exhibit a positive deviation from

Raoult's law), then ak>xk and in the evaluation of its chemical potential, component k "acts as

if" the solution contains more of k than the mole fraction suggests. Similarly, if γk< 1 (a

nonideal solution where the component k exhibits a negative deviation from Raoult's law) so

that ak<xk, the component "acts as if" there is less of it present than the composition

suggests. Therefore for non-ideal multicomponent system, the formula below is not valid

anymore.

(5.4.3)

Whereby, for non-ideal system, γ is needed. Thus formula becomes:

(5.4.4)

5.4.5.2 Relative Volatility

The relative volatility of two components can be expressed as the ratio of their k

values. From the K-values, the relative volatility for each component can be determined and

more accurate. (Sinnott, 2005):

j

ij

K

Ki

(5.4.5)

Where, Ki = light components

Kj = heavy components

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5.4.5.2.1 Key Component

Key component is component whose volatility that is vapor pressure characteristics relatives

to each other make them adjacent in the listing of the component in the feed. These key

components are separate into two as follows (Geankoplis,2003) :

1. Light key component is component whose percent recovery is greater in the

distillate than in the bottom. Acetic acid is chosen as light key component.

2. Heavy key component is the lightest component whose percent recovery is greater

in the bottom than in the distillate. Hexadecanoic acid is chosen as heavy key

component.

5.4.5.3 Bubble and Dew Point (Non-ideal system)

In order to estimate the number of stages, condenser and reboiler temperature, the

dew and bubble points must be calculated first. By definition, a saturated liquid is at its

bubble point (any rise in temperature will cause a bubble vapor to form), and a saturated

vapor is at its dew point (any drop in temperature will cause a drop of liquid to form) (Sinnott,

2005).

Bubble point: yi 0.1kixi (5.4.6)

Dew point : xi 0.1/ kiyi (5.4.7)

5.4.5.4 Minimum theoretical Stages

The Fenske equation (Fenske,1932) is used to estimate the minimum stages required at total

reflux (Sinnott, 2005):

(5.4.8)

Where,

D = subscript for distillate

B = subscript for bottom

Nm = minimum theoretical stages at total reflux

XHK = concentration of heavy key component

XLK = concentration of light key component

αavg= average relative volatility

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5.4.5.5 Minimum Reflux Ratio

The number of stages required for separation will be dependent on the reflux ratio

used. As the reflux ratio is reduced a pinch point will occur at which separation can only be

achieved with an infinite number of stages. Colburn (1941) and Underwood (1948) have

derived equations for estimating the minimum reflux ratio for multicomponent distillations. As

the Underwood equation is more widely used , the equation can be stated in the form

(Sinnott, 2005):

i

dii,x

= Rm + 1 (5.4.9)

Where,

i = the relative volatility of component i with respect to some reference

component, usually the heavy key

R m = the minimum reflux ratio

Xi,d = concentration of component i in the tops at minimum reflux

and is the root of the equation:

qx

i

fii1

,

(5.4.10)

Where xi,f = the concentration of component i in the feed, and q depends on the condition of

the feed.

5.4.5.6 Column Efficiency

A quick estimate of the overall column efficiency can be obtained from correlation

given by O’Connell (1946) in the form of an equation (Sinnott, 2005):

E0 = 51 – 32.5 log (μa αa) (5.4.11)

Where,

μa = molar average viscosity,mNs/m2

αa = average volatility of the light key

The overall column efficiency is correlated with the product of the relative volatility of the light

key component and the molar average viscosity of the feed, estimated at the average column

temperature. The overall column efficiency is relatively high in the range 50-100% (Seader,

2004)

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5.4.5.7 Number of stages using Lewis Matheson method

Estimation of the actual physical number of plates required in the distillation column is

usually done by dividing the actual theoretical stages by the overall plate efficiency (Sinnott,

2005):

(5.4.12)

Besides that, Lewis Matheson method is using in calculation of number of ideal stages. Feed

point also can be determined from this method:

1. For Top-Down:

(5.4.13)

2. For Bottom-up:

(5.4.14)

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5.4.5.8 Approximate Column Sizing

A trial and error approach is necessary in plate design. Starting with a rough plate

layout, checking key performance and revising the design until a satisfactory design is

achieved (Sinnott, 2005). The design procedures are as follows:

1. Determination of the vapour and liquid rate, based on the reflux ratio and feed

condition.

2. Estimation of the system physical properties.

3. Selection on a trial plate spacing.

4. Based on the flooding condition, the column diameter is determined.

5. Try to make a plate layout with downcomer area, active area, hole diameter, hole

area, weir height, weir length, and plate thickness.

6. The weeping rate is checking.

7. The plate pressure drop is checking.

8. The down-comer backup is checking .

9. Determination of plate layout details

10. Confirmation on the percentage flooding based on the chosen column diameter.

11. Entrainment is checking.

12. Determination of the column wall thickness and column head selection.

13. The design is finalize with the drawing and data specification sheet.

5.4.5.9 Plate Spacing

The overall height of the column will depend on the plate spacing. Plate spacing from

0.15 m to 1m are normally used. In this distillation column, the plate spacing used is 0.50 m

as it is in the range of 0.15 m to 1 m (Sinnott, 2005).

5.4.5.10 Column Diameter

The column diameter is computed to avoid flooding where the liquid begins to fill the

column and leave with vapor because it cannot flow downward at the required rate (Seader,

2004).The principle factor on determining the column diameter is the vapor flow rate. The

column diameter can be calculated by calculating the top and the bottom net area at its

maximum volumetric flow rate.

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The Liquid-vapor flow factor, FLV is given by:

FLv =

5.0

L

V

Vw

Lw

(5.4.15)

Where:

Lw = liquid mass flowrate, kg/s

Vw = vapor mass flowrate, kg/s

5.4.5.10.1 Flooding velocity

The flooding condition fixes the upper limit of vapour velocity. A high vapour velocity

is needed for high plate efficiencies, and the velocity will normally be between 70 to 90 per

cent of that which would cause flooding. For design, a value of 80 to 85 per cent of the

flooding velocity should be used. The flooding velocity can be estimated from the correlation

given by Fair (1961,referred to Sinnott,2005):

(5.4.16)

Where,

Uf = flooding vapour velocity, m/s, based on the net column cross-sectional

area,An

K1 = a constant

5.4.5.11 Weir Liquid Crest

The height of the liquid crest over the weir can be estimated using the Francis weir

formula. For a segmental downcomer this can be written as (Sinnott, 2005):

how =

3/2

750

w

w

LxI

L

(5.4.17)

where lw = weir length, m

how = weir crest, mm liquid

Lw = liquid flow-rate, kg/s

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5.4.5.12 Weep Point

The vapor velocity at the weep point is the minimum value for stable operation.

Minimum vapor velocity through the holes based on the holes area, ûh (Sinnott, 2005):

ûh = 5.02

)(

)4.25(9.0

v

dhk

(5.4.18)

where

ûh = minimum vapour velocity through the holes(based on the hole area), m/s,

dh = hole diameter, mm,

K2 = a constant, dependent on the depth of clear liquid on the plate

5.4.5.13 Plate Pressure Drop

The pressure required is automatically developed by the reboiler, which generates

vapor at the pressure sufficient to overcome the pressure drop in the column and in the

condenser. The overall pressure drop is calculated to determine the pressure and

temperature in the reboiler and the pressure drop per plate must be checked to make sure

the plate will operate properly without flooding. The pressure drop across the plate can be

divided into two parts which are the friction loss in the holes and the pressure drop due to the

holdup of liquid on the plate. It is usually given as an equivalent head in millimeters or inches

of liquid (Sinnott, 2005):

ldt hhh (5.4.19)

Where

ht = total pressure drop per plate, mm of liquid

hd = friction loss for dry plate, mm of liquid

hl = equivalent head of liquid on plate, mm of liquid

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5.4.5.13.1 Dry plate drop

Pressure drop through the holes can be predicted from a modification of equation for

flow through an orifice (Sinnott, 2005):

hd =

L

v

C

U

o

h

2

51

(5.4.20)

Where uh = vapor velocity throught holes, m/s

ρv = vapor density

ρL = liquid density

Co = orifice coefficient

The orifice coefficient is a function of the plate thickness, hole diameter and the hole of

perforated area ratio.

5.4.5.13.2 Residual head

Residual head is a function of liquid surface tension, froth density and froth height.

Taking residual head as a fixed value of 12.5 mm of water, the equation for estimating the

residual head proposed by Hunt et al. (1955, referred to Sinnott, 2005):

Residual head,hr =

L

3105.12 (5.4.21)

Total Drop can be determined using this equation:

Pressure drop per plate,hT = hd +( hw + how ) + hr (5.4.22)

5.4.5.14 Downcomer Liquid Back Up

The liquid area and the plate spacing must be such that the level of the liquid and forth in the

down comer is well below the top of the outlet weir on the plate above. The backup of liquid

in the down comer is caused by the pressure drop over the plate and the resistance to flow in

the down comer itself.

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Head loss by Cicalese et al (1947, referred to Sinnott, 2005):

hdC =

2

166

ap

w

LxA

L

(5.4.23)

where Lw = liquid flow rate in downcomer, kg/s,

Aap = either the downcomer area Ad or the clearance area under the downcomer

Aap; whichever is the smaller, m2.

The clearance area under the downcomer is given by:

Aap = haplw (5.4.24)

where hap is height of the bottom edge of the apron above the plate. This height is normally

set at 5 to 10 mm below the outlet weir height (Sinnott, 2005):

hap = hw – (5 to 10 mm) (5.4.25)

Back up in the downcomer,hb = hw + how + hT + hdc (5.4.26)

5.4.5.15 Downcomer residence time

Sufficient residence time must be allowed in the down comer for the entrained vapor

to disengage from the liquid stream; this is to prevent heavily aerated liquid being carried

under the downcomer. At time of at least 3 second is recommended. The down comer

residence time, tr is given by (Sinnott, 2005):

(5.4.27)

Where,

tr = residence time, s,

hbc = clear liquid back-up, m.

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5.4.5.16 Check Entrainment by Fair

Entrainment can be estimated from the correlation given by Fair (1961), Figure 5.4.13, which

gives the fractional entrainment (kg/kg gross liquid flow) as a function of the liquid-vapour

factor FLV, with the percentage approach to flooding as a parameter. The percentage flooding

is given by (Sinnott, 2005):

Flooding percentage = F

V

u

U %100 (5.4.28)

5.4.5.17 Perforated Area

The area available for perforation will be reduced by the obstruction caused by

structural members (the support rings and beams), and by the use of calming zones.

Calming zones are unperforated strips of plate at the inlet and outlet sides of the plate. The

width of the support ring for sectional plates will normally be 50 to 75mm: the support ring

should not extend into down comer area. A strip of imperforated plate will left round the edge

of cartridge-type trays to stiffen the plate. A cartridge type construction is used; allowing 50

mm unperforated strips round. Formula used is list below (Sinnott, 2005):

Mean length, unperforated edge strips = (Dc –0.05) x x (5.4.29)

Mean length of calming zone, approx = weir length + width of unperforated strip (5.4.30)

Total area available for perforation, Ap = Active area – (Area of unperforated edge + Area of

calming zones) (5.4.31)

5-120

5.4.6 CALCULATION FOR CHEMICAL DESIGN

5.4.6.1 Step 1: Obtained composition and flow rate

Composition and flow rate at feed,F; distillate,D and bottom,W are obtained from figure 5.4.2.

5.4.6.2 Step 2: Obtained K-values

From table 5.4.1, the average activity coeffients is calculated based on K-values. Therefore,

based on the value, it is show that the system is non-ideal system.

Table 5.4.1 : Average activity coefficients

Number of tray ACO DO Acetic Gum

Tray1 10.4332 22.0111 5.2563 46.5074

Tray2 10.4668 13.9794 4.9210 38.3746

Tray3 10.3886 12.0192 4.7993 35.8138

Tray4 10.2905 18.9198 4.7438 35.0642

Tray5 10.1914 22.7024 4.6991 34.6213

Tray6 10.1110 23.6861 4.6128 26.7363

Tray7 10.0327 42.6745 4.4954 24.3179

Tray8 9.9548 9.9136 4.2639 18.9130

Tray9 9.8422 9.5379 4.0870 14.1124

Tray10 9.7408 9.4201 4.0128 12.7745

AVERAGE 10.1452 18.4864 4.5891 28.7236

STDEV 0.2396 9.6974 0.3654 10.5931

5.4.6.3 Step 3: Determination of relative volatilities

Table 5.4.2 shows the average relative volatility for each component. The average relative

volatility is based on light key. Acetic acid is chosen as light key. So the average relative

volatility, αavg is 497.26. It shows that the component is volatile as it has greater volatility. The

greater relative volatility, the mixture is easier to separate.

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Table 5.4.2: average relative volatility

No.of trays α(ACO) α(DO) α(Acetic) α(Gum)

Tray1 1 85.6000 1053.3788 0.6599

Tray2 1 47.4561 728.3269 0.6112

Tray3 1 39.3427 650.7129 0.5953

Tray4 1 62.0185 638.1988 0.5921

Tray5 1 75.0035 635.8290 0.5911

Tray6 1 66.2164 438.9700 0.5189

Tray7 1 111.5893 372.6323 0.4967

Tray8 1 20.6083 229.8526 0.4347

Tray9 1 14.2100 124.8799 0.3613

Tray10 1 12.3553 99.7943 0.3373

AVERAGE 1 53.4400 497.2576 0.5199

STD 0 31.0754 285.0185 0.1050

5.4.6.4 Step 4: Determination of dew and bubble point

The system is a non-ideal system and the bubble point and dew point is calculated

based on the relationship between K-values at each tray and temperature that are plotted

into graph and equation forms. Figure 5.4.4 to 5.4.7 shows variation of K-values with

temperature for all components.

Figure 5.4.4: graph of K value for hexadecanoic acid

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Figure 5.4.5: graph of K value for Tetradecene

Figure 5.4.6: graph of K value for Acetic acid

5-123

Figure 5.4.7: graph of K value for Octacosene

5.4.6.4.1 Dew Temperature (Top column)

Operating Temperature = 355.93 K

Operating Pressure = 11 kPa

Based on equation 5.4.7 for dew point, value close to 1.0, therefore dew temperature

355.93 K is accepted.

Table 5.4.3: Method to find dew temperature at the top of the column

Component yi = XD K y=KXD ∑Xi = ∑y/K

ACO 0.00215 -0.66217 -0.00143 0.00215

DO 0.49889 -5.66899 -2.82820 0.49889

Acetic Acid 0.49896 -4.53711 -2.26382 0.49896

TOTAL 1.00000 1.00000

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5.4.6.4.2 Bubble Point (Bottom Column)


Operating Pressure = 12 kPa

Based on equation 5.4.6 for bubble point, ii xk value should close to 1.0. This is trial and

error method as ii xk value is not 1 at temperature 541.21 K. Therefore, using goal and

seek function, the bubble point is at 570.43 K where ii xk value is closed to 1.

Table 5.4.4: Method to find bubble temperature at the bottom of the column

Component Xi=XB K ∑yi = ∑KXi

ACO 0.9961 0.9895 0.9857

DO 0.0010 13.3364 0.0133

Gum 0.0029 0.3342 0.0010

TOTAL 1.0000 1.0000

5.4.6.4.3 Bubble Point for Feed


Operating Pressure = 13.00 kPa

Based on equation 5.4.6 for bubble point, ii xk value should close to 1.0. This is trial and

error method as ii xk value is not 1 at temperature 398.62 K. Therefore, using goal and

seek function, the bubble point at feed is 450.70 K.

Table 5.4.5: Method to find bubble temperature of the feed

Component Xi=XF K ∑yi = ∑KXi

ACO 0.60744 0.06758 0.04105

DO 0.19570 2.72792 0.53385

Acetic Acid 0.19512 2.17852 0.42506

Gum 0.00175 0.02292 0.00004

TOTAL 1.00000 1.00000

5-125

5.4.6.5 Step 5: Calculate minimum theoretical stages using Fenske equation

Minimum number of stages is calculated using Equation 5.4.8:

Nm = avg

BD x

)25.497log(

)11^1008.5/9961.0()00215.0/49896.0log(

Nm = 5 stages

5.4.6.6 Step 6: Estimation of Minimum Reflux Ratio

By using Underwood method (equation 5.4.10) to estimate minimum reflux, q = 1.

qx

i

fii1

,

i

fii x ,=1 – 1 = 0

Table 5.4.6: minimum reflux ratio base on q value

θ

Component Xif αi αi Xif 2.51

ACO 0.60744 1.0000 0.6074 -0.4013

DO 0.19570 53.4400 10.4581 0.2054

Acetic Acid 0.19512 497.2576 97.0224 0.1961

Gum 0.00175 0.5199 0.0009 -0.0005

Total 0.0003

This is trial and error method, so, the value of = 2.51 which is close to 0.

Therefore for the equation 5.9:

i

,ixi d = Rm + 1, Rm +1 can be determine using θ= 2.51.

Table 5.4.7 shows the summary calculation to determine Rm +1 and also based on mole

fraction and relative volatilities at top tray.

5-126

Table 5.4.7: Summary calculation for the equation to determine Rm +1

Component Xid αi αi Xid αi-θ αi Xid / αi-θ

ACO 0.00215 1.000 0.00215 -1.51362 -0.0014

DO 0.49889 53.440 26.66069 50.92640 0.5235

Acetic Acid 0.49896 497.258 248.11020 494.74394 0.5015

Total 1.0236

Rm + 1 = 1.0236

Therefore, the minimum reflux ratio, Rm = 0.0236

1R

R

m

m

= 0.0230

For specimen calculation, for R=2,

R+1 = 3

R/(R+1)= 0.67

Figure 5.4.8: Erbar-Maddox correlation (Sinnott, 2005)

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Figure 5.4.8 is a Erbar-Maddox correlation. From Erbar- Maddox correlation, value Nm/N can

be determined. Therefore,

N

Nm = 0.20

Nm/N = 0.20

N =23stages

However, iteration needs to be performed to obtain optimum reflux ratio. For other reflux

ratio, the summary is in table 5.4.8:

Table 5.4.8: Reflux ratio

R 2 3 4 5 6

Nm/N 0.2 0.25 0.28 0.35 0.42

N 23 18.776 16.764 14.412 11.176

Deviation 4.6940 2.0117 3.3529 2.2353

Table 5.4.8 shows iteration between reflux ratio and stages in order to determine optimum

reflux ratio. Value for Nm/N is from figure 5.4.8. The optimum reflux ratio is near this value

which is 5. Therefore, the required number of stages is 14 stages.

5.4.6.7 Step 7: Determination of Column Efficiency using O’Connell’s correlation

At average temperature,

T avg = (5.4.32)

=

= 448.57 K

Then, log μ is obtained from equation 5.4.33,

log μ = μAx (5.4.33)

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Table 5.4.9: Viscosity data

Component Vis A Vis B log μ Viscosity mol frac

ACO 0.428231 -

0.448606 0.955536 9.026849 0.607436

DO 0.017500 -

0.424580 0.041256 1.099654 0.195698

Acetic Acid -0.011000 -

0.450630 -0.024435 0.945290 0.195115

Gum -0.039509 -

0.636560 -0.062154 0.866654 0.001752

Using equation 5.4.33, viscosity at average temperature for each component can be

determined as summarize in table 5.4.9 above. Therefore,

Molar average viscosity of feed , μavg = 0.607436 (9.026849) + 0.195698 (1.099654) +

0.195115(0.945290) + 0.001752 (0.866654)

= 5.8844 mNs/m2

Therefore, from equation 5.4.11, column efficiency,

E0 = 51 – 32.5 log (μa αa)

From previous, αa= 497.26

Hence the column efficiency, Eo = 51 – 32.5 log (5.8844 x 497.26)

= 61.65 %

5.4.6.8 Step 8: Determination of number of stages using Lewis Matheson method

Constant molar overflow is assumed and the material balance and equilibrium

relationship equations are solved stage by stage starting at the top and bottom of the

column. The procedure is to start the calculation at the top and bottom of the column and

proceed toward the feed point. The initial estimates of the component distributions in the

products are then revised and the calculations repeated until the iteration stop when ratio of

Light key/ Heavy key at top down and bottom up is close to ratio of light key / heavy key at

feed. Table 5.4.10 to 5.4.12 shows summarization of top down, bottom up and results

obtained after iteration performed. Summarize table for stage by stage is shown in Appendix

A4.

5-129

Top down Equation:

Table 5.4.10: Summary of top-down calculation

Lo 616.31 kmol/ hr

D 123.26 kmol/ hr

R 5

V1 739.57 kmol/ hr

Lo/V1 0.83

From equation 5.4.13:

y2 = 0.83 (x1-xo) + y1

Bottom up Equation:

Table 5.4.11: Summary of bottom-up calculation

V’ = Vo 739.57 kmol/ hr

F 315.21 kmol/ hr

L’ = Lo+F 931.52 kmol/ hr

B 191.95 kmol/ hr

B / L’ 0.206

V’ / L’ 0.794


XB1= 0.794 yB + 0.206 xB

5-130

Table 5.4.12: Results after Iteration

Component Composition (Top-down) Composition (Feed) Composition (Bottom-up)

ACO 0.9778 0.9398 7.389E-06

DO 0.0000 0.0049 1.0000

Acetic acid 0.0735 0.0264 7.578E-09

Gum 0.0102 0.0289 1.754E-09

Summary:

1. At Top-down: 3 stages

2. At Bottom-up: 11 stages

3. Feed Tray is at Tray 4

4. Number of ideal stages = Top-down + Bottom-up

= 14 stages

5. Actual stages = Number of ideal stages (5.4.34)

0E

= (14-1) / 0.62

= 21 stages

Therefore, Number of actual stages is 21 stages

6. Feed tray location:

a) From top = (3-0.5) / (0.62)

= 4 trays

b) From bottom= (11-0.5) / (0.62)

=17 trays

Therefore, feed tray is on the 4th Tray.

5-131

5.4.6.9 Step 9: Calculation for density and relative molar mass (RMM)

Table 5.4.13: Properties of components at feed, distillate and bottom

Component MW feed,Xf distillate,XD Bottom, XB Liquid density (kg/m3)

ACO 256.43 0.60744 0.00215 0.99612 881.58

DO 196.38 0.19570 0.49889 0.00100 774.10

Acetic Acid 60.05 0.19512 0.49896 5.0774E-11 1051.50

Gum 392.73 0.00175 7.7961E-07 0.00288 804.59

Table 5.4.13 shows properties of component at feed, distillate and bottom. The properties

are then used to calculate relative molar mass and density at top and bottom product. The

formulas used are listed as below (Sinnott, 2005):

1. Relative molar mass = ∑ MW(X) (5.4.35)

2. Mean liquid density, L = iix (5.4.36)

3. Mean Vapor density, V = STP

OP

OP

STP

STP P

Px

T

Tx

V

MW

(5.4.37)

Calculation for average relative molar mass, RMM :

Using equation 5.4.35,

RMM of Feed = 0.60744 (256.428) + 0.19570 (196.378) + 0.19512 (60.052)

+ 0.00175 (392.730)

= 206.5991 kg / kmol

RMM of Top Product = 2.1522x10-3 (256.428) + 0.4988900 (196.378) +

0.4989571 (60.052)

= 128.49 kg / kmol

RMM of Bottom Product = 0.99612 (256.428) + 0.00100 (196.378) +

2.88x10-3 (392.730)

= 257 kg / kmol

5-132

Calculation for density :

1. Top product

Using equation 5.4.36:

Liquid density, L = iiDx ,

= 2.1522x10-3 (881.5780) + 0.49889 (774.0980) + 0.4989571

(1051.50)

= 912.74 kg / m3


Vapor density, V = STP

OP

OP

STP

STP P

Px

T

Tx

V

MW

= (128.49 / 22.4) kg/m3 (273 / 355.93) K (0.11 / 1.0) bar

= 0.4840 kg / m3

2. Bottom product


Liquid density, L = iiBx ,

= 0.99612 (881.5780) + 0.00100 (774.098) + 2.88x10-3

(804.593)

= 881 kg / m3


Vapor density, V = STP

OP

OP

STP

STP P

Px

T

Tx

V

MW

= (257/ 22.4) kg/m3 (273 / 541.21) K (0.12 / 1.0) bar

= 2.7269 kg / m3

5-133

5.4.6.10 Step 10: Flow rate Calculation

The liquid and vapor mass flow rate above and below feed point is calculated and then used

to obtain Liquid-vapor flow factor, FLV.

Above the feed point:

1. liquid mass flow rate,Lm = D(R+1)

= [(315.21 kmol/hr x 206.60 kg/kmol)/3600 s] x 3

= 13.20 kg/s

2. Vapor mass flow rate,Vm = Lm + D

= 13.20 + 4.3993

= 17.60 kg/s

Below the feed point:

1. Liquid mass flow rate,Ln = F + Lm

= 18.09 + 13.20

= 31.29 kg/ s

2. Vapor mass flow rate, Vm = Ln – W

= 31.29 – 13.69

= 17.60 kg/ s

5-134

Table 5.4.14 below shows summary of physical properties at distillate and bottom

product.

Table 5.4.14: Physical properties at distillate and bottom product

Distillate product Bottom product

Temperature (K) 355.93 541.21

ρL, kg/m3 912.74 881

ρV, kg/m3 0.4840 2.7269

Liquid flowrate (kg/s) 13.20 31.29

Vapor flow rate (kg/s) 17.60 17.60

5.4.6.11 Step 11: Calculation of Column Diameter

This step is to determine the diameter of the column. Procedure in Column diameter

calculation is:

1. Determination of Liquid-vapor flow factor,FLV to get K1 value

2. Based on K1 value, flooding velocity can be obtained

3. Finding maximum volumetric flow rate, Q. From this, net area required, An are

estimated

4. Column cross area sectional, As are determined

5. Then, column diameter can be obtained

The Liquid-vapor flow factor, FLV at top product can be obtained from equation 5.4.15:

FLv =

5.0

L

V

Vw

Lw

= 0.0172

5-135

The Liquid-vapor flow factor, FLV at bottom product can be obtained from equation 5.4.15:

FLv =

5.0

L

V

Vw

Lw

= 0.10

Take plate spacing as 0. 50 m, from figure 5.4.9 below (Sinnott, 2005), value for k1 can be

obtained.

Figure 5.4.9: Flooding velocity, sieve plates

Hence, from figure 5.4.9 value of K1 for top and bottom are:

Top k1 = 0.09

Bottom k1 = 0.07

5-136

Correction for surface tension:

k1 = ( / 0.02)0.2 (5.4.38)

which liquid surface tension is 0.02 N/m (Sinnott, 2005).

Value of surface tension, at top is 0.03117 N/m and 0.0268 N/m at bottom. Surface tension

is obtained as calculation in Appendix A4. Hence:

1. = 0.098

2. = 0.075

Using equation 5.4.16, Flooding velocity,Uf:

Therefore, for top and bottom pruduct, flooding velocity are:

1. = 4.2692 m/s

2. = 1.3514 m/s

Design for 85% flooding at maximum flow rate (Sinnott, 2005):

Therefore, Ûv for top column,

= 3.6288 m/s

And for bottom column,

= 1.1487 m/s

5-137

Therefore, Maximum volumetric flow rate at top (Using equation 5.4.39):

Q = V

Vm

(5.4.39)

Q = 4840.0

60.17 = 36.36 m3/s

And maximum volumetric flow rate at bottom (Using equation 5.4.40):

Q = V

Vn

(5.4.40)

Q = 7269.2

60.17 = 6.45m3/s

In order to calculate the column diameter, an estimate of the net area is required:

Net area required, An = Q / (5.4.41)

Using equation 5.4.41, for the top column:

An = 6288.3

36.36= 10.02 m2

and for the bottom column:

An = 1487.1

45.6 = 5.62 m2

5-138

Column cross area sectional, As

Take down comer area as 12% of total net area, An (Sinnott, 2005).

The column cross area sectional, As for top column,

As = 88.0

nA =

88.0

02.10 = 11.39 m2

The column cross area sectional, As for bottom column,

As = 88.0

nA =

88.0

62.5

= 6.38 m2

Column diameter,Dc

Column diameter for the top column:

Dc =

5.04

sxA

=

5.039.114

x = 3.807 m

Column diameter for the bottom column:

Dc =

5.04

sxA

=

5.038.64

x= 2.8511 m

5.4.6.12 Step 12: Provisional Plate Design

For plate design, down comer area, active area, holes area, hole size and weir height are

calculated first. The equation involve for calculation are shown below (Sinnott, 2005):

(5.4.42)

Downcomer area: Ad = 12% x AC (5.4.43)

Active area: Aa = Ac – 2 Ad (5.4.44)

Hole area, take design 10% of active area: 10% x Aa (5.4.45)

Weir length: lW = DC x (LW/ DC) (5.4.46)

5-139

5.4.6.12.1 Column Area, Ac

Column area is calculated using equation 5.4.42,

Column Area, Ac=4

2D

= π (2.8511)2 / 4

= 6.38 m2

5.4.6.12.2 Down-comer area, Ad

Take downcomer area as 12% of total. From equation 5.4.43

Ad = 12% x AC

= 0.12 x 6.38

=0.766 m2

5.4.6.12.3 Net area,An

An = Ac – Ad

= 6.38 - 0.766

= 5.614 m2

5.4.6.12.4 Active Area, Aa

Active area is calculated by using equation 5.4.44

Aa = Ac-2Ad

= 6.38 - 2(0.766)

= 4.851 m2

5-140

5.4.6.12.5 Hole area, Ah

Using equation 5.4.45, take 10% of active area, Aa (Sinnott, 2005):

Ah = 10% x Aa

=0.1 x 4.851

= 0.4851 m2

Figure 5.4.10: Relation between downcomer area and weir length

(Ad / Ac) x 100% = (0.766/6.38) = 12 %

From the figure 5.4.10, Iw / Dc = 0.77

From equation 5.4.46, weir length,

Iw = 0.77 x 2.8511

= 2.195 m

5-141

Table 5.4.15 shows the summary for Provisional Plate Design.

Table 5.4.15: Summary of Provisional Plate Design

Column diameter,Dc 2.8511 m

Column area,Ac 6.38 m2

Downcomer area,Ad 0.766 m2

Net area,An 5.62 m2

Active area ,Aa 4.85 m2

hole area, Ah 0.485 m2

Weir length,Iw 2.195 m

5.4.6.13 Step 13: Check Weeping

Take this values as suggested in Chemical Engineering Design volume 6,

Weir height, Hw = 50mm

Hole diameter,dh = 5mm

Plate thickness = 5mm

Maximum liquid rate, Lw = Ln = 31.29 kg/s

Minimum liquid rate at 70% turn down (Sinnott, 2005),

Lw = 0.7 x 31.29

= 21.90 kg/s

5-142

5.4.6.14 Step 14: Weir Liquid Crest

From equation 5.4.17, Maximum Weir Liquid Crest:

How =

3/2

750

w

w

LxI

L

=

3/2

195.2881

29.31750

X= 47.31 mm liquid

and Minimum weir liquid crest:

How =

3/2

750

w

w

LxI

L

=

3/2

195.2881

90.21750

X= 37.25 mm liquid

At minimum rate,

Clear liquid depth, Hw + How = 50 + 37.25 = 87.25 mm

Therefore, from figure 5.4.11, K2 = 30.8

Figure 5.4.11: Weep point Correlation (Eduljee, 1959)

5-143

5.4.6.15 Step 15: Weep Point

The vapor velocity at the weep point is calculated Using equation 5.4.18,

Minimum vapor velocity through the holes based on the holes area,Uh:

Uh = 5.02

)(

)4.25(9.0

v

dhk

= 5.0)7269.2(

)0.54.25(9.08.30

= 7.53 m/s

5.4.6.16 Step 16: Plate Pressure Drop

Figure 5.4.12: Relation between per cent perforated area with orifice (Sinnott, 2005)

5-144

For plate thickness/hole diameter = 5/5 =1

Percent perforated area = (Ah / Aa) x 100 = (0.485/ 4.85) x 100 = 10

Therefore, from the figure 5.4.12, Co = 0.84

Maximum vapor velocity through holes, Uh max = hA

Q (5.4.47)

Therefore, Uh max = 6.45 / 0.485

= 13.30 m/s

Dry plate drop, hd


hd =

L

v

C

U

o

h

2

51

=

881

7266.2

84.0

30.1351

2

= 39.57 mm liquid

Residual Head, hr


Residual head,hr =

L

3105.12

=

881

105.12 3

=14.20 mm liquid


Pressure drop per plate,hT = hd +( hw + how ) + hr

= 39.57 + 87.25 + 14.20

= 141 mm liquid

5-145

5.4.6.17 Step 17: Downcomer Liquid Back Up

The height of the bottom edge of the apron above the plate,Hap


The height of the bottom edge of the apron above the plate,Hap

= Hw - 10

= 50 – 10

= 40 mm

= 0.04 m

Area under apron, Aap


Area under apron, Aap = hap x Iw

= 0.04 x 2.195

= 0.0878 m2

Since it is less than dA which is 0.766m2, thus it can be used to calculate the head loss in

down comer

Head loss in down comer,hdc


Head loss by Cicalese et al (1947),

hdC =

2

166

ap

w

LxA

L

=

2

0878.0881

29.31166

x

= 27.14 mm

Using equation 5.4.26,

Back up in the downcomer,hb = hw + how + hT + hdc

= 87.25 + 141 + 27.14

= 255.39 mm liquid

= 0.255 m

5-146

Rule: hb < ½ (plate spacing + weir height)

0.26 < 0.28

So tray spacing is acceptable

Downcomer Residence Time, tr

From equation 5.4.27, Downcomer Residence Time, tr:

= 5.51 s

Therefore, tr is greater than 3.0 s which is recommended. So tr is satisfactory

5.4.6.18 Step 18:Check Entrainment by Fair

Uv= nA

Q =

62.5

453.6 = 1.149 m/s

From equation 5.4.28,

Flooding percentage = F

V

u

U %100=

351.1

%100149.1 = 85 %

5-147

From Figure 5.4.13, Value = 0.035. Value is below 0.1 so the column diameter proposed

earlier is acceptable (Sinnott, 2005).

Figure 5.4.13: Entrainment correlation for sieve plates (Fair, 1961)

5-148

5.4.6.19 Step 19: Perforated Area

Figure 5.4.14: Relation between Lh/Dc vs Lw/Dc

From figure 5.4.14,

At Iw/Dc = 0.77

= 99 0

Angle subtended at plate = 180 – 99 = 81o

Mean length, unperforated edge strips, Ls

Allowing 50 mm perforated strip round plate edge with 50 mm wide calming zone. From

equation (5.4.29):

Mean length,unperforated edge strips ,Ls= (2.851 – 0.05) x x180

81

= 3.960 m

5-149

Area of unperforated edge strips, Aes

= (50 x 10-3) m x Ls

= (50 x 10-3) m x 3.960

= 0.198 m2

Mean length of calming zones


Mean length of calming zones = 2.195 + 0.05

= 2.245 m

Area of calming zone, Au

Area of calming zone, Au = 2 x 0.05 x (mean length of calming zones) (5.4.48)

= 2 x 0.05 x 2.245

= 0.225 m2

Total area available for perforation, Ap


Total area available for perforation, Ap = Active area – (Area of unperforated edge + Area of

calming zones)

= 4.852 - 0.198 - 0.225

= 4.429 m2

5-150

The ratio of Ah / Ap = 0.485/ 4.429 = 0.11

From Figure 5.4.15,

Ip/dh = 2.7

Acceptable because range between 2.5 – 4.0 (Sinnott, 2005)

Figure 4.12: Relation between Ah/ApvsIp/dh

Figure 5.4.15: Relation between Ah/Ap vs Ip/dh

5.4.6.20 Step 20: Number of Holes

Area of one hole,A1 = 4

2

HD =

4

)005.0( 2 = 1.9635 x 10–5 m2

Number of holes = 1A

Ah = 5109635.1

485.0

= 24,700 holes

5-151

5.4.6.21 Step 21: Column Height

Total Column Height = tray spacing x no. of stages

=0.5 x 21

=11 m

Actual height:

= 11 m + 2 m

= 13 m

5-152

Table 5.4.16: Chemical Design Sheet for Distillation Column

Chemical Design Specification Sheet

Item No : T-102

Function: To obtaine higher conversion in reactor 101 and 102

Operating Condition

Operating Temperature (oC)

Feed

Distillate

Bottom

125.47

82.78

268.06

Operating Pressure (kPa)

Feed

Distillate

Bottom

13

11

12

Stream Flow rate (kg/s)

Feed Flow rate 18.09 Distillate flow rate 4.40

Bottom Flow rate 13.69

Column specifications

Design type

Material of construction

Tray

Number of trays

Reflux Ratio

Vertical

Stainless Steel

Sieve trays

21

5

Column Diameter (m)

Column Height (m)

Column cross sectional

area (m2)

tray spacing (m)

2.851

13

6.384

0.5

Sieve plate Design

Plate thickness (mm)

Downcomer area (m2)

Net Area (m2)

Active Area (m2)

5

0.77

5.62

4.85

Hole diameter (mm)

Hole area (m2)

5

0.49

Weep Point Weir Design

Minimun vapor velocity (m/s)

Maximum liquid flowrate (kg/s)

Turn Down

7.53

31.29

70%

Weir length (m)

Weir Height (mm)

Weir liquid crest:

Maximum (mm liquid)

Minimum (mm liquid)

2.20

50

47.31

37.25

5-153

Hole Design Plate pressure Drop

Area of one hole (m2)

Number of holes

1.963 x 10-5

24,711

Total Pressure drop (mm

liquid)

141

Plate layout Downcomer Liquid backup

Angle, θ

Mean length unperforated edge

strips (m)

Area of unperforated edge

strips (m2)

Mean length of calming

zone (m)

Area calming zone (m2)

Area of perforation (m2)

81o

3.96

0.198

2.25

0.22

4.429

Height of liquid backup (m)

Area under apron (m2)

Residence time in

downcomer, tr (s)

0.04

0.0878

5.51

References:

Sinnott, R.K., 2005. Chemical Engineering Design. 4th edition: Vol 6. Coulson &

Richardson’s.

Perry, R.H. and Green, D.W. (1997). “Perry’s Chemical Engineering Handbook.” 7th ed.

USA: McGraw-Hill, Inc

Seader J.D & Henley E. (1998), Separation Process Principles, John Wiley & Sons, New

Jersey.

Documents

CHAPTER 5.T-102(5.4)