Diethyl Ether (DEE): Equipments Design

23

CHAPTER 5

EQUIPMENT DESIGN

In this chapter, detailed equipment design and mechanical design of

5.1 Fixed Bed Catalytic Reactor Process Design:

Reaction temperature =250 0 C ( 523K)

Catalyst: γ - alumina

Density of catalyst particle: 1392 kg/m3 [8]

Catalyst porosity: 0.52 [8]

Type of reactor: Shell and tube heat exchanger type in which catalyst is placed inside the

tube.

Reaction is exothermic: It is carried out in isothermal manner. Water is to be circulated in

liquid form on shell side to maintain the isothermal condition.

Mass of catalyst required in commercial scale plant = 6579.711 kg

Superficial velocity of feed gas V=0.802 m/s

Capacity of plant =50000 MTA of diethyl ether (DEE)

Let no. of working days per annum=340 days

Production rate of diethyl ether (DEE) = (50000*1000)/(340*24)

=6127.45 Kg/hr

!""=#$%%&'()*

2

&'()*2 +#1&'()*&,-(%

(5.1) [3]

"./03"4"=#%(567%8%&'()*

&'()*2 +#1&'()*&,-(% +#2&'()*

2 +#9&,-(% 2

Design equation (5.2) [3]

:

;= <

!>

?@ABCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC?DE9B [4]

24

In table 5.1 conversion of ethanol and rate of reaction data is given. Unit of rate of reaction

is mol/(gm catalyst sec)

Table 5.1: rate of reaction and conversion data

r (total) 1/r

Ethanol

conversion

2.77216E-06 360729.1 0

2.24531E-06 445373.6 0.1

1.81423E-06 551197.8 0.2

1.45502E-06 687277 0.3

1.15111E-06 868729.7 0.4

8.90654E-07 1122770 0.5

8.31259E-07 1202994 0.525

4.67523E-07 2138934 0.7

2.9333E-07 3409130 0.8

From the graph (appendix A)

Area= 340000 unit

Weight of catalyst= 6579711 gm

= 6579.711 Kg

Bulk density =0.9333 gm/cc [8]

Volume = 6579.711/9333

= 7.049942 m3

Feed rate = 0.1382 Kmol/sec

= 0.1382 x 43.312

= 5.99 Kg/sec

25

Density = PM/RT

= (1500 x 43.312) / ( 8.314 x 523 )

= 14.94 Kg/m3

Feed rate = 5.99 / 14.94

= 0.401 m3/sec

Superficial velocity = 0.805 m/sec

Total Crosse section area = feed rate / space

= 0.401 / 0.805

= 0.499 m2

MOC of tube = Stainless steel

Tube OD = 0.0508 m

Tube ID = 0.04328 m

Crosse section area of tube = (∏/4) x ID2

= (∏/4) x (0.04328)2

= 0.00147 m2

Total number of tube required

N = Total Crosse section area / Crosse section area of tube

= 0.499/0.00147

= 340

Length of the tube (L) =total volume / (N x Crosse section area of tube)

= 7.05 / (340 x 0.00147)

= 14 m

26

Area = N x ∏ x OD x L

= 340 x ∏ x 0.0508 x 14

= 764.78 m2

Heat duty (Q) = 2445180.91 J/sec

Calculation of fixed bed side film coefficient hi ;

dp = diameter of catalyst

= 0.003 m

Pipe diameter

dt = 0.04328 m

dp/dt = 0.003/0.04328

= 0.06931

(hidt /k) =0.813 e-6dp/dt( dp G/µ) 0.9

Thermal conductivity K = 0.04366 W/mK

Viscosity µ = 1.58235 x 10-5 pa.sec

Mass velocity G = 0.87 Kg/m2sec

On calculation

hi = 416.32637 W/m2K

hi dp/k = 3.6(dpG/µ ε)0.365

on calculation

hi = 49.789923 W/m2K

Take lesser value

hi = 49.789923 W/m2K

27

Calculation of shell side heat transfer, h0

Shell side heat transfer coefficient calculated here [11]

Tube pitch Pt =1.25d0

=1.25 x 0.0508

= 0.0635 m

Type of arrangement = Equilateral triangular

Equivalent diameter de = 1.1/d0 (Pt – 0.907 d02)

= 1.1/0.0508[0.06352 – 0.907*0.0508 2]

= 0.03663 m

Shell side mass flow rate m ;

∆H = m*Cp*∆T

Here coolant used is dowtherm Q because operating temperature is 523 K and dowtherm Q is

stable up to 603 K ( Properties from dowtherm Q product technical data)

Properties of dowtherm Q

Cp = 1811 J/Kg K

Viscosity µ = 1.28 x 10-3 pa.sec

Thermal conductivity K = 0.1156 W/mK

∆T= 60 K

m = 2445180.91/(1811 x 60)

= 22.5 Kg/s

Density = 927.6 Kg/ m3

Circulation rate qv = (22.5/927.6)

= 0.024 m3/sec

28

Shell inside diameter, Ds :

Db =d0 (Nt /K1 )1/n1

K1 = 0.319 and n1 = 2.142

Db = 50.8(340/0.319)1/2.142

= 1.315m

Let clearance between shell internal dia and bundle (Db),

Db = 15 mm

Let Ds= 1.315 + 0.015 m

= 1.330 m

Baffle spacing

Bs= 0.4Ds

= 0.4 x 1.33

= 0.532m

Shell side flow area As = (Pt-d0)DsBs/Pt

= (0.0635-0.0508)/0.0635(1.330 x 0.532)

= 0.1416 m2

Gs = m/As

= 22.5 / 0.1416

= 158.83 kg/m2 sec

Reynolds number,

Re = deGs/µ

= 0.03669 x 158.83 / 0.00128

= 4545.36

Prandlt number,

Pr = Cp µ/K

29

= 1811 x 0.00128 / 0.1156

= 20.05

(h0 de/k)= 0.027 Re0.8Pr0.3

From calculation

h0 = 150.50 W/m2K

Overall heat transfer coefficient U0 ;

1/ U0 =1/h0+1/h0d +d0 ln(d0 /di)/2Kw+d0 l/di hid +d0 l/di hi

=1/150.50 + 1/5000 + {0.0508 ln(0.0508/0.04328)}/(2*16) +

(0.0508/0.04328)*(1/5000) + 0.0508/(0.04328 x 49.78)

U0 = 37.06 W/m2K

Shell side pressure drop

Ps =8 Jf(Ds/de)(L/Bs)(ρsus2/2)

Jf = 0.07 from Jf vs Nre graph [11]

us= Gs/ρs

= 158.83 / 927.6

= 0.171 m/sec

= 8*0.07 x (1.330/0.03663) x (14/0.5323) x ( 985.728 x 0.0692/2)

= 7335.7 Pa

Tube Side pressure drop

Pt =8 Jf(L/di)(ρsus2/2)

Jf = 0.03 from Jf vs Nre graph [11]

=8 x 0.03 x (14/0.04328) x (14.95 x 0.8022)/2

= 0.3760672 KPa

Pressure drop across the bed

Blake – plummer equation

!= "

1.75(1 # $)%&'

$*+,"

P = 18.07 KPa

30

Total tube side pressure drop

Pt = 18.45 KPa

5.1.1 Mechanical Design of reactor

Shell and tube type reactor [6]

(a) Shell side

Material carbon steel - (Corrosion allowance- 3mm)

Number of passes – 1

Fluid – dowtherm Q

Working pressure – 0.3 N/mm2

Design pressure – 0.33 N/mm2

Inlet temperature – 25 0C

Outlet temperature – 85 0C

Segmental baffles (25% cut ) with tie rods and spacers

Maximum allowable stress - 80 N/mm2

Shell thickness; [6]

ts =PD/(2fJ+P)

= 0.33 x 1400/((2 x 80 x 0.85)+0.33) + 3 mm

= 6.38 mm

Nozzle thickness (diameter -75mm)

tn=PD/(2fJ-P)

= 0.33 x 75/( 2 x 80 – 0.33)

= 0.155 mm + 3 mm

= 3.155 mm

Head

Head thickness (th) = PCrW/2fJ

Crown radius = 1400 mm

Knuckle radius = 140 mm

31

W=1/4(3+ (Rc/R1)1/2)

= 1/4(3 + (1400/140)1/2)

= 1.54

th = 0.33 x 1400 x 1.54 / (2 x 0.85 x 80) + 3mm

= 8.23mm

Transverse Baffles

Spacing between baffles= 0.4Ds

= 0.4 x 1.4

= 0.56m

Thickness of baffles = 5mm

Tube Side [6]

Tube and tube sheet material - stainless steel

Number of tubes – 340

Outside diameter – 50.8 mm

Length – 14m

Tube pitch - 0.0635m



Inlet temperature – 2500C

Outlet temperature - 2500C

Permissible stress – 74.5 N/mm2

tf =PD0/(2fJ+P)

= 1.65 x 50.8 / (2 x 74.5 x 0.85 + 1.65)

= 0.65 mm

No corrosion allowance, since the tubes are of stainless steel.

Design of Gasket and Bolt Size [6]

Gasket material – flat metal jacketed, asbestos fill (iron or soft steel)

Gasket factor, m= 3.75

Minimum design stress = 52.4 N/mm2

32

Basic gasket seating width – b 0

Internal dia. Of Gasket – 1400 mm

Do/Di = ((Y-Pm)/(Y-P(m+1)))0.5

= ((52.4 – 0.33 x 3.75)/(52.4 – 0.33 x 4.75))0.5

= 1.0032

Do = 1.4045 m

N = (1.4045-1400)/2 = 0.0022648mm use 35mm

b0 = ½N = 0.0175mm

G= (1.4045+1400)/2

= 1.4022m

Effective Gasket seating width, b= 0.5b01/2

= 2.09 mm

Bolts

Minimum bolt load at atm. Condition, Wm1 = 3.14bGYa

= 3.14 x 2.09 x 1402.2 x 52.4

= 483360.87 N

At operating condition,

Wm2=3.14(2b)GmP+3.14G2P

= 3.14 x 2 x 2.09 x 1402.2 x 3.75 x 0.33 +3.14 x 1402.22 x 0.33

= 532176.24 N

Wm1 < Wm2 so Wm2 is controlling load

Number of bolts = 1402.2/(2.5*10)

= 56

Am2= 532176.24/80 = 6652.203 mm2

33

Diameter of bolts = [(Am2/no. of bolts) x 3.14/4]1/2

= [(6652.203)/56 x (4/3.14)]1/2

=12.29 mm

Bolt area, Ab = 2 x 3.14 x YaGN/fa

= 2 x 3.14 x 52.48 x 1402.2 x 35 / 80

=202204.36 mm2

Pitch of bolts = 4.75*18

= 85.6 mm

Pitch circle dia.= (85.6*56)/3.14

=1526.62mm

Flange Thickness,

K= 1/[0.3+1.5WmhG/HG]

= 1/[0.3 + 1.5 x 532176.24 x 62.52136 /( 509382.1 X 1402.2)]

= 2.7

tf = G(p/kf)1/2+c

= 1402.2 x (0.33/2.7/80) ½ + 3

= 70.62 mm

5.2 Heat exchanger Design

For heat exchanger tube side is waste water and shell side is cooling water is used. Here we

assume over all heat transfer coefficient (U) is 800 W/m2K.In table 5.1 tube side and shell

side fluid inlet, outlet temperature and mass flowrate values given. [11]

Table 5.2: tube side and shell side flowrate and temperature

tube side shell side

flow rate(Kg/sec) 0.6714 6.12

inlet temperature(K) 401 308

outlet temperature(K) 310 318

34

U=800 W/m2K (assumed) [11]

LMTD= [(401-318)-(310-308)/ln((401-318)/(310-308))]

= 21.74 K

Q = 256454.44 J/sec

Q = UA(LMTD)

A=256454.44/(800 x 21.74)

= 14.74 m2

Material of construction (MOC) of tube = Stainless steel

Tube OD = 0.02 m

Tube ID = 0.016 m

Length of tube (L) = 5 m

Area of tube = ∏ x ID x L

= ∏ x (0.04328) x 5

= 0.303 m2

Total number of tube required

N = total area / area of tube

= 14.74/0.303

= 49

Tube side heat transfer coefficient

Cross section area = n x (∏/4) x ID2

= 49 x (∏/4) x (0.016)2

= 0.0098 m2

Velocity (u) = 0.000692/0.0098

= 0.0706 m/sec

35

Density = 969.972 Kg/m3

Viscosity = 0.000345 Pa.sec

hi = 4200(1.35 + 0.02t)u0.8/ID0.2

= 4200 (1.35 + 0.02 x 82.5) (0.0706)0.8/(0.016)0.2

= 3466.1561

Shell side

Water flow rate = 6.12 Kg/sec

Pitch (P) = 1.25 x OD

= 1.25 x 0.02

= 0.025 m

Equivalent diameter de = 1.1/d0 (Pt – 0.907 d02)

= 1.1/0.02[0.0252 – 0.907*0.022]

= 0.0144 m

Shell inside diameter, Ds :

Db =d0 (Nt /K1 )1/n1

K1 = 0.319 and n1 = 2.142

Db = 0.02(49/0.319)1/2.142

= 0.21 m

Let clearance between shell internal dia and bundle (Db),

Db = 15 mm

Let Ds= 0.21 + 0.015 m

= 0.225 m

Baffle spacing

Bs= 0.4Ds

= 0.4 x 0.225 = 0.09 m

36

Shell side flow area As = (Pt-d0)DsBs/Pt

= (0.025-0.02)/0.025(0.225 x 0.09)

= 0.00405 m2

Gs = m/As

= 6.12 / 0.00405

= 1530 kg/m2 s

Reynolds number,

Re = deGs/µ

= 0.0144 x 1530 / 0.000853

= 25815.515

Prandlt number,

Pr = Cp µ/K

= 4184 x 0.000853 / 0.610

= 5.85

(h0 de/k)= 0.023 Re0.8Pr0.3

From calculation

h0 = 5594.0996 W/m2K

Overall heat transfer coefficient U0 ;

1/ U0 =1/h0+1/h0d +d0 ln(d0 /di)/2Kw+d0 l/di hid +d0 l/di hi

=1/5594.0996 + 1/5000 + {0.02 ln(0.02/0.016)}/(2*16) +

(0.02/0.016) x (1/5000) + 0.02/(0.016 x 3466.1561)

U0 = 1648.18 W/m2K

Shell side pressure drop

Ps =8 Jf(Ds/de)(L/Bs)(ρsus2/2)

Jf = 0.03

us= Gs/ρs

= 1530 / 1000

= 1.53 m/sec

= 8 x 0.07 x (0.225/0.0144) x (5/0.09) x (1000 x 1.532/2) = 234.28 KPa

37

Tube Side pressure drop

Pt = (8Jf(L/di) + 2.5)(ρtut2/2)

= ( 8 x 0.008 x (5/0.016) + 2.5)(969.69 x 0.0712 /2)

= 54.99 Pa

5.2.1 Mechanical Design for heat exchanger

Shell and tube type heat exchanger [6]

(a) Shell side

Material carbon steel - (Corrosion allowance- 3mm)

Number of passes – 1

Fluid – water



Inlet temperature – 25 0C

Outlet temperature – 85 0C

Segmental baffles (25% cut ) with tie rods and spacers

Shell thickness;

ts =PD/(2fJ+P)

= 0.44 x 300/((2 x 80 x 0.85)+0.44) + 3 mm

= 3.96 mm

Nozzle thickness (diameter -75mm)

tn=PD/(2fJ-P)

= 0.44 x 75/( 2 x 80 – 0.44)

= 0.21 mm + 3 mm

= 3.21 mm

Head




38

W=1/4(3+ (Rc/R1)1/2)

= 1/4(3 + (300/30)1/2)

= 1.54

th = 0.44 x 300 x 1.54 / (2 x 0.85 x 80) + 3mm

= 4.49 mm

Transverse Baffles

Spacing between baffles= 0.4Ds

= 0.4 x 0.3

= 0.12 m

Thickness of baffles = 5mm

Tube Side

Tube and tube sheet material - stainless steel

Number of tubes – 49

Outside diameter – 20 mm

Length – 5 m

Tube pitch - 0.025 m



Inlet temperature – 1280C

Outlet temperature - 370C

Permissible stress – 74.5 N/mm2

tf =PD0/(2fJ+P)

= 0.55 x 20 / (2 x 74.5 x 0.85 + 0.55)

= 0.086 mm

No corrosion allowance, since the tubes are of stainless steel.

Design of Gasket and Bolt Size [6]

Gasket material – flat metal jacketed, asbestos fill (iron or soft steel)

Gasket factor, m= 3.75

39

Minimum design stress = 52.4 N/mm2

Basic gasket seating width – b 0

Internal dia. Of Gasket – 300 mm

Do/Di = ((Y-Pm)/(Y-P(m+1)))0.5

= ((52.4 – 0.44 x 3.75)/(52.4 – 0.44 x 4.75))0.5

= 1.0043

Do = 301.29 m

N = (301.29 - 300)/2 = 0.502 mm use 35mm

b0 = ½N = 0.0175 m

G= (301.29 + 300)/2

= 300.65 mm

Effective Gasket seating width, b= 0.5b01/2

= 2.09 mm

Bolts

Minimum bolt load at atm. Condition, Wm1 = 3.14bGYa

= 3.14 x 2.09 x 300.65 x 52.4

= 103635.28 N

At operating condition,

Wm2=3.14(2b)GmP+3.14G2P

= 3.14 x 2 x 2.09 x 300.65 x 3.75 x 0.44 +3.14 x 301.652 x 0.44

= 131402.52 N

Wm1 < Wm2 so Wm2 is controlling load

Number of bolts= 300.65/(2.5*10)

= 12

40

Am2= 131402.52/80

= 1642.53 mm2

Diameter of bolts= [(Am2/no. of bolts) x 3.14/4]1/2

= [(1642.53)/12 x (4/3.14)]1/2

=13.19 mm

Bolt area, Ab = 2 x 3.14 x YaGN/fa

= 2 x 3.14 x 52.48 x 300.65 x 35 / 80

= 43350.36 mm2

Pitch of bolts = 4.75*18

= 85.6 mm

Pitch circle dia.= (85.6*12)/3.14

= 327.13 mm

Flange Thickness,

K= 1/[0.3+1.5WmhG/HG]

= 1/[0.3 + 1.5 x 131402.52 x 13.4 /( 31221.65 X 300.65)]

= 1.75

tf = G(p/kf)1/2+c

= 300.65 x (0.44/1.75/80) ½ + 3

= 23.99 mm

Use 24 mm

5.3 Distillation column Design:

Operating pressure at top = 1 atm = 101.325 KPa

Reflux ratio = 3.49

Number of plates = 40

Distillation molar rate D = 0.0327 Kmol/sec

Liquid molar rate L= D x R

= 0.0327 x 3.49

= 0.114 Kmol/sec

41

Vapor molar rate = D x (R + 1)

= 0.0327 x (3.49 + 1)

= 0.1468 Kmol/sec

Vapor density ρv = 3.91 Kg/m3

Liquid density ρl = 653.64 Kg/m3

Vapor and liquid flowrate is given in table 5.2

Table 5.3: vapor and liquid flowrate

vapor liquid

molar flow rate 0.1468 0.1141

mass rate 10.8649 8.4451

vol. rate 2.7750 0.0129

Vload = Q [ρv / (ρl - ρv)]0.5

= 2.77 [ 3.91/(653.64 – 3.91)]0.5

= 0.2154 m3/sec

q = 0.0129 m3/sec

Single pass

Dt = 1.7 m (from graph of Vload and liquid flowrate)

System factor S = 1

Flooding factor = 0.8 ( 80 % flooding)

Flow path length L = 0.75 x Dt / number of pass

= 0.75 x 1.7 / 1

= 1.275 m

C* = 0.125

C = S x C*

= 1 x 0.125

= 0.125

Aamin = [ vapor load + 1.36qL]/ (C x F)

= [ 0.2154 + 1.36 x 0.0129 x 1.275 ]/(0.125 x 0.8) = 2.37 m2

42

U* = 0.170 m/sec

U* = 0.007(ρl - ρv)0.5

= 0.007 x (653.64 – 3.91)

= 0.178 m/sec

U* = 0.008 x (Ts (ρl - ρv)) 0.5

= 0.008 x ( 0.457 (653.64 – 3.91)) 0.5

= 0.137 m/sec

Use smallest value

U* = 0.137 m/sec

u = U* x S

= 0.137 x 1

= 0.137 m/sec

Admin = q/(u x f)

= 0.0129/(0.137 x 0.8)

= 0.1171 m2

Admin < 0.11 x Aa

0.1171 < 0.11 x 0.1171 m2

0.1171 < 0.2607 m2

Admin = 2 x 0.1171

= 0.2342 m2

At = Aamin + 2 Admin

= 2.37 + 2 x 0.2342

= 2.84 m2

Atmin = 1.28 Vload /(0.8 x 0.125)

= 1.28 x 0.2154/ (0.8 x 0.125)

= 2.75 m2

At > Atmin

Take At = 2.84 m2

43

Diameter = (At x 4 / 3.14)0.5

= (2.84 x 4 / 3.14)0.5

= 1.9 m

Ad/(AtN) = 0.2342/(2.84 x 1)

= 0.0823

Weir length

Lw/Dt = 0.657

Lw = 0.657 x 1.9

= 1.25 m

Weir hight

H/ Dt = 0.12

H = 0.12 x 1.9

= 0.228 m

Number of valve units

Assume 120-175 units/ m2 active area

Active area = 2.37 m2

Number of units = 285 to 417 units/plate

Assume

Number of units = 350 units/plate

Holes area = 350/845

= 0.4142 m2

Pressure drop

Tray MOC – MS density = 7700 kg/m3

Thickness of tray = 14 gauge = 0.188cm

Type of valve V4 K1 = 2.73 K2 = 13.6

∆Pdry = 0.135 tn (ρm /ρl) + K1Vn2(ρv /ρl)

= 0.135 (0.188)(7700/653.64) + 2.73 (6.692)(3.91/653.64)

= 1.032 cm liquid

44

∆Pdry = K2Vn2(ρv /ρl)

= 13.6 (6.692)(3.91/653.64)

= 3.65 cm liquid

∆Pt = ∆Pdry + 55.4(q/Lw)0.67 + 0.04hw

= 3.65 + 55.4(0.0129/1.25)0.67 + 0.04 x 50

= 8.44 cm liquid

= 0.076 psi

Hde = 55.4(q/Lw)0.67 + 0.1 hw + (∆Pt + 1.66)( ρl / (ρl - ρv))

= 55.4(0.0129/1.25)0.67 + 0.1 x 50 + (8.44 + 1.66)(653.64/(653.64-3.91))

= 17.96 cm liquid < 0.6 TS

%Flooding = Vload / (0.78ATC)

= 0.2154 / (0.78 x 2.84 x0.125)

= 77.60%

5.3.1 Mechanical design of distillation column

Mechanical design of distillation column including support. [14]

Operating pressure = 101.325 Kpa

Design pressure = 1.1 x 101.325 = 111.45 Kpa = 0.11145 N/mm2

Design temperature = 423 K

MOC = carbon steel

Diameter = 1900 mm

Thickness of the column

tc = PD/(2fJ - P)

= 0.44 x 300/((2 x 80 x 0.85) - 0.44) + 3 mm

= 3.065 mm

But take 8mm

Head

Torispherical head [6]



45


W=1/4(3+ (Rc/R1)1/2)

= 1/4(3 + (1900/190)1/2)

= 1.54

th = 0.11145 x 1900 x 1.54 / (2 x 0.85 x 80) + 3mm

= 5.39 mm

Use 8 mm same as column diameter

Total vessel dead load

!=("!+0.8#$ )%&'

= 1.15 x 3.14 x 1.9 x (19 + 0.8 x 1.9) x 0.008 x 7700 x 9.81

= 119736.89 N

Column support design

Skirt diameter = 1900mm

Stress due to dead load

Fds = W/(D + t)t

= 119736.89/(3.14 x (1900 + t) x t)

Stress due to wind load

Fws = 11071.56/(3.14 x (1900 + t) x t)

Total compressive stess = Fds + Fws

Maximum stress = 0.125Et/D = Fds + Fws

E = 190 N/mm2

By solving this

t = 41.42 mm

So take thickness 45 mm

For this thickness

Fcompressive < Fs

Ftensile < Fs

Engineering

Diethyl Ether (DEE): Equipments Design