In pressure vessel fresh feed is mixed with recycled stream. In pressure vessel pressure is maintained in such a way that feed remains in liquid form.
Assuming pressure in tank = 16 atm
Fluid to be handled = 129286 kg/hr
Temperature of this fluid = 128 oC
At this temperature
ρEO = 696 kg/m3
ρWater = 921 kg/m3
volumetric flow rate of water = 107400./921
= 116.65 m3/hr
EO = 21885.6/696
= 31.44 m3/hr
So total vol. flow rate of fluid = Vo = 116.65 + 31.44
= 148 m3/hr
Suppose of residence time = 10 min = 0.166 hr
Residence time = volume of vessel/volumetric flow rate of fluid
Volume of vessel = τ * Vo
= 10/60 * 148
= 24.66 m3
Assume pressure vessel = 75 % full.
Total volume of vessel = V/.75
= 24.66/.75
= 33 m3
Suppose L/D = 2.5
L = 2.5 D
Volume of vessel = V = (π/4)*D2L
Putting the value of L in above equation, we get
D = 2.56 m
L = 6.40 m
5.2: MECHANICAL Design of Pressure Vessel
Material of Construction:
Most suitable material of construction is mild steel
Corrosion Allowance:
Corrosion allowance is taken as 2 mm as a first estimate for designing purpose.
Design Pressure:
For pressure vessel Design pressure = 10 % above operating pressure
So design pressure = 1.1 *16
= 17.6 atm
= 1783.2 kPa
Design Temperature:
Design Temperature = 127 oC
Design Stress:
Design Stress is taken as the maximum stress of the material at design temperature.
Design stress at temperature = 127 oC
f = 120 N/mm2
Design of Cylindrical Section
Thickness of shell = 1783.3*2.56/(2*0.85*120)-1783.3*10-3
= 11.24 mm
For purpose of safety we assume efficiency of joints = 0.85
e = 22.57 mm
Adding corrosion allowance = 2 mm
Wall thickness = 24.5 mm
Design of Domed Head
Three types of domed heads are used which are given below
Among these three heads upto 15 bars most expensive heads are torispherical heads.
So we have selected torispherical head.
Head thickness = (Pi * Rc * Cs)/2f J+Pi(Cs-0.2)
Cs = stress concentration factor
Rc = crown radius Rk = knuckle radius
Rk / Rc 0.06 Rc Di
Rk/Rc = 0.06 Rc = Di = 2.56 m
Rk = 0.06 * 2.56
= 0.1536
Cs = stress concentration factor= 0.25 * [3+(2.56/0.1536)1/2]
= 1.77 mm
e = 1783.32*1.77*2.56/(2*.85*120) + 1783.2*10-3 (1.77-.2)
= 39 mm
WEIGHT OF VESSEL
Wv = 240 * Cv * Dm (Hv + 0.8 Dm) t
Cv = 1.08 for vessel
Hv = Height of vessel = 6.40 m
g = 9.81 m/sec2
t = wall thickness = 13.25 * 10-3 m
Dm = mean vessel diameter = (Di + t * 10-3) m
Dm = (2.56 + 24.5 * 10-3)
= 2.57325 m
Wv = 74753 N
Fluid Weight
Wf = 129324 * 10/60 = 21554 kg = 21554 * 9.8
= 211229 N
FITTINGS,PLATEFORMS WEIGHT
= 360 + 150 + (1.7 * 1000) * (1.2*1000)
= 33418 N
Total Weights = 9260 + 211229 + 33418
= 300444.28 N
PRIMARY STRESSES
a) Longitudinal and circumferential stresses due to pressure
δn = PD1/2t = 1.7832 * 2.56 * 103 / (2 * 24.55)
= 86 N/mm2
δL = PDi/4t = 1.7832 * 2.56 * 103 / (4*24.55)
= 43 N/mm2
b) The direct stress due to weight of vessel
δw = W / π(Di + t) * t
= 300444 / π (2.56 *103 + 13.25) * 24.55
= 2.756 N/mm2
c) Bending Stresses
WIND LOADS
Mx = wx2/2
Assume wind pressure = 1280 N/m2
Dm = 2.57325 m
Loading per linear meter = 1280 * 2.57325
= 3294 N/m
Bending moment at bottom = Mx = 3294/2 * 6.42
= 67456 Nm
BENDING STRESSES
δb = ± M / Iv (Di/2 + t)
Iv = second moment of area
Iv = π / 64 (Do4 – Di4)
Do = 2586.5 mm
Di = 2560 mm
Iv = π / 64 ((2586.5)4 – (2560)4)
= 8.866 * 1010
δb = {67456 Nm / 8.866 * 1010}* (2560/2 + 13.25) * 103 mm/1m
= ± 0.984 N/mm2
d) Torsional Shear Stresses
τ = I/Ip (Di/2 + t)
For preliminary vessel design. These are neglected.
PRINCIPAL STRESSES
δ1 = ½[ δn + δz + {(δn – δz)2 + 4 τ2}1/2]
δw = -ive (compressive)
δz = δL + δw ± δb
= 86 – 2.756 + 0.984
= 84 N/mm2
δ1 = ½ [86 + 84 + {(86-84)2 + 0}1/2]
= 86 N/mm2
δ2 = ½[ δn + δz - {(δn – δz)2 + 4 τ2}1/2]
= 84 N/mm2
δ3 = 0.5 P (-ive compressive)
As δb is very small, so for both downwind and upwind δz will be nearly equal.
As there is no torsional stresses τ = 0, so principal stresses will be only δz and δn .
δ3 = -0.5 * 0.892 = -0.446 N/mm2
Stresses in a cylindrical shell under combined loading
ALLOWABLE STRESS INTENSITY
δ1 – δ2 = 86-84 = 2 N/mm2
δ1 – δ3 = 86 – (-0.446) = 86.446 N/mm2
δ2 – δ3 = 84 – (-0.446) = 84.446 N/mm2
Maximum Stress Intensity = δ1 – δ3 = 86.446 N/mm2
Design Stress = f = 120 N/mm2
Maximum Stress Intensity < Design Stress
CHECK ELASTIC STABILITY (BUBLING)
Critical Bubling Stress = δc = 2 * 104 (t/Do)
δc = 2 * 104 (13.25/2586.5)
= 102 N/mm2
Maximum Compressive Stress is well below critical bubling stress, so design is satisfactory.
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