Monday 11 April 2011

PRESSURE VESSEL DESIGN


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/mm

 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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