Design Procedure with Relevant Equations for Tall Distillation Column with varying Thickness

Design Procedure with Relevant Equations for Tall Distillation Column with varying Thickness

1)   Column Shell Thickness ( ts ) :- The maximum thickness is at the top of the shell end and is determined only on the basis of  Circumferential Stresses.

                               ts  = (PDi / 2fJ – P) + c

Here , ts  = Shell Thickness (unit - mm)

P = Design Pressure

Di  = Inner diameter of shell

f = Allowable stress of shell material

J = Joint Efficiency = 1(for distillation column)

c = Corrosion Allowance

Note :- All stresses are in N/mm²

2)   Axial Stress Due to Pressure (fap) :-

                       

                                   fap  = PDi / 4 ( ts - c)

Here , P = Design Pressure

Di  = Inner diameter of shell

ts  = Shell Thickness that calculated above

c = Corrosion Allowance

Axial Stress Due to Pressure is the same throughout the column height.

3)   Stresses due to Dead Loads :-

A)  Compressive stress due to weight of shell at height  ‘X’ :-

fds = Weight of shell / Cross section of shell

      =  π/4 (DO ² - Di ²) ρshell  X

           π/4 (DO ² - Di ²)

Here,

Outer diameter of shell (DO)= Di  + 2 ts

ρshell  = Density of shell material

X = Height of column under consideration

B)  Compressive stress due to weight of Insulation at height  ‘X’ :-

fdins  = π Dins  tins ρins X

                 π Dm ( ts - c)

          = Weight of insulation per unit height X

                               π Dm ( ts - c)

Here, Dins = Diameter of Insulation

 tins = Thickness of insulation

 ρins = Density of insulation

 Dm = Mean diameter of shell= (DO  + Di )/2

C)  Compressive stress due to weight of liquid in the column up to a height  ‘X’ :-

fd(liq) = ∑ Weight of liquid per unit height X

                                π Dm ( ts - c)

Here,

Weight in terms of height X is given by

= (X / tray spacing ) π/4 Di ² x Weight of liquid,tray etc.

D) Compressive stress due to weight of attachments such as internals, tophead, platforms and ladder up to a height  ‘X’ :-

fd(att) = ∑ Weight of attachments per unit height X

                                π Dm ( ts - c)

Here,

fd(att) = Weight of head + (Weight of attachments x (X))

                                     π Dm ( ts - c)        

 

E)   Total Compressive Dead Weight stress (fdx ) :-

fdx  = fds + fdins + fd(liq) + fd(att)

   
      4)   Stress due to wind load at a distance X :-

         
      fwx = Mw / Z

Here, Z = Modules of Section for the area of shell

              = π/4 DO ²  ( ts - c) 

Mw  = Bending moment due to wind load at a distance X

       = Wind load x Distance / 2

= 0.7 Pw DO X²  / 2

Here, Pw = Wind Pressure

fwx = 1.4 Pw  X²  / π Do ( ts - c)        

     
       5)   Determination of Height (X) :-

    
         fwx  + fap - fdx  = ft(max)

Here, ft(max) = Permissible Tensile Stress of shell material

If Joint Efficiency J is to be considered,then,

fwx  + fap - fdx  - fall  x J = 0

The above equation can be stated in the form of quadratic equation,  a X² + b X + c = 0 , from which we can find the value of X.

         6)   Stress due to Eccentricity load (fe) :-

              
         fe = We X e / π/4 DO ²  ( ts - c) 

Here, We  = Summation of Eccentric load

 e = Eccentricity

         7)   Stress due to Seismic load (fsx) :-

          
       fsx = Msx / π/4 DO ²  ( ts - c) 

Where,

Msx  = Bending Moment at X

        = 4SWX²   (3H - X / H²)

S – Semismic coefficient

W – Total weight of column

H – Total height of column