Saturday, November 12, 2011

Plate Thickness Calculations for Digesters and Other Pressure Vessels

Hi Friends,

In earlier posts, we have discussed in detail the process design and equipment design calculations for various technological equipment including pressure vessels used in Alumina refineries. I admire your level of stamina and patience in going through such complicated calculations with utmost interest. In present post, we wish to present the design calculations used for estimating the plate thickness of the pressure vessels like Digesters and Flash tanks operative in Alumina refineries. We have carried out sample calculations for Digester vessel installed in medium pressure digestion circuit of Alumina refinery.

As such, many methods and empirical relations have been developed by designers and equipment manufacturers based on their rich experience on the subject. Here, we will discuss the simplified  formula which gives most authentic and reliable results compared to others. Since the plate thickness of pressure vessels is directly proportion to its pressure and diameter and inversely proportion to allowable stress of material of vessel, thus the engineering formula used for thickness calculation can be presented as follows-
                                                                      P x D
                                                  t = -----------
                                                        2 x J x f
Here, P = Design pressure of vessel in kg per cm2,
          D = Diameter of vessel in mm,
          J  = Joint efficiency of welding,
          f  = Maximum permissible stress for material of plate in kg per cm2.
          t  = Plate thickness of vessel in mm.
Welding of pressure vessels are done by duly qualified and certified welders. The welding joint efficiency figures for thickness calculations is taken as per the following norms-
J = 1.00 for class-A type, J = 0.85 for class-B type and  J = 0.50 for class-C type.
The maximum permissible stress for plates of carbon steel as well as stainless steel ranges from 1000 kg/cm2 to 1800 kg/cm2 thus for design calculation purpose, lower value at 1000 kg/cm2 is generally considered. The sample calculations for estimation of plate thickness of Digester vessels are given below for clarity in explanation.

Sample Calculation:
Let us work out the plate thickness for the Digester vessels for Alumina refinery adopting Medium pressure digestion technology. The maximum operating pressure for such Digesters is 7.0 kg per cm2,
Thus design pressure for Digesters, P = 1.20 x 7.0 = 8.40 kg per cm2.
Diameter of Digester = 4.00 meter = 4 x 1000 mm (assumed),
For class-A type welding, Joint efficiency J = 1.00,
Maximum permissible stress of steel plate, f = 1000 kg/cm2,
                                                                                 8.4 x 4.0 x 1000
Thus the plate thickness of Digester vessel, t = ------------------------  = 16.80 mm.
                                                                                  2 x 1.0 x 1000 
Taking the design margin of 15%, 
Plate thickness = 1.15 x 16.80 = 19.32 mm.
Hence, the minimum plate thickness for Digester vessels operative for Medium pressure digestion technology must be 20 mm.

The specifications, drawings and fabrications of pressure vessels are carried out as per the guidelines and standards of American Society of Mechanical Engineers (ASME). Trust, the subject has been elaborated in simplified manner. Please put your views / suggestions / remarks / comments, if any.

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Thanks and regards.

Kunwar Rajendra


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  7. Please provide derivation of formula ..

    1. Please refer Chemical Engineering Handbook by Perry and Chilton.

      Rajendra Kunwar