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Calculation of Icremental Volumes in Storage Tanks
2

Calculation of Icremental Volumes in Storage Tanks

Calculation of Icremental Volumes in Storage Tanks

(OP)
Hi,
I need some help with the following problem:

Given Data

StorageTank(Shell Height=59'-4")and(E=29,000000psi)and the fluid to be stored is Oil.
The Shell Body is divided in 6 Rings.(Butt Welded)..
The first ring has 117.25 inches, and the other 5 Rings have the same width (118.25 inches).
The inside diameter at the bottom of the Tank is 168'-6". There is also a Bottom Crown of 8 and 7/16 inches.

Requested: To calculate the incremental volumes per 1/16 inches in the body of the shell tank.
Regards,

OnePoint

RE: Calculation of Icremental Volumes in Storage Tanks

It depends on what you need it for.

We occasionally have customers who want a capacity table (usually not in 1/16" increments) just for informational purposes.  In those cases, we make up a table on spreadsheet, based on tank dimensions only.  Just cross sectional area times 1/16" times appropriate gallon/feet/inch conversions.

If a certified gauge table is needed, you're looking at something more complicated- check with the people that strap tanks.  I think API publishes one or more standards on appropriate procedures.  I don't know to what extent they go in preparation of these tables.  You could do an elastic shell design and calculate changes in volume due to shell movement, etc.

RE: Calculation of Icremental Volumes in Storage Tanks

Well, if you're looking to evaluate volume to that kind of accuracy, I can just about guarantee that you cannot achieve such accuracy. Based on a 0.0625" change in a 712" high tank, you are looking for an accuracy of roughly 0.01%. Nothing in the real world of tank farms is anywhere close to accurate to 0.01%. As JStephen pointed out in his post, are you expecting to incorporate the change in diameter as the tank strain changes due to changes in the head pressure as the liquid level changes? Don't forget to include shell rotation at the bottom shell to floor seam! How about volumetric expansion/contraction in a 24 hour cycle with a hot day and clear, cool night? How about accounting for the increase in volume as the shell corrodes? How accurate is the as built diameter compared to the drawings?

I'd say the premise of the request for measurements to that kind of accuracy needs to be re-evaluated.

jt

RE: Calculation of Icremental Volumes in Storage Tanks

(OP)
Hi JStephen and jte,
Thanks for your answers.I was asked by my superviser to solve this problem a few days ago. I am quite new in this area of expertise. I have managed so far to do some calculations. I am not sure if I am on the right track.The following is what I have considered. There is also a crown at the bottom of the tank. The height of this crown is 8.43 inches. That crown is within the first ring(117.75 width inches).
How should I extract the volume of the crownn(cone-like shape)?
I would appreciate some suggestions.

Best regards,

OnePoint

________________________________________________________
Given Data

Oil storage tank(Butt Welded Model)
Material(Elasticity modulus: 29X106 psi)
Liquid in tank: Oil, S.G. = 0.86

Shell height: 59’ – 4” = 712”
Inside radius (for ring 1) = 84’ – 3” = 1011”
Bottom crown = 8.4375”
6 rings, heights and thickness as follows:

Ring no    Ring width (in)    Thickness (in)
1    117.75    1.233
2    118.25    0.977
3    118.25    0.784
4    118.25    0.590
5    118.25    0.396
6    118.25    0.313

1. Inside radii are calculated for all the rings, using the inside radius for Ring 1 and plate thicknesses of each Ring, as follows:

Outside radius, Ring 1 =  inside radius1 + plate thichness1 = 1011” + 1.233” = 1012.233”

Assumption: outside diameter for tank is constant.

For rings 2 – 6,  inside radius = outside radius – plate thickness

e.g. Ring 2, IR2 = 1012.233”- 0.977” = 1011.256”

2. The inside(underformed/unstressed) circumferences are calculated below,


Ring1 : C1 = 2 x 3.141592483x1011.000”=6352.300” (529.358’)

Ring2: C2 = 2 x 3.141592483x1011.256”= 6353.909” (529.492’)

Calculations for inside radii and inside ring circumferences are summarized in table below:

Ring no    Thickness (in)    Outside radius (in)    Inside radius (in)    Circumference (in)    C (ft)
1    1.233    1012.233    1011.000    6352.300    529.358
2    0.977    1012.233    1011.256    6353.909    529.492
3    0.784    1012.233    1011.449    6355.121    529.593
4    0.590    1012.233    1011.643    6356.340    529.695
5    0.396    1012.233    1011.837    6357.559    529.797
6    0.313    1012.233    1011.921    6358.084    529.840
3. Incremental volumes per course are calculated for each ring.

The fully stressed circumferences are: C’=C+ ? C

Formula for liquid head stress (correction in feet) using the empty tank circumference(s):
 
 Delta(C)=WxHxC(squered)/12x2x3.141xExT
where:

W = weight of oil, p/ft3
H = height of liquid above ring, ft
C = inside circumference for empty rings, ft
E = modulus of elasticity for steel, psi
T=  thickness of the rings

For simplification, a constant K, is taken as:

 K=62.3/24x3.141xE  
E = 29X106 psi, therefore K = 2.84924 X10-8

Then Delta(C)=Kx(SGxHxsqueredC)/T
Calculations for the circumference corrections (?C) and the fully stressed circumferences (C’) are included in the table below:

Ring no    C (ft)    ? C (ft)    C’ (ft)
1    529.358    0.055    529.413
2    529.492    0.069    529.562
3    529.593    0.086    529.680
4    529.695    0.115    529.810
5    529.797    0.171    529.968
6    529.840    0.217    530.057
            
The formula for the incremental volume per inch (barrels/inch), using the fully stressed circumference, for each of the rings:
 The stressed(Corrected) circumference is C'= 2x3.1415xR'and  A'=3.141xR'xR'

Therefore R'=C'/2PI    

Inc.Vol. = PI(C'x12/2PI)x(C'x12/2PI)x1/F (inches),
Where correction factor for barrels, F=9702

Results for incremental volumes are attached below:

Ring no    Inc. Vol., in barrels/in
1    331.040
2    331.226
3    331.374
4    331.537
5    331.734
6    331.846

Average fully stressed circumference = 529.748’
Average fully stressed diameter = 168.624’

4. Uncorrected incremental volumes (using unstressed circumferences)
   Uncorrected Volume=
Ring no    C (ft)    Barrels/in
1    529.358    330.972
2    529.492    331.139
3    529.593    331.266
4    529.695    331.393
5    529.797    331.520
6    529.840    331.575

    
The incremental volumes for 1/16” increments:

Ring no    Volume, no correction, barrels/in    Corrected  volume,barrels/in    ?V ,barrels per1/16” increments
1    330.972    331.040    0.0043
2    331.139    331.226    0.0054
3    331.266    331.374    0.0068
4    331.393    331.537    0.0090
5    331.520    331.734    0.0134
6    331.575    331.846    0.0170


RE: Calculation of Icremental Volumes in Storage Tanks

If you don't have accurate measurements for the tank, there's not a lot of point in going into that much detail in the calculations.

Shell plates can be stacked flush inside, flush outside, or aligned on centerline.  Just depends on who did it.

The crown in the floor is intended partly to accommodate settlement.  A tank usually settles more in the center than at the shell.  So the crown may or may not be there, or may be reduced, once the tank is in service.

If you don't have an actual survey of the tank showing floor profile, exact circumference, etc., just assume a plates are stacked flush inside, ignore shell movement, and you've got a simple spreadsheet to whip up.

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