6 replies to this topic

[Dacs]

I've been developing some spreadsheets for vessel sizing and I come up with a method to estimate the wetted surface area of a horizontal vessel with boot (with 2:1 Elliptical, Hemispherical and Flat Heads)

The inputs are
1. Vessel Diameter
2. Boot Diameter
3. Liquid Level
4. Head Type

The difference of this spreadsheet from what I've seen before is that this doesn't rely on approximations per se, but the algorithm actually creates a wireframe mesh of the surface and it calculates the surface area, triangle by triangle.

The value depends on the number of iterations (obviously the higher, the better).

The results are promising, since from what I'm getting, the values are less than 0.5% from calculated from Mathematica.

Thing is, I do not have a way of checking the values generated other than using Mathematica (for integrating the actual surface integrals involved).

So can anyone help me verify the values generated by my spreadsheet?

If anyone is genuinely interested, let me know and I'll attach the spreadsheet. And if this indeed works, I'm more than happy to share this with all of you since I bet we'll be needing this for relief load calculations during fire cases.

I haven't been able to attach the actual file since I *may* be violating company rules if I upload the actual file without removing proprietary algorithms.

[djack77494]

The results are promising, since from what I'm getting, the values are less than 0.5% from calculated from Mathematica.

Thing is, I do not have a way of checking the values generated other than using Mathematica (for integrating the actual surface integrals involved).

Dacs,
If I may say so, you're definitely overthinking this problem. As I understand, your spreadsheet agrees within 0.5% of the results from Mathematica, which you trust. Sounds like "No Problem" to me. Are you trying to get even closer results? The whole concept of using a numerical integration technique to get the surface area of a vessel blows my mind. I know there are analytical solutions, perhaps with some approximation, that show up all over the place. They are more than adequate for engineering work. So what I don't understand is, "Why overwork the problem?"

[Dacs]

I totally understand your concern, and I agree with your statement. This is really an overkill.

While relief load calculations would probably won't benefit as much as in having a more accurate wetted surface area calculation would (in as much as it really helps if we're right on the money), I feel that:

1. The techniques that I used in doing the spreadsheet can be used in a lot of problems (that may as well include problems outside of process engineering). Imagine running an arbitrary number of nested iterations without macros in Excel. My company is paranoid in running macros in our system that I just decided to get it done without one.
2. It certainly does help if we can come up with something that will give us more accurate results. And as I said, I'm more than willing to share it with you. I just need to make sure that it runs right.
3. The actual purpose of the spreadsheet is not only determining the wetted area, but I'm actually developing a three-phase horizontal vessel sizing spreadsheet in which if circumstances permit, I'm also willing to share (don't worry, I would do so without violating anything).
4. This is my way of sharing something productive to the community.

Or maybe, I may have too much time on my hands

So let me rephrase my intent: I developed a spreadsheet that calculates (I believe, more accurately) the wetted surface area of a horizontal vessel with boot. Can anyone tell me on (other) ways to verify my calculations? I just want to eliminate my bias in the calculation.

I'll work on the spreadsheet so that I can freely release it without any issues.

[joerd]

You may check out an article by Rick Doane, Accurate Wetted Areas for Partially Filled Vessels, Chemical Engineering, December 2007. Even though he claims to have an analytical solution, there are some implicit assumptions, so his equation gives you a very close approximation.
I'll be interested to see what you come up with.

[Dacs]

Joerd:

Thank you for the reference.

Upon a little digging, I saw the pertinent equations involved.
<img src="http://img17.imagesh...ellipaccur.png" border="0" class="linked-image" />
I can't tell if there are other equations involved since I have yet to see the full article.

Anyways, I tried running my simulation with:

Diameter = 3 m
Height = 2 m

for a single 2:1 Elliptical head

Here are the values that I got:
1. Above Equation: 6.11 m
2. My spreadsheet (# Iterations-X: 30, # Iterations-Y: 30): 6.66 m
3. Mathematica: 6.68 m
<img src="http://img211.images...athematica.jpg" border="0" class="linked-image" />

To be honest, I'm at lost here. Can anyone (with time to spare) check if I got the equation for 2:1 Elliptical and the corresponding surface integral right?

The article claims that it has 2% error but if based from Mathematica, it goes around with 8% error.

Here's the stripped down spreadsheet BTW. This is only for reference so I won't be held responsible for any errors that this spreadsheet may produce (this is still a WIP).

I'd love to hear comments from you to make this better.

Attached Files

•  Wetted_Surface_Area.xls   226.5KB   380 downloads

[Archer]

Dacs:

I calculated a surface area of 6.676 m2, which agrees with your result from Mathematica. That means that your integral is likely to be correct, as is your implementation in the spreadsheet (the error is very small, likely rounding). Joerd and I analyzed Doane's article and found that it can be off by over 10% for some wetted area calculations, but these errors were typically for almost full or almost empty vessels. I believe that there was a typo in his original equation, but has been a while since I looked at the article.

I recommend using Mathematica or your numerical method since you already have them available. For anyone using Doane's equation, it is not completely accurate simply for the fact that there is no general closed form equation for the wetted area of a partially filled horizontal vessel. Nevertheless, it gets you close.

[Elizabeth_I]

this forum is just amazing! i didnt expect to find the answers to my questions here, but i really did!
Thank you so much:)



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Edited by Elizabeth_I, 28 April 2011 - 04:50 AM.