Silo Volume Calculations-How do you?

Just x-checking that my method for calculating silo volume is correct.
If we have a standard silo, cone bottom & cylinder top, with a level Tx towards the bottom of the code, ranged in mm.

I have seen a few different methods, but none of them seem to take into account the correct volume of a cone calculation. With a Level Tx in the cone, as the level goes above the Level Tx & presents a reading, the base of the cone is changing, therefore the calculation needs to account for this.


To get an accurate volume, we need to do 3x calculations:
1. Small Cone - Volume below Level Tx
2. Large Cone - Volume of complete cone, with Level Tx used to determine the Base of the Cone
3. Cylinder - Volume of Cylinder based on Level Tx reading-Large Cone height.

Calculations:
Small Cone
ConeSmall := ConeHeight2LevelTx * PI * (ConeRadius@LevelTx^2) * 0.3333 * 1000
Large Cone
//ConeAngle is a Constant
ConeRadius@Level := (ConeHeight2LevelTx + LevelTxRaw) / TAN(RAD(ConeAngle))
ConeLarge := (LevelTxRaw + ConeHeight2LevelTx) * PI * (ConeRadius@Level^2) * 0.3333 * 1000
Cylinder
VolumeTotal := ((CylinderRadius^2) * PI * (LevelTxRaw - ConeHeightfromLevelTx2Cylinder)) + ConeLarge

Obviously there is some checking on what the current reading is so as to put the correct formula to use.

Does this look like how you guys would do it?

See http://www.plctalk.net/qanda/showthread.php?t=21418

Your calculations look OK, and theoretically should give you the filled volume of a silo, provided it is filled with a liquid.

The real world always gets you, and filling a silo with granular material throws in a bunch of factors that will make an accurate fill volume very difficult to achieve.

Granular material will build into a conical pile when filling, and deplete to an inverted cone when emptying. The angle of the cone, called the "angle of repose", is determined by the density, surface area, shape, and coefficient of friction of the granular material, things which are often not constant.

So now we have factors caused by filling and emptying, but what if the filling point is not central in the top of the silo, the cone will be "slewed" towards the filling point. The placement of the Tx in the bottom cone is essentially looking at the height of the material directly above it, and if not central.....

And now add factors like the silo can be emptying while being filled, or fill/empty in cycles, and you can see the problems this would introduce to get an accurate volume.

It is for reasons like this that in a lot of applications, silos have weight cells on them to determine the contents, but this relies on a constant density. Sometimes "gauging" probes are used to factor this variation into the equations.

Other methods include mass flowmeter measurement of filling and emptying to determine the contents.


Just how accurate did you want your silo measurements ?

How about using load cells? I would think it would be more accurate with load cells.

robb676 said:

How about using load cells? I would think it would be more accurate with load cells.

Click to expand...

Load Cells, although preferred , are a nightmare to install on silo's. Piping, services and fluctuating amounts of cooling or heating medium in silo jackets prevent reliable readings.

Alaric said:

See http://www.plctalk.net/qanda/showthread.php?t=21418

Click to expand...

Thanks Alaric,
Couple of questions.
1. I tried searching the forum first, using Silo Volume but got nothing. Had you this saved, or used a different search key?
2. The Lookup table is not a bad idea, but then the values still have to be loaded somewhere. I think I prefer the method of calculating the changing diameter based on level.

daba said:

Your calculations look OK, and theoretically should give you the filled volume of a silo, provided it is filled with a liquid.

Click to expand...

Yep, this is for a liquid

The real world always gets you, and filling a silo with granular material throws in a bunch of factors that will make an accurate fill volume very difficult to achieve.

Granular material will build into a conical pile when filling, and deplete to an inverted cone when emptying. The angle of the cone, called the "angle of repose", is determined by the density, surface area, shape, and coefficient of friction of the granular material, things which are often not constant.

So now we have factors caused by filling and emptying, but what if the filling point is not central in the top of the silo, the cone will be "slewed" towards the filling point. The placement of the Tx in the bottom cone is essentially looking at the height of the material directly above it, and if not central.....

And now add factors like the silo can be emptying while being filled, or fill/empty in cycles, and you can see the problems this would introduce to get an accurate volume.

It is for reasons like this that in a lot of applications, silos have weight cells on them to determine the contents, but this relies on a constant density. Sometimes "gauging" probes are used to factor this variation into the equations.

Other methods include mass flowmeter measurement of filling and emptying to determine the contents.

Click to expand...

Interesting comments, have never had to do a granular material before, but will keep this one in th eback of the mind for future reference.
This site also has flow meters for x-checking what tanker delivers, & there has always been discrepancies.

Just how accurate did you want your silo measurements ?

Click to expand...

Who knows, at least so it is representative & close to what the tanker delivery reports.

robb676 said:

How about using load cells? I would think it would be more accurate with load cells.

Click to expand...

Existing site, Level Tx's already there. Large tanks, process is storage only, not used for batching.

lostcontrol said:

1. I tried searching the forum first, using Silo Volume but got nothing. Had you this saved, or used a different search key?

Click to expand...

"Conical"

Yep, this is for a liquid

Click to expand...

Depending on the accuracy you need and size of the tank and plumbing, you may want to keep in mind that the conical bottom of the tank is not a true cone, it has a flat spot (making it a frustum) where the pipe attaches to the point of the cone. If you are using a pressure sensor to measure the height of the fluid then you probably need to account for the fluid in the pipe down to where the sensor is mounted.

P.S.
At the bottom of the thread I linked Peter makes some comments about exponents that is worth reading the whole thread for.

How would piping and cooling and heating affect the install of load cells? When we did it we just raised the corners up some to place the cells. It was super easy.

Why would piping, heating and cooling affect the installation of load cells ?

I'm not sure either. If you think that the silo needs to flex a few inches (so the load cells can read) then you'd have to install flexible couplings on every pipe and wire that connects to the silo.

At my coal plant, we have many silo's (from 1t to 700t of granular material...) that are mounted on load cells. The load cells are annoyingly accurate and repeatable. The load cells require no flexible couplings, the support beams of the silo only flex a few .001" under load (its a strain gauge).
I would not sell product by the reading on the load cells (they arent that good) but on an 800t silo, we can fill to 750t indicated and not overflow the thing.

I'm sure they are expensive to retrofit though.

-John

robb676 said:

How would piping and cooling and heating affect the install of load cells? When we did it we just raised the corners up some to place the cells. It was super easy.

Click to expand...

Rigid connection affect repeatabilty and linearity. There are special flex connections that require to be installed to prevent the load cells from binding.

If the silo is jacketed for cooling, calibration must always be done with the jacket full.

If the silo has steam jacket, the inrush of steam will actually place force on the laod cells.

I know all this stuff as i worked for a scale company for almost 10 years.