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kWh Per Ton Calculation Question

01/09/2008 8:26 AM

Hi All,

Question time again. I am trying to come up with an easy model for my operators to determine the energy requirements to melt different materials. I have a database with a whole lot of Thermodynamic information, but to try and explain to someone what it all means will take forever (mainly because I do not understand it all myself ).

I know that I can use the Heat of Forming information of a metal at a certain temperature to calculate the kWh required per ton of metal. But for the life of me I cannot figure out how ......

Let me show you what I have .....

H° for Fe at 1823K is 80668.865 J/gmol

80668.865 / Mol mass (55.85) = 1444.384 J/g (or kJ/kg)

1 kW = 1J/s Thus 1444.384/3600 = 0.401218kW/kg

Thus 401.218 kW/ton.

If that is right then I am satisfied to use said figure, but I know that we use approximately 660kW/t to produce steel from Scrap, so where am I going wrong? Then also I was told that to melt Aluminum would use the same energy as steel, but if I use the same calculation with Aluminum I get a value of 604kW/ton. Now what?

Am I totally off the track. Can some of you brilliant Thermodynamic experts shed some light on this for me?

Regards,

TC

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#1

Re: kWh Per Ton Calculation Question

01/09/2008 9:44 AM

Hi T4T,

Until someone with a better answer comes by, I'll throw my six eggs worth in....

Not sure what you mean by heat of forming.

If I understand the question correctly, you want to know how much energy to melt metals?

If so, what you need to know is - specific heat capacity of the metal, latent heat of fusion of the metal, melting point of the metal, mass of the metal.

First, to calculate how much energy it takes to heat the metal to its melting point:

Mass of metal x specific heat capacity (SHC) of the metal x temperature rise, ΔT(melting point of the metal - room temp)

Once the metal is at its melting point, you need to supply energy to break the bonds in the crystal lattice of the solid metal to turn it into a liquid. This energy is called the latent heat of fusion. (its called latent because it appears hidden, as you pump in the energy the temperature does not change)

Energy to melt the metal = latent heat of fusion (LHF) of the metal x mass of metal.

Once all the metal has melted, then the temperature will start to rise again. Think of ice cubes in a drink. As long as there is still some ice, the drink stays cool, as all the heat the drink absorbs goes to melt the ice, before it can raise the temperature of the drink.

So the total energy needs are

(mass of metal x ΔT x SHC) + (mass of metal x LHF)

I hope this helps!

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Guru
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#2

Re: kWh Per Ton Calculation Question

01/09/2008 10:16 AM

As far as the difference in the calculation and energy used; have you considered the efficiency of the process, the waste heat, and the energy to operate the equipment?

The system used to melt the two different metals may be the same, and operate at only one temperature, thus the energy cost of operating the equipment would be the same. If you have a furnace that melts steel, it would definitely melt aluminum without modification, however, it would take less time.

Most workers do not want to spend allot of time doing complex calculations. The best method would be to provide a Excel spreadsheet where all they have to do is input the quantity, and the energy use would be displayed. Depending on the accuracy needed, you could print a completed table for the most common amounts.

Also a ton of aluminum will take up allot more volume then a ton of steel. The same weight of the two metals may take different quantity of processes to complete.

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#3

Re: kWh Per Ton Calculation Question

01/09/2008 11:39 AM

Er, it's kWh per ton (not kW per ton; shoot the pedant).

In calculating energy consumption, the energy loss routes need to be established and an appropriate allowance made.

401/660 ≈ 61%. Reasonable, though could do better. It's always worth looking at cost-effective ways of reducing the 660kWh/ton towards the 401kWh/ton figure. Better insulation, perhaps?

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#4

Re: kWh Per Ton Calculation Question

01/10/2008 2:01 AM

Hi all,

Thanks for the comments and answers I will make a few comments back.

Zaphod congrats, you got a good answer mark from me. It was exactly what I was looking for, namely some formula to calculate THEORETICAL energy requirement.

Techno, thanks for your comments. As I said above, i am looking for theoretical calculations first, then I will work in efficiency in the table I give to the operator. I do not know what your background is but the energy requirement for melting Steel and Aluminium is very close to 1:1. Thus it will not be faster to melt aluminium than melting steel (my opinion), if all else stays the same (furnace, energy input etc.). In my case it is not really that they do not want to make the complex calculation, it is more a case of lack of skills and knowledge. So they cannot make the calculation, I have to do it for them. But, because I did not have a plain formula, it took me a few hours to calculate what the different energy requirement would be if we change the material to be melted next. Yes, i am going to print out a table of figures and stick it to the wall, for myself I am going to build a little database with the relevant constants and then can do a quick reference calculation when I want to something different, say Iron Silicide, or Ferro manganese ....

PWSlack: I was just checking to see if you're awake ;). Off course it is kWh per ton, because it takes time. In other words it will take X kW to melt 1 ton in 1 hour. As I mentioned the theoretical values to melt aluminium and steel should be the same. Then you work on volume and temperature and furnace efficiency etc and it will be different. But again, I will keep on posting my progress and continue to study and figure things out.

Thanks for all your help guys, I cannot express how much I have learnt from being part of CR4. It is easier and more productive to post a question here and get all the comments form a host of people, than to ask the question to my colleague with his Masters degree in Metallurgy sitting 6 feet away.

Regards,

TC

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Guru
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#5
In reply to #4

Re: kWh Per Ton Calculation Question

01/10/2008 9:54 AM

I have worked in a Machine shop as a machinist and a welder.

Aluminum melts faster by volume and by temperature.

By weight it would be about the same.

Aluminum melts at a lower temperature. 660 °C

Depending on the carbon content, steel melts between 1540°C and 1400°C,

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#6
In reply to #4

Re: kWh Per Ton Calculation Question

01/10/2008 10:08 AM

Thanks TC,

Its nice to be able to exercise the old grey matter, and doubly nice when it helps someone.

I have a degree in Materials Science and Engineering, and have run into people like your metalurgist before !!!

Its having to deal with those kind of people that makes this forum so refreshing!

Onwards and upwards !!!

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