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Energy Balance: Problem With Heat Capacity And Enthalpy Of Vaporizatio

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#1 SosaBaby

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Posted 15 January 2021 - 08:37 AM

Hello Everyone,

 

I have been doing an exercise about Mass and Energy balance of a Chemical process reported in the Perry Handbook 9th Edition in the section Thermodynamics pag 4-9.

 

The industrial process is the production of DME (Dimethyl ether) from the dehydratation of MeOH ( Methanol).

 

The reaction is: 2CH3OH--> CH3OCH3 + H2O  (exothermic, T = 250°C and P =10 bar for maintain the Liquid phase)

 

The PFD scheme is:

 

Attached File  IMG_20210114_121626.jpg   52.24KB   0 downloads

 

 

 

The mass balance results of all the streams results are reported in this table (the Pressure is always constant at 10 bar), and they are not important for get to the point, only the T values of each stream.

 

Attached File  IMG_20210114_121731.jpg   28.91KB   0 downloads

 

 

 

I have to calculate the Enthalpy of stream 5 -> H5, at 250°C is all VAPOR. The Perry solves like that:

 

H5 = ΔHf(DME) + Cp(DME)*(250 - 25) + ΔHf(MeOH) + Cp(MeOH)*(250 - 25) + ΔHf(H2O) + Cp(H2O)*(250 - 25)

 

So, the reference state is IDEAL GAS at 25°C (298°K).

 

 

My FIRST QUESTION is: 

 

Is this the unique route for calculate H5? I can remember that many times it is used an approximate Cp at the average temperature ( in this case 113°C) and at the aggregation state of the component. Is this possible ? What do you think?

 

My SECOND QUESTION is:

 

The ideal gas heat capacities CP of the thee species are reported from the solved exercise as: 43.9 J/molK (MeOH) , 65.7 J/molK ( DME) and 33.6 J/molK (H2O). I think that they are taken from the handbook in the Tab 2-75 (pag 2-149): "Heat Capacity at constant P of Inorganic and Organic Compounds in the Ideal Gas State Fit to HyperBolic Functions", because the Cp is calculated in the IG state and it is the only table that have the parameters constant C1, C2.... in the right temperature range.

 

But, what is the hyperbolic function for calculate Cp using C1,C2,C3,C4,C5.. ? ?

I can't find in the handbook. Will you calculate the Cp in another way?

 

 

Attached File  IMG_20210114_123421.jpg   26.97KB   0 downloads

 

 

 

Then, I have to calculate the Enthalpy of stream 7 -> H7, at 75°C is ALL LIQUID. The Perry solves like that:

 

H7 = ΔHf(DME) + Cp(DME)*(75 - 25) - ΔHvap(DME) + ΔHf(MeOH) + Cp(MeOH)*(75 - 25)  - ΔHvap(DME) + ΔHf(H2O) + Cp(H2O)*(75 - 25) - ΔHvap(H2O)

 

So, the difference is that, as the reference is vapor, it is necessary to substract for the vaporization enthalpy.

 

My THIRD QUESTION is:

 

Is this procedure for calculate the enthalpy of a liquid stream a little bit confusing? Due to the reference state that is ideal gas. Is there any alternative?

 

My FOURTH QUESTION:

 

The vaporization enthalpy ΔHvap of the three species are reported from the solved exercise as: 35.75 Kj/mol (MeOH) , 14.19 Kj/mol (DME), 42.99 Kj/mol (H2O). I think that they are taken from the handbook in the Tab 2-69 (pag 2-120): "Heats of Vaporization of Inorganic and Organic Liquids" where it is reported C1,C2,C3,C4 for each component and i think the ΔHvap has to be calculated with a simple polynomial function (C1 + C2*T..).

 

But..Which Temperature (T) i have to consider in the polynomial function..75°C ( 348°K) ? or the Tsat at 10 bar?

What do you suggets? Are they any other methods for calculate the ΔHvap?

 

 

I would be glad if someone can help me a little in these questions because i may have terrible gaps in Thermochemistry.

 

Thanks and sorry for the long message.

 

Sosababy


Edited by SosaBaby, 15 January 2021 - 08:38 AM.


#2 PingPong

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Posted 17 January 2021 - 04:49 AM

I don't have Perry 9th edition, and maybe nobody on this forum has it.

From your text it seems that Chapters 4 and 2 are much different from the older editions.

 

Without the full text of the exercise it is not clear for outsiders what this is really about.

 

Formulas, tables or graphs for ideal gas specific heats can be found in many sources. I would expect that the table in Perry 9th has the formula in the small print at the bottom of that Tab 2-75, maybe on the last page only.

 

The book "Properties of Gases and Liquids" will have formulas for it in the Appendix.

 

Also look at the NIST webbook:

https://webbook.nist...sk=1#Thermo-Gas

https://webbook.nist...sk=1#Thermo-Gas

https://webbook.nist...sk=1#Thermo-Gas

Simply interpolate the tables.



#3 SosaBaby

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Posted 18 January 2021 - 03:07 PM

I don't have Perry 9th edition, and maybe nobody on this forum has it.

From your text it seems that Chapters 4 and 2 are much different from the older editions.

 

Without the full text of the exercise it is not clear for outsiders what this is really about.

 

Formulas, tables or graphs for ideal gas specific heats can be found in many sources. I would expect that the table in Perry 9th has the formula in the small print at the bottom of that Tab 2-75, maybe on the last page only.

 

The book "Properties of Gases and Liquids" will have formulas for it in the Appendix.

 

Also look at the NIST webbook:

https://webbook.nist...sk=1#Thermo-Gas

https://webbook.nist...sk=1#Thermo-Gas

https://webbook.nist...sk=1#Thermo-Gas

Simply interpolate the tables.

Thank you really much. I have found the formula at the bottom of the tables of the hyperbolic function, and also the one for the enthalpy of vaporization






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