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# Calculating Heat Capacity With Changing Temperature And Pressure

5 replies to this topic
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### #1 BeigeSponge

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Posted 19 March 2022 - 06:20 PM

I am designing a packed bed reactor and in order to perform my heat balance I need to calculate the heat capacities. Given the reactor is adiabatic and I aim to also calculate the pressure drop, the temperature and pressure will vary along the length. Therefore, I need to be able to calculate the heat capacities depending on temperature and pressure, are there any equations to do this?

My other line of thinking is, if I assume ideal gas and use the heat capacity at constant volume (my reactor volume is obviously not expanding) then if my I am correct, the heat capacity is only dependent on temperature and I could then use Shomate equations etc to determine Cp at differing temperatures.

Ideally, I'd like to not make that assumption because I am operating at a moderate pressure (around 30 bar) and ideal gas is not a safe assumption in this scenario.

Any guidance would be much appreciated.

Thanks,

### #2 PingPong

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Posted 20 March 2022 - 05:17 AM

...........

My other line of thinking is, if I assume ideal gas and use the heat capacity at constant volume (my reactor volume is obviously not expanding) then if my I am correct, the heat capacity is only dependent on temperature and I could then use Shomate equations etc to determine Cp at differing temperatures.

...........

You should use the heat capacity at constant pressure, not at constant volume. That reactor volume is constant is irrelevant.

............

Ideally, I'd like to not make that assumption because I am operating at a moderate pressure (around 30 bar) and ideal gas is not a safe assumption in this scenario

..............

Whether it deviates much from ideal gas also depends on temperature and gas composition which you did not bother to mention.

Most accurate would be to use a process simulator. If you do not have access to a professional simulator like Hysys or Aspen+ or PRO/II or Chemcad then you can use freeware like DWsim  https://sourceforge....projects/dwsim/

### #3 BeigeSponge

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Posted 20 March 2022 - 05:41 PM

...........

My other line of thinking is, if I assume ideal gas and use the heat capacity at constant volume (my reactor volume is obviously not expanding) then if my I am correct, the heat capacity is only dependent on temperature and I could then use Shomate equations etc to determine Cp at differing temperatures.

...........

You should use the heat capacity at constant pressure, not at constant volume. That reactor volume is constant is irrelevant.

............

Ideally, I'd like to not make that assumption because I am operating at a moderate pressure (around 30 bar) and ideal gas is not a safe assumption in this scenario

..............

Whether it deviates much from ideal gas also depends on temperature and gas composition which you did not bother to mention.

Most accurate would be to use a process simulator. If you do not have access to a professional simulator like Hysys or Aspen+ or PRO/II or Chemcad then you can use freeware like DWsim  https://sourceforge....projects/dwsim/

The temperature is 623K, so not too high temperature. The composition of the feed is:

0.2% CH4, 5.1% CO2, 8.49% CO, 0.2% Ar, 36.46% H2, 15.1% N2, 34.45% H20.

Lots of small molecules so may be be quite ideal.

### #4 PaoloPemi

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Posted 21 March 2022 - 02:26 AM

take care to use a correct way to solve the reactor or provide additional details if you wish to receive comments...
about fluid properties of course there are differences assuming constant pressure or volume...

however predicted enthalpy departures at 623 K 30 Bar are not very large (from ideal model)
as example

Cp 2.11 Cv 1.57 Kj/Kg-K with LKP model

Cp 2.13 Cv 1.57 Kj/Kg-K with PRX model

(Prode Properties, free version)

of course it depends from the degree of accuracy you wish to obtain...

### #5 BeigeSponge

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Posted 25 March 2022 - 12:23 PM

take care to use a correct way to solve the reactor or provide additional details if you wish to receive comments...
about fluid properties of course there are differences assuming constant pressure or volume...

however predicted enthalpy departures at 623 K 30 Bar are not very large (from ideal model)
as example

Cp 2.11 Cv 1.57 Kj/Kg-K with LKP model

Cp 2.13 Cv 1.57 Kj/Kg-K with PRX model

(Prode Properties, free version)

of course it depends from the degree of accuracy you wish to obtain...

I ended up plotting compressibility factor and comparing it to ideal gas, you're right, it approximates well. In that case, is my understanding correct that Cp only varies with temperature and therefore I can just use the shomate equation and calculate Cp via this and then input it into my rate equation?

### #6 PaoloPemi

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Posted 26 March 2022 - 02:21 AM

differences (ideal vs. real) can be higher at different operating conditions,
you can calculate / plot differences (ideal vs. real) for example in Excel with tools as Prode and see if ideal gas behaviour is suitable (or not) for your application...