Thermal expansion for supercritical fluids 2

[130684]

Dears,

I have double pipe heat exchanger with cold ethylene flowing in tube side at 55 barg and 10 C; it is heated by LP steam (1 barg, in shellside) to 35 C. The duty of the heat exchanger is Q = 2219 kW (normal conditions).

If the cold high pressure ethylene is blocked in the heat exchanger between the isolation valves of it, thermal expansion of the fluid might occur. The heat exchanger is proteceted by a Relief Valve set @ 66 barg.

My question is: does anybody know how to calculate the relief flow and the relief temperature for this case?

I did it with the following methods, but the results are completly different.

1: Relieving flow for thermal expansion of GASES:
M = Q x [(ro2 - ro3)/ro2]/(h3 - h2) , kg/h where: 2 is for relieving temperature and 3 is for relieving temperature +1 C.
- the relieving temperature was assumed to be maximum shelside temperature (120 C)

2. Isochoric flash:
Considering a fixed volume (HX pipe + additional pipe) in which the fluid exists, a mass of fluid at operating temperature is calculated based on the density, m=ro(actual) * V(system).

Then, the fluid is brought to the set pressure and the temperature is modified till the volume of the contained fluid a9based on initial mass) is equal to the volume of pipe (this is the point where the RV starts to open). Choosing Dt=1s, the heat Q=2219kWx1s = 2219 kJ is added to the system. The new volume is calculated at the temperature where the valve starts to open + the temperature increase due to the heat input (Trelief = Tset + DT, where DT = Q/(m*Cp) x 1s)).
The relief flow is: m = ro(v) x DV/Dt , kg/s

I incline to use the second method even if in the attached file the example assumes ideal vapor phase.
Could you please let me know you opinion?

Thanks!

 

[PaoloPemi]

if you wish to define a simple model I would proceed as follows
calculate the volume of the system, calculate the density of the fluid at operating conditions and the initial mass (volume / density) of fluid in the system, since you know the mass of fluid in the system and the volume you can calculate the (initial) density and temperature at discharging pressure (psv set)
now you can define the amount of heat exchanged (in a certain time step) and calculate the new temperature (with some rigorous procedure, see below, or assuming constant properties), then calculate the new density,
since you know the volume of the system, you can calculate the qty discharged (in that time step) as difference of (initial) mass of fluid - volume of system / density of fluid
you can proceed with additional steps, if required.

I would presume that modeling the fluid as ideal could introduce large errors, I prefer to solve these problems in Excel with the help of a process library (Prode Properties, see prode.com), you may use an equivalent system if available.

 

[PaoloPemi]

of course, mass of fluid = recipient volume * fluid density
sorry for the typo

 

[don1980]

I do this the same way Paolo describes. It's an easy calculation - same as that for a thermal expansion of liquid. If you can find a Mollier diagram for this fluid, then it's easier to visualize the problem, and you can get the specific volume values (density) from that plot.

 

[130684]

Thank you very much for you answers.
I still have some issues that are a bit unclear and I would appreciate your support for helping me understand them.

"since you know the mass of fluid in the system and the volume you can calculate the (initial) density and temperature at discharging pressure (psv set)"

1. the pressure at which the second temperature/density are calculated is the set pressure of the relief valve or the relief pressure (110% x Set pressure)?

2. which equations have you used for the calculation of the density and temperature? (at relief (or set) pressure)
I calculated the temperature (and implicitly the density) with Hysys, keeping the pressure constant and varying temperature untill the volume of the fluid inside reaches the volume of system. Seems that ok?

Thanks!

 

[don1980]

The final state (state-2) is relieving pressure and not set pressure. Use the density at state-2 to determine the volume of fluid that must be relieved. I would use 1 hr worth of heat to determine the state-2 temperature. Since this is supercritical, a continuous heat input will cause the fluid temperature to continue rising throughout the relief event.

You can easily find a pressure-enthalpy diagram for ethylene on the internet. I think this will help visualize the problem.

 

[PaoloPemi]

as written by don1980 use the relieving pressure,
a pressure-enthalpy diagram for ethylene could be useful to understand the whole process,
of course you can utilize a process simulator, selecting SRK or PR results should be roughly equivalent,
you may define the procedure as a sequence of basic (flash) operations,
-volume and pressure
-enthalpy and pressure
these units are generally available in simulators,
for example Prode Properties exports in Excel the macros VPF() to solve for volume and pressure and HPF() to solve for enthalpy and pressure, I would presume that your simulator has similar features

 

[130684]

Thank you both. you're comments were very useful.