Process flow diagram: pressure and velocity changes with temperature

[uby]

Pressure and velocity changes with temperature in open flow tube

Hello everyone,

I have a process in which a gas goes through a heater. I want to calculate the physical properties of the stream coming out of the heater. Here is a description of the streams:

Input to the heater:
molar flow rate is 1 mole per minute
pressure(P) is 2 atm
temperature(T) is 298K
gas velocity(u) is 1 cm per second

Output from the heater:
molar flow rate is 1 mole per minute
pressure is unknown
temperature is 1073K
gas velocity is unknown

How do I go about solving for the pressure and velocity of the output, assuming that the gas is compressible (i.e. - the density is free to change)?

Assuming an ideal gas equation of state: P = rho*R*T/M where rho = density, R = gas constant, and M = molar mass of the gas species.

Continuity (molar flux in equals molar flux out) requires that the molar flow rates be equal, but not necessarily the volumetric flow rates since density is free to change.

I end up getting stuck at the equation when combining ideal gas and continuity expressions:
P1*u1*T2/T1 = P2*u2

I cannot figure out how P2 and u2 individually change.

Help?

Thanks!

 

[Q_Goest]

Hi uby. The way to do this is to go back to basic principals and perform an analysis on the heat transfer and pressure drop through the heat exchanger. I'd suggest breaking up the flow through the heat exchanger into smaller chunks (ie: control volumes) and performing a pressure drop analysis on each bit of the flow along with a heat transfer analysis to determine how temperature (really the enthalpy) of the flow changes. As heat is added, the fluid properties change, and as fluid properties change, pressure drop along a given length of tube inside the heat exchanger also change.

 

[uby]

Hi Q_Goest, Thanks for your reply!

I'm not sure I agree with (or I fail to understand) your suggestion. Isn't the ideal gas equation of state derived from similar principles as the heat transfer equations (i.e. - work and heat in the forms of enthalpy and internal energy)? The ideal gas equation of state states that the increase in temperature should manifest itself as a change in pressure AND/OR velocity/fluid density. I'm not sure I gain any additional information from performing heat transfer calculations. Think of this as a state function: I don't care how or at what rate the fluid temperature increases, all I care about is what happens after it reaches a specified temperature. Shouldn't the equation of state give that to me directly?

 

[Q_Goest]

Consider how one could calculate the outlet temperature of a HX if there was no heat transfer (ie: it was a straight piece of pipe). If there were no heat transfer, the http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation" equation could be applied since there would be no change in the fluid states other than the drop in pressure. If density change is significant however (or if there are any large changes in the fluid properties), we can't apply the DW equation for the entire flow, we would need to break it up into smaller lengths such that the change in properties in each small length of pipe would be sufficiently small so that the DW equation is suitably accurate. This is what a piping pressure drop type program would do for you. It's a kind of 1 dimensional FEA analysis. Note that if the fluid is 2 phase, the DW equation won't work, but there are others that will.

But if there is also heat transfer, we need to incorporate that into our analysis of the fluid flow. Let's assume we have a pipe with one fluid on the outside and another on the inside. There's http://en.wikipedia.org/wiki/Convection" through the pipe wall. And finally there is convective heat transfer again on the inside of the pipe wall to the fluid. What a piping program would do is to break up the pipe into sections and analyze each section of pipe as it does with the pressure drop.

It sounds like you're having problems figuring out how to calculate fluid properties though. Although you can treat the fluid as an ideal gas (assuming it remains a gas), there are properties such as enthalpy that you can't get from the ideal gas equation of state. For those properties, and because I'm recommending doing what amounts to a 1 dimensional FEA analysis, I'd suggest getting a fluids properties database such as REFPROP and integrate it into your anlaysis.

 

[alphy]

Dear scientist,

Thank you for sharing your process flow diagram and the specific details of your problem. It appears that you are trying to determine the pressure and velocity of a gas stream after it has gone through a heater. You have correctly identified the ideal gas equation of state and the continuity equation as key principles to consider in your calculations.

To solve for the pressure and velocity of the output, you will need to use the ideal gas equation and the continuity equation together. As you have mentioned, continuity requires that the molar flow rates be equal, but the volumetric flow rates may not be equal due to changes in density. This means that you will need to use the ideal gas equation to relate the pressure, temperature, and molar flow rate of the input stream to the pressure, temperature, and molar flow rate of the output stream. You can then use the continuity equation to relate the velocity of the input stream to the velocity of the output stream.

To solve for the pressure and velocity of the output stream, you will need to use algebraic manipulation to rearrange the equations and solve for the unknown variables. In this case, you have correctly identified the equation P1*u1*T2/T1 = P2*u2 as the key equation to use. By rearranging this equation, you can solve for P2 and u2 individually.

I hope this helps to guide you in your calculations. If you encounter any further difficulties, please do not hesitate to reach out for further assistance. Good luck with your research!

Best,