# Heat Exchanger Design - finding necessary variables

I'm working on a project to design a shell and tube heat exchanger. There's a mixture of 68.4% C,3H6 and 31.4% C3H8 being cooled from 135 $^\circ$F and 321 psia to 100 $^\circ$F and 285 psig. The volumetric flow rate of the hydrocarbon stream is 200 GPM. The cooling water on the outside is initially at 85 F and 60 psig and exit pressure of 50 psi.

I'm not sure if my process is correct, but I found the average of the inlet and outlet pressure and temperature in the hydrocarbon stream and then used those values in the ideal gas equation to find the densities of each hydrocarbon, I then took the average of the two densities and multiplied by the volumetric flow rate to find the mass flow rate of the hydrocarbon stream. I was then going to use the equation $$Q =m^o C_{p1} (T_2-T_1)(0.684) + m^oC_{p2}(T_2-T_1)(0.314)$$ to find the heat transfer of the hydrocarbon stream and then balance it with the water stream. I'm not exactly sure how to find the specific heats of the hydrocarbons. I checked perry's handbook but couldn't find anything at the average temperature. I'm just looking for any advice on whether or not this would be a correct procedure and if so, where could I find the specific heats of the hydrocarbons.

## 2 Answers

I found the average of the inlet and outlet pressure and temperature in the hydrocarbon stream and then used those values in the ideal gas equation to find the densities of each hydrocarbon

Why would you find the density of each hydrocarbon? you now have a mixture flow and you need to find the thermal properties of this mixture for your heat transfer calculations (at the average temperatures).

1) Density (to calculate mass flow rate): $$\frac{1}{\rho _{mix}} = \sum \frac{x_i}{\rho _i}$$ where $x$ is the mass fraction of component i in the mixture.

(Note: since the flow mass rations are close to 70% and 30%, taking arithmetic average of densities won't be quite accurate.)

2) Specific Heat: $$Cp_{mix} = \sum x_i Cp_i$$

And finally the equation becomes: $$Q = m^o_{mix} Cp_{mix} (T_2 - T_1)$$

Between 135 F and 100 F I don't think the heat capacity or density would vary much so using average properties should be fine. If you want to be more conservative you can use the higher Cp between inlet and outlet as this would yield the highest cooling water flow requirement. If you want to be more accurate for whatever reason then you could integrate the function Cp(T) from T1 to T2. The equation should be quite easy to integrate directly.

Note that mass in should be equal to mass out, ie volume flow*density at the inlet and outlet should be equal. Since you only have one number for volumetric flow rate, I would use the higher density of the two (inlet/outlet) to calculate the mass flow.

Specific heats of hydrocarbons as functions of temperature should be in Perry's somewhere at the back. Otherwise, I like using NIST Chemistry Webbook.