How do I find out which compressor would fulfill my volume flow rate
requirements based on Free Air Delivery as the only volume flow rate
given in the catalogue?
- Calculate the mass flow rate of air given your required duty. You can do this by looking up or calculating the density of air, $\rho_\text{out}$, at your outlet conditions ($300 \space \frac{\text{ft}^3}{\text{min}}$ at $18 \space \text{psig}$ and $T_\text{out}$) and then dividing your volumetric flow rate by this density.
$$\dot{m}=\dot{V}_\text{out} \cdot \rho_\text{out}$$
- Convert mass flow rate $\dot{m}$ to standard volumetric flowrate, $\dot{V}_\text{std}$, (probably $\text{SCFM}$, or Standard Cubic Feet per Minute in your case) since this is the number vendors use to rate their compressors. You can do this by dividing the mass flow rate by air density at standard conditions, $\rho_\text{std}$.
$$\dot{V}_\text{std}=\frac{\dot{m}}{\rho_\text{std}}$$
$$\dot{V}_\text{std}=\dot{V}_\text{out} \cdot \left( \frac{\rho_\text{out}}{\rho_\text{std}} \right) $$
Provide this standard volumetric flowrate along with:
- available suction pressure and temperature
- required discharge pressure and temperature (note: often air compressor packages come with cooling options since compressing heats up air)
- utility power details (3-phase 240 VAC? continuous or intermittent duty?)
Here's an example setup worked out:
My process simulator (DWSIM 5.8) gives $\rho_\text{out}=0.163758 \space \frac{\text{lbm}}{\text{ft}^3}$ for $T_\text{out}=80^{\circ}F$ (?) and $P_\text{out}=32.7 \space \text{psi}$ (this is $18\space\text{psig}$ assuming atmospheric pressure is $14.7\space\text{psig}$)
It gives $\rho_\text{std}=0.0763781 \space \frac{\text{lbm}}{\text{ft}^3}$ for $T=60^{\circ}F$ and $P_\text{out}=14.696 \space \text{psi}$ (probably standard conditions in United States)
Plug it all together and you have:
$$\dot{V}_\text{std}=\left( 300 \space \frac{\text{ft}^3}{\text{min}} \right) \cdot \left( \frac{0.163758 \space \frac{\text{lbm}}{\text{ft}^3}}{0.0763781 \space \frac{\text{lbm}}{\text{ft}^3}} \right)=643.21317 \space\frac{\text{ft}^3}{\text{min}}$$
$$\dot{V}_\text{std}=650\space\text{SCFM}$$
Note: This value is only valid for the exact pressures and temperatures I assumed. You didn't provide an outlet temperature so I filled one in. Also, I didn't take pressure drop across the ducting into account (I simply used $18 \space\text{psig}$).
What would be the best system to change the pressure of the compressor (116 psi) to the required pressure (18 psig). How can I
control the pressure while achieving the required flow rate in the
system. (Is the varying cross sectional duct with pressure regulation
valves the best option)?
If you purchase a compressor that has a much higher maximum operating discharge pressure (ex: the $118 \space\text{psig}$ screw compressor you mentioned), then you can use a pressure regulator (which also would have to be sized for your mass flow rate and compressor outlet conditions) to reduce the pressure to that needed by your duct system. You'll also want to make sure a pressure relief valve (sometimes included with compressor packages if you request one) capable of relieving the maximum flow rate of air back to atmosphere in order to prevent equipment damage or injury in case accidental block-in causes dangerous pressure release (especially important with positive displacement compressors like a screw compressor).
Some air compressor packages offer a recycle system that automatically sends air from the discharge directly back to the compressor suction in order to reduce flow; it's less efficient but cheaper than a "VFD" option (variable frequency drive) which lowers the compressor rate of rotation to something less than what the nature of AC power imposes on induction motors typically used in small air compressors.
What's confusing me is that the catalogues specify the flow rate as
Free Air Delivery, whereas, in my system, since I have a duct, it
would incorporate an impediment, and thus change the flow rate of the
compressor.
You're correct in thinking that restricting flow from a compressor will decrease the flow rate from the compressor. All fluid compressors have what is called a "pump curve" and any given outlet piping and ducting system will have a "system curve". Both curves are plotted with "head" ("pressure" but in a more generalized form) versus flow rate.
Image by Baltakatei derived from work by Ryan Toomey, licensed CC BY-SA 4.0
The point at which the pump and system curves cross determines the flow rate through your system (the "operating point"). Adding a restriction (such as narrowing the duct) steepens the yellow system curve, driving the actual flow rate towards the left on the plot. Using a VFD or recycle line permits shifting the pump curve down or to the left.
A screw compressor is a form of "positive displacement" pump. Positive displacement pumps have a pump curve that is very steep (as opposed to those of "centrifugal pumps"), meaning they do not respond strongly to discharge pressure if their mechanical configuration doesn't change. That said, screw compressors can achieve lower flowrates (in other words: achieve higher "turn down") without the use of a VFD or recycle line by utilizing adjustable suction and discharge port apertures ("slide valves") which change the timing for exactly when gas in a flute begins and ends compression. However, all these are bells and whistles that cost money and increase complexity.
