Receiver Tank Calculations

Receiver Tank

My colleague, Lee Evans, wrote a blog about calculating the size of receiver tanks within a compressor air system.  (You can read it here: Receiver Tank Principle and Calculations).  But, what if you want to use them in remote areas or in emergency cases?  During these situations, the air compressor is not putting any additional compressed air into the tank.  But, we still have potential energy stored inside the tanks similar to a capacitor that has stored voltage in an electrical system.  In this blog, I will show how you can calculate the size of receiver tanks for applications that are remote or for emergency systems.

From Lee Evans’ blog, Equation 1 can be adjusted to remove the input capacity from an air compressor.  This value is Cap below.  During air compressor shutdowns or after being filled and removed, this value becomes zero.

Receiver tank capacity formula (Equation 1)

V = T * (C – Cap) * (Pa) / (P1-P2)

V – Volume of receiver tank (cubic feet)

T – Time interval (minutes)

C – Air requirement of demand (cubic feet per minute)

Cap – Compressor capacity (cubic feet per minute)

Pa – Absolute atmospheric pressure (PSIA)

P1 – Tank pressure (PSIG)

P2 = minimum tank pressure (PSIG)

 

Making Cap = 0, the new equation for this type of receiver tank now becomes Equation 2.

Receiver tank capacity formula (Equation 2)

V = T * C * (Pa) / (P1-P2)

With Equation 2, we can calculate the required volume of a receiver tank after it has been pre-charged.  For example, EXAIR created a special Air Amplifier to remove toxic fumes from an oven.  The Air Amplifier was positioned in the exhaust stack and would only operate during power failures.  In this situation, product was being baked in an oven.  The material had toxic chemicals that had to cross-link to harden.  If the power would go out, then the product in the oven would be discarded, but the toxic fumes had to be removed.  What also doesn’t work during power outages is the air compressor.  So, they needed to have a receiver tank with enough volume to store compressed air.  From the volume of the oven, we calculated that they need the special Air Amplifier to operate for 6 minutes.  The compressed air system was operating at 110 PSIG, and the Air Amplifier required an average air flow of 10 cubic feet per minute from the range of 110 PSIG to 0 PSIG.  We are able to calculate the required receiver volume to ensure that the toxic fumes are evacuated from the oven in Equation 2.

Receiver tank capacity formula (Equation 2)

V = T * C * Pa / (P1 – P2)

V = 6 minutes * 10 cubic feet per minute * 14.7 PSIA / (110 PSIG – 0 PSIG)

V = 8 cubic feet.

Receiver tanks are more commonly sized in gallons.  In converting 8 cubic feet to gallons, we get a 60-Gallon Receiver Tank.  EXAIR recommended the model 9500-60 to be used near the oven to operate the special Air Amplifier during power outage.

Another way to look at Equation 2 is to create a timing equation.  If the volume of the tank is known, we can calculate how long a system will last.  In this example for scuba diving, we can use this information to configure the amount of time that a tank will last.  The diver has a 0.39 cubic feet tank at a pressure of 3,000 PSIG.  I will use a standard Surface Consumption Rate, SCR, at 0.8 cubic feet per minute.  If we stop the test when the tank reaches a pressure of 1,000 PSIG, we can calculate the time by using Equation 3.

Receiver tank timing formula (Equation 3):

T = V * (P1 – P2) / (C * Pa)

T – Time interval (minutes)

V – Volume of receiver tank (cubic feet)

C – Air demand (cubic feet per minute)

Pa – Absolute atmospheric pressure (PSIA)

P1 – Initial tank pressure (PSIG)

P2 – Ending tank pressure (PSIG)

By placing the values in the Equation 3, we can calculate the time to go from 3,000 PSIG to 1,000 PSIG by breathing normal at the surface.

T = 0.39 cubic feet * (3,000 PSIG – 1,000 PSIG) / (0.8 cubic feet per minute * 14.7 PSIA)

T = 66 minutes.

What happens if the diver goes into deeper water?  The atmospheric pressure, Pa, changes.  If the diver goes to 100 feet below the surface, this is roughly 3 atmospheres or (3 * 14.7) = 44.1 PSIA.  If we use the same conditions above except at 100 feet below, the time will change by a third, or in looking at Equation 3:

T = 0.39 cubic feet * (3,000 PSIG – 1,000 PSIG) / (0.8 cubic feet per minute * 44.1 PSIA)

T = 22 minutes. 

If you have any questions about using a receiver tank in your application, you can contact an EXAIR Application Engineer.  We will be happy to solve for the proper volume or time needed for your application.

 

John Ball
Application Engineer
Email: johnball@exair.com
Twitter: @EXAIR_jb

Receiver Tank Principle and Calculations

 

Visualization of the receiver tank concept

A receiver tank is a form of dry compressed air storage in a compressed air system.  Normally installed after drying and filtration, and before end use devices, receiver tanks help to store compressed air.  The compressed air is created by the supply side, stored by the receiver tank, and released as needed to the demand side of the system.

But how does this work?

The principle behind this concept is rooted in pressure differentials.  Just as we increase pressure when reducing volume of a gas, we can increase volume when reducing pressure.  So, if we have a given volume of compressed air at a certain pressure (P1), we will have a different volume of compressed air when converting this same air to a different pressure (P2).

This is the idea behind a receiver tank.  We store the compressed air at a higher pressure than what is needed by the system, creating a favorable pressure differential to release compressed air when it is needed.  And, in order to properly use a receiver tank, we must be able to properly calculate the required size/volume of the tank.  To do so, we must familiarize ourselves with the receiver tank capacity formula.

An EXAIR 60 gallon receiver tank

Receiver tank capacity formula

V = ( T(C-Cap)(Pa)/(P1-P2) )

 

Where,

V = Volume of receiver tank in cubic feet

T = Time interval in minutes during which compressed air demand will occur

C = Air requirement of demand in cubic feet per minute

Cap = Compressor capacity in cubic feet per minute

Pa = Absolute atmospheric pressure, given in PSIA

P1 = Initial tank pressure (Compressor discharge pressure)

P2 = minimum tank pressure (Pressure required at output of tank to operate compressed air devices)

An example:

Let’s consider an application with an intermittent demand spike of 50 SCFM of compressed air at 80 PSIG.  The system is operating from a 10HP compressor which produces 40 SCFM at 110 PSIG, and the compressed air devices need to operate for (5) minutes at this volume.

We can use a receiver tank and the pressure differential between the output of the compressor and the demand of the system to create a reservoir of compressed air.  This stored air will release into the system to maintain pressure while demand is high and rebuild when the excess demand is gone.

In this application, the values are as follows:

V = ?

T = 5 minutes

C = 50 CFM

Cap = 40 SCFM

Pa = 14.5 PSI

P1 = 110 PSIG

P2 = 80 PSIG

Running these numbers out we end up with:

This means we will need a receiver tank with a volume of 24.2 ft.³ (24.2 cubic feet equates to approximately 180 gallons – most receiver tanks have capacities rated in gallons) to store the required volume of compressed air needed in this system.  Doing so will result in a constant supply of 80 PSIG, even at a demand volume which exceeds the ability of the compressor.  By installing a properly sized receiver tank with proper pressure differential, the reliability of the system can be improved.

This improvement in system reliability translates to a more repeatable result from the compressed air driven devices connected to the system.  If you have questions about improving the reliability of your compressed air system, exactly how it can be improved, or what an engineered solution could provide, contact an EXAIR Application Engineer.  We’re here to help.

Lee Evans
Application Engineer
LeeEvans@EXAIR.com
@EXAIR_LE

Compressed Air Calculations, Optimization, and Tips

EXAIR uses our blog platform to communicate everything from new product announcements to personal interests to safe and efficient use of compressed air. We have recently passed our 5 year anniversary of posting blogs (hard for us to believe) and I thought it appropriate to share a few of the entries which explain some more of the technical aspects of compressed air.

Here is a good blog explaining EXAIR’s 6 steps to optimization, a useful process for improving your compressed air efficiency:


One of the Above 6 steps is to provide secondary storage, a receiver tank, to eliminate pressure drops from high use intermittent applications. This blog entry addresses how to size a receiver tank properly:

Here are 5 things everyone should know about compressed air, including how to calculate the cost of compressed air:

These next few entries address a common issue we regularly assist customers with, compressed air plumbing:

In a recent blog post we discuss how to improve the efficiency of your point of use applications:

Thanks for supporting our blog over the past 5 years, we appreciate it. If you need any support with your sustainability or safety initiatives, or with your compressed air applications please contact us.  

Have a great day,
Kirk Edwards
@EXAIR_KE

Advanced Management of Compressed Air – Storage and Capacitance

Receiver Tank Drawing

Last week I attended the Advanced Management of Compressed Air Systems seminar put on by the Compressed Air Challenge.  For those unfamiliar with the Compressed Air Challenge, it’s an organization focused on delivering reliable and sustainable compressed air that has maximized efficiency.  Many of the industry’s best practices are preached, if not mandated, and the ultimate goal is to reduce compressed air use as much as possible.  This fits in line with EXAIR products, their design for maximum efficiency, and the recurring ability of our customers to reduce their compressed air use by using our products.

The “advanced” seminar dives into compressed air system profiles, explores the math and theory behind system design, explains the various types of system controls, and shows how to balance compressed air supply and demand.  These things are great not only on their inherent value, but also because when Brian Farno, Russ Bowman, and I attended the Fundamentals of Compressed Air Systems seminar, we kept raising our hands asking questions that were “too advanced”.  The material presented here answered many of those questions, and sparked a few new ones.

One of the questions that came to me during the training had to do with the capacitance of a compressed air system.  When storing the energy of a compressed air system in a receiver tank, there has to be a pressure gradient in order for there to be energy storage.  If a receiver tank has the same inlet and outlet pressure, it is merely part of the system plumbing and provides no benefit to the system when demand peaks.  So I thought to myself, “if a pressure drop is needed across a receiver tank to achieve system capacitance, and the capacitance of the system is related to the value of that differential, a system could theoretically be supplied enough compressed air volume with the right pressure specs”.

So, I looked to the formula used for sizing a receiver tank.

V = (T x (C – R) x Pa)/P1-P2

Where:

V = Receiver volume in cubic feet

T = Time of the event in minutes (amount of time for which the receiver tank must be able to provide compressed air at the needed rate)

C = Intermittent demand amount (how much flow or “Q”) in CFM

R = Flow into tank during event (through needle valve, spare air in system, etc.) in CFM

Pa = Absolute atmospheric pressure (14.7 PSIA)

P1 = Initial receiver tank pressure (in PSI)

P2 = Final receiver tank pressure (in PSI)

Ok, nothing new there.  First grade stuff.  Plugging in some theoretical values we could say:

T = 1 minute

C = 50 cubic feet per minute

R = 0 cubic feet per minute.  In this example we’ll assume there is no residual compressed air flow and that the receiver tank must deliver all the airflow for the duration of the event.

Pa = 14.7

P1 = 100 PSIG

P2 = 90 PSIG

Using these values, the volume calculates to be 73.5 cubic feet.  But, most receiver tanks are sized in gallons so we can multiply by 7.48 to get the figure in gallons.  (7.48 gallons = 1 cubic foot)  This yields an approximate value of 550 gallons.  In plain terms, for the application above, we would need a 550 gallon receiver tank with an inlet pressure of 100 PSIG and an outlet pressure of 90 PSIG to provide compressed airflow over the needed (1) minute duration.

That’s a big tank.

Now, back to my thought on pressure differentials – if we increase the ΔP, we can decrease the size of the receiver tank.  Let’s say the inlet pressure to the receiver tank can be as high as 130 PSIG (a wet tank, in line before any filters or dryers).  This will quadruple the pressure differential and reduce the size of the tank by 75% to 138 gallons.  Great!

Well, great for a new system, but what about one already in place?  What if the application needs 50 CFM of compressed air flow for 1 minute, and the shop already has a 175 gallon tank.  We can work the equation in reverse to determine the necessary pressure differential that will ensure the system has enough capacitance to sustain the event (approximately 32 PSI).  It’s good to know the math.

As a whole, the seminar was a great success and the presenters proved why they’re experts in the field of compressed air.  We’re not too shabby here at EXAIR either.  If you have an application need, give us a call.

Lee Evans
Application Engineer
LeeEvans@EXAIR.com
@EXAIR_LE