Understanding Expansion Factor

Expansion factor is defined as the fractional change of the volume of a substance from a change in its temperature. Simply said, as a substance temperature increases, its volume increases. This is important when determining the amount of fluid that will expand in a hydronic system and subsequently the expansion tank needed to accommodate this increase.

We will look at fluid expansion with an end towards what is considered the accurate estimation as documented in the ASHRAE Fundamentals Handbook. The equation is fundamentally:

Net expansion = gross expansion of fluid minus expansion of piping and components

This is typically expressed as a fraction that is then multiplied by the total system volume of the hydronic system to calculate the expanded fluid. To that end, the gross expansion is the difference in specific volumes at two temperatures divided by the starting (lower temperature) specific volume.

Gross Expansion Factor of Fluid = ((v2-v1))/v1 = v2/v1-1

Where:

v1: specific volume of the fluid at temperature t1 (higher temperature)

v2: specific volume of the fluid at temperature t2 (lower temperature)

The expansion of the piping and components can be cumbersome to calculate because different component materials (boilers/chillers, air separators, heat exchangers, etc.) may be at potentially different temperatures, so an estimation is needed to be made. The traditional approach is to make all components materials homogeneous with the system piping and all at the same stop/start temperatures. The formula for calculating the change in volume of a solid or liquid due to thermal expansion is:

Expansion Factor of Piping and Components = β(t2-t1)

Where:

β: coefficient of the ratio of volumetric expansion of the piping material ((in³/in³)^oF) The coefficient can be estimated:

β≅3α

Making the equation:

Expansion Factor of Piping and Components = 3α(t2-t1)

Where:

α: Coefficient of the ratio of linear expansion of the piping material (in/in^oF)

For the exacting-minded, the actual equation for the growth factor of the expansion of piping and components is:

Expansion Factor of Piping and Components = (α(t2-t1)+1)^3-1

This is the integration of the circumferential and linear growth of a hollow cylinder (pipe). The approximation of 3α(t2-t1) follows the equation with less than 1 percent difference over the temperature range from -100^oF to 350^oF, which makes the 3α(t2-t1) a more convenient equation estimation.

Linear expansion coefficients (α) for common materials are shown in the following table:

Material	α (in./in./oF)
Ductile Iron	6.20E-06
PVC	3.00E-05
Cast Iron	6.11E-06
Steel	6.67E-06
HDPE	8.00E-05
Concrete	5.50E-06
Copper	9.44E-06

And yes, this paper uses English units because who could argue with the exact science behind the inch, foot, yard, and pound and Fahrenheit? USA, Liberia, and Myanmar can’t all be wrong! Even the United Kingdom abandoned and switched to Celsius decades ago. Oh well, go ‘Merica!

It is important to review the specific weight of water and discuss the differences of heating and chilled water systems. The chart shows the profile of specific weight and the typical chilled water and typical heating system zones. The fact that water density in a heating water system decreases at a considerably greater rate than in a chilled water system, shows that a single linear approximation equation is not a n accurate option. In fact, as will be shown, the piping can expand greater than the water at lower temperatures.

The net expansion of water starting at 70^oF in a hydronic heating system as influenced by the piping material is shown in the following chart for steel piping:

Charts can be deceiving in assessing the influence of the component expansion. This impact of steel pipe expansion on the net expansion of the water in the piping system is shown in the following table.

This reveals a dramatic impact on the expansion of the water in the heating system. Employing the same methodology to the chilled water system starting at 40^oF, the impact of the steel piping has an even greater influence on the net expansion.

Chilled Water System
Temp (oF)	Gross Exp.	Net Exp.	% Reduction
40	0.00%	0.00%	–
50	0.02%	0.00%	-24.82%
60	0.10%	0.06%	58.43%
70	0.19%	0.13%	68.85%
80	0.32%	0.24%	75.11%
90	0.50%	0.40%	79.96%
100	0.68%	0.56%	82.29%
110	0.91%	0.77%	84.54%

This shows that at times the lower temperature piping expands faster that the water.

Propylene Glycol

The mixture of propylene glycol has the effect of increasing specific weight and increasing the slope of the rate of change.

The resulting net expansion of various propylene concentrations are shown for typical heating and chilled hydronic loops. The chart for heating shows the expansion factor with 70oF as the starting temperature.

Net Expansion Heating System
Temp (oF)	Water	10%PG	20%PG	30%PG	40%PG	50%PG	60%PG
70	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
80	0.11%	0.22%	0.27%	0.33%	0.38%	0.40%	0.45%
90	0.27%	0.44%	0.55%	0.66%	0.76%	0.81%	0.91%
100	0.42%	0.67%	0.83%	0.99%	1.15%	1.22%	1.37%
110	0.63%	0.93%	1.14%	1.34%	1.53%	1.67%	1.86%
120	0.86%	1.21%	1.48%	1.70%	1.93%	2.14%	2.36%
130	1.10%	1.49%	1.82%	2.07%	2.32%	2.62%	2.86%
140	1.36%	1.78%	2.16%	2.44%	2.72%	3.10%	3.37%
150	1.65%	2.12%	2.51%	2.84%	3.15%	3.56%	3.85%
160	1.95%	2.47%	2.85%	3.25%	3.58%	4.02%	4.34%
170	2.28%	2.82%	3.20%	3.65%	4.01%	4.48%	4.84%
180	2.62%	3.16%	3.57%	4.06%	4.47%	4.95%	5.35%
190	2.99%	3.48%	3.95%	4.48%	4.94%	5.43%	5.88%
200	3.37%	3.81%	4.34%	4.90%	5.42%	5.91%	6.42%

The chart for chilled hydronic systems shows the net expansion with the lowest temperature that concentration of propylene glycol is anticipated to start expanding. For example, 40% propylene glycol starts expanding from -10oF (its lowest anticipated temperature).

There are many aspects of expansion that can be further explored as to their significance:

• Is the component and piping expansion coefficient truly linear?
• Should the final temperature of a heating loop and the starting temperatures of a chilled hydronic loop be better represented as (ts+tr)/2? Where ts = supply temperature and tr = return temperature?

The entire specific volumes are included at the final pages of this paper and can be used to develop a simple spreadsheet to use lookup functions and piping material inputs to accurately calculate the expansion factor for any system input (between -50^oF and 240^oF). For other heat transfer and antifreeze fluids, simply add these to your spreadsheet for future reference.

Sam Fuller
Technical Engineer
Wessels Company

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August Employee Spotlight 2024

Wessels is proud to introduce our newest employee, Nathan Blank. He recently joined our Engineering Department as a Design Engineer. He graduated with a degree in mechanical engineering from Purdue University in Indianapolis. In his free time, he can be found playing Uncharted 4 and is rated as one of the top players in the world! He also enjoys watching Surf’s Up, weightlifting, and the Indy Fuel hockey team. Please join us in welcoming Nathan Blank to Wessels Company.

Nathan’s Fast Facts:
Favorite Color: Purple
Favorite Food: Chicken thighs
Likes: Indy Fuel
Fun Fact: He ran 150 miles when he was 10!

Nathan Blank
Engineer
Email: [email protected]

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How To: Quickly Adjust Vessel Pre-charge Pressure

The proper way of setting the pre-charge air pressure for a tank in operation is to isolate the tank from the system, drain off all expanded fluid, and measure the air pressure in the tank. The pre-charge air pressure can then be reset to its optimal setting. Depending on the tank size, this process can take a lengthy amount of time. To reduce the service time on an operating tank, there are alternative techniques that can be used.

Fixing a system expansion tank quickly requires some basic understanding of its operation and the principles of compressed gas (air). The expansion tank absorbs the system’s expanded fluid caused by temperature increase. The tank air volume controls the pressure increases in the system. A very large, oversized tank will register a very low pressure increase because the relative air cushion volume change is small. A properly sized expansion tank should show a pressure increase of 20-40 psi from empty to “full” of expanded fluid.

The air cushion in an expansion tank follows the principles of Boyle’s law. Boyle’s law states that pressure times volume of a contained gas equals a constant. If the compressed gas is pressurized to twice the starting pressure, the resulting volume of the compressed gas is 1/2 of the original volume. Simply stated, Boyle’s law is:

Air loss over time

Air or nitrogen gas can find its way out of the sealed tank. The points of minute air loss that may not be easily observed through standard bubble testing are threaded connections, the air charge valve, bulkhead fitting (bottom system connection on select tanks), and the bladder itself. The bladder is butyl, which has very low permeability. Higher pressure can drive more air through the bladder by means of diffusion. As the high-pressure water is “starved” for oxygen/air, it will pull molecules through the bladder over time.

As air is lost through the tank bladder or threaded connections, the result is the same as under-inflated air charge pressure. The tank will back fill with water until the air pressure in the tank equals the system water pressure. This will result in the same issues as an undersized expansion tank.

Annual Bladder Tank Check

Schedule a preventative maintenance event every 12 months. NOTE: there should be a drain valve between the system isolation valve and the tank. If one is not present, have one installed.

1. Isolate the tank from the system.
2. Drain the water from the bladder. Drain must be located between shut off valve and tank.
3. Read the pre-charge air pressure. It should be approximately equal to ((static height above the tank)/2.31+10 psig), or the same as the pressure reducing valve setting (auto fill valve) feeding water to the system.
4. Adjust to required pre-charge air pressure. If low, retest threaded connections with soap solution.
   If pressure is within range, re-establish next PM event for 12-month period.

Setting the Pre-Charge “On-the-Fly”

With the tank in operation, a common question is “Can I adjust the pre-charge pressure in the tank without draining the tank first completely?” The answer to this question is “Yes,” providing we have working understanding of the compression air cushion of the expansion tank. As we approach the tank, we will notice that the tank is operating and the pressure P1. As we drain water from the isolated expansion tank and measure the captured water in a known volume bucket, a lower pressure P2 should be observed. Armed with these three data points, plus the size of the tank on the job, and the needed pre-charged pressure for the tank at startup, we can adjust the pressure P2 to ensure that, as the tank empties, it will ramp down to that required pre-charge pressure.

Let’s look at the variables needed to to be identified to set the pre-charge pressure with a somewhat full tank:

V_t            Tank total volume in gallons.

V_w           Water drawn from the operating expansion tank in gallons.

p₁            Measured pressure before the water draw in psig.

p₂            Measured pressure after the water draw in psig.

p_a            Atmospheric pressure (sea level typically 14.7 psia).

p_pre         Required tank pre-charge at system startup in psig.

With these known variables, we will calculate:

PE           Potential energy needed in the tank in GAP (gallons absolute pressure in psia).

V₁           Air volume of the operating expansion tank in gallons.

V₂           Air volume of the expansion tank after the water draw in gallons.

The expansion tank can be thought of as a container of potential energy of (p_pre + p_a) x V_t at the startup of the system. Boyle’s law p₁V₁ = p₂V₂ means that this potential energy should remain the same at any condition of the tank. If we see that the potential energy has dropped, we can increase the air pressure in the tank until that potential energy is met.

We will first calculate the potential energy required by the tank’s air cushion, PE.

PE = (p_pre + p_a) x Tv

We will start with Boyle’s Law to help find V₂ then adjust P₂ to meet the required potential energy.

(p₁ + p_a)V₁ = (p₂ + p_a)V₂

As we draw off water, the resulting air cushion size relationship is:

V₁ = V₂-V_w (V_w is the known draw water volume)

Substituting shows:

(p₁ + p_a)(V₂-V_w) = (p₂ + p_a)V₂

Solving for V₂:

V₂ = V_w(p₁ + p_a)/(p₁-p₂)

Because we want the potential energy to match the tank’s empty condition, we solve:

(p_2(new) + p_a)V₂ = PE

(p_2(new) + p_a) = PE/V₂

p_2(new) = PE/V₂ – p_a

Example: An NLA-800L (211 gallons) at the job site has a pressure reading of 60 psig. After isolating the tank and drawing off 8-gallons of water, the pressure reading drops to 52 psig. Atmospheric pressure is at sea level (p_a = 14.7 psia). Find the required increase in pressure required after the draw of water to ensure the tank pre-charge pressure is 12 psig.

V_t            Tank total volume 211 gallons

V_w           Water drawn from the operating expansion tank 8 gallons.

p₁            Measured pressure before the water draw 60 psig.

p₂            Measured pressure after the water draw 52 psig.

p_a            Atmospheric pressure 14.7 psia.

p_pre         Required tank pre-charge at system startup 12 psig.

The potential energy at tank startup should be:

PE = (p_pre+p_a) x V_t

PE = (12+14.7) x 211 = 5,634 GAP (gallons absolute pressure in psia)

Solving for V₂:

V₂ = V_w(p₁ + p_a)/(p₁-p₂)

V₂ = 8 (60 + 14.7)/(60-52)

V2 = 74.7 gallons

We can solve for the current potential energy in the air cushion V₂ at pressure p₂ of 52 psig and see that:

PE₂ = (p₂+p_a) x V₂

PE₂ = (52+14.7) x 74.7 = 4,982 GAP (gallons absolute pressure in psia)

Now, determine the pressure p2(new) needed to bring the potential energy to the correct value of 5,634 GAP:

p_2(new) = PE/V₂ – p_a

p_2(new) = 5,634/74.7 – 14.7

p_2(new) = 61 psig

It is important to reiterate that the best way to make sure the pre-charge pressure is correct is to drain the tank completely of any stored water and measure and adjust the pressure as needed. Often the method of drawing off a small amount of water will expedite the troubleshooting of an expansion tank at the job site. Regardless of findings and calculations, a tank should never be pressurized beyond the ASME working pressure of the tank. If calculations show that a high pressure is needed to reach the necessary potential energy, do not adjust if this could cause a dangerous or lethal situation. It is recommended that the entire tank be drained if this condition occurs.

Sam Fuller
Technical Engineer
Wessels Company

Download PDF Version of “How To: Quickly Adjust Vessel Pre-charge Pressure”

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How To: Select Nitrogen Cylinders to Pre-Charge a Bladder Tank

At times, an expansion tank pre-charge must be increased using compressed air. Wessels recommends dry, oil-free air like the compressed air used in our factory, which is taken to below -50°F and processed through a dryer. Another option is to use compressed nitrogen because it is an inert gas that avoids oxidation and moisture content that can corrode the system. Nitrogen also provides more consistent pressure and is readily available. But how many cylinders are needed to pre-charge a bladder tank to the desired pressure? There are several factors that need to be considered: the size of the compressed gas cylinders, the size of the expansion tank accepting the nitrogen, and the pressure that is needed for the pre-charge.

Additionally, we need to think in terms of stored potential energy. With the product pV (where p is absolute pressure and V is volume) equal to potential energy in joules (ft-lbf), we can calculate the energy in a cylinder of gas and compare it to the potential energy requirement of the bladder tank.

To make the units more conducive to gallons and psia, let’s use pV in terms of GAP (gallons times absolute pressure in psia). Gas cylinders are rated in cubic feet. This is actually the cubic feet of gas at 150 psig (164.7 psia) that, when released, would make up that amount of volume in cubic feet at 0 psia. In terms of potential energy in terms of GAP, the amount of energy in each cylinder is equal to 100 times the “rated” cubic feet of the cylinder. A 20 cubic foot cylinder charged to 2,200 psig yields a potential energy of 20 x 100 = 2,000 GAP.

Some common size cylinders whereas the rating in Cubic Feet based on 150 psig:

Be aware that the rating for the cylinders is referenced above 0 psia. If charging a tank to a pressure greater than 0 psia, which of course is any expansion tank, the potential energy will be somewhat less, but this will yield a close approximation. For example, if the tank at the job site is 250 gallons and needs to be charged from 40 psig to 90 psig, this requires the potential energy to be increased:

250 gallons × (90-40) psia=12,500 GAP

Bottle “H” is rated for 244 Cu.Ft. or 24,400 GAP above 0 psig. To recalculate the potential energy above 90 psig, a simple ratio should be used:

The 14.7 factor to convert psig to psia drops out of the equation and yields:

For the above example, the resulting cylinder potential energy above the 90-psig set point for the expansion tank calculates thusly:

The potential energy above 90 psig for the “J” 330 cu.ft. is 23,402 GAP and is large enough to handle the tank in this example. An alternative is to take two (2) “Q” tanks which also have the necessary GAP requirement for the example expansion tank.

An excel spreadsheet is available to download for evaluating most potential jobs.

Written by:
Sam Fuller
Technical Sales Engineer
Wessels Company

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March Employee Spotlight 2024

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How To: Understand Data Tags

Every pressure vessel manufactured by Wessels Company is equipped with a metal data tag affixed to its front side, positioned below the smart bracket system. This data tag serves as a quick reference for essential vessel information.

All vessels that adhere to the ASME code have a corresponding U stamp on the tag. You can learn more about the ASME code and Wessels’s certification here: Wessels and ASME Specification | Wessels Company (westank.com)

Each vessel that adheres to the ASME code is also given a specific National Board number, which is the manufacturing organization’s sequential identifier for a specific pressure-retaining item so it can be tracked. The number circled is either a five- or six-digit number, found in the upper right corner of the data tag. Maintenance engineers can use the National Board number as a reference for technical support or warranty information.

Crucial operational parameters such as maximum and minimum working pressures and temperatures are prominently featured on the tag. These values are denoted as Maximum Allowable Working Pressure (MAWP) and Minimum Design Metal Temperature (MDMT), respectively. For instance, the specified MAWP for this vessel is 200 pounds per square inch (psi), accompanied by a maximum working temperature of 240°F.

Additionally, the tag includes the manufacturing year, affirming its origin in the United States. H.D. denotes Head Dimension, indicating the size of the vessel’s top, while SH signifies the shell thickness or steel gauge employed in its construction.

In the lower left corner of the tag you can find the CRN (Canadian Registration Number), a mandatory identifier for vessels intended for installation and registration within Canada. Meanwhile, the tank type is often delineated on the lower right side; for example, this particular vessel is identified as a 35-gallon expansion tank.

The name of the manufacturer can also be found on the tag, and in this case, the manufacturer is Wessels Company. For more information about data tags, you can call our warehouse at 317-888-9800 or watch this short video.

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February Employee Spotlight

We are pleased to introduce our new Operations Manager, Kevin Smith, who joined our team at the beginning of 2024. Kevin graduated from Indiana Wesleyan University in 2003 with an associate degree in Business Management. He highlights his coworkers as his favorite part of working at Wessels. Beyond his professional endeavors, Kevin pursues outdoor hobbies such as hiking, kayaking, and camping, alongside his passion for woodworking. He treasures quality time spent with loved ones, including his family, friends, and three rescue cats: Cuddles, Pokie, and Tiger. Kevin learned to play the card game Euchre when he was only 9 years old and has been playing in a monthly Euchre club for 30 years! Wessels extends a warm welcome to Kevin as he embarks on this new role.

Kevin fast facts:
Favorite color: Green
Favorite food: Tenderloin
Likes: Spending time with friends & family

Kevin Smith
Operations Manager
E-mail: [email protected]
Phone: 317-888-9800 ext: 1027

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