# Radiant Expansionism

John Siegenthaler, P.E.

All closed-loop hydronic radiant heating systems require an expansion tank to accommodate the increases volume of the heated fluid.

The classic method of sizing an expansion tank looks at the volume of the water when the system is at it highest temperature, and compares it to the volume of the water when the system is filled. A tank volume is then calculated that will accept the increased volume without allowing the system pressure to climb high enough to open the relief valve.

## The 'Classic' Sizing Procedure

Here's a quick review of the classic sizing procedure for a diaphragm-type expansion tank in any type of closed-loop hydronic heating system:Step 1 -- Estimate the system's fluid volume (not including any assumed expansion tank). You can use Table 1 to estimate the volume contained in the system piping.

If you're using tubing or pipe not included in this table, the volume, in gallons per foot, can be determined using Formula 1:

where:

d = internal diameter of pipe (in inches)

You'll also need to look up the fluid volume contained in the system's heat source. Most boiler manufacturers provide this data on their technical literature.

Add the tubing/piping volume to that of the heat source and any other miscellaneous system components (buffer tank, heat exchangers, etc.) and call the total estimated system volume (Vs).

Step 2 -- Determine the required air-side pressure in the expansion tank using Formula 2:

where:

Pa = the proper air side pressure (before adding water to the system) (psi)

H = the height of liquid in the system above the inlet to the expansion tank (ft.)

Dc = the density of the system fluid at its initial (cold) fill temperature (lb. / cubic ft.)

5 = an allowance for 5 psi static pressure at top of system

Formula 2 can be used for systems containing either water or antifreeze solutions. It requires the density of the "cold" fluid used to fill the system. For water use a value of 62.4 lbs./cubic ft. For other fluids look up their density at 60 degrees F in manufacturers literature.

The number 5 at the end of the formula assumes that 5 psi of static pressure is desired at the top of the piping system to help push air out through vents, as well as to suppress vapor pocket formation in high temperature systems. This number can be adjusted up or down. Higher values will result in larger expansion tank sizes and vice versa.

The value "H" in Formula 2 is the vertical distance from the inlet of the expansion tank to the top of the piping system (in ft.). The greater this height is, the greater the static pressure on the tank, and thus the higher the air-side pressurization required to ensure the diaphragm remains fully expanded when the system is filled.

Adjust the air pressure in the diaphragm to the calculated value before you add fluid to the system. This ensures that the diaphragm will not be partially compressed when the system is filled, reducing the acceptance volume of the tank when it's needed (e.g. when the fluid starts to heat up).

Step 3 - Calculate the required minimum expansion tank volume using Formula 3:

where:

Vt = the required minimum volume of the expansion tank gallons)

Vs = the system volume (gallons)

PRV = the pressure at which the pressure relief valve opens (psi)

Pa = the correct air side pressure (psi)

Dh = the density of the system fluid at its final (hot) temperature (lb. / cubic ft.)

Dc = the density of the system fluid at its initial (cold) fill temperature (lb. / cubic ft.)

The volume of the system (Vs) was found in Step 1. The air side pressurization (Pa) was found in Step 2, as was the density of the fluid when the system will filled (Dc). The pressure relief valve setting (PRV) on most residential and light commercial systems is 30 psi.

All that's left is to look up the density of the fluid when the system is at maximum temperature. For water use the graph shown in Figure 2. For antifreeze solution look up the density in the manufacturer's literature for the concentration being used.

Here's an example: Let's say that the top of a piping system is 25 ft. above the expansion tank connection. The system is filled with water at 60 degrees F. Based on the amount of piping and boiler volume it's estimated that the system contains 22 gallons of water. The boiler is equipped with a 30 psi relief valve. The maximum operating temperature of the system will be 200 degrees F. What's the minimum expansion tank volume required?

Solution: The air side pressurization is calculated using Formula 2:

From Figure 2, the density of water at 200 degrees F is 59.9 lbs./cubic ft. Putting the numbers in Formula 3 yields:

Remember, this is the minimum expansion tank volume required for this system. Using a larger volume tank is fine. An oversized tank reduces the variation in system pressure between its temperature extremes, albeit at a higher cost.

## Conservative But Flawed

The above procedure sizes the expansion tank such that the maximum system pressure is 5 psi lower than the relief valve setting assuming all the system fluid reaches the same maximum temperature at the same time (presumably at design load conditions).But in reality, does all the system fluid reach this maximum temperature at the same time? Can you have a system where 200-degree F water is supplied to the heat emitters, and 200-degree F water returns from the heat emitters? Certainly not if any heat is being released. The return side of the distribution system will always be cooler than the supply side.

Now think about a large radiant floor heating system. Perhaps the water in the boiler is in the range of 180 degrees F at design load conditions. But what's the temperature of the water out in the floor circuits? If it's a slab on grade system, say for a large garage facility, the average water temperature in the floor circuits might only be around 100 degrees F. Furthermore, the vast majority of the fluid volume in such a system is in those floor circuits rather than the boiler and near-boiler piping.

Imagine, for example, a facility with a 300,000 Btu/hr. system consisting of a boiler with a volume of 35 gallons, some near-boiler piping with a total volume of 4.5 gallons, and 9,500 ft. of 5/8-inch PEX tubing in the floor slab. The volume in the floor circuits is approximately 132 gallons. That's 77 percent of the total system volume. Assume the proper air side pressurization is 12 psi, and the system has a 30 psi relief valve.

If we sized the expansion tank for this system assuming all the fluid reaches the same temperature as the boiler (e. g. 180 degrees F) the minimum expansion tank volume would be:

Now compare this to a situation in which we size two hypothetical expansion tanks: One for the fluid in the boiler and near boiler piping that reaches 180 degrees F, and another for the fluid in the floor circuits that (conservatively) reaches 110 degrees F at design load.

For the fluid volume that reaches 180 degrees F the minimum expansion tank volume would be:

For the fluid volume that reaches 110 degrees F the minimum expansion tank volume would be:

Now think of the volumes of these two hypothetical expansion tanks being put together into a single tank having a total volume of 3.8+4.2= 8.0 gallons.

That's about half the tank volume calculated with the procedure that assumes all fluid gets to 180 degrees F.

I should also point out that even the second calculation is conservative because it ignores the temperature drop of the fluid in the floor circuits and near boiler piping when the system is operating. This temperature drop tends to lower the average fluid temperature and hence reduce to total expansion volume.

## Where Does This Matter?

Last year, I helped design a radiant floor heating system containing 21 miles of 3/4-inxh PEX tubing. The floor circuits held approximately 2,100 gallons of fluid. The boilers and near boiler piping held about 225 gallons of fluid. 90 percent of the system's volume was in the floor circuits.Using the first procedure the required minimum expansion tank volume would have been 223 gallons. Using the corrected procedure the required minimum expansion tank volume was 89 gallons. The savings realized using the smaller expansion tank was several hundred dollars.

True, on smaller residential systems the difference in expansion tank volume determined by these two approaches is small and the savings are probably minimal. However, many of you are designing larger snowmelt systems and commercial floor heating systems where the difference in the expansion tank volumes can be substantial. In some jobs the corrected calculation procedure could make the difference between an expansion tank that hangs below the air separator, versus one that must be floor-mounted. The latter is one more piece of equipment competing for the precious floor space in most mechanical rooms.

Also remember, glycol solutions expand more than water as they change in temperature. This further increases the difference in the calculated expansion tank volumes. Think about this on your next big snowmelt project.

As I mentioned earlier, technically there's nothing wrong about over-sizing an expansion tank. It simply increases the cost of the job. Some large jobs, without a doubt can absorb this cost.

But we can make the same argument for pipe sizing, closer tube spacing, and oversized wiring. Good designers assess the alternatives and then decide. What we've discussed is simply a tool that lets you compare expansion tank requirements in radiant systems. It's a method that goes beyond "seat of the pants" selection methods. Use it when it's appropriate.