*How To Size Thermal Expansion Tanks For Hot Water Systems*

In Part 1 of this series, we looked at where thermal expansion tanks are needed. When it is determined that a tank should be included in the plumbing system, the next task is to determine the correct size for the tank. Referring to sizing tables in an expansion tank manufacturer’s catalog is the easiest method, although not the best method, for sizing thermal expansion tanks. Sizing tables provided by the manufacturers, give the tank model number and size based on the water heater’s volume and the system supply pressure. These tables, however, are based on three important assumptions that designers need to be aware of.

*First*, for most manufacturers, the tables are based on a maximum allowable line pressure of 150 psi. This is the maximum allowable working pressure of most water heaters and thermal expansion tanks. It is also the setting of the water heater relief valve. In other words, the thermal expansion tank, if selected by the tables, could accommodate the thermal expansion up to a system pressure of 150 psi, which is the relieving point for the water heater relief valve. Remember that the purpose of the thermal expansion tank is to avoid the relief valve from relieving. Sizing the thermal expansion tank for a maximum allowable pressure of 135 psi, which is 10% below the relief valve set point, is a better alternative.

*Second*, the manufacturer’s tables are based on a tank precharge pressure of 40 psi. Precharge is the air pressure on the airside of the tank bladder. This setting, by the way, is not founded upon an engineering principle but is the Department of Transportation’s limitation for transporting tanks. To reduce the size of the thermal expansion tank, the precharge air pressure should be set equal to the line pressure of the system, not the 40 psi tank precharge pressure that is set from the factory. (Note: if expansion tanks are sized by an engineer based on a precharge air pressure equal to line pressure, the plumbing drawings and specifications should instruct the contractor to charge the expansion tank with air pressure equal to the line pressure.) Since the manufacturer’s sizing table is based on a tank precharge pressure of 40 psi, they do not accurately size an expansion tank when the precharge pressure is equal to the line pressure,.

*Third*, most manufacturers’ sizing tables are based on a 40^{0}F temperature rise of the stored water. Think about this for a moment. The water heater is typically sized based on a 100^{0}F temperature differential. For instance, often we assume cold water enters the water heater at 40^{0}F and is heated and stored at 140^{0}F. If we design the water heater to raise the water temperature 100^{0}F, a conservative approach is to size the thermal expansion tank to accommodate the amount of water expansion resulting from the same 100^{0}F temperature increase. This is, of course, a worst-case scenario (complete emptying of the tank and filling with 40^{0}F cold water). Designing the expansion tank based on only a 40^{0}F temperature rise is less than conservative.

To design a thermal expansion tank for a maximum allowable pressure less than 150 psi, a precharge air pressure different from 40 psi, and a temperature differential greater than 40^{0}F, we can’t consult the manufacturer’s tables. Also, on large systems, the storage tank sizes are often larger than the values given in the tables. So what do we do? We must calculate the proper expansion tank size using engineering *equations*. Here is a simplified method for sizing expansion tanks. A more detailed method is presented in the ASPE Design Handbook, Volume 4.

To select a thermal expansion tank, the total tank capacity and the acceptance volume must be determined. The total tank capacity is the volume of the tank. The acceptance volume is the amount of water that the tank will accept with air pressure on the air-side of the diaphragm.

First, determine the expansion volume of the water in your system. This is the volume of water the expansion tank will have to accommodate, which is also called the “acceptance volume.” The volume of expanded water depends upon the specific volume of water at the entering and heated temperatures and the volume of stored water.

(1) V_{ACC} = V_{T} x (Vs_{2}/Vs_{1} – 1)

where,

V_{ACC} = Acceptance Volume (gallons)

Vs_{2} = Specific volume of water at heated temperature, (ft^{3}/lb)

Vs_{1} = Specific volume of water at entering temperature, (ft^{3}/lb)

V_{T} = Water heater storage tank volume (gallons)

The specific volume of saturated water at various temperatures can be found in tables of thermodynamic properties, or there is a handy table in the ASPE Data Book Volume 2, Table 6-5 Thermal Properties of Water. Here is a good number to remember. Water heated from 40^{0}F to 140^{0}F will expand by 1.7%. For example, let’s assume we have a 120-gallon water heater and the water is heated from 40^{0}F to 140^{0}F.

V_{ACC} = 120 (0.01629/0.01602 – 1) = 120 (.017) = 2.0 gallons

This is the amount of water that the thermal expansion tank would have to accept to prevent pressure spikes in the system. I know that this is a simplified approach. I have ignored the expansion of the heater tank and the hot water piping. It is my experience that the impact of these factors is small and has little effect on the ultimate tank selection.

Keep in mind that when we complete the calculations, we select expansion tanks that come in rather large size increments. That’s why including factors that do not significantly impact the total amount of thermal expansion needed, can safely be omitted from the calculations. If you want to be more precise the equations provided in the ASPE Design Handbook include the expansion of pipe material.

By the way, I also don’t bother correcting for altitude. We typically don’t need that much accuracy. Also, since we are assuming a 100-degree water temperature differential in the calculations, we have some built-in conservatism.

The final step is to determine the total capacity of the expansion tank. The equation for total expansion tank capacity is derived from Boyle’s law. When the precharge pressure will equal the line pressure, use equation (2) below.

(2) V_{ET} = V_{ACC} / (1- P_{1}/P_{2})

where,

P_{1} = Static water line pressure, (psia)

P_{2} = Maximum desired tank pressure, (psia)

V_{ACC} = Acceptance volume, (gallons)

V_{ET} = Total volume of the expansion tank, (gallons)

(*Note that the pressures are absolute pressures (psia). Add 14.7 to gauge pressure to convert to absolute pressure. Also, note that this equation assumes that the air precharge pressure is equal to the line pressure. This equation should not be used if the precharge pressure does not equal the line pressure.)*

If the expansion tank has a 150 psi allowable working pressure, I use 149.7 psia (135 + 14.7 = 149.7) for P_{2}, which is 10% below the set point of the relief valve. Using our example above, let’s assume that the actual line pressure and precharge pressure is 80 psi.

V_{ET} = 2.0 / (1 – 94.7/149.7) = 5.44 gallons

Given a calculated total tank capacity of 5.44 gallons and an acceptance capacity of 2 gallons, consult the manufacturer’s data and select a tank that meets your specific application.

If the precharge pressure does not equal the line pressure, equation (2) cannot be used. The appropriate equation for a precharge pressure that does not equal the line pressure is equation 3 below.

(3) V_{ET} = V_{ACC} / [(P_{1}/P_{2}) – (P_{1}/P_{3})]

where,

P_{1} = Precharge pressure, (psia)

P_{2} = Static water line pressure, (psia)

P_{3} = Maximum desired tank pressure, (psia)

V_{ACC} = Acceptance volume, (gallons)

V_{ET} = Total volume of the expansion tank, (gallons)

For the preceding example, if the expansion tank has a factory precharge of 40 psig and it is not increased to the line pressure of 80 psig, then the required total capacity of the expansion tank increases from 5.4 gallons to 9.4 gallons.

Some manufacturer’s now also have sizing calculators based on these engineering equations on their websites. Click here for an example.

The sizing method described above is for thermal expansion tanks installed in a hot water system. If you are sizing tanks for a booster pump system, the procedure is different.

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