# Modeling a Vacuum Breaker

by Jeff Sines, Senior Product Engineer at Engineered Software, Inc.

In a fluid transmission pipeline with changes in elevation there could be conditions in which the pressure in the piping system goes below the vapor pressure of the fluid.  When this occurs, the liquid in the pipeline turns to vapor and the flow in the pipeline becomes erratic, resulting in pressure surges, flow reversals, and water hammer. This low pressure condition can collapse the piping and also cause physical damage to the pipeline by rupturing welds or seams. To prevent this from happening, vacuum breakers are installed in pipelines to allow air to enter the pipe to prevent a vacuum from forming. In this situation, the pipe will no longer be fully charged, which is an assumption that PIPE-FLO uses to perform its calculations using the Bernoulli equation.

There is no native vacuum breaker component in the PIPE-FLO program. Instead, various PIPE-FLO devices can be used to simulate a vacuum breaker.

We will look at an example to see how to simulate a vacuum breaker in a system with elevation changes that can result in vacuum forming in the pipelines. In the system shown below in Figure 1, a supply sump is locate at Elevation 100 ft and a pump supplies the fluid to the system.  The pipeline rises to the 200 ft elevation and then proceeds downhill to Elevation 120. At Elevation 120 the fluid flows on to the outlet tank located at 180 ft. In addition, the system is designed to isolate the Outlet tank and allow flow to the Alternate tank at Elevation 120. There is a vacuum breaker installed at the 200 foot elevation set to open just below atmospheric pressure (0 psig), which is modeled as a pressure boundary called "Vacuum bkr" and a flow boundary called "Vent". Both are closed in Figure 1.

Figure 1.
Design Case Vacuum Breaker Model

The calculated results for the Design Case is shown in Figure 2 with a flow rate of 1010 gpm. Note that the pressure at Elevation 200 is 0.288 psig which is above the set pressure of the Vacuum breaker. Also, the pressures at all the junctions are above 0 psig.

Figure 2. Calculated Design Case Vacuum Breaker Model

Figure 3 shows the condition in which the Outlet tank at 180 ft is isolated and the path to the Alternate tank at 120 ft is opened. The flow rate through the system will increase due to the change in elevation head which creates a siphon effect. Notice that PIPE-FLO calculates a flow rate of 1675 gpm and the calculated pressure at Elevation 200 is a -24.6 psig, which is less than absolute zero, or 0 psia. This condition cannot occur in real life because an absolute vacuum cannot be achieved (-14.7 psig). When the pressure at Elevation 200 drops below the vapor pressure of the liquid, vapor bubbles would form and flows and pressures would become erratic, potentially damaging the pipeline.

Figure 3. Alternate Flow Lineup

## The Real World

A properly designed system would include a vacuum breaker at Elevation 200 ft to minimize or prevent a vacuum from forming in the pipeline. When the pipeline to the Alternate outlet tank is opened and the pipeline to the Outlet tank closed, the pressure at Elevation 200 begins to drop as the flow rate in the downward flowing pipe P-{006} begins to increase. Once the pressure at Elevation 200 goes below the set pressure of the vacuum breaker, the vacuum breaker opens to break the siphon in the pipeline. The flow rate will be determined by the amount of dynamic head loss and static head (elevation and pressure differences) that the pump must overcome.

With the vacuum breaker open, air would be admitted into the pipeline so the pipe would no longer be fully charged, and the fluid can then free fall down Pipe P-{006} from Elevation 200 into the Alternate outlet tank. The elevation at which the P-{006} becomes fully charged again will depend on the amount of head loss from the fully charged elevation to the Alternate Tank, and the pressure (vacuum) that is obtained at the vacuum breaker and is felt on the surface of the liquid at the point at which the pipeline is fully charged.

How much flow the pump will deliver and at what elevation pipe P-{006} becomes fully charged again depends on the capacity of the vacuum breaker and what pressure (or vacuum) is obtained at the high point of the system. PIPE-FLO can be used to answer these two questions

## Modeling the System with PIPE-FLO®

#### CASE #1: INFINITE CAPACITY VACUUM BREAKER

Figure 4 below shows the system assuming a very large capacity vacuum breaker that can admit enough air to keep the pressure at the high point at atmospheric pressure with the vacuum breaker open.  Notice the pipeline between the Elevation 200 node and the Inlet node is closed, and the pipelines to the Vacuum bkr pressure source and the Vent flow demand are opened. This is the same as breaking the siphon.

Figure 4. Alternate Vacuum Breaker Lineup

Now we have two physical systems:

• The first system includes the Supply sump, the Pump, pipelines, and the pressure demand called Vacuum bkr.
• The second system includes the Vent flow demand, pipelines, and the Alternate outlet tank.

The flow rate through the pump to the Vacuum bkr at Elevation 200 ft is calculated to be 1021 gpm.

To determine the elevation at which Pipe-{006} becomes fully charged again, set the flow rate into the Vent flow demand to the value calculated leaving the Vacuum bkr. Setting the Vent demand to 1021 gpm simulates the flow down pipe P-{006} but this results in the pressure at the vent dropping to -30.71 psig, once again a physically impossible condition. In this scenario with a large capacity vacuum breaker open, the pressure of the liquid inside the pipe will be at atmospheric pressure until the pipe becomes fully charged again. Converting -30.71 psig to feet of head results in -70.94 feet (= -30.67*2.31), which means the pipe will become fully charged at 129.1 feet (=200 ft -70.94 ft).

Another way to determine this level in PIPE-FLO is to iteratively change the elevation of the vent demand and Inlet node until the calculated pressure at those two nodes equals zero, as was done in Figure 5 below. The elevation was determined to be 128.89 feet, very close to the 129.1 feet determined by the first method.

Figure 5. Iteratively determining the elevation at which the pipe becomes fully charged.

#### CASE #2: SMALL VACUUM BREAKER THAT ALLOWS A VACUUM AT THE HIGH POINT

Figure 6 below shows the system in which a smaller vacuum breaker is installed and the vacuum at the high point is -4 psig (or about 8.1 inches of mercury vacuum). In the PIPE-FLO model, the pressure boundary "Vacuum bkr" was changed to -4 psig and a flow rate of 1170 gpm was calculated. The pressure at the Vent is calculated to be -29.57 psig. The elevation at which the pipe becomes fully charge will have a vacuum of -4 psig felt on it, so the difference (-29.57 - (- 4) = 25.57 psi ) can be converted to feet (25.57 psi x 2.31 = 59.07 ft) which can then be used to determine the fully charged elevation (200 - 59.07 = 140.93 ft).

Figure 6. System with -4 psig vacuum at the high point

To perform the elevation calculation iteratively as shown in Figure 7 below, the flow at the Vent demand was set to 1170 gpm and the elevation changed iteratively unitl the pressure at the Vent was calculated to -4 psig. An elevation of 140.82 feet was determined iteratively. This is within reasonable engineering accuracy for the 140.93 ft elevation calculated previously.

Figure 7. Iteratively determining the elevation at which the pipe becomes fully charged with a vacuum of - 4 psig at the vacuum breaker.

## Summary

### Key Points About Modeling the Vacuum Breaker

The previous analysis makes some key assumptions about what is happening in the piping system. The head loss caused by the two-phase flow between the vacuum breaker and the elevation at which the pipe becomes fully charged is neglected in this analysis. Depending on the nature of the two-phase flow (slug flow, bubbly flow, annular flow, etc.), this assumption will introduce a level of error in the flow rate and elevation calculations. The methods presented above will get the engineer "in the ballpark" and if more accurate results are needed, software that can calculate the head loss and pressure drop for two-phase flow should be used.

Additionally, the value of vacuum that will be obtained will depend on the capacity of the vacuum breaker.