Total Condenser Flow with a Two Stage Economizer

The unit is a 400 ton, R-134a, four-stage compressor, with a two-stage flash gas economizer. To perform a heat balance and diagnose a condenser problem, the total flow of refrigerant through the condenser needs to be known.
The full flow through the condenser is the sum of the evaporator and the compressor side loads from the economizer.
The gas in the economizer is part liquid, part vapor, the vapor goes to the compressor, the liquid proceeds toward the evaporator.
Multi-stage compressors have an ability to introduce gas in between impellor stages. This gas is taken from the economizer which lowers the pressure in the economizer stage, the result is an increase in refrigeration effect and a reduction of heat exchange surface area (which reduces first costs, maintenance costs, and is very desirable).
Below is a basic arrangement of the two-stage economizer and four-stage compressor system (no valves or controls are shown). The arrows mark the basic direction of flow and the numbered points mark the location of where the data points are associated with the points on the pressure enthalpy diagram (next figure).
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Point 1, is the compressor suction, point two, is the discharge of the first stage. Point 3, is the mixture of gas from the first stage and the low side economizer is, point 4.
Point 5, is the discharge of the second stage, point 6 is the mixture of the second stage and the high side economizer is, point 7.
Point 9, is the discharge of the compressor, point 10, the liquid leaving the condenser, point 11, is the high side liquid condition, and point 12, is the low side liquid condition.
The system above is plotted on a pressure-enthalpy diagram below:

The first step is to determine the mass flow of refrigerant through the evaporator. The unit is a 400-ton unit, to find the mass flow of refrigerant multiply 400 X 200 Btu/minute/per ton, and divide by the enthalpy difference between point 1, and point 12, or, 163 – 73 = 90 Btu/pound/minute, so (400 X 200)/90 = 888.8 pounds per minute.
889 pounds per minute are flowing through the evaporator (I rounded up), we can now determine the ratio of the pounds of flash gas to pounds of liquid in the low side from the enthalpy values at points 11, 12, and 4 as follows:
(Point 11 – Point 12)/ (Point 4 – Point 11), or (83 – 73)/ (165 – 83) = .122
To find the flash gas flow multiply .122 by 889 to get, 108.5 pound per minute of flow for the flash gas from the low side economizer.
Next step is to find the flow from the high side economizer.
The flow is cumulative through the compressor, so, our new flow is 889 + 108.5 = 997.5 pound per minute to the third stage.
We need to find the ratio of gas to liquid again using the same approach except this time using points, 10, 11, and 7. (Point 10 – Point 11)/ (Point 7 – Point 10) = (101 – 83) / (171 – 101) = .257
Using the flow of 997.5 multiplied by .257 we get, 256 pounds per minute flow from the high side economizer.
So, to find the full flow to the condenser, 889 + 108.5 + 256 = 1253.5 pounds of refrigerant per minute through the condenser.
Note: Point 3 and 6 are internal to the compressor and not likely obtainable in the field, since you have the two ratios needed now, the points can be found using the pressure enthalpy diagram as follows:
Point 3 = (Point 2 enthalpy + (low side ratio X Point 4 enthalpy))/ (1 + (low side ratio))
Point 3 = (169 + (.122 X 165))/ (1 + .122) = 168.6
Point 6 = (Point 5 enthalpy + (high side ratio X Point 7 enthalpy))/ (1 + (high side ratio))
Point 6 = (176 + (.257 X 171))/ (1 + .257) = 174.9
Point 3 and point 6 are in reasonable agreement to the design information with error likely attributed to me reading the scaling on the chart.
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