## Can you explain the pump math behind the GPM calculation?

**Background**

In a properly running pump station, each time the well level reaches the turn-on point, pumps will be turned on in alternation as driven by the pump control system. The design of such systems requires that the ongoing pumping load (in terms of fluid throughput) be shared equally among the two or three pumps.

While the pumps may have slightly different performance (in terms of GPM throughput), over time their run times in relation to each other ought to converge upon a stable fixed value. That this in fact occurs is assumed and forms the basis for all calculations for GPM. The AlarmAgent RTU will detect sudden drops in the performance of a given pump via the resulting sudden and sustained change in run time ratios.

The following assumptions set the "ground rules" under which the pump performance algorithms in the AlarmAgent RTU work. These assumptions are for "Standard" pump systems. "Non-Standard" systems include variable-speed drives and non-alternating pump control strategies. Pump performance math can only give meaningful GPM or efficiency information when the pumping strategy conforms to the assumptions of the pump math.

**General Pump Station Parameters and Assumptions**

The controller algorithm, however implemented, seeks to guarantee that over time each pump will pump equal volumes.

Station wells and pump GPM ratings are sized to accommodate maximum expected flow over the life of the station. Pumps are replaced/overhauled when performance drops to ~90% of their GPM rating. This would typically take about 10 years of operation.

Actual flow (and hence actual cycle timing) depends on weather, season, time of day and population changes. Assumptions about the actual flow are:

1. Each pump encounters flows with identical statistics.

2. Flow variations between pumps will average zero to over 250 cycles (~3 days).

A typical pump cycle is ~15-30 minutes. The minimum would be 3 minutes, the maximum about 10-12 hours. Older stations or drier conditions tend to have longer cycle times than newer stations or wetter conditions.

Pumps are sized so that they can completely drain a full well (with 0 additional inflow) in 15 to 240 seconds (_ - 4 minutes). Pumps sizes outside this range may have a loss of accuracy or precision in their reported efficiency. Specifically, if the pump can drain the well in less than 15 seconds, the efficiency figure will peg at a value corresponding to the highest reportable 15 second drain rate. If the pump takes longer than 4 minutes (considered the more likely case), then there will be a gradual loss of significant figures in the reported figure. Until, if the pump takes longer than 8 hours the reported value becomes zero.

Pumps may be forced on when the well is not actually full in order to perform maintenance, tests, or when the fill time has exceeded sepsis limits.

Pumps are never run dry. This implies that pump runtime is always limited by how long it takes to empty the well. Once the station performance is known, bounds can be placed on minimum expected runtimes if the well was full. Then, this can be exploited to distinguish manually forced cycles from those initiated by the full-well condition.

**Role of the RTU**

A cycle for a single pump consists of T1, the time the pump is off (and the well is filling). and T2, the time the pump is pumping.

T1 and T2 are the only things that the RTU can measure. The pump math algorithm can only operate upon this data set.

All volumes and flows are relative. Scaling to physical units depends on the well size, float location, control algorithm, calibrations against direct measurement, etc�