### Well-pump energy calculation method

To calculate electrical energy for well pumps, we first calculate the energy needed to lift and pressurize the water for delivery to the home, then divide by the overall efficiency of the pump and motor system (Wateright 2003 and Greenberg 2005). The amount of energy required is a function of the amount of water consumed by the household. We estimate annual indoor water consumption using the following equation developed through a water end-use metering study (Mayer et al. 1999).

AIC = (37.2 x occupants + 69.2) x 365            Equation 26

where:

AIC            = Annual indoor water consumptions (gallons)

Occupants = total number of household occupants

365           = converts daily to annual consumption

Outdoor water consumption is estimated using data from Mayer et al. (1999). Because outdoor water use depends heavily on house-specific usage patterns (e.g., landscaping or swimming pools), we allow the user to select their outdoor water usage category, shown in Table 22.

Table 22. Outdoor Annual Water Consumption per Household

 Outdoor water usage categorya Outdoor water consumption (thousand gallons per year) Roughly 5 min/day 10b Roughly 30 min/day 50b Roughly 45 min/day 84.7c Roughly 1.25 hours/day 150d Roughly 2 hours/day 200b Roughly 2.75 hours/day 300 Roughly 3.5 hours/day 400

Notes:

a Watering times assumes a typical garden house with 5 gal/min flow rate.

b These values are drawn from Mayer et al., table 5.14. All other values are extrapolations extending the range for use as a user input.

c This is the mean value of outdoor water use reported by Mayer et al. (146,100 gallons mean annual household consumption, with 58% of that amount allocated to outdoor uses).

d Default value.

Equation 27

where:

WP       = Annual average water power (hp)

TDH     = Total Dynamic Head (feet)

GPM     = Annual average flow rate of well (gallons per minute)

= Annual water consumption (gallons per year) ÷ 525,600 (min/year)

3960    = Unit conversion constant (feet•gallons/minute to horsepower)

To calculate total dynamic head (TDH), we use the following equation.

where:

In practice, dynamic head would be a function of the depth to water and also include a term for friction losses in the piping. To simplify our calculations and make it easier for the user to describe their well system, we calculate dynamic head using the well depth (which will always be greater than the depth to water) and ignore piping friction losses, under the assumption that these two factors approximately cancel each other out. As a default, we assume that the average residential well in the U.S. is 150 feet deep. Because pressurization head (the pressure at which water is delivered to the piping in the house) is normally expressed using units of pressure (rather than feet of head), we convert from pressure to head using a ratio of 2.31 feet of head per psi. We assume 50 psi as a typical pressurization level for residential water systems supplied by wells. Pressurization head is only included if the user indicates that the water pressure in their house is provided by a water pump (versus gravity flow from storage).

EP = WP x 0.746 x 1/eff           Equation 29

where:

EP       = Electrical power (kW)

WP      = Water power (hp)

eff         = Overall efficiency of pump and motor system (decimal value, 0 to 1)

The efficiency of pump and motor systems can vary widely depending on the type of pump and motor, well configuration, and maintenance practices. Representative values for efficiency are not published, but it has been suggested that overall efficiencies between 0.15 and 0.60 are typical. For modeling in HES, we assume a combined efficiency of 0.40 for residential well pump/motor systems. For modeling best available pump/motor systems, we assume a combined efficiency of 0.60.

Finally, we calculate annual energy consumption for well pumping using the following equation:

PumpingEnergy = EP x 8760            Equation 30

where:

8760      = hours per year

 The Mayer et al. study shows that indoor water use is relatively constant across the country, but outdoor water use can vary by a factor of 20 or more between regions of the country. A possible future improvement to our water use model would be to use the Mayer et al. study to estimate the relationship between climate and outdoor water use.