A Guide To Water Well Casing and Screen Selection   -   28

9.0  APPENDICIES AND TABLES

 

9.1  APPENDIX I

Well Efficiency

Well loss and formation loss in a pumping well. The concept of pumped well efficiency was first presented by Jacob in 1947. Basically, he defines "well efficiency" as the formation loss (the head loss required to produce flow) divided by the total drawdown observed in the well. This quotient is expressed as a percentage.

To the right is a simplified sketch illustrating this concept. Since ground-water flow through porous media is laminar in nature, the head loss required to produce the flow through the aquifer is proportional to the first power of the well discharge:

Formation loss = BQ
Where: B = formation loss coefficient.

The formation loss therefor is the difference between the static (non-pumping) water level and that water level observed in the aquifer (or gravel pack) adjacent to the casing or screen, (e.g. a small diameter piezometer placed in the gravel pack would measure only formation loss).

As the water enters the well bore through the screen openings, the velocity increases such that the flow becomes turbulent. The turbulence is caused by the "jetting" action through the well screen slots and the change in direction of the water as it enters laterally and is forced to move axially. The head loss associated with this turbulent flow is known as the well loss and varies as the second power of the discharge.

Well loss = CQ2
Where: C = Well loss coefficient.

The formation loss coefficient then is related strictly to aquifer type, while the well loss coefficient is a function of well screen design and geometry (effective area of opening, type and nature of slots or louvers). The total drawdown S observed in the well is simply the sum of the formation loss plus the well loss.

Total drawdown observed in well:
S=BQ + CQ2

The pumped well efficiency is a measure of the effectiveness of the well screen as a transmitting medium between the aquifer (or gravel pack) and the well bore. This effectiveness (or well efficiency) is quantitatively expressed as:

Pumped Well Efficiency:

Rearranging the above equation results in:

Pumped Well Efficiency:

As can be seen in the above equation, the well efficiency is not a constant but varies inversely with discharge (i.e. efficiency is maximum for low discharges and minimum for high discharges).


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