The Well / Aquifer Model (Initial Test Results) - 17
5.3 Pumped Well Efficiency
With consideration of all factors contributing to head loss as
specified in equation (4), a less rigorous theoretical approach to the problem of
screen loss can be formulated. To understand this latter approach, the concept of
"well efficiency" must be introduced. This concept of pumped well efficiency was
first presented by Jacob in 1947. Basically, Jacob defines well efficiency as the
formation loss (the laminar head loss required to produce flow in the aquifer) divided
by the total drawdown as observed in the well. This quotient is expressed as a
percentage.
Figure 15
Figure 15 is a simplified sketch
illustrating this concept. Since ground-water flow through porous media is laminar
in nature, the head loss required to produce flow through the aquifer is proportional
to the first power of the well discharge:
Formation loss = BQ
where:
B = formation loss coefficient
Q = well discharge
Formation loss is defined as the difference between the static
(non-pumping) water level in the aquifer and the water level observed in the aquifer
(or gravel pack) immediately adjacent to the well casing or screen.
As water enters a well through screen openings, its velocity
increases as the jetting action produces a turbulent flow condition. The turbulence
caused by the jetting action through the well screen, as well as the change in direction
of the water as it is forced to move axially, results in an additional head loss term.
Head loss associated with this turbulent flow is known as well loss and varies
approximately as the second power of the discharge.
Well loss = CQ2
where C = Well loss coefficient
The formation loss coefficient (B) is related to aquifer
characteristics, while well loss coefficient (C) is a function of well screen design,
geometry, and effective area of opening. The total drawdown, observed in the well,
can be stated as a sum of formation loss plus the well loss:
s = BQ + CQ2 (26)
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