The Well / Aquifer Model (Initial Test Results)   -   25


7.2   Effective Well Radius

Effective well radius is defined as that hypothetical empirically determined radius which, if substituted in the drawdown equation of the well, will yield the actual drawdown outside the screen of the well.

An example of this definition can be seen using the data from Figure 49 (Appendix IV) (data record 1). The theoretical Theim equation describing drawdown vs distance from a pumping well can be written:

where:

sw = drawdown measured in pumping well (ft)
Qp = prototype (field) discharge = 6Qm (gpm)
Qm = model discharge (gpm)
T  = model transmissivity = Km 5 (gpd/ft)
Km = model hydraulic conductivity = 26 (gpd ft2)
r2 = distance from model well where drawdown = 0. (r2 = 100 in.)
re = effective well radius (inches)

Using the data from data record 1, equation (39) becomes

sw = 55 ft

From Fig. 49 (Appendix IV), the actual drawdown as measured in the well was

60 - 5.46 = 54.5 ft

Practically speaking, effective well radius as used in these analyses is a measure of the effect of screen and gravel pack on drawdown. Figs. 49 through 73 (Appendix IV) are semi-logarithmic plots of head of water in the model vs the logarithm of distance from the center of the well screen for all 25 tests. Effective well radius is calculated in all of the Figures represents the horizontal extrapolation of the water level in the well (at the edge of the screen 5 inches away from the center of the well) to the intersection of the least-squares line of piezometric head vs distance.

For example, if, as shown on Figure 49, the water level in the well had been 10 ft above the Pressure Transducer reference level instead of 5.46 as was actually measured, the effective well radius would have been about 9.5 inches instead of the 7.44 calculated. Therefore, the larger the effective well radius, the larger the influence the screen/ gravel combination has on well efficiency.

Figure 74 shows a plot of percentage screen open area vs. effective well radius. A hyperbola was fit to the data but, as can be seen in the Figure, little correlation exists. With the exception of the three unstable tests (10, 11, 16) the effective well radius, ranging from 6.3 to 9.5 inches, was fairly independent of the percentage of screen open area.

Fig. 74


7.3   Percentage of Screen Open Area, Entrance Velocity, and Well Efficiency

One of the primary objectives of the present investigation was to investigate the effect of screen entrance velocity on well efficiency for various screen open area percentages. As entrance velocity is a component of both frictional head loss and well efficiency, it is important to understand the interrelationships. The concept of well efficiency measures the magnitude of this frictional head loss term related to a percentage of total well drawdown. The theoretical relationship between percentage of screen open area and well efficiency is hyperbolic in form, as shown in Figure 40 (Appendix II). This Figure is a plot of percentage of screen open area vs well efficiency for the Silverado aquifer, with all screens masked to allow a 1/6 circumference of open area.


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