Ground Water, continued
Permeability of Water-bearing MaterialsThe rate of movement of ground water is determined by the size, shape, quantity, and degree of interconnection of the interstices and by the hydraulic gradient. The capacity of a water-bearing material for transmitting water under hydraulic head is its permeability. The coefficient of permeability may be expressed as the rate of flow of water, in gallons a day, through a cross-sectional area of 1 square foot under hydraulic gradient of 100 percent at a temperature of 60 deg. F. (Meinzer's coefficient; see Stearns, 1927, p. 148.) The coefficient of transmissibility is a similar measure and may be defined as the number of gallons of water a day transmitted through each 1-foot strip extending the height of the aquifer under a unit-gradient (Theis, 1935, p. 520). The coefficient of transmissibility may also be expressed as the number of gallons of water a day transmitted through each section 1 mile wide extending the height of the aquifer, under a hydraulic gradient of 1 foot to the mile.
The coefficient of transmissibility is equivalent to the coefficient of permeability (corrected for temperature) multiplied by the thickness of the aquifer.
The coefficient of permeability of water-bearing materials can be determined in the laboratory (methods summarized by V.C. Fishel in Wenzel, 1942, pp. 56-58) or in the field. Pumping tests were made in Grant and Stevens Counties between June 1, 1941, and October 1, 1942, by Melvin S. Scanlan of the Division of Water Resources of the Kansas State Board of Agriculture and Woodrow W. Wilson of the Federal Geological Survey. Discharge measurements were made using a Collins flow meter (Pl. 8) and measurements of drawdown and recovery were made using a steel tape or an electrical measuring device, or both.
Theis (1935) has shown that to the extent that Darcy's law governs the motion of ground water under natural conditions and under the artificial conditions caused by pumping, an analogy exists between hydrologic conditions in an aquifer and thermal conditions in a similar thermal system. Darcy's law is analogous to the law of the flow of heat by conduction, hydraulic pressure being analogous to temperature hydraulic gradient to thermal gradient, permeability to thermal conductivity, and specific yield to specific heat. From his equation expressing the relation between the draw-down and the rate and duration of discharge of a well, Theis developed the following recovery formula for determining the transmissibility of an aquifer (as defined above):
T = (264q / s) log10(t / t1)
in which T = coefficient of transmissibility
The residual drawdown (s) is computed by subtracting the static water-level measurement (Table 5) from water-level measurements made after pumping stops (Fig. 9). The proper ratio
log10(t / t1) / s
is determined graphically by plotting log10(t / t1) against corresponding values of s (Fig. 9). This procedure is simplified by plotting t / t1 on the logarithmic coordinate of semi-logarithmic paper. For any convenient value of log10(t/t1), the corresponding value of s may be found by inspection, provided the curve passes through the origin. If the curve does not pass through the origin, it can be made to do so approximately by applying an empirical correction to the 264 formula as follows:
T = (264q / s) log10[(t +/- c) / t1]
in which c is a correction factor (Wenzel, 1942, p. 127). Only one (well 115) of the curves for tests in Grant and Stevens Counties passed through the origin. The correction factors needed to make the other curves pass through the origin ranged from -185 to +147.
Figure 9--(A) Recovery curve for well 115. (B) Curve for pumping test on well 115 obtained by plotting s against t/t1.
The weighted average discharge (q) of well 115 was 680 gallons a minute (Table 5). When values for s, (t / t1), and q are substituted in the Theis recovery formula, the coefficient of transmissibility of the water-bearing material at the pumped well is found to be 43,573. Dividing the coefficient of transmissibility by the average thickness of the saturated water-bearing material in the vicinity of the well, 295 feet, the average coefficient of permeability is found to be about 148. (The temperature of the water was 60 deg. F., hence no temperature correction is needed.) Data on seven pumping tests in Grant and Stevens Counties are listed in Table 6.
Table 5--Data on pumping test of well 115, Grant County, made on September 25, 1942, by Melvin Scanlan, Woodrow W. Wilson, and Thad G. McLaughlin.
The irrigation wells listed in Table 6 obtain water primarily from the Rexroad (?) formation but also from the lower part of the Meade formation. As indicated by the pumping tests, these deposits have low to moderate permeabilities, but because of the great thickness of saturated material the coefficient of transmissibility generally is large. Some wells, such as 299, penetrated deposits consisting primarily of silt, whereas wells 244 and 247 encountered thick deposits of sand and gravel. Two of the wells listed in Table 6 (30 and 56) penetrated the entire thickness of saturated material above the Cretaceous deposits.
Table 6--Results of pumping tests in Grant and Stevens Counties.
(b) Coefficient of transmissibility divided by thickness of saturated water-bearing material; temperature of water 60 deg. F., hence no correction for temperature is needed.
The Rexroad (?) formation in places contains beds of saturated sand and gravel in which the ground water is confined by overlying beds of clay which are relatively impermeable. Wells drilled to these water-bearing beds encounter water under artesian head, and in Lakin Draw and North Fork Cimarron Valley the head is sufficient to cause a few of them to flow. Artesian water has been en-countered in many wells in Grant, Haskell, and Stevens Counties, but the water generally is not under sufficient head to flow at the surface.
The only flowing wells in this area are near Ulysses. Well 47 encountered artesian water at a depth of about 160 feet, and in 1943 it had a measured yield of 1.25 gallons a minute. A feebly flowing well about 2 miles southeast of Ulysses in North Fork Cimarron Valley was reported to be 220 feet deep.
Kansas Geological Survey, Grant, Haskell, and Stevens Geohydrology|
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Web version May 2002. Original publication date July 1946.