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Ground Water

Ground Water, continued

Permeability of the Water-bearing Materials

The permeability of a water-bearing material--that is, its capacity to transmit water under hydraulic head--may be determined in the field by tests of ground-water velocity or by discharging-well methods.

Ground-water Velocity Method

In 1904, Slichter (1906, pp. 7-16) made tests of the velocity of the underflow in the Arkansas valley 2 miles west of Garden City and at Holcomb (referred to as Sherlock in Slichter's report) in Finney County. The method developed and used by Slichter consists of driving several small wells into the water-bearing formation in such a manner that the movement of water is from one well toward one or more of the other wells. A salt is introduced into the up-gradient well and the electrolyte thus formed is allowed to move down-gradient toward the other wells, where its arrival is detected electrically. The rate of movement of the electrolyte and hence the rate of movement of the ground water is computed from the elapsed time between the introduction of the salt in the up-gradient well and its detection in a well located downgradient. Slichter made several tests at each location and found that the natural velocity of the ground water 2 miles west of Garden City ranged from 1.3 to 10.3 feet per day and averaged 6 .6 feet per day. He found that the natural velocity of the ground water at Holcomb ranged from 2.0 to 22.9 feet per day and averaged 8.9 feet per day. The wells used in making the velocity tests ranged from 11 to 65 feet in depth, and tapped only the alluvial deposits of the valley.

Slichter did not compute permeability after determining the natural velocity of the ground water. Permeability can be computed, however, by using the equation Pm = (7.48 pvCt)/I, in which Pm is Meinzer's coefficient of permeability, p is the porosity of the water-bearing material, v is the velocity of the ground water in feet per day, and I is the hydraulic gradient in feet per foot (Wenzel, 1942, p. 71). The coefficient of permeability as defined by Meinzer is expressed as the number of gallons of water a day, at 60 deg. F., that is conducted laterally through each mile of the water-bearing bed under investigation (measured at right angles to the direction of flow), for each foot of thickness of the bed, and for each foot per mile of hydraulic gradient (Stearns, 1927, p. 148).

The average hydraulic gradient 2 miles west of Garden City is 7.5 feet to the mile or 0.00142 foot per foot, and the average velocity of the ground water as determined by Slichter was 6.6 feet per day. The temperature of the ground waters in the area where Slichter's work was done averages about 60 deg. F., so that no correction for temperature is needed. By using an assumed porosity of 30 percent and substituting these values in the above equation, the coefficient of permeability of the water-bearing materials 2 miles west of Garden City is computed to be about 10,400.

Using the same equation, but substituting 8.9 feet per day for v, the coefficient of permeability of the water-bearing material at Holcomb is computed to be about 14,000.

Theis Recevery Method

Theis (1935) developed the following formula for determining permeability from the recovery of the water level in a well:

T = (264q/s) log10 (t/t1)

in which T = coefficient of transmissibility
q = pumping rate (in gallons a minute)
t = time since pumping began (in minutes)
t1 = time since pumping stopped (in minutes)
s = residual drawdown at the pumped well (in feet) at time t1

The coefficient of transmissibility is the product of the field coefficient* of permeability and the thickness of the saturated portion of the aquifer. The Theis formula is based on the assumption that if a well is pumped at a constant rate of discharge for a known period and then left to recover, the residual drawdown at any instant will be the same as if the discharge of the well had been continued, but a recharge well having the same (flow) had been introduced at the same point at the instant the discharge actually stopped (Wenzel, 1942, p. 95). It does not assume equilibrium conditions.

(* - The field coefficient of permeability differs from Meinzer's definition of coefficient of permeability chiefly in that it does not include a temperature correction.)

The value of (log10 t/t1)/s is determined graphically by plotting log10 t/t1 against corresponding values of s. Most of the points should fall on a straight line and this straight line should pass through the origin. If the straight line does not pass through the origin, it may be made to do so by empirically applying a correction factor to t. With the empirical correction factor the Theis formula is as follows:

T = (264q/s) log10 [(t +/- c)/t1]

where c is the value whose magnitude is such that the straight line determined by plotting log10 [t +/- c)/t1] against s will pass through the origin (Wenzel, 1942, p. 96).

Pumping tests to determine the permeability of the water-bearing material by the Theis recovery method were made on six wells in the Finney-Gray area. The field tests were conducted by Woodrow Wilson, of the Federal Geological Survey, and Melvin Scanlan, of the Division of Water Resources, Kansas State Board of Agriculture. The results of one test were obviously in error so they have been omitted from this discussion. In computing the results of the other five tests, it was necessary to apply the correction factor to make the straight lines pass through the origin. The results of the five tests are given in table 4.

Sumary

The coefficients of permeability of the alluvium in the Arkansas valley determined by using the ground-water velocity method were 10,400 and 14,000, as compared with 1,030 computed for well 454 by the Theis recovery method. The latter figure, 1,030, is probably more nearly of the right order of magnitude. Certain inherent errors of the ground-water velocity method as used by Slichter may be pointed out. Errors in determining the velocity of the ground water may have been caused by an increase in the hydraulic gradient caused by the rise of water in the up-gradient well at the time the salt was introduced and by the fact that the water-bearing material under study is highly lenticular, allowing greater velocity along certain "pipes" of more permeable material. The wide range in velocities obtained by Slichter indicates that certain measurements were made along "pipes" of this kind, and other measurements were made along "pipes" of material having a very low permeability. For lenticular material of this type, it would be very difficult to evaluate the ground-water velocities obtained in order to arrive at an average velocity.

Wells 160 and 450 tap the same water-bearing formations, but the computed coefficient of permeability of the material at well 450 is about 2 1/2 times greater than that of the material at well 160. A comparison of the specific capacities and the thickness of water-bearing materials at the two wells also show that the water-bearing material at well 450 has a greater permeability than the material at well 160. Well 160 has a specific capacity of 32, and the thickness of the water-bearing material is about 160 feet; whereas the thickness of water-bearing material at well 450 is about 148 feet, yet well 450 has a specific capacity of 46.

 Kansas Geological Survey, Finney and Gray County Geohydrology Comments to webadmin@kgs.ku.edu Web version April 2002. Original publication date Dec. 1944. URL=http://www.kgs.ku.edu/General/Geology/Finney/06_gw2.html