2 Saga of the Dakota Aquifer
The Homestead Act of 1862 opened the northernmost portion of the United States’ Louisiana Purchase of 1803 to settlement. Homesteaders could purchase 160 acres (0.65 km2) of land for $18 with the obligation that it be farmed for five years. The southern part of the Dakota Territory grew from about 10,000 people in 1870 to close to 100,000 in 1880 (Fabry, 2016). High rainfall in the 1870s led to the general belief that “rain follows the plow.” However, the drought of 1886-1889 led to the drilling of many wells for irrigation. The famous artesian well in Woonsocket, South Dakota, USA (Book Cover) was drilled in 1888 and had an initial wellhead pressure of 250 psi (1.7 MPa) and flowed 8000 gal/min (30 m3/min). The drought of 1886-1889 came to the attention of the United States Congress because of its implications for the future of farming in the new states of North and South Dakota. John Wesley Powell, second director of the United States Geological Survey two years after its founding, was called to testify.[2]
“While the Dakota sandstone is one of the most important of the known artesian reservoirs, the amount of land which can be redeemed to agriculture through its aid is yet so small that disastrous results might follow if great expectations were aroused in regard to it.” (Artesian Aquifers are discussed in the GW-Project book by Woessner and Poeter (2020)).
“Such is the complexity of conditions and so great is the danger of disaster through expensive exploitation in ignorance of the true conditions that the subject demands the most skillful investigation which can be bestowed.”
– Powell testimony (1890)
Indeed, skillful investigations were carried out by N. H. Darton[3] (1896, 1901, 1909) and continued throughout the 20th century by pre-eminent United States Geological Survey (USGS) hydrogeologists. Among these, Bredehoeft et al. gave high praise to Darton in the opening paragraph of their 1983 paper.
“The Dakota aquifer in South Dakota is one of the classic artesian aquifers. Many modern ideas concerning artesian aquifers stem from N. H. Darton’s investigation of the Dakota aquifer in the 1890s and early 1900s. This paper is based to a large extent upon Darton’s data and is a tribute to Darton’s ability as a hydrologist.”
Bredehoeft et al. (1983) incorporated several further quotes from Darton (1909, page 60). Of two included below, the first is directly part of this book’s story and the second is parenthetical. The first is Darton’s conceptualization of how outcrops in the Black Hills in the western part of South Dakota provided the driving potential (as discussed in the GW-Project book by Woessner and Poeter (2020)) for flow to the east where the thousands of irrigation wells were completed.
“The evidence of this pressure, as found in many wells in eastern South Dakota, is conclusive that the water flows underground for many hundreds of miles. Such pressures can be explained only by the hydrostatic influence of a column of water extending to a high altitude on the west. If it were not for the outflow of the water to the east and south the initial head which the waters derived from the high lands of the intake zone would continue under the entire region, but owing to this leakage the head is not maintained, and there is a gradual diminution toward the east known as ‘hydraulic grade,’ a slope sustained by the friction of the water in its passage through the strata.”
Darton’s “evidence” was contained in a map of the potentiometric surface of the Dakota aquifer system (Figure 2). From this map and T. C. Chamberlin’s (1885) elucidation of geologic and physical principles that explained artesian conditions, Darton drew a cross-sectional model of the Dakota aquifer system (Figure 3), which is often included in textbooks on hydrogeology. The second quote by Bredehoeft et al. (1983) lamented that Darton’s recognition of leakage through a confining layer was forgotten for many decades.
“Another factor which undoubtedly somewhat influences the hydraulic grade in the Great Plains region is a certain but unknown amount of general leakage through the so-called impermeable strata, especially when under great pressure.”
By 1923 some 10,000 wells were drilled in South Dakota and eventually 15,000 by 1958 (Davis et al., 1961). The original pressure in the Woonsocket well had declined to 130 psi (0.9 MPa) by 1892 and its flow reduced to 1150 gal/minute (4.3 m3/min). By 1915 the pressure had declined further to 45 psi (0.3 MPa) and by 1923 to 35 psi (0.24 MPa) (Meinzer and Hard, 1925). With the passage of 35 years, Meinzer and Hard reflected on the prescience of Powell’s testimony of 1890.
“It is exceedingly interesting and gratifying to note that in March, 1890, when the excitement over the artesian wells must have been about at its maximum, Maj. J. W. Powell, Director of the United States Geological Survey made a statement on the subject before the Committee on Irrigation of the House of Representatives which must have seemed unduly conservative at that time but which clearly indicated the temporary character of the high pressures and discharges and gave an estimate of permanent yield that appears remarkably accurate after 34 years of artesian development and decline.”
Although Meinzer and Hard’s report primarily summarized numerous surveys and measurements of pressures and flows in irrigation wells over time, a four-page section, “Withdrawal of stored water and compression of the Dakota Sandstone,” planted the seed of Meinzer’s 1928 cornerstone paper “Compressibility and Elasticity of Artesian Aquifers.” The difficulty Meinzer addressed in that paper was a mass balance problem.
- Between 1886 and 1923, the average groundwater withdrawal was 3000 gallons/minute[4] (gallons/minute or gpm) (11.4 m3/min) from a row of 18 townships (R65 – R48W), where a township is 6 miles × 6 miles.
- But steady-state lateral flow through a representative cross section of the aquifer based on Darcy’s law, Q = KiA, brings to the townships only 500 gal/min (1.9 m3/min). Darcy’s Law is discussed in the GW-Project book by Woessner and Poeter (2020).
- K = 6.25 × 10–4 ft/s (1.9 × 10–4 m/s) (hydraulic conductivity)
- i = 5 ft/mile (~1m/km) based on the potentiometric map (hydraulic gradient from Figure 1)
- A = 6 miles (~10,000 m) × 60 ft (~20 m) (representative cross-sectional area of the aquifer is one township wide times thickness of the aquifer)
- Q = KiA = (6.25 × 10–4 ft/s) (5 ft/ mi) (6 mi × 60 ft) (60 s/min) (7.5 gal/ft3) = 500 gallons/minute (~2000 liters/minute) (mean west-to-east discharge transecting a north-south boundary of a township)
Calculations (1) and (2) above leave the problem of finding approximately 2500 gal/min (9.5 m3/min), which is the difference between the extraction rate of 3000 gal/min (11.4 m3/min) and the cross-sectional flow rate of 500 gal/min (1.9 m3/min). Meinzer concluded that the excess production must be drawn from preexisting connate water stored in the pores of the aquifer. Meinzer drew circumstantial evidence for this behavior from a variety of hydromechanical observations:
- F.H. King (1892, pages 67-69) wrote that “One of the surprising observations made during this study is that a heavily loaded moving train has the power of disturbing the level of water in the non-capillary spaces of the soil, but in just what manner this is brought about is not easy to see.” (The water level response is shown in Figure 4 of this book following this discussion of evidence.) … “The strongest rises in the level of the water are produced by the heavily loaded trains which move rather slowly. A single engine has never been observed to leave a record, and the rapidly moving passenger trains produce only a slight movement, or none at all.”
- Terzaghi (1925) conducted laboratory experiments in which porosity (void volume divided by total volume) of a pre-compacted sand was measured in response to changes of axial stress (force per unit area) (The pressure response is shown in Figure 5 of this book following this discussion of evidence.) The sample went through several loading and unloading cycles. Although unloading produced permanent compaction, reloading followed the initial trend after the previous cycle’s axial stress was reached. Relevant to Meinzer was that porosity reduction between points a and b in Figure 5 was similar to that needed to account for the missing volume of water in his calculation.
- Schureman (1926) presented data that showed the water levels in an 800-ft deep well in Longport, New Jersey were in phase with ocean tides recorded at Atlantic City seven miles to the northeast. The two locations are on a barrier island that is about 1000 feet (~305 m) wide in the Atlantic Ocean off the east coast of the United States (The tide and well water level responses are shown in Figure 6 of this book following this discussion of evidence.) The correlation had to be due to a mechanical loading effect because 300 feet (90 m) of intervening clays meant that water could not possibly communicate directly with the deep sand (Thompson, 1926).
- Pratt and Johnson (1926) attributed land subsidence at Goose Creek in Galveston Bay to oil, gas, and water extraction from rock pores in the underlying formations (The subsidence is shown in Figure 7 of this book following this discussion of evidence.) In the first three instances above, an applied mechanical load produced a fluid pressure response associated with the reduction of pore volume. Subsidence at Goose Creek showed the converse was also true, namely, that fluid extraction could lead to loss of pore volume.
Meinzer concluded that the difference between extraction volume and recharge volume could be resolved by a decrease in aquifer volume. The change in aquifer volume was considered to occur only through vertical consolidation, ΔVpore/Vpore=Δb/b, where Δ indicates the change in, or the difference between, the pore volume before and after pumping, Vpore is the initial pore volume, and b is the initial aquifer thickness. Limiting deformation to one dimension is an idealization of a three-dimensional problem, but frequently invoked for aquifers of large areal extent. The assumption of zero lateral strain (strain is a measure of the relative change in a length, area, or volume) reduces the problem to just the vertical dimension with vertical strain defined to be εv = – db/b = 4.4 in/60 ft = 0.6 % (Meinzer, 1928, page 281), where the sign convention for εv is that compression is considered to be positive. The vertical strain of 0.6 % meant that the required porosity decrease was from an initial 38.2 % to 37.6 %. With these definitions, Meinzer’s line of reasoning implied that water displaced by 4.4 inches (0.11 m) of aquifer compression over the 648 square miles (1680 km2) of the 18 townships would be sufficient to yield 2500 gal/min (9.5 m3/min) for 38 years. Thus, “compressibility of artesian aquifers” in the title of Meinzer’s paper solved the mass balance problem. It provided a clear exposition of the physical basis of groundwater storage in a confined aquifer.
