flowing wells: terminology, history and role in the

Hydrol Earth Syst Sci 24 6001ndash6019 2020httpsdoiorg105194hess-24-6001-2020copy Author(s) 2020 This work is distributed underthe Creative Commons Attribution 40 License

Flowing wells terminology history and rolein the evolution of groundwater scienceXiao-Wei Jiang1 John Cherry2 and Li Wan1

1MOE (Ministry of Education) Key Laboratory of Groundwater Circulation and EvolutionChina University of Geosciences Beijing 100083 China2G360 Institute for Groundwater Research University of Guelph Guelph Ontario N1G 2W1 Canada

Correspondence Xiao-Wei Jiang (jxwcugbeducn)

Received 2 June 2020 ndash Discussion started 22 June 2020Revised 10 November 2020 ndash Accepted 10 November 2020 ndash Published 21 December 2020

Abstract The gushing of water from flowing wells at-tracted public attention and scientific curiosity as early asthe 17th century but little attention has been paid to theinfluence of flowing wells on the evolution of groundwaterscience This study asserts that questions posed by flowingwells since the early 19th century led to the birth of manyfundamental concepts and principles of physical hydrogeol-ogy Due to the widespread occurrence of flowing wells inbasins with regional aquitards there is a long-lasting mis-conception that flowing wells could only occur in regionallyconfined aquifers However the recognition of possible oc-currence of flowing wells in unconfined aquifers was antic-ipated at the turn of the 20th century based on observed in-creases in hydraulic head with depth in topographic lows ofbasins without apparent aquitards This was later verified inthe 1960s by field and modeling studies that gave birth toquantitative analysis of topographically driven groundwaterflow systems which was a paradigm shift in hydrogeologyFollowing this paradigm several preconditions for flowingwells established in the 19th century were found unneces-sary Intermingled in the evolution of flow system conceptsare inconsistencies and confusion concerning the use of theterm ldquoartesianrdquo so we propose avoidance of this term Thishistorical perspective of the causes of flowing well condi-tions and the influence of flowing wells on groundwater sci-ence could lead to a deeper understanding of the evolution ofgroundwater science and guide future studies on hydraulicsof flowing wells

1 Introduction

The primary motivation for the study of groundwater is itsimportance as a resource (Back and Herman 1997 Freezeand Cherry 1979) Groundwater from springs was utilized inthe Middle East some 10 000 years ago (Beaumont 1973)and produced from shallow flowing wells in the WesternDesert of Egypt in the first millennium BCE as dug wellsreached greater depths (Commander 2005) However hy-drogeology did not emerge as a distinct science until the19th century (Fetter 2004) which corresponds to a pe-riod when deeper-drilled flowing wells became a substan-tial source of water supply in Europe (Howden and Mather2013) It was acknowledged that the recognition of the greatvalue of flowing wells in Europe in the 18th century stim-ulated the advancement of water well drilling technology(Davis and De Wiest 1966) and the maturation of geologicaland hydrological sciences in the 19th century led to the birthof hydrogeology in the 19th century (Meyer et al 1988)However little attention has been paid to the importanceof the scientific questions prompted by flowing wells in theearly evolution of groundwater science in the 19th century

This review aims to demonstrate that flowing wells con-tributed to not only the birth but also the evolution of severalaspects of hydrogeology Freeze and Back (1983) dividedphysical hydrogeology into three domains ie physics ofgroundwater flow well hydraulics and regional groundwa-ter flow Following these domains studies directly or indi-rectly related to flowing wells are divided into four threads(Fig 1) covering all of the three domains The first threethreads shown in Fig 1 stem from flowing wells in confined

Published by Copernicus Publications on behalf of the European Geosciences Union

6002 X-W Jiang et al Flowing wells terminology history and the role in the evolution of groundwater science

Figure 1 Four threads of evolution of physical hydrogeology stemmed from flowing wells The yellow ellipses are field phenomena offlowing wells the purple boxes are papers directly related to flowing wells and the white boxes are papers less or not directly related toflowing wells but have connections to previous or follow-up studies on flowing wells The publications labeled with a ldquolowastrdquo are the sevenclassical studies identified by both Freeze and Back (1983) and Anderson (2008)

aquifers while the fourth is from flowing wells in uncon-fined aquifers Following Freeze and Cherry (1979) a con-fined aquifer is a saturated permeable geologic unit that isconfined between two aquitards while an unconfined aquiferis the saturated part of a permeable geologic unit in whichthe water table forms the upper boundary The seven classi-cal studies that were selected by both Freeze and Back (1983)and Anderson (2008) as benchmark papers of physical hy-drogeology (groundwater hydrology) have been included inthe four threads Moreover four out of the seven papers aredirectly related to flowing wells implying that flowing wellscan be considered at least one of the roots of physical hy-drogeology

The paper is organized as follows We first introduce theterms used to represent flowing wells with conceptual ex-amples of the root difference between confined and uncon-fined sources for these wells (Sect 2) Section 3 summarizesthe history of drilling flowing wells in selected regions thathave inspired hydrogeologists Sections 4 through 7 then his-torically sequence the principal hydrogeological publicationsthrough which flowing wells played a major role in the evo-lution of the science as we know it today Finally concludingremarks are given in Sect 8

2 Terms related to flowing wells and confusion ofldquoartesianrdquo

21 Terms representing flowing wells

In the groundwater hydrology hydrogeology or hydrologytextbooks available to the authors we found that the phe-

nomenon of a well that overflows at the surface is defined orat least mentioned in 34 textbooks The widely used termsinclude ldquoflowing wellrdquo ldquoartesian wellrdquo and ldquoflowing artesianwellrdquo which appear in 17 15 and 13 textbooks respectively(sometimes more than one term is used in one book) Otherless frequently used terms include ldquoartesian flowing wellrdquoldquooverflowing wellrdquo and ldquofree flowing wellrdquo For convenienceof discussion we divide these six terms into two categoriesthose using the term ldquoartesianrdquo and those not using ldquoarte-sianrdquo

The terms ldquoflowing wellrdquo ldquooverflowing wellrdquo and ldquofreeflowing wellrdquo stem purely from the phenomenon of wateroverflow at the well outlet presumably at grade level Theterm ldquooverflowing wellrdquo has been used in Britain since atleast as early as the 1820s (Anonymous 1822) and currentlyis still widely used in Britain as found in several textbooks(Hiscock and Bense 2014 Price 1996 Rushton 2003) Tothe best of the authorsrsquo knowledge the term ldquoflowing wellrdquowas first used in the USGS (United States Geological Survey)hydrogeologic report The Requisite and Qualifying Condi-tions of Artesian Wells (Chamberlin 1885) and is currentlythe one most widely used The term ldquofree flowing wellrdquocan be found in three textbooks available to us (Fitts 2013Kruseman and de Ridder 1990 Nonner 2003) By includ-ing the adjectives ldquoflowingrdquo ldquooverflowingrdquo or ldquofree flow-ingrdquo these terms have clear meaning to represent wells thatgroundwater could flow out of without the aid of pumping

The number of textbooks that use one or two of the termsldquoartesian wellrdquo ldquoflowing artesian wellrdquo or ldquoartesian flowingwellrdquo is as high as 28 indicating the popularity of the ad-jective ldquoartesianrdquo The term ldquoartesian wellrdquo originates from

Hydrol Earth Syst Sci 24 6001ndash6019 2020 httpsdoiorg105194hess-24-6001-2020

X-W Jiang et al Flowing wells terminology history and the role in the evolution of groundwater science 6003

ldquowell of Artoisrdquo (ldquoArtesiardquo is the historical Latin name ofArtois an ancient province in northern France) It is unques-tionable that it was the phenomenon of water overflow atthe surface which attracted peoplersquos attention to wells of Ar-tois drilled in 1126 (Fuller 1906 Norton 1897) The termldquoartesian fountainrdquo was applied in French scientific litera-ture to represent flowing wells in 1805 (Lionnais 1805)and the term ldquoartesian wellrdquo was widely used in FranceBritain and the United States in the 1820s and 1830s (Arago1835 Buckland 1836 de Thury 1830 Garnier 1822 Stor-row 1835) Currently an artesian well is synonymous witha flowing well in the majority of European textbooks wehave inspected (Hendriks 2010 Kruseman and de Ridder1990 Price 1996 Rushton 2003 Brassington 2017 Davie2008 de Marsily 1986 Houmllting and Coldewey 2019) and inat least eight textbooks in North America (Deming 2002Domenico and Schwartz 1998 Driscoll 1986 Pinder andCelia 2006 Yeh et al 2015 Hornberger et al 2014 Fitts2013 Alley and Alley 2017) Since the late 19th centurythe term artesian well was not restricted to flowing wells butwas divided into flowing artesian wells and non-flowing arte-sian wells (Carpenter 1891 Norton 1897 Slichter 1899)In the 10 textbooks in North America that we inspected (Fet-ter 2001 Freeze and Cherry 1979 Batu 1998 Kasenow2010 LaMoreaux et al 2009 Mays 2012 McWhorter andSunada 1977 Heath 1983 Schwartz and Zhang 2003 Toddand Mays 2004) the term flowing artesian well is used torepresent a flowing well and an artesian well is equivalentto a well penetrating a confined aquifer but not necessarilyflowing at the surface

Due to the widespread occurrence of aquitards it wasinitially believed that only a confined aquifer bounded byaquitards has the possibility for the static water level tohave hydraulic head higher than the ground surface eleva-tion ie flowing wells could occur only in confined aquifersLater studies found that flowing wells could also occur inan unconfined aquifer ie a homogeneous aquifer withoutaquitards (Hubbert 1940 Toacuteth 1966 Versluys 1930) Be-cause the adjective ldquoartesianrdquo indicates the type of aquiferin Artois ie a confined aquifer according to the defini-tions given by the USGS the term ldquoflowing artesian wellrdquowas restricted to flowing wells in confined aquifers (Lohman1972b) and it was explicitly pointed out that ldquoa flowing welldoes not necessarily indicate artesian conditionsrdquo (Heath1983) To differentiate flowing wells in confined and un-confined aquifers Toacuteth (1966) defined confined-flow flow-ing wells and unconfined-flow flowing wells as two end-members of flowing wells while Freeze and Cherry (1979)defined geologically controlled flowing wells and topograph-ically controlled flowing wells As shown in Fig 2 geo-logically controlled flowing wells are equivalent to Toacutethrsquosconfined-flow flowing wells while topographically con-trolled flowing wells correspond to Toacutethrsquos unconfined-flowflowing wells Note that in geologically controlled flowingwells topography is still the driving force of groundwater

flow from the topographic highs to topographic lows There-fore we avoid the terms of geologically controlled and topo-graphically controlled flowing wells and we use the termi-nology by Toacuteth (1966) in the following discussion

22 Confusing uses of ldquoartesianrdquo in the literature

The adjective ldquoartesianrdquo which was initially used in termsldquoartesian fountainrdquo and ldquoartesian wellrdquo has been appliedto such terms as ldquoartesian waterrdquo ldquoartesian aquiferrdquo andldquoartesian pressurerdquo Following the definitions given by theUSGS (Lohman 1972a) and as used in many USGS pub-lications the term ldquoartesian aquiferrdquo is equivalent to ldquocon-fined aquiferrdquo ldquoartesian waterrdquo refers to groundwater fromor within a confined aquifer and ldquoartesian pressurerdquo is thewater pressure in a confined aquifer An artesian basin wasdefined by Meinzer (1923b) to be a basin in which water isconfined under artesian pressure implying that the hydraulichead being greater than the elevation of ground surface is nota necessary condition The Great Artesian Basin in Australiais one of the largest artesian basins in the world and is wellknown for its numerous flowing wells in confined aquifersIn the United States there are many artesian basins like theartesian basin of the Dakotas (Darton 1905 Swenson 1968)the great Paleozoic artesian basin of the Mississippi Valleyregion (Meinzer 1923a) the Roswell artesian basin in NewMexico (Fiedler and Nye 1933) and the Grand Junctionartesian basin in Colorado (Jacob and Lohman 1952) all ofwhich had many flowing wells in the initial stage of ground-water development but many of which currently have staticwater levels significantly below grade

The different meanings of ldquoartesianrdquo caused confusion notonly to beginners of hydrogeology but also to professionalhydrogeologists which has been realized by some textbookauthors Deming (2002) and Younger (2007) both chose pho-tos of a flowing well for their cover image but they havequite opposite viewpoints on ldquoartesianrdquo Deming (2002) heldthe opinion that ldquoartesianrdquo implies that the hydraulic head isgreater than the elevation of ground surface defining ldquoarte-sian aquiferrdquo to be identical to confined aquifer would makethe definition not only conceptually useless but also etymo-logically incorrect because wells drilled in Artois could flowspontaneously On the contrary Younger (2007) believed thatldquoartesianrdquo is a synonym of ldquoconfinedrdquo and pointed out thatldquoartesianrdquo is also widely misused to refer to any well fromwhich water flows without pumping a phenomenon which isnot restricted to confined aquifers Younger also discouragedfurther use of ldquoartesianrdquo because it lacks intuitive meaningin modern English

To sum up hydrogeologists are keenly interested in flow-ing wells but the literature is confusing concerning the quali-fier of ldquoartesianrdquo This confusion has likely led to the ground-water community underestimating the role that flowing wellshave played in the evolution of its science Given that themeaning of the adjective ldquoartesianrdquo has a few meanings in

httpsdoiorg105194hess-24-6001-2020 Hydrol Earth Syst Sci 24 6001ndash6019 2020


Figure 2 (a) Geologically controlled or confined-flow flowing wells (b) topographically controlled or unconfined-flow flowing wells (mod-ified from Freeze and Cherry 1979) It is assumed that the screened intake for the respective well is at its bottom

the literature the meaning can be unclear unless it is definedin each publication of use There is no necessity to preservethis term in groundwater science therefore we propose thatits use be avoided

3 The history of drilling flowing wells in selectedregions

Here we briefly review the history of both shallow and deepflowing wells in regions that most directly contributed to thedevelopment of modern groundwater science

31 France

As early as 1126 a shallow flowing well tapping the con-fined fringe of the chalk aquifer was identified in Artois innorthern France (Margat et al 2013) In the early 19th cen-tury the technique of cable-tool drilling (also called percus-sion drilling) resulted in drilling of deeper flowing wells inFrance Garnier (1822) published the first technical guide-book on drilling ldquoartesianrdquo wells It was stated that with theexception of some provinces there are few parts of Francewhere artesian wells are not to be expected Garnier obtaineda prize from the Society for the Encouragement of Industrydue to the publication of this book which reflects the interestof the French government in flowing wells

According to Arago (1835) most flowing wells up tothat time ranged in depth from 36 to 177 m Between 1833and 1841 a flowing well with a depth of 548 m was drilledin Grenelle within the Paris Basin The water level in thisflowing well could rise to a height of 33 m above groundsurface in a pipe supported by a wooden scaffolding acces-sible by steps In 1855 an article titled The Artesian Wellat Grenelle in France was reproduced in California Farmerand Journal of Useful Sciences in the United States (Anony-mous 1855) It was commented that ldquoThis splendid achieve-ment at that date may be looked upon as the pioneer effortand at the present time and within a very few years the mostastonishing results may be expectedrdquo In 1861 another flow-ing well with a depth of 586 m was completed in Passy nearParis which is the last flowing well in Paris still in use todayDarcy (1856) and Dupuit (1863) were both inspired by flow

rate measurements at different orifices in these deep flowingwells The details are given in Sect 5

32 Italy

According to Norton (1897) nearly equal in antiquity withthe flowing wells of Artois are those of Modena in north-ern Italy which might have disputed with Artois on the rightto provide their name to flowing wells It was noteworthythat two well-borerrsquos augers were used in the municipal coatof arms indicating the influence of wells on the town Gio-vanni Cassini (1625ndash1712) referred to flowing wells in Mod-ena and Bologna and developed one himself at the castle ofUrbin (Merdinger 1955) A shallow flowing well can be ob-tained by digging to a depth of sim 20 m and boring a hole forthe next sim 15 m by using an auger (Biswas 1970)

Based on the famous flowing wells of ModenaBernardino Ramazzini (1633ndash1714) and Antonio Vallisnieri(1661ndash1730) connected flowing wells to the water cycleand pioneered the theory of artesian water pressure in thelate 1600s and early 1700s (Duffy 2017) The details are in-troduced in Sect 41

33 Great Britain

By the end of the 1700s some shallow flowing wells hadbeen dug in Great Britain In 1785 a flowing well (artificialspring) with a depth of sim 37 m was dug sim 91 m away fromthe Derwent River in Derby (ldquoDarwentrdquo Darwin 1785)One of the first flowing wells near London was completedin 1794 (Buckland 1836) The successful experiences of wa-ter supply from flowing wells led to sinking of more flowingwells According to Macintosh (1827) James Ryan obtaineda patent on boring for minerals and water in 1805 while JohnGoode obtained a patent on boring for the purpose of obtain-ing and raising water in 1823 indicating that drilling was ac-tive in Great Britain in the early 19th century According toan article in Monthly Magazine and British Register (Anony-mous 1822) two flowing wells with depths of 32 and 37 mwere drilled in the town of Tottenham in 1821 and manyflowing wells had existed for a period of time in various partsof the country by 1822

The publication of Garnier (1822) in France aroused fur-ther interest in flowing wells in Great Britain (Farey 1823)



Although many flowing wells had been drilled in the Lon-don Basin many boreholes failed to become flowing wellsTherefore Buckland (1836) called for a theory of flowingwells The experience gained from the costly failures im-proved understanding of conditions necessary for the suc-cess of a flowing well the details of which are discussed inSect 41

34 The United States

Accompanying the increase in population due to immigrationand western expansion in the US there was a higher demandof water resources for drinking and for agriculture As a re-sult of the increased drilling technology since the 19th cen-tury deep groundwater was utilized by drilling numerouswells many of which were flowing wells at least in the ini-tial stage of development Here we list some regions whereflowing wells were drilled resulting in significant advancesin groundwater science

Development of the CambrianndashOrdovician aquifer systemin the northern US Midwest can be traced to 1864 when aflowing well with a depth of 217 m was drilled in Chicago(Konikow 2013) By the end of the 19th century flowingwells were common in topographically low areas in the Mis-sissippi Missouri and Illinois river valleys near Lake Michi-gan and around Lake Winnebago in northeastern Wiscon-sin (Young 1992) At the beginning of the 21st centurythere were still many flowing wells newly drilled in Michi-gan (Gaber 2005) Chamberlinrsquos (1885) classic report basedon the hydrogeologic conditions in Wisconsin is consideredone of the roots of groundwater science in Wisconsin (An-derson 2005) In 1876 a flowing well with a depth of 293 mand an initial flow rate of 3270 m3 dminus1 drilled in Prairie duChien Wisconsin was named ldquoThe Greatest Artesian Foun-tain in Americardquo (Meiter 2019) A photo of this flowing wellserved as the frontispiece of Chamberlin (1885) and Freezeand Back (1983) and the cover image of Deming (2002) andit was also cited in Anderson (2005)

In the US Great Plains interest in groundwater emergeddue to the irrigation demands beginning in the 1880s due tothe widespread drought In early 20th century flowing wellswere common in topographic lows near rivers eg in theArkansas River valley of southeastern Colorado much ofSouth Dakota and parts of southeastern North Dakota andnortheastern Nebraska in the Missouri River valley (Darton1905) In South Dakota and North Dakota within the GreatPlains some 400 deep wells were drilled into the Dakotasandstone by 1896 of which over 350 were flowing wells(Darton 1897) Due to the introduction of the jetting methodof drilling in around 1900 thousands of small-diameter wellswere drilled to the Dakota sandstone during the following2 decades There were about 10 000 deep wells in SouthDakota in 1915 and between 6000 and 8000 deep wells inNorth Dakota in 1923 (Meinzer and Hard 1925) Due tothe increased withdrawal of deep groundwater many flowing

wells became non-flowing wells accompanied by decreasingflow rates in the flowing wells that still flowed The conditionof flowing wells led to improved understanding of the pat-tern of groundwater circulation in confined aquifers (Darton1905) while the changing production rates led to the birth ofthe concept of compressibility and the role of compressibilityon production in confined aquifers (Meinzer and Hard 1925Meinzer 1928) The details are discussed in Sect 61

In flowing wells of the Dakota aquifer it was noted thatldquothe pressure increases for several hours or even days af-ter the flow is shut off and when opened the flow de-creases in the same way until the normal flow is reachedrdquo(Meinzer 1928) Several decades later based on field obser-vations of decreasing flow rate with time in flowing wells inthe Grand Junction artesian basin and in the Roswell arte-sian basin in New Mexico constant-drawdown aquifer testswere proposed to obtain hydraulic parameters (Jacob andLohman 1952 Hantush 1959) More details are discussedin Sect 62

35 Australia

The Great Artesian Basin which covers one-fifth of the to-tal area of Australia is one of the largest and best-knowngroundwater basins in the world (Ordens et al 2020) Thefirst shallow flowing well was dug to a depth of 43 m by us-ing an auger near a spring in New South Wales in 1878 whilethe first deep machine-drilled flowing well was completedin 1887 at a depth of 393 m near Cunnamulla Queensland(Williamson 2013) By the end of the 19th century therewere already around 1000 flowing wells on the continent(van der Gun 2019) The exploitation of flowing wells andartesian water contributed to the emergence of hydrogeologyas a discipline in Australia (Williamson 2013) and the de-velopment of such sources has played a vital role in the pas-toral industry in the arid and semiarid regions of Australia(Habermehl 2020)

Due to the occurrence of intervening aquifers andaquitards the Great Artesian Basin is a multilayered con-fined aquifer system Although head drawdowns of up to100 m have been recorded in highly developed areas hy-draulic heads in the Jurassic and Lower Cretaceous aquifersare still above ground surface throughout most of the basin(Habermehl 2020) A comprehensive review of the historyand recent research status of the basin can be found in Or-dens et al (2020)

36 Canada

The hydrogeology of the Canadian Prairies has been studiedsince the beginning of the 20th century Groundwater in thisregion is largely obtained from surficial Pleistocene glacialdrift and the underlying bedrock of Tertiary or Cretaceousage Due to the occurrence of a large number of flowingwells either in the glacial drift or in the bedrock great at-



tention was paid to the relation between topography geologyand areas with flowing wells during basin-scale groundwatersurveys (Meyboom 1966) A similarity between the poten-tiometric surface and the local topography was widely ob-served in many parts of the Canadian Prairies (Jones 1962Meyboom 1962 Toacuteth 1962 Farvolden 1961)

The Trochu area in central Alberta which covers an areaof 67 km2 is representative of the hydrogeology of the Cana-dian Prairies There were 10 shallow flowing wells rangingin depth from 9 to 27 m in topographic lows (Toacuteth 1966)Because the glacial deposits have low contents of clay theyare efficient for infiltration of rainfall and evaporation of soilwater Combined with previous theoretical findings on topo-graphically driven flow systems (Hubbert 1940 Toacuteth 19621963) these flowing wells were considered to be controlledby topography and typical manifestations of groundwaterdischarge (Toacuteth 1966) The details are discussed in Sect 7

37 China

As early as in the 11th century deep drilling using bam-boo pipes was employed in Sichuan Province China toreach brines from 100 m deep boreholes (Vogel 1993) Inthe 16th century a flowing well in Beijing became a site oftourism known as ldquoManjingrdquo (literally meaning a well full ofwater) In the 17th century due to the success of developingflowing wells for brines ldquoZiliujingrdquo (meaning flowing well)became the name of a town in Sichuan Province In 1835 the1001 m deep flowing well at Shenhai (frequently mistaken tobe Xinhai in the English literature) was constructed for pro-ducing brines and gases (Vogel 1993) However these earlydrilling techniques and experiences of drilling deep flow-ing wells did not substantially produce follow-on activityin the development of groundwater science in China In theearly 1950s the large demand of groundwater in (semi)aridregions led to exploration of groundwater and resulted in theestablishment of hydrogeology as a distinct discipline in sev-eral universities In the late 1950s the success of drillingsome flowing wells led to a campaign for finding more flow-ing wells for agriculture in many basins of the country Un-fortunately due to overexploitation flowing wells have dis-appeared in many regions including the North China Plain

One of the most intensively studied groundwater basins isthe Ordos Plateau in northwestern China composed mainlyof a thick sandstone aquifer of Cretaceous age up to around1000 m thick Because the overlying thin Quaternary de-posits have much higher permeability and there is no con-tinuous aquitard within the Cretaceous sandstone the OrdosPlateau can be conceptualized as a thick unconfined aquifer(Hou et al 2008 Jiang et al 2018) As early as the 1950sseveral flowing wells were established in deep boreholes inthe Cretaceous sandstone in topographic lows subsequentlynumerous flowing wells were drilled for agricultural waterFor example in the Wudu lake catchment on this plateauwith an area of approximately 200 km2 there were 15 flow-

ing wells in 2015 (J Z Wang et al 2015) In recent yearsadditional flowing wells have been drilled The majority offlowing wells in this catchment range in depth from 70 to300 m with one well reaching the bottom of the Cretaceoussandstone at a depth of 800 m

To reduce costs the flowing wells drilled into the Creta-ceous sandstone are cased only in the very shallow part thatcorresponds to the Quaternary deposits These wells providea prime example to study the hydraulics of flowing wellsin a macroscopically homogeneous basin The steady-statehydraulics of flowing wells in homogeneous basins is intro-duced in Sect 73

4 Confined-flow flowing wells and confined flowbounded by aquitards (1690sndashcurrent)

41 Conditions of confined-flow flowing wells

Based on his observations of flowing wells in Modena Italyin 1691 Ramassini plotted a geological section showing theoccurrence of flowing wells penetrating a confined aquiferreceiving its water from an underground reservoir at a higherlevel in the surrounding mountain (Biswas 1970) There-fore for the occurrence of flowing wells Ramassini alreadysuspected the role of topography or the hydraulic gradi-ent between the well and the underground reservoir in thesurrounding mountain (de Vries 2007) Unfortunately hethought the source of water in the underground reservoir inthe surrounding mountain was more likely to be from the seaLater Valniseri argued in 1726 that the source of water in theflowing wells of Modena must be rainfall and snowmelt inthe adjacent Apennine Mountains (Duffy 2017) which wasthe start of thinking about the simultaneous control of topog-raphy and precipitation on flowing wells

In the evolution of thinking about groundwater it wasuniversally accepted by the early 19th century that the wa-ter from flowing wells came from rainfall which found itsway through the pores or fractures of a permeable stratumsandwiched between two water-tight strata at depth (Gar-nier 1822) De Thury (1830) summarized three conditionsof flowing wells In his words the first is to reach a flowof deep water coming from higher basins and passing alongthe bosom of the Earth between compact and impermeablerocks the second is to afford this deep water the possibilityof rising to the surface by using an artificially bored welland the third is to prevent the spreading of the ascending wa-ter into the surrounding sand or rock by inserting tubes intothe bored well

Following the successful drilling of flowing wells inFrance the theory of the mechanism of flowing wells becamewell understood in Britain For example Buckland (1836)illustrates the cause of two flowing wells in the confinedaquifer of the London Basin The successful experiencescoupled with the costly failures of drilling in Britain led to



the recognition of three necessary conditions for the successof a flowing well (Bond 1865)

(1) The existence of a porous stratum having a suf-ficient outcrop on the surface to collect an adequateamount of rainfall and passing down between twoimpermeable strata (2) the level of the outcroppingportion of the porous stratum must be above that ofthe orifice of the well so as to give a sufficient riseto the water and (3) there must be no outlet in theporous stratum by which its drainage can leak outeither in the shape of a dislocation by which it canpass into lower strata or a natural vent by whichit can rise to the surface at a lower level than thewell

Based on his North American experience with the Wis-consin portion of the CambrianndashOrdovician aquifer systemChamberlain (1885) published The Requisite and QualifyingConditions of Artesian Wells and listed seven conditions offlowing wells which include the following

(1) A pervious stratum to permit the entrance andthe passage of the water (2) a water-tight bed be-low to prevent the escape of the water downward(3) a like impervious bed above to prevent escapeupward for the water being under pressure fromthe fountain-head would otherwise find relief inthat direction (4) an inclination of these beds sothat the edge at which the waters enter will behigher than the surface at the well (5) a suitableexposure of the edge of the porous stratum so thatit may take in a sufficient supply of water (6) anadequate rainfall to furnish this supply and (7) anabsence of any escape for the water at a lower levelthan the surface at the well

In fact the seven prerequisites given by Chamber-lain (1885) are inclusive of the three conditions given byde Thury (1830) and Bond (1865) several decades ear-lier However Bond (1865) did not cite de Thury (1830)and Chamberlin (1885) did not cite either Bond (1865) orde Thury (1830) therefore we assume their findings wereobtained independently

42 Confined flow bounded by aquitards

In the late 1890s Darton (1897) with the USGS investigatedthe occurrence of flowing wells in the Dakotas and plottedthe cross section of the Dakota aquifer (Fig 3) By construct-ing contours of hydraulic head of the Dakota confined aquiferacross South Dakota which shows the head loss through theconfined aquifer Darton (1905) concluded that groundwa-ter discharged by the flowing wells in the east had flowedhundreds of kilometers horizontally through the aquifer fromoutcrops in the west This study popularized the pattern of

groundwater flow in a confined aquifer that outcrops in topo-graphic highs as shown in Fig 2a There was also a long-lasting conceptual model for the Great Artesian Basin ofAustralia that each aquifer can be considered to be laterallycontinuous across the extent of the basin (Habermehl 2020)

As shown in Fig 3 groundwater flow in a confinedaquifer which is bounded by the adjacent aquitards is simi-lar to flow through a pipe Such a flow pattern is commonlyutilized to interpret groundwater age in confined aquiferswhich is known as piston flow age (Bethke and Johnson2008 Hinkle et al 2010) Because many hydrogeochemicalprocesses are dependent on travel time through the aquiferhydrochemical facies (Back 1960 1966) usually evolvealong the flow path bounded by aquitards Therefore sucha flow pattern which stemmed from analyzing confined-flowflowing wells is the cornerstone of sampling and analyzinggroundwater geochemistry and isotopes in confined aquifers

5 Darcyrsquos law and steady-state well hydraulics inspiredby flowing wells (1850sndash1910s)

51 The birth of Darcyrsquos law evoked by flowing wells

It is widely known that Darcyrsquos law which represents the be-ginning of groundwater hydrology as a quantitative sciencein 1856 (Freeze and Back 1983) was established based onsand column experiments In fact the sand column experi-ments were designed to confirm a linear correlation betweenflow rate and head loss in sands which was first recognized inflowing wells (Brown 2002 Ritzi and Bobeck 2008) Flow-ing wells were important sources of water supply in the ParisBasin since the early 19th century and this led to flow ratesbeing measured at different elevations of discharge orificesin several flowing wells in the 1840s (Fig 4) In fact suchexperiments can be regarded as constant-head (drawdown)tests at multiple discharge orifices in single wells As shownin Fig 4a in either September or November the flow ratesincreased linearly as the elevation of discharge orifice de-creased Henry Darcyrsquos (1803ndash1858) interest in this linearcorrelation instigated his famous lab experiments with sandcolumn (Brown 2002 Ritzi and Bobeck 2008)

Theoretically the head loss from the recharge area to thedischarge orifice can be divided into head loss in the aquiferand head loss along the well pipe According to the Chezyequation describing head loss at high flow velocities in pipeshead loss in the well pipe should be proportional to the squareof flow rate Based on the linear trend between head loss andflow rate shown in Fig 4a it was inferred that the head lossin the short-distance well pipe with high velocities is lim-ited compared with the well loss in the long-distance aquiferwith low velocities To identify the control of flow velocityon head loss Darcy conducted pipe flow experiments dur-ing 1849 and 1851 and proposed equations on the depen-dence of head loss on flow rate At low velocity the head



Figure 3 The profile of the Dakota confined aquifer and the confined flow bounded by aquitards (modified from Darton 1897)

Figure 4 (a) The changes in flow rate with elevation of discharge orifice of a flowing well (data from Darcy 1856) (b) the device formeasuring flow rate (only one discharge orifice is open during measurement) The higher flow rate in November shown in (a) can be a resultof higher hydraulic head surrounding the flowing well probably due to the contribution of groundwater recharge

loss was found to be linear to discharge rate which can bewritten as

hL =La

πr4 q (1)

and at high water velocity the head loss was found to belinear to the square of discharge rate which can be written as

hL =Lb

πr5 q2 (2)

where L is length r is pipe radius q is the volume dischargerate and a and b are empirical coefficients of proportionalityEquation (1) verified the Poiseuille (1841) equation by exper-iments under completely different circumstances and Eq (2)can be considered another form of the Chezy equation Notethat Eq (2) led to the co-naming of the DarcyndashWeisbach pipefriction formula About 30 years later Reynolds (1883) fullyquantified the occurrence and differences between laminarand turbulent flow by introducing the Reynolds number

By assuming that head loss from a position in the aquiferwith constant head away from the flowing well to the dis-charge orifice occurs in both the aquifer and the well pipeequations similar to the following forms were obtained

h1+aLprime

πr prime4q1+

bH1

πr5 q21sim= h2+

aLprime

πr prime4q2+

bH2

πr5 q22 (3a)

(h1minush2)+b

πr5

(H1q

21 minusH2q

22

)sim=minusC (q1minus q2) (3b)

where Lprime is flow distance in the aquifer from the positionwith constant head to the flowing well r prime is radius represen-tative of pores in the aquifer h1 and h2 are the elevationsof the discharge orifices measured from the ground and canbe considered aquifer potentiometric heads H1 and H2 arethe lengths of well pipes from the bottom to the dischargeorifice and C is an unnamed constant From the angle of aconstant-head well test the first part of the left-hand side ofEq (3b) is the difference in aquifer head loss at the well cre-ated by changing the elevation of the discharge orifice andthe second part is the difference in the well loss from riserpipes with different flow distances The linear relationshipbetween h1ndashh2 and q1ndashq2 shown in Fig 4a indicates that thesecond part on the left-hand side of Eq (3b) is negligibleTherefore Eq (3b) changes into

h1minush2 sim=minusC (q1minus q2) (4)

where C can be interpreted as the slope shown in Fig 4aTo confirm Eq (4) in 1855 Darcy conducted the sand col-

umn experiments by assuming that water flow through sands



Figure 5 Plot from Dupuit (1863) showing the radial flow toward a flowing well penetrating a confined aquifer which caused head loss witha cone of depression in the potentiometric level (ldquoniveau piezometriquerdquo) It is clear that the potentiometric level of the cone of depression isstill above the land surface

is similar to water flow through the aquifer and obtained thewell-known empirical equation of Darcyrsquos law Note that thecoefficient today known as hydraulic conductivity was notnamed by Darcy Hubbert (1940) rigorously interpreted hy-draulic conductivity and examined Darcyrsquos law in the light ofthe microscopic NavierndashStokes flow theory which raised thesophistication of understanding of Darcyrsquos law

52 Steady-state well hydraulics in confined aquifersDupuit equation

In 1850 Jules Dupuit (1804ndash1866) succeeded Henry Darcyas Chief Director for Water and Pavements and started hisresearch on groundwater hydraulics The field data shownin Fig 4a triggered Dupuit to quantify the constant C inEq (4) Dupuit realized that groundwater flow would radi-ally converge to the flowing well and head loss in the con-fined aquifer away from the flowing well would form a coneof depression (Fig 5)

In radial flow Darcyrsquos law can be written as

q = k(2πxB)dydx (5)

where B is the thickness of the confined aquifer x is the ra-dius within the cone of depression and y is the correspondinghead with reference to the elevation of the discharge orificeDupuit (1863) obtained the following equation by integrat-ing Eq (5) from the radius of the well rw to the radius ofinfluence R

h0minushw =q

2πkBln

(R

rw

) (6)

where hw is the elevation of the discharge orifice and h0 isthe hydraulic head at the radius of influence which equalsthe initial hydraulic head of the flowing well when thewell has been closed for a duration of time By comparingEqs (4) and (6) it can be interpreted that C = 1

2πkB ln(Rrw

)

Dupuit (1863) explicitly stated that Eq (6) is supported bythe measurements of flow rate versus elevation of dischargeorifice of flowing wells reported in Darcy (1856)

Although Eq (6) was derived based on the hydrogeologiccondition of a flowing well in a confined aquifer it is appli-cable to non-flowing wells in a confined aquifer A limita-tion of the equation is the difficulty of determining the ra-dius of influence in the field Thiem (1906) improved Eq (6)by integrating Eq (5) between two wells within the coneof depression and obtained an equation to determine hy-draulic conductivity which is known as the Thiem equilib-rium method Although the Thiem equation (Thiem 1906)was introduced in almost all textbooks Dupuitrsquos pioneeringstudy on steady-state radial flow to a flowing well in con-fined aquifers (Dupuit 1863) which is applicable to a non-flowing well in confined aquifers was seldom mentioned intextbooks

Dupuit (1863) also derived similar equations for a well inunconfined aquifers by neglecting the vertical hydraulic gra-dient which is currently known as the DupuitndashForchheimer



approximation Although the vertical hydraulic gradient isneglected the DupuitndashForchheimer approximation is stilluseful in interpreting regional-scale groundwater flow prob-lems (Haitjema and Mitchell-Bruker 2005)

6 Compressibility of confined aquifers and transientwell hydraulics inspired by flowingwells (1920sndashcurrent)

61 Compressibility of confined aquifers conceptsinstigated by flowing wells

In the 1920s groundwater resources were undergoing devel-opment in the United States therefore much of the effort ofthe USGS turned toward developing an inventory of wellsand their production (Domenico and Schwartz 1998) Theinventory of groundwater resources in the Dakota aquifer in-dicated that the number of flowing wells that were still flow-ing was decreasing The imbalance between groundwaterdischarge through flowing wells and groundwater rechargeled to significant insight into the role of aquifer compress-ibility (Meinzer 1928 Meinzer and Hard 1925)

Groundwater development in the Dakota aquifer startedwith flowing wells in the 1880s After active drilling inthe 1900s investigations in the 1910s showed that manyflowing wells had stopped flowing To determine the ground-water budget a study area of 18 townships near Ellen-dale North Dakota (ranges 48 to 65 west along town-ship 129 north) with a total of 320 flowing wells sup-plied by the Dakota sandstone was selected The rate ofdischarge through flowing wells was estimated to be closeto 0189 m3 sminus1 (3000 gallons per minute) during the 38-year period from 1886 to 1923 but the rate of lateralrecharge through eastward percolation was inferred to beless than 0063 m3 sminus1 (1000 gallons per minute) (Meinzerand Hard 1925) Although these estimates could be very in-accurate they were sufficient to demonstrate the excess ofdischarge through flowing wells over recharge Meinzer andHard (1925) concluded that most of the water dischargedthrough the flowing wells was taken out of storage in thesandstone aquifer indicating that the sandstone aquifer wascompressible It was also observed that the artesian headwould increase gradually for some time after a flowing wellwas shut off which is a manifestation of elasticity of theaquifer medium (Meinzer and Hard 1925)

By summarizing these observations of flowing wells ndashas well as the evidence of compressibility and elasticity ofcompacted sand land subsidence in an oil field water levelfluctuations produced by ocean tides and water level fluc-tuations produced by railroad trains ndash Meinzer (1928) con-cluded that confined aquifers are compressible and elasticAlthough geochemical and numerical studies several decadeslater showed that leakage also contributed to well dischargein the Dakota aquifer (Bredehoeft et al 1983 Leonard et

al 1983 Swenson 1968) this did not undermine the role offlowing wells that had intrigued the interest of hydrogeolo-gists

Several years later by assuming that discharge of ground-water from storage as head falls is similar to release of heatas temperature decreases Theis (1935) recognized that con-fined aquifers possess a property analogous to heat capacityand derived the equation characterizing the transient behav-ior of hydraulic head due to discharge of a well Theisrsquos solu-tion was not understood by the groundwater hydrology com-munity until Jacob (1940) defined the coefficient of storageas a combination of vertical compressibility of the porousmedium and compressibility of water Thereafter numerousefforts were devoted to determining the aquifer parametersusing transient well hydraulics and identifying the behaviorof drawdown or flow rate in other aquifers (leaky aquifersunconfined aquifers)

62 Transient well hydraulics in flowing andnon-flowing wells in confined aquifers

In the early 1930s the high demand for groundwater led toevaluation of groundwater in different parts of the UnitedStates and pumping tests using the Thiem equilibriummethod were conducted to obtain hydraulic conductivity inseveral regions (Lohman 1936 Theis 1932 Wenzel 1936)Unfortunately it was found to be difficult to consistently ob-tain aquifer parameters because of the increasing drawdownwith time (Wenzel 1936)

To interpret the time-varying drawdown Charles Ver-non Theis (1900ndash1987) assumed that groundwater flow dis-turbed by a sink withdrawing water was analogous to heatconduction disturbed by a sink withdrawing heat and resortedto Clarence Isador Lubin (1900ndash1989) a mathematician atthe University of Cincinnati for the solution of temperaturedistribution of a uniform plate under two different conditions(White and Clebsch 1993) The first condition is the intro-duction of a sink kept at a temperature which corresponds tothe constant-drawdown aquifer test problem and is applicableto flowing wells and the second condition is the introductionof a sink with a uniform heat flow rate which correspondsto the constant-rate pumping test problem It was fortunatethat the solution of the second problem was readily avail-able in the field of heat conduction (Carslaw 1921) In thisway Theis (1935) obtained the analytical solution of time-dependent drawdown induced by pumping and opened thedoor to determining aquifer parameters using transient wellhydraulics

When a flowing well has been shut off for a duration oftime upon reopening the discharge rate decreases with timewhich can be considered a constant-drawdown aquifer testBased on Smith (1937) solution to the analogous problem inheat conduction (the first problem raised by Theis) Jacob andLohman (1952) derived a solution to the constant-drawdownwell test problem in a confined aquifer and verified the re-



sults based on flowing wells in the Grand Junction artesianbasin Colorado Several years later after the classical workon constant-rate pumping problem in leaky aquifers (Han-tush and Jacob 1955) Hantush (1959) derived a solution tothe constant-drawdown well hydraulics to a flowing well inleaky aquifers In fact constant-drawdown tests can also becarried out in non-flowing wells either by using a speciallydesigned pump or by connecting the well to a pressurizedwater container at the surface (Mishra and Guyonnet 1992)Such constant-drawdown tests have been found to be particu-larly useful in low-permeability aquifers (Jones 1993 Tave-nas et al 1990 Wilkinson 1968)

In summary although the door of transient well hydraulicswas directly opened by Theis (1935) based on constant-ratepumping tests constant-drawdown well tests triggered byflowing wells belong to an indispensable component of tran-sient well hydraulics and are still receiving active attention inthe current century (Chang and Chen 2002 Wen et al 2011Tsai and Yeh 2012 Feng and Zhan 2019) It is worth notingthat current models on transient well hydraulics did not fullyaccount for the relationship between groundwater rechargefrom precipitation and groundwater discharge in wells egthe higher flow rate in November than that in Septembershown in Fig 4a can not be explained by current theories

7 Unconfined-flow flowing wells and topographicallydriven flow systems (1890sndashcurrent)

71 Qualitative understanding of topographicallydriven groundwater flow and unconfined-flowflowing wells

At the turn of the 20th century there was initial field evi-dence of topographically driven groundwater flow namelyupward groundwater flow below surface waterbodies (King1899) and increase in hydraulic head with depth in the dis-charge area (Pennink 1905) in homogeneous aquifers Ver-sluys (1930) explicitly pointed out that the occurrence ofartesian pressure exceeding the land surface corresponds toan increase in hydraulic head with depth and would neces-sarily lead to upward groundwater flow By calculating headdistribution based on the analogy between temperature andhydraulic head Versluys concluded that aquitards are notnecessary conditions of flowing wells Due to the poor un-derstanding of the potential of subsurface water Versluyswrongly assumed that pressure head difference is the driv-ing force of groundwater flow

Based on the principle of conservation of mass and thelaws of thermodynamics Hubbert (1940) defined the poten-tial of subsurface water and obtained graphical solutions toregional groundwater flow in a homogeneous and isotropicaquifer with a symmetrical topography between two streams(Fig 6) Hubbert (1940) found that flowing wells could oc-cur in topographic lows without an overlying confining bed

and pointed out that a confined aquifer outcrops in the high-lands and is overlain by impermeable strata in the lowlandsas shown in Fig 2a is by no means a necessary condition forflowing wells

Because there was no aquitard in the studies of Ver-sluys (1930) or Hubbert (1940) the pattern of groundwaterflow is mainly controlled by topography Such flowing wellsin homogeneous unconfined aquifers driven by topographybelong to unconfined-flow flowing wells (Toacuteth 1966)

72 Quantitative analysis of topographically drivengroundwater flow systems

In the 1950s and 1960s the high demand for water on theCanadian Prairies led to institutional programs of groundwa-ter exploration and research The phenomena described byKing (1899) and Hubbert (1940) such as the mean watertable closely follows the topography and flowing wells oc-cur in topographic lows were quite common in the CanadianPrairies (Meyboom 1962 1966 Toacuteth 1962 1966) Basedon the field observations two similar but slightly differentconceptual models of topographically induced groundwa-ter flow (Fig 7) were developed by Toacuteth (1962) and Mey-boom (1962) Because the mean water table which closelyfollows the topography can be considered a priori knownToacuteth (1962) solved the Laplace equation for a homogeneousunit basin with a known water table that changes linearlyfrom the divide to the valley (Fig 7a) Based on intuitivethinking founded on field observations Meyboom (1962)considered the permeability difference between the shallowand deep aquifers and qualitatively obtained the flow pattern(Fig 7b) They agreed that the combination of the two mod-els ldquogives a good description of the unconfined region ofgroundwater flow in the western Canadian Prairiesrdquo (Toacuteth2005)

According to Toacuteth (1962) groundwater discharge couldcover the entire lower half of the unit basin and the wholedischarge area has higher hydraulic head than the corre-sponding elevation of water table which fulfills the defini-tion of ldquoartesian waterrdquo by Meinzer (1923b) To quantify theoccurrence of flowing wells in topographic lows of homoge-neous unconfined aquifers J Z Wang et al (2015) examinedthe zone with flowing wells under different water table undu-lations and basin width-to-depth ratios By fixing the basindepth increases in water table undulation and decreases inbasin length both led to increased hydraulic gradient betweenrecharge and discharge areas Based on the distribution ofhead exceeding surface (termed artesian head in their paper)it was found that the zone with flowing wells is always withinthe discharge area and the ratio of its size to the whole basinis proportional to the hydraulic gradient (Fig 8) Thereforein homogeneous basins the hydraulic gradient is the maincontrol factor for flowing wells

When the undulation of the topography is more complexToacuteth (1963) analytically obtained a flow net showing the si-



Figure 6 The flow net of groundwater flow between two rivers obtained by Hubbert (1940) and the head in selected piezometers (modifiedfrom Fetter 1994)

Figure 7 Topographically driven flow systems (a) homogeneous basin (modified from Toacuteth 1962) and (b) heterogeneous basin with ahigher permeability layer in the bottom (modified from Meyboom 1962)

multaneous occurrence of several local flow systems one in-termediate flow system and one regional flow system in a ho-mogeneous basin Note that the Canadian Prairies is semiaridand the impetus for advancing flow systems thinking camefrom the need to understand terrain patterns of soil salinityvegetation and groundwater chemistry for which the spatialvariations are flow system based Several years later R Al-

lan Freeze who was a proteacutegeacute of Meyboom combined theideas of Meyboom and Toacuteth together in his PhD thesis by nu-merically simulating steady-state regional groundwater flowin heterogeneous basins with any desired water table con-figuration (Freeze 2012) As reported in Freeze and With-erspoon (1967) heterogeneity would perturb the distributionof flow systems but does not affect the basic flow pattern in-



Figure 8 (a) The geometry of a unit basin with a length of L depth of |D| and three scenarios of water table undulations (correspondingto different α) (bndashj) the distribution of head exceeding surface in the unit basin under three different water table undulations and basinlength-to-width ratios (L|D|) (modified from Wang et al 2015)

duced by topography (Fig 9) It was also found that confinedaquifers need not outcrop to produce flowing well conditions(Fig 9b and c) In some recent studies it was found thatdepth-decaying hydraulic conductivity would lead to weak-ening of regional flow systems and thus deepening of localflow systems (Jiang et al 2009 2011 Wang et al 2011Zlotnik et al 2011)

As illustrated above although horizontal flow dominateswhen the basin width-to-depth ratio is high andor hydraulicconductivity in the deep layer is much higher vertical com-ponents of groundwater flow are widespread in either thickunconfined aquifers or aquitards overlying confined aquiferswhich is quite different from the flow pattern shown inFigs 2a and 3 The spatial distribution of groundwater age inthick unconfined aquifers is also more complicated than thatin a confined aquifer (Jiang et al 2010 2012) Thereforequantitative analysis of the topographically driven ground-water flow systems became a paradigm shift in hydrogeol-ogy This paradigm shift has been expressed by others insimilar words Anderson (2008) comments that ldquoThe Toacutethmodel is an important early exploration of the analysis ofregional flow systemsrdquo Bredehoeft (2018) points out thatldquoToacutethrsquos conceptual model of groundwater flowrdquo representsthe beginning of a new era in hydrogeology and termed theparadigm shift to be ldquothe Toacuteth revolutionrdquo

In his book about flow systems Toacuteth (2009) states thatsince the 1960s hydrogeologyrsquos basic paradigm has shiftedfrom confined flow in aquifers (aquitard-bound flow) tocross-formational flow in drainage basins ie flow pathschange from through a confined aquifer to across aquitardsand different depths of aquifers in heterogeneous basins Al-though cross-formational flow (inter-aquifer leakage) had al-ready been anticipated by Chamberlin (1885) it was iden-tified in the Dakota artesian basin through aquitards inthe 1960s (Swenson 1968) and it was recently identified

in the Great Artesian Basin through faults (Pandey et al2020 Smerdon and Turnadge 2015) Moreover although theconcept of flowing wells in the context of aquitard bound-ing is introduced in almost every groundwater textbookthe concept of unconfined-flow flowing wells in homoge-neous basins has been included in few textbooks (Domenicoand Schwartz 1998 Freeze and Cherry 1979 Heath 1983Kasenow 2010 Lohman 1972b) Therefore the acceptanceof the new paradigm is a slow process

73 Hydraulics of unconfined-flow flowing wells

The steady-state hydraulics of confined-flow flowing wellshad been examined by Glee in the 1930s but the study ofunconfined-flow flowing wells is most recent Z Y Zhang etal (2018) simulated the water exchange between the uncon-fined aquifer and a flowing well in a three-dimensional ho-mogeneous unit basin As a result of the increasing hydraulichead with depth in the discharge area of the aquifer hydraulichead in the shallow part is smaller than hydraulic head ofthe flowing well and in the deep part it is larger than hy-draulic head of the flowing well Therefore there is ground-water inflow from the aquifer to the flowing well (Qin) in thedeep part and groundwater outflow from the flowing well tothe aquifer (Qout) in the shallow part Because Qin is largerthan Qout cumulative flow rate at the well outlet is above 0(Fig 10a) which results in water overflow at the surface Insome extreme cases eg if the water table coincides with theground surface or the shallow part is casedQout equals 0 andcumulative flow rate at the well outlet is determined by Qin(Fig 10b) Z Y Zhang et al (2018) found that the simulta-neous occurrence of inflow and outflow could also occur ina thick confined aquifer Therefore the third condition pro-posed by both de Thury (1830) and Bond (1865) as well asthe seventh condition given by Chamberlin (1885) is not anecessary condition for flowing wells Moreover as shown



Figure 9 The distribution of equipotential lines and area of flowing wells in homogeneous (a) and heterogeneous basins (b c) (modifiedfrom Freeze and Witherspoon 1967) Also shown in (a) is the streamlines showing the pattern of groundwater flow from the recharge to thedischarge area

Figure 10 Conceptual cross-sectional views of flow around flow-ing wells (a) A flowing well with Qin gtQout (b) a flowing wellwith Qin gtQout = 0 (modified from Z Y Zhang et al 2018)Qw means the flow rate at the well outlet

in Fig 10a groundwater in the shallow part of the aquifercould not enter the flowing well indicating that the well out-let is a ldquowindowrdquo to the deep groundwater ie groundwatersampled at the well outlet could represent deep groundwa-ter (Zhang et al 2019) This has been verified in the flow-ing wells in the Ordos Plateau China by using hydrochem-istry and stable isotopes such as 2H 18O 87Sr86Sr and 26Mg(H Wang et al 2015 H Zhang et al 2018)

Based on the plots shown in Figs 6 to 10 several quali-fying conditions of flowing wells proposed in the 19th cen-tury have been found to be unnecessary since the turn of the20th century Although the transient behavior of groundwaterflow to flowing wells in confined aquifers has been studied inthe 1950s (Hantush 1959 Jacob and Lohman 1952) therehas been no research on transient groundwater flow to flow-

ing wells in unconfined aquifers Moreover research cou-pling groundwater recharge from precipitation and ground-water discharge through flowing wells which is critical tointerpret the increased flow rate with time as shown in Fig 4aand the sustainability of flowing wells is also missing

8 Conclusions and suggestions

The evolution of nearly all domains of physical hydroge-ology can be connected to flowing wells The advent ofmodern cable-tool drilling equipment in Europe in the early19th century made flowing wells common in the 19th cen-tury Because flowing wells are spectacular visual evidenceof groundwater occurrence they became the impetus for bothqualitative and quantitative groundwater science The pursuitof answers to fundamental questions generated by flowingwells in confined aquifers bounded by aquitards moved thescience forward for more than a century until pumping be-came the main form of groundwater development Moreoversince the turn of the 20th century flowing wells in uncon-fined aquifers were an impetus for the paradigm shift fromaquitard-bound flow to cross-formational flow driven by to-pography

Given the spectacular flowing wells in Paris and Lon-don in the early 19th century it was not a coincidence thatDarcy (1856) did his monumental laboratory experimentssoon after he did pipe flow experiments prompted by flowingwells He was followed by his colleague Dupuit (1863) to de-velop the hydraulics of steady flow to wells The term ldquoflow-



ing wellrdquo was introduced by Chamberlain (1885) in his clas-sic USGS report which provided a comprehensive explana-tion of flowing wells using hydrogeological principles Basedon field investigations of the CambrianndashOrdovician aquifersystem in Wisconsin he recognized the role of confiningbeds in creating flowing well conditions and also that theseconfining beds are leaky This was followed soon after by theclassic work by Darton (1897 1905) who studied the Dakotaaquifer Meinzer and Hard (1925) and Meinzer (1928) de-duced from declining discharge of flowing wells and excessof discharge over recharge that confined aquifers are elasticand have storage capability related to compressibility Thisprompted Theis (1935) of the USGS to initiate transient wellhydraulics for non-leaky aquifers although leakage recog-nized decades earlier set the stage for Hantush to pioneer thehydraulics of pumping wells and flowing wells in aquiferswith leaky confining beds in the 1950s (Hantush and Jacob1955 Hantush 1959)

The wide occurrence of regional-scale confined aquifersshowing ubiquitous flowing wells in sedimentary rocks inFrance Britain the United States and Australia resulted inconfined flow in aquifers being a broadly useful concep-tualization However this resulted in the common miscon-ception that flowing wells must occur in confined aquifersbounded by aquitards and the confusion of the term ldquoarte-sianrdquo Versluys (1930) and Hubbert (1940) realized flow-ing wells can occur in entirely unconfined and homoge-neous conditions controlled only by topography which wassupported by Toacutethrsquos (1962 1963) and Freeze and Wither-spoonrsquos (1967) quantitative studies of topographically drivengroundwater flow systems An introduction to confined-flow and unconfined-flow flowing wells has been given byToacuteth (1966) in a journal paper and included in the textbookby Freeze and Cherry (1979) while quantitative analysis oftopographically driven groundwater flow systems has beenconsidered to be a paradigm shift in modern hydrogeology(Bredehoeft 2018 Madl-Szonyi 2008 Toacuteth 2005) Gener-ally in Earth sciences it takes decades for a paradigm shiftto achieve completeness when completeness is judged by theparadigm being the primary basis for teaching as manifestedin what is included in textbooks For example the paradigmshift from steady-state to non-steady-state well hydraulics inconfined aquifers that began in the 1930s was completed bythe late 1950s and transient well hydraulics has been in-cluded in almost all groundwater textbooks since then

Although there have been great advances in how we thinkabout groundwater flow systems and the current paradigmis well advanced it is not yet comprehensive The miscon-ception that flowing wells must occur in confined aquifersis still impeding the acceptance of the new paradigm whichis reflected by the limited number of textbooks introducingflowing wells in unconfined aquifers Based on the summaryof the role of flowing wells in the evolution of many conceptsand principles of groundwater hydrology acknowledgementof the role of flowing wells as the main root of groundwa-

ter hydrology would lead to a deeper understanding of thescience of groundwater Avoidance of the term ldquoartesianrdquo isneeded to eradicate confusion in terminology that crept intogroundwater science long after the classic work by DarcyDupuit and others established the foundation A complete de-scription of confined-flow and purely unconfined-flow flow-ing wells and their connections to evolution of hydrogeologyand quantitative methods for topographically driven ground-water flow systems are expected in all future groundwatertextbooks However because purely confined flow and purelyunconfined flow are two end-members of groundwater flowclearer concepts for the simultaneous control of aquitards andtopography on the occurrence of flowing wells are needed

Code and data availability No data sets were used in this article

Author contributions XJ and JC prepared the article with contribu-tions from LW

Competing interests The authors declare that they have no conflictof interest

Special issue statement This article is part of the special issueldquoHistory of hydrologyrdquo (HESSHGSS inter-journal SI) It is not as-sociated with a conference

Acknowledgements The authors thank Vitaly Zlotnik of the Uni-versity of NebraskandashLincoln for discussion on the ambiguous termldquoartesianrdquo Eileen Poeter of the Colorado School of Mines andJohn Hermance of Brown University for suggestions on improvingthe article The authors also thank the handling editor Okke Bate-laan and two reviewers (Garth van der Kamp and an anonymousone) for suggestions

Financial support This study was supported by the Teaching Re-form Funds of the China University of Geosciences the NationalNatural Science Foundation of China (41772242) the NationalProgram for Support of Top-notch Young Professionals and the111 Project (B20010)

Review statement This paper was edited by Okke Batelaan and re-viewed by Garth van der Kamp and one anonymous referee



References

Alley W M and Alley R High and Dry Meeting the Challengesof the Worldrsquos Growing Dependence on Groundwater Yale Uni-versity Press New Haven 2017

Anderson M P The Wisconsin Roots of Ground Water Hydrol-ogy Groundwater 43 142ndash145 httpsdoiorg101111j1745-65842005tb02294x 2005

Anderson M P Groundwater Benchmark Papers in HydrologyIAHS Press Oxfordshire 2008

Anonymous The Social Economist NO 1 ndash Bored springs or ar-tificial fountains obtained by boring the earth Mon Mag BritRegist 54 32ndash35 1822

Anonymous The Artesian Well at Grenelle in France in Califor-nia Farmer and Journal of Useful Sciences Vol 4 21 pp 1855

Arago M On springs artesian wells and sprouting fountains Ed-inburgh New Philosoph J 18 205ndash246 1835

Back W Origin of hydrochemical facies of ground water in theAtlantic Coastal Plain in Proceedings of 21st International Ge-ological Congress Copenhagen 87ndash95 1960

Back W Hydrochemical facies and ground-water flow patternsin northern part of Atlantic Coastal Plain Report 498A USGSWashington DC 1966

Back W and Herman J S American Hydrogeology at the Millen-nium An Annotated Chronology of 100 Most Influential PapersHydrogeol J 5 37ndash50 httpsdoiorg101007s1004000502551997

Batu V Aquifer Hydraulics A Comprehensive Guide to Hydroge-ologic Data Analysis John Wiley amp Sons Inc New York NY1998

Beaumont P A Traditional Method of Ground-Water Util-isation in the Middle East Groundwater 11 23ndash30httpsdoiorg101111j1745-65841973tb02984x 1973

Bethke C M and Johnson T M Groundwater Age and Ground-water Age Dating AnnuRev Earth Planet Sci 36 121ndash152httpsdoiorg101146annurevearth36031207124210 2008

Biswas A K The History of Hydrology North-Holland Publish-ing Company Amsterdam 1970

Bond F T The geology of mineral springs Popul Sci Rev 4203ndash213 1865

Brassington R Field Hydrogeology 3rd Edn John Wiley amp SonsLtd Hoboken NJ 2017

Bredehoeft J D The Toth Revolution Groundwater 56 157ndash159httpsdoiorg101111gwat12592 2018

Bredehoeft J D Neuzil C E and Milly P C Regional flowin the Dakota aquifer a study of the role of confining layersReport 2237 USGS Alexandria Virginia 1983

Brown G O Henry Darcy and the making of a law Water ResourRes 38 11-11ndash11-12 httpsdoiorg1010292001wr0007272002

Buckland W Geology amp Mineralogy Considered with Referenceto Natural Theology Routledge London 1836

Carpenter L G Artesian Wells of Colorado and Their Relationto Irrigation The State Agricultural College Fort Collins CO1891

Carslaw H S Introduction to the Mathematical Theory of the Con-duction of Heat in Solids Macmillan London 1921

Chamberlin T C The requisite and qualifying conditions of arte-sian wells in Fifth Annual report of the United States Geologi-cal Survey to the Secretary of the Interior 1883ndash1884 edited by

Powell J W Washington Government Printing Office Wash-ington DC 125ndash173 1885

Chang C-C and Chen C-S An integral transform approach fora mixed boundary problem involving a flowing partially pene-trating well with infinitesimal well skin Water Resour Res 381071 httpsdoiorg1010292001wr001091 2002

Commander D P Artesian Water in Water Encyclopedia editedby Lehr J H and Keeley J John Wiley amp Sons Inc 1ndash5httpsdoiorg101002047147844Xgw56 2005

Darton N H Preliminary Report on Artesian Waters of a Por-tion of the Dakotas in Seventeenth Annual Report of the UnitedStates Geological Survey Government Printing Office Washing-ton 609ndash694 1897

Darton N H Preliminary report on the geology and undergroundwater resources of the central Great Plains Report 32 1905

Darcy H Les fontaines publiques de la ville de Dijon DalmontParis 1856

Darwin E An account of an artificial spring of water Philos TRoy Soc Lond 75 1ndash7 1785

Davie T Fundamentals of Hydrology 2nd Edn Routledge Oxon2008

Davis S N and De Wiest R J M Hydrogeology John Wiley andSons New York 1966

de Marsily G Quantitative Hydrogeology Academic Press Or-lando FL 1986

Deming D Introduction to Hydrogeology The McGraw-HillCompanies Inc New York NY 2002

de Thury H Observations on the cause of the spouting of over-flowing wells or artesian fountains Edinburgh New PhilosophJ 9 157ndash165 1830

de Vries J J History of Groundwater Hydrology in The Hand-book of Groundwater Engineering 2nd Edn edited by DelleurJ W CRC Press Boca Raton 2007

Domenico P A and Schwartz F W Physical and Chemical Hy-drogeology 2nd Edn John Wdey amp Sons lnc New York NY1998

Driscoll F G Groundwater and Wells 2nd Edn Johnson Divi-sion St Paul Minnesota 1986

Duffy C J The terrestrial hydrologic cycle an his-torical sense of balance WIREs Water 4 e1216httpsdoiorg101002wat21216 2017

Dupuit A J E J Eacutetudes theacuteoriques et pratiques sur le movementdes eaux dans les canaux deacutecouvertes et agrave travers les terrainespermeacuteables 2nd Edn Dunod Paris 1863

Farey J On artesian wells and boreholes Mon Mag Brit Regist56 309 1823

Farvolden R N Groundwater resources Pembina area AlbertaResearch Council of Alberta Alberta 1961

Feng Q and Zhan H Constant-head test at a partially penetrat-ing well in an aquifer-aquitard system J Hydrol 569 495ndash505httpsdoiorg101016jjhydrol201812018 2019

Fetter C W Applied Hydrogeology 3rd Edn Pearson EducationInc Essex 1994

Fetter C W Applied Hydrogeology 4th Edn Pearson EducationInc Essex 2001

Fetter C W Hydrogeology A Short History Part 2 Groundwa-ter 42 949ndash953 httpsdoiorg101111j1745-65842004t01-14-x 2004



Fiedler A G and Nye S S Geology and Ground-Water Re-sources of the Roswell Artesian Basin New Mexico USGS Wa-ter Supply Paper 639 USGS Washington DC 1933

Fitts C R Groundwater Science 2nd Edn Academic PressWaltham MA 2013

Freeze R A Vignettes of a Life in Hydrogeology Groundwater50 485ndash490 httpsdoiorg101111j1745-6584201200921x2012

Freeze R A and Back W Benchmark Papers in Geology Phys-ical Hydrogeology Hutchinson Ross Publishing Company NewYork NY 1983

Freeze R A and Cherry J A Groundwater Prentice-Hall IncEnglewood Cliffs NJ 1979

Freeze R A and Witherspoon P A Theoretical analysis of re-gional groundwater flow 2 Effect of water-table configurationand subsurface permeability variation Water Resour Res 3623ndash634 httpsdoiorg101029WR003i002p00623 1967

Fuller M L Significance of the term ldquoartesianrdquo in Underground-Water Papers 1906 edited by Fuller M L Government PrintingOffice Washington 9ndash15 1906

Gaber M S Michigan Flowing Well Handbook Michigan Depart-ment of Environmental Quality Water Bureau Michigan 2005

Garnier F De LrsquoArt du Fontenier Sondeur et des Puits ArteacutesiensImprimerie de Madame Huzard Rue de lrsquoEperon St Andreacute desArt Paris 1822

Habermehl M A Review The evolving understanding ofthe Great Artesian Basin (Australia) from discovery to cur-rent hydrogeological interpretations Hydrogeol J 28 13ndash36httpsdoiorg101007s10040-019-02036-6 2020

Haitjema H M and Mitchell-Bruker S Are Water Tables a Sub-dued Replica of the Topography Groundwater 43 781ndash786httpsdoiorg101111j1745-6584200500090x 2005

Hantush M S Nonsteady flow to flowing wells inleaky aquifers J Geophys Res 64 1043ndash1052httpsdoiorg101029JZ064i008p01043 1959

Hantush M S and Jacob C E Non-steady radial flow in an infi-nite leaky aquifer Eos Trans Am Geophys Union 36 95ndash100httpsdoiorg101029TR036i001p00095 1955

Heath R C Basic Ground-Water Hydrology USGS Reston Vir-ginia 1983

Hendriks M Introduction to Physical Hydrology Oxford Univer-sity Press New York 2010

Hinkle S R Shapiro S D Plummer L N Busenberg E Wid-man P K Casile G C and Wayland J E Estimates of tracer-based piston-flow ages of groundwater from selected sites ndash Na-tional Water-Quality Assessment Program 1992ndash2005 US Geo-logical Survey Washington DC 2010

Hiscock K M and Bense V F Hydrogeology Principles andPractice 2nd Edn John Wiley amp Sons Ltd Oxford 2014

Houmllting B and Coldewey W G Hydrogeology Springer-Verlag GmbH Berlin Germany 2019

Hornberger G M Wiberg P L Raffensperger J P andDrsquoOdorico P Elements of Physical Hydrology 2nd EdnJohns Hopkins University Press Baltimore MA 2014

Hou G C Liang Y P Su X S Zhao Z H Tao ZP Yin L H Yang Y C and Wang X Y Groundwa-ter Systems and Resources in the Ordos Basin China ActaGeolog Sin 82 1061ndash1069 httpsdoiorg101111j1755-67242008tb00664x 2008

Howden N and Mather J History of Hydrogeology Tay-lor amp Francis Group LLC Boca Raton FL 2013

Hubbert M K The Theory of Ground-Water Motion J Geol 48785ndash944 httpsdoiorg101086624930 1940

Jacob C E On the flow of water in an elastic artesianaquifer Eos Trans Am Geophys Union 21 574ndash586httpsdoiorg101029TR021i002p00574 1940

Jacob C E and Lohman S W Nonsteady flow to awell of constant drawdown in an extensive aquiferEos Trans Am Geophys Union 33 559ndash569httpsdoiorg101029TR033i004p00559 1952

Jiang X W Wan L Wang X S Ge S M and Liu J Ef-fect of exponential decay in hydraulic conductivity with depthon regional groundwater flow Geophys Res Lett 36 L24402httpsdoiorg1010292009GL041251 2009

Jiang X W Wan L Cardenas M B Ge S and Wang X S Si-multaneous rejuvenation and aging of groundwater in basins dueto depth-decaying hydraulic conductivity and porosity GeophysRes Lett 37 L05403 httpsdoiorg1010292010gl0423872010

Jiang X W Wang X S Wan L and Ge S An analyticalstudy on stagnant points in nested flow systems in basins withdepth-decaying hydraulic conductivity Water Resour Res 47W01512 httpsdoiorg1010292010WR009346 2011

Jiang X-W Wan L Ge S Cao G-L Hou G-C HuF-S Wang X-S Li H and Liang S-H A quantitativestudy on accumulation of age mass around stagnation pointsin nested flow systems Water Resour Res 48 W12502httpsdoiorg1010292012wr012509 2012

Jiang X W Wan L Wang X S Wang D Wang HWang J Z Zhang H Zhang Z Y and Zhao K YA multi-method study of regional groundwater circulation inthe Ordos Plateau NW China Hydrogeol J 26 1657ndash1668httpsdoiorg101007s10040-018-1731-4 2018

Jones J F Reconnaissance groundwater study Swan Hills andadjacent areas Alberta Research Council of Alberta Alberta1962

Jones L A Comparison of Pumping and Slug Tests for Es-timating the Hydraulic Conductivity of Unweathered Wis-consian Age Till in Iowa Groundwater 31 896ndash904httpsdoiorg101111j1745-65841993tb00862x 1993

Kasenow M Applied Ground-Water Hydrology and Well Hy-draulics 3rd Edn Water Resources Publications LLC High-lands Ranch Colorado 2010

King F H Principles and conditions of the movements of ground-waters in Nineteenth Annual Report of the United States Geo-logical Survey Part 2 USGS Washington DC 59ndash295 1899

Konikow L F Groundwater depletion in the United States (1900ndash2008) US Geological Survey Scientific Investigations Re-port 2013-5079 USGS Reston Virginia 2013

Kruseman G P and de Ridder N A Analysis and Evaluation ofPumping Test Data 2nd Edn International Institute for LandReclamation and Improvement Wageningen the Netherlands1990

LaMoreaux P E Soliman M M Memon B A LaMoreaux JW and Assaad F A Environmental Hydrogeology 2nd EdnTaylor and Francis Group LLC Boca Raton FL 2009

Leonard R B Signor D C Jorgensen D G and Helgesen J OGeohydrology and hydrochemistry of the Dakota aquifer cen-



tral United States J Am Water Resour Assoc 19 903ndash912httpsdoiorg101111j1752-16881983tb05939x 1983

Lionnais Historie de 1a ville de Naney Description de 1a fontaineartesienne de Jarville Lionnais Nancy 1805

Lohman S W Geology and ground-water resources of the Eliza-beth City area North Carolina Report 773A USGS Washing-ton DC 1936

Lohman S W Definitions of Selected Ground-Water Terms ndash Re-visions and Conceptual Refinements USGS Washington 1972a

Lohman S W Ground-Water Hydraulics Report Geological Sur-vey Professional Paper 708 USGS Washington DC 1972b

Macintosh A The Repertory of Patent Inventions and Other Dis-coveries and Improvements in Arts Manufactures and Agricul-ture Bibliotheca Regia Monacensis London 1827

Madl-Szonyi J From the Artesian Paradigm to Basin HydraulicsThe Contribution of Jozsef Toth to Hungarian HydrogeologyPublishing Company of Budapest University of Technology andEconomics Budapest 2008

Margat J Pennequin D and Roux J-C History of French hy-drogeology in History of Hydrogeology edited by Howden Nand Mather J Taylor amp Francis Group LLC Boca Raton FL2013

Mays L W Ground and Surface Water Hydrology John Wi-ley amp Sons Inc Hoboken NJ 2012

McWhorter D B and Sunada D K Ground-Water Hydrologyand Hydraulics Water Resources Publications LLC HighlandsRanch Colorado USA 1977

Meinzer O E The occurrence of ground water in the UnitedStates with a discussion of principles Report 489 USGS Wash-ington DC 1923a

Meinzer O E Outline of ground-water hydrology with defini-tions Report 494 USGS Washington DC 1923b

Meinzer O E Compressibility and elasticity ofartesian aquifers Econ Geol 23 263ndash291httpsdoiorg102113gsecongeo233263 1928

Meinzer O E and Hard H A The artesian water supply of theDakota sandstone in North Dakota with special reference to theEdgeley quadrangle Chapter E in Contributions to the hydrologyof the United States 1923ndash1924 Report 520E USGS Washing-ton DC 73ndash95 1925

Meiter J A The Guide to Wisconsin Flowing Artesian WellsNeshkoro Wisconsin 2019

Merdinger C J Water Supply through the Ages Part I Early His-tory Military Eng 47 280ndash285 1955

Meyboom P Patterns of groundwater flow in the Prairie Profilein Proceedings of Third Canadian Hydrology Symposium 8ndash9 November 1962 Calgary Alberta 5ndash20 1962

Meyboom P Groundwater Studies in the Assiniboine Riverdrainage basin Part 1 The evaluation of a flow system in south-central Saskatchewan Bulletin 139 Geologic Survey of CanadaOttawa 1ndash65 1966

Meyer G Davis G and LaMoreaux P E Historical perspec-tive in Hydrogeology The Geology of North America Vol 0ndash2edited by Back W Rosenshein J S and Seaber P R TheGeological Society of America Boulder Colorado 1988

Mishra S and Guyonnet D Analysis of Observation-Well Re-sponse During Constant-Head Testing Groundwater 30 523ndash528 httpsdoiorg101111j1745-65841992tb01528x 1992

Nonner J C Introduction to Hydrogeology 2nd EdnA A Balkema Publishers Lisse 2003

Norton W H Artesian Wells of Iowa Iowa Geological SurveyAnnual Report 6 Iowa Geological Survey Iowa City Iowa 113ndash428 httpsdoiorg10170772160-52701330 1897

Ordens C M McIntyre N Underschultz J R Ransley TMoore C and Mallants D Preface Advances in hydrogeo-logic understanding of Australiarsquos Great Artesian Basin Hydro-geol J 28 1ndash11 httpsdoiorg101007s10040-019-02107-82020

Pandey S Singh D Denner S Cox R Herbert S J Dick-inson C Gallagher M Foster L Cairns B and GossmannS Inter-aquifer connectivity between Australiarsquos Great ArtesianBasin and the overlying Condamine Alluvium an assessmentand its implications for the basinrsquos groundwater managementHydrogeol J 28 125ndash146 httpsdoiorg101007s10040-019-02089-7 2020

Pennink J M K Over de beweging van grondwater De Ingenieur20 482ndash492 1905

Pinder G F and Celia M A Subsurface hydrology John Wi-ley amp Sons Inc Hoboken NJ 2006

Poiseuille J L Recherches expeacuterimentales sur le mouvement desliquides dans les tubes de trelsquos-petits diamelsquotres comptes rendusAcadeacutemie des Sciences Paris 1841

Price M Introducing Groundwater Chapman amp Hall London1996

Ramazzini B De Fontium mutinensium amiranda scaturigine trac-tatus physico-hydrostaticusm Cramer and Perachon Genevae1691

Reynolds O An experimental investigation of the circum-stances which determine whether the motion of watershall be direct or sinuous and of the law of resistancein parallel channel Philos T Roy Soc 174 935ndash982httpsdoiorg101098rspl18830018 1883

Ritzi R W and Bobeck P Comprehensive principles ofquantitative hydrogeology established by Darcy (1856)and Dupuit (1857) Water Resour Res 44 W10402httpsdoiorg1010292008wr007002 2008

Rushton K R Groundwater Hydrology Conceptual and Compu-tational Models John Wiley amp Sons Ltd London 2003

Schwartz F W and Zhang H Fundamentals of Ground WaterJohn Wiley amp Sons New York NY 2003

Slichter C S Theoretical investigation of the motion of groundwaters 19th Annual Report of the United Stated Geological Sur-vey Government Printing Office Washington 1899

Smerdon B D and Turnadge C Considering the potential effectof faulting on regional-scale groundwater flow an illustrative ex-ample from Australiarsquos Great Artesian Basin Hydrogeol J 23949ndash960 httpsdoiorg101007s10040-015-1248-z 2015

Smith L P Heat Flow in an Infinite Solid Bounded In-ternally by a Cylinder J Appl Phys 8 441ndash448httpsdoiorg10106311710319 1937

Storrow C S A Treatise on Water-Works for Conveying andDistribution Supplies of Water Hilliard Gray Boston Mas-sachusetts 1835

Swenson F A New theory of recharge tothe artesian basin of the Dakotas GSA Bul-letin 79 163ndash182 httpsdoiorg1011300016-7606(1968)79[163NTORTT]20CO2 1968



Tavenas F Diene M and Leroueil S Analysis of the in situconstant-head permeability test in clays Can Geotech J 27305ndash314 1990

Theis C V Ground water in Curry and Roosevelt Coun-ties 10th Bienn Rept 1930-32 New Mexico State EngineerSanta Fe 99ndash160 1932

Theis C V The relation between the lowering of the Piezometricsurface and the rate and duration of discharge of a well usingground-water storage Eos Trans Am Geophys Union 16 519ndash524 httpsdoiorg101029TR016i002p00519 1935

Thiem G Hydrologische methoden Gebhardt Leipzig 1906Todd D K and Mays L W Groundwater Hydrology 3rd Edn

John Wiley amp Sons New York 2004Toacuteth J A theory of groundwater motion in small drainage basins

in central Alberta Canada J Geophys Res 67 4375ndash4388httpsdoiorg101029JZ067i011p04375 1962

Toacuteth J A theoretical analysis of groundwater flow insmall drainage basins J Geophys Res 68 4795ndash4812httpsdoiorg101029JZ068i016p04795 1963

Toacuteth J Mapping and interpretation of field phenomena for ground-water reconnaissance in a prairie environment International As-sociation of Scientific Hydrology Bulletin Alberta Canada 1120ndash68 httpsdoiorg10108002626666609493458 1966

Toacuteth J The Canadian School of HydrogeologyHistory and Legacy Groundwater 43 640ndash644httpsdoiorg101111j1745-658420050086x 2005

Toacuteth J Gravitational Systems of Groundwater Flow TheoryEvaluation Utilization Cambridge University Press New York2009

Tsai C-S and Yeh H-D Wellbore flow-rate solution for aconstant-head test in two-zone finite confined aquifers Hy-drol Process 26 3216ndash3224 httpsdoiorg101002hyp83222012

van der Gun J The Global Groundwater Revolution in the OxfordResearch Encyclopedia Oxford University Press New York1ndash30 httpsdoiorg101093acrefore97801993894140136322019

Versluys J The origin of artesian pressure P Roy Acad Sci Am-sterdam 33 214ndash222 1930

Vogel H U The great well of China Scient Am 268 116ndash1211993

Wang H Jiang X W Wan L Han G and Guo H Hydro-geochemical characterization of groundwater flow systems inthe discharge area of a river basin J Hydrol 527 433ndash441httpsdoiorg101016jjhydrol201504063 2015

Wang J Z Jiang X W Wan L Woumlrman A Wang H WangX S and Li H An analytical study on artesian flow conditionsin unconfined-aquifer drainage basins Water Resour Res 518658ndash8667 httpsdoiorg1010022015wr017104 2015

Wang X S Jiang X W Wan L Ge S and Li H L A newanalytical solution of topography-driven flow in a drainage basinwith depth-dependent anisotropy of permeability Water ResourRes 47 W09603 httpsdoiorg1010292011WR0105072011

Wen Z Zhan H Huang G and Jin M Constant-head test in aleaky aquifer with a finite-thickness skin J Hydrol 399 326ndash334 httpsdoiorg101016jjhydrol201101010 2011

Wenzel L K The thiem method for determining permeability ofwater-bearing materials and its application to the determinationof specific yield results of investigations in the Platte river valleyNebraska Report 679A USGS Washington DC 1936

White R R and Clebsch A C V Theis The Man and His Contri-butions to Hydrogeology in Selected Contributions to Ground-Water Hydrology by C V Theis and a Review of His Life andWork edited by Clebsch A US Geological Survey Washing-ton DC 1993

Wilkinson W B Constant Head in Situ Permeabil-ity Tests in Clay Strata Geacuteotechnique 18 172ndash194httpsdoiorg101680geot1968182172 1968

Williamson W H The history of hydrogeology in Australia inHistory of Hydrogeology edited by Howden N and Mather JTaylor amp Francis Group LLC Boca Raton FL 2013

Yeh J T C Khaleel R and Carroll K C Flow Through Het-erogeneous Geologic Media Cambridge University Press NewYork NY 2015

Young H L Summary of ground-water hydrology of theCambrian-Ordovician aquifer system in the northern MidwestUnited States A in Regional aquifer system analysis Re-port 1405A USGS Washington DC 67 pp 1992

Younger P L Groundwater in the Environment Blackwell Pub-lishing Ltd Malden MA 2007

Zhang H Jiang X W Wan L Ke S Liu S A HanG Guo H and Dong A Fractionation of Mg isotopesby clay formation and calcite precipitation in groundwa-ter with long residence times in a sandstone aquifer Or-dos Basin China Geochim Cosmochim Ac 237 261ndash274httpsdoiorg101016jgca201806023 2018

Zhang Z Y Jiang X W Wang X S Wan L and Wang JZ A numerical study on the occurrence of flowing wells inthe discharge area of basins due to the upward hydraulic gra-dient induced wellbore flow Hydrol Process 32 1682ndash1694httpsdoiorg101002hyp11623 2018

Zhang Z-Y Jiang X-W Wang X-S Wan L and Wang J-ZWhy mixed groundwater at the outlet of open flowing wells inunconfined-aquifer basins can represent deep groundwater im-plications for sampling in long-screen wells Hydrogeol J 27409ndash421 httpsdoiorg101007s10040-018-1842-y 2019

Zlotnik V A Cardenas M B and Toundykov D Effectsof multiscale anisotropy on basin and hyporheic groundwaterflow Groundwater 49 576ndash583 httpsdoiorg101111j1745-6584201000775x 2011


Abstract

Introduction

Terms related to flowing wells and confusion of ldquoartesianrdquo

Terms representing flowing wells

Confusing uses of ldquoartesianrdquo in the literature

The history of drilling flowing wells in selected regions

France

Italy

Great Britain

The United States

Australia

Canada

China

Confined-flow flowing wells and confined flow bounded by aquitards (1690sndashcurrent)

Conditions of confined-flow flowing wells

Confined flow bounded by aquitards

Darcys law and steady-state well hydraulics inspired by flowing wells (1850sndash1910s)

The birth of Darcys law evoked by flowing wells

Steady-state well hydraulics in confined aquifers Dupuit equation

Compressibility of confined aquifers and transient well hydraulics inspired by flowing wells (1920sndashcurrent)

Compressibility of confined aquifers concepts instigated by flowing wells

Transient well hydraulics in flowing and non-flowing wells in confined aquifers

Unconfined-flow flowing wells and topographically driven flow systems (1890sndashcurrent)

Qualitative understanding of topographically driven groundwater flow and unconfined-flow flowing wells

Quantitative analysis of topographically driven groundwater flow systems

Hydraulics of unconfined-flow flowing wells

Conclusions and suggestions

Code and data availability

Author contributions

Competing interests

Special issue statement

Acknowledgements

Financial support

Review statement

References


Figure 1 Four threads of evolution of physical hydrogeology stemmed from flowing wells The yellow ellipses are field phenomena offlowing wells the purple boxes are papers directly related to flowing wells and the white boxes are papers less or not directly related toflowing wells but have connections to previous or follow-up studies on flowing wells The publications labeled with a ldquolowastrdquo are the sevenclassical studies identified by both Freeze and Back (1983) and Anderson (2008)

aquifers while the fourth is from flowing wells in uncon-fined aquifers Following Freeze and Cherry (1979) a con-fined aquifer is a saturated permeable geologic unit that isconfined between two aquitards while an unconfined aquiferis the saturated part of a permeable geologic unit in whichthe water table forms the upper boundary The seven classi-cal studies that were selected by both Freeze and Back (1983)and Anderson (2008) as benchmark papers of physical hy-drogeology (groundwater hydrology) have been included inthe four threads Moreover four out of the seven papers aredirectly related to flowing wells implying that flowing wellscan be considered at least one of the roots of physical hy-drogeology

The paper is organized as follows We first introduce theterms used to represent flowing wells with conceptual ex-amples of the root difference between confined and uncon-fined sources for these wells (Sect 2) Section 3 summarizesthe history of drilling flowing wells in selected regions thathave inspired hydrogeologists Sections 4 through 7 then his-torically sequence the principal hydrogeological publicationsthrough which flowing wells played a major role in the evo-lution of the science as we know it today Finally concludingremarks are given in Sect 8

2 Terms related to flowing wells and confusion ofldquoartesianrdquo

21 Terms representing flowing wells

In the groundwater hydrology hydrogeology or hydrologytextbooks available to the authors we found that the phe-

nomenon of a well that overflows at the surface is defined orat least mentioned in 34 textbooks The widely used termsinclude ldquoflowing wellrdquo ldquoartesian wellrdquo and ldquoflowing artesianwellrdquo which appear in 17 15 and 13 textbooks respectively(sometimes more than one term is used in one book) Otherless frequently used terms include ldquoartesian flowing wellrdquoldquooverflowing wellrdquo and ldquofree flowing wellrdquo For convenienceof discussion we divide these six terms into two categoriesthose using the term ldquoartesianrdquo and those not using ldquoarte-sianrdquo

The terms ldquoflowing wellrdquo ldquooverflowing wellrdquo and ldquofreeflowing wellrdquo stem purely from the phenomenon of wateroverflow at the well outlet presumably at grade level Theterm ldquooverflowing wellrdquo has been used in Britain since atleast as early as the 1820s (Anonymous 1822) and currentlyis still widely used in Britain as found in several textbooks(Hiscock and Bense 2014 Price 1996 Rushton 2003) Tothe best of the authorsrsquo knowledge the term ldquoflowing wellrdquowas first used in the USGS (United States Geological Survey)hydrogeologic report The Requisite and Qualifying Condi-tions of Artesian Wells (Chamberlin 1885) and is currentlythe one most widely used The term ldquofree flowing wellrdquocan be found in three textbooks available to us (Fitts 2013Kruseman and de Ridder 1990 Nonner 2003) By includ-ing the adjectives ldquoflowingrdquo ldquooverflowingrdquo or ldquofree flow-ingrdquo these terms have clear meaning to represent wells thatgroundwater could flow out of without the aid of pumping

The number of textbooks that use one or two of the termsldquoartesian wellrdquo ldquoflowing artesian wellrdquo or ldquoartesian flowingwellrdquo is as high as 28 indicating the popularity of the ad-jective ldquoartesianrdquo The term ldquoartesian wellrdquo originates from
















31 France




32 Italy



33 Great Britain












35 Australia



36 Canada






37 China






























hL =La

πr4 q (1)


hL =Lb

πr5 q2 (2)



h1+aLprime

πr prime4q1+

bH1

πr5 q21sim= h2+

aLprime

πr prime4q2+

bH2

πr5 q22 (3a)

(h1minush2)+b

πr5

(H1q

21 minusH2q

22















h0minushw =q

2πkBln

(R

rw

) (6)


2πkB ln(Rrw

)








































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References















31 France




32 Italy



33 Great Britain












35 Australia



36 Canada






37 China






























hL =La

πr4 q (1)


hL =Lb

πr5 q2 (2)



h1+aLprime

πr prime4q1+

bH1

πr5 q21sim= h2+

aLprime

πr prime4q2+

bH2

πr5 q22 (3a)

(h1minush2)+b

πr5

(H1q

21 minusH2q

22















h0minushw =q

2πkBln

(R

rw

) (6)


2πkB ln(Rrw

)








































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References









35 Australia



36 Canada






37 China






























hL =La

πr4 q (1)


hL =Lb

πr5 q2 (2)



h1+aLprime

πr prime4q1+

bH1

πr5 q21sim= h2+

aLprime

πr prime4q2+

bH2

πr5 q22 (3a)

(h1minush2)+b

πr5

(H1q

21 minusH2q

22















h0minushw =q

2πkBln

(R

rw

) (6)


2πkB ln(Rrw

)








































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References




37 China






























hL =La

πr4 q (1)


hL =Lb

πr5 q2 (2)



h1+aLprime

πr prime4q1+

bH1

πr5 q21sim= h2+

aLprime

πr prime4q2+

bH2

πr5 q22 (3a)

(h1minush2)+b

πr5

(H1q

21 minusH2q

22















h0minushw =q

2πkBln

(R

rw

) (6)


2πkB ln(Rrw

)








































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References




















hL =La

πr4 q (1)


hL =Lb

πr5 q2 (2)



h1+aLprime

πr prime4q1+

bH1

πr5 q21sim= h2+

aLprime

πr prime4q2+

bH2

πr5 q22 (3a)

(h1minush2)+b

πr5

(H1q

21 minusH2q

22















h0minushw =q

2πkBln

(R

rw

) (6)


2πkB ln(Rrw

)








































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References









h0minushw =q

2πkBln

(R

rw

) (6)


2πkB ln(Rrw

)








































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References




































































References





























































































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

Canada

China

















Competing interests


Acknowledgements

Financial support

Review statement

References















































































































Abstract

Introduction





France

Italy

Great Britain

The United States

Australia

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Competing interests


Acknowledgements

Financial support

Review statement

References

flowing wells: terminology, history and role in the

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