Case Study

Interpretation of Pumping Test with RadialCollector Well Using a Reservoir Model

Emmanuel Kwame Appiah-Adjei1; Longcang Shu2; Kwaku Amaning Adjei3;Chengpeng Lu4; and Mingjiang Deng5

Abstract: This study proposes a reservoir model for evaluation of aquifer parameters from a long duration pumping test conducted with aradial collector pumping well and nine observation wells in an unconfined aquifer in the Tailan River basin of China. The proposed model,based on the concept of double continuum, was used to conceptualize the pumping test site into conduit and porous reservoirs coupled by alinear flow exchange for simulating flow during the pumping test. The set of model equations developed from the concept were solved by aniterative method. The model-simulated hydraulic heads agree reasonably well with the observation heads in both the pumping and observationwells at an average normalized root mean square error of 10.99 and 8.06%, respectively, during pumping but were weaker in the recoveryperiod. This notwithstanding, the specific yield estimates compare well with the range obtained for a numerical modeling of the entire aquiferbasin. Significantly, the model was applied successfully in simulating sustainable withdrawal rates from the aquifer and may be a useful toolfor analyzing flows to radial collector wells for applications in water resources management.DOI: 10.1061/(ASCE)HE.1943-5584.0000598.© 2012 American Society of Civil Engineers.

CE Database subject headings: Aquifers; Porous media; Pumps; Groundwater management; Parameters; China; Reservoirs.

Author keywords: Aquifer; Porous media flow; Pumping test; Groundwater management; Parameters; China.

Introduction

Reliable and accurate estimates of aquifer parameters are very im-portant in groundwater resource assessment, quantification of avail-able resources, and sustainable exploitation of aquifers (Mjemahet al. 2009; Jat et al. 1995). Therefore, several techniques, suchas flood wave response, tidal response, water balance calculationson fluctuations of water table in response to recharge and dischargerate, and laboratory drainage experiments, are available for estimat-ing these parameters. Most of these techniques require very specificand/or exhaustive data, which are not always available. Thus therelatively simple technique of pumping test analysis has become

the standard and widely used approach for determining aquiferparameters of most formations (Samuel and Jha 2003; Moench1994).

Commonly, the data from pumping tests are interpreted using ananalytical solution. As such, several analytical solutions are avail-able for this purpose. Generally, the type of analytical solution ap-propriate for interpretation of any pumping test data depends onfactors like the hydrogeologic condition of the aquifer medium(i.e., whether unconfined, leaky, or confined), conditions of thetest wells (e.g., partially or fully penetrating), mode of pumping(i.e., constant or variable) during the test, and influence of existinghydrogeological boundaries (e.g., recharge or barrier boundaries)on the data (Fetter 2001; Kruseman and de Ridder 1994).

One of the earliest analytical solutions for interpreting pumpingtest data was presented by Theis (1935) and was for ideal confinedaquifer conditions (i.e., constant pumping rate, fully penetratingpumping well, infinite extent of aquifer, etc.). Subsequently, moreimproved solutions were developed by Hantush and Jacob (1955);Cooper and Jacob (1946); Walton (1962); Hantush (1964), andmany others to predict the behavior of confined aquifers to includeleaky, partially penetrating, and/or variable pumping conditions.Analytical solutions for interpreting unconfined aquifer tests werelater initiated through Boulton’s (1955, 1963) delayed yield con-cept and have been improved upon by the works of Neuman(1972, 1975); Moench (1993); Streltsova (1973, 1976); Huntand Scot (2005), and many others over the years. The analyticalsolutions for unconfined aquifers are more complex than thosefor confined aquifers because the number of parameters derivedfrom them is greater owing to the delayed yield concept includedin their solutions.

Usually, vertical wells are used in conducting pumping tests,and thus the solutions discussed earlier were developed taking intoconsideration flow to such wells. However, in recent times, hori-zontal and radial collector wells are becoming a common featurefor accessing groundwater because of their economical nature

1Ph.D. Student, State Key Laboratory of Hydrology, Water Resourcesand Hydraulic Engineering, Hohai Univ., No. 1 Xikang Rd., Nanjing210098, China; and Lecturer, Geological Engineering Dept., KwameNkrumah Univ. of Science and Technology, PMB, Kumasi, Ghana(corresponding author). E-mail: emmaappiah_adjei@yahoo.com

2Professor, College of Hydrology and Water Resources, Hohai Univ.,No. 1 Xikang Rd., Nanjing 210098, China; and Professor, State KeyLaboratory of Hydrology, Water Resources and Hydraulic Engineering,Hohai Univ., No. 1 Xikang Rd., Nanjing 210098, China.

3Ph.D. Student, State Key Laboratory of Hydrology, Water Resourcesand Hydraulic Engineering, Hohai Univ., No. 1 Xikang Rd., Nanjing210098, China; and Lecturer, Civil Engineering Dept., Kwame NkrumahUniv. of Science and Technology, PMB, Kumasi, Ghana.

4Ph.D. Student, State Key Laboratory of Hydrology, Water Resourcesand Hydraulic Engineering, Hohai Univ., No. 1 Xikang Rd., Nanjing210098, China.

5Senior Engineer, Dept. of Water Resources of Xinjiang, Xinjiang830063, China.

Note. This manuscript was submitted on September 13, 2011; approvedon February 3, 2012; published online on February 6, 2012. Discussionperiod open until May 1, 2013; separate discussions must be submittedfor individual papers. This paper is part of the Journal of Hydrologic En-gineering, Vol. 17, No. 12, December 1, 2012. © ASCE, ISSN 1084-0699/2012/12-1397-1407/$25.00.

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(Maurer 1995) and their relative efficiency for aquifer remediation(Hunt 2005). More so, these wells have significantly higher wellscreen exposure to the aquifer than vertical wells, can produce largequantities of water under moderate drawdown conditions, and areparticularly suitable for accessing shallow highly permeable aqui-fers in which vertical wells have low yields (Ball and Herbert 1992;Sawyer and Lieuallen-Dulam 1998; Patel et al. 2010). The head andflow distribution around these types of wells are different from ver-tical wells; hence the data from them are interpreted using specificanalytical or semianalytical solutions developed by Bear (1979);Cleveland (1994); Hantush and Papadopoulos (1962); Schafer(1996), etc. Like all analytical solutions, the accuracy of the resultsobtained from these solutions depend on the validity of the assump-tions invoked in their derivation, the accuracy of their curve fittingprocess, and the relative importance of extraneous effects on thefield test conditions for data collection (Moench 1994). Mostly,the basis for the derivation of an analytical solution does not exactlymatch the conditions of the field data acquisition and, thus, maylimit its interpretation. Because of this limitation, numerical meth-ods may often be preferred for evaluating flow to these wells(Conger and Trichel 1993; Losonsky and Beljin 1992). Thenumerical methods when applied in analyzing pumping test dataoften make it possible to eliminate some of the simplificationsand assumptions on which the analytical solutions are based (Lebbeet al. 1992).

This study proposes a new method, i.e., reservoir model, basedon an application of the double-continuum concept for interpreta-tion of long duration pumping test data obtained from an uncon-fined formation in the Tailan River basin of northwest China. Thedeveloped model comprises two reservoirs dealing with conduitflow in the radial collector pumping well and diffuse flow in theporous aquifer around the collector well coupled by an exchangeflow between the two reservoirs, which was estimated using the

hydraulic head difference between the reservoirs. This modelwas successfully used to simulate the pumping test conditionsof the aquifer system and pumping scenarios that may be usedto maximize groundwater withdrawals from the aquifer while stillensuring that there is sustainable management of the resource,which serve as the backbone for economic development in thestudy area.

Study Area and Data Acquisition

Tailan River Basin

The study area is within the Tailan River basin located in thewestern part of the Tianshan Mountains and the north marginalzone of the Tarim basin in the Xinjiang Autonomous Region inthe northwest part of China (Fig. 1). The basin is divided into fivegeomorphologic units: a middle-low mountainous area, an inter-mountain deep stripping area, a low mountain anticlinal regionof Gumubiezi, a mountain front alluvial–pluvial fan area, and analluvial plain area (Sun et al. 2011; Wang 2010), and slopes fromthe north to the south.

The total drainage area of the basin is about 3;871 km2 and ispart of the arid regions of China with a typical arid climate of scarceprecipitation and strong evaporation potential (Sun et al. 2011).Mean annual precipitation and pan-evaporation of the area rangefrom 100 to 250 mm and 1,000 to 1,800 mm, respectively, whilethe mean annual temperature is 7.9°C (Sun et al. 2011; Wang2010). Mean annual runoff of the basin is about 742 × 106 m3

and is seasonally distributed; June to August accounts for69.9%, September to November accounts for 16.6%, Decemberto February accounts for 4.5%, and March to May accounts for9% (Wang 2010). Glacier thawing runoff contributes nearly

Fig. 1. Study location in Xinjiang, China, with the pumping (F2) and observed (G01–G10) wells

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21 to 50% of the river discharge in the basin (Yang 2005;Wang 2010).

The basin area is mainly underlain by variegated sandstone,mudstone, and breccias among other formations of the pretertiaryera. Local structural features in the area were developed as a resultof tectonic activities in the depression unit at the northern margin ofthe Tarim basin; hence, folds and faults are common structures inthe area. Overlying the structured formations in the area, however,are thick and uneven unconsolidated quaternary sediments, whichare widely distributed over the whole basin. The quaternary sedi-ment thickness ranges from 170 to about 700 m and is, mainly,multilayered with abundant groundwater storage (Wang 2010).Piedmont alluvial–pluvial fan deposits, widely distributed in thebasin and composed of coarse gravel to fine sand sediments, serveas the aquifer formation in the area. The aquifer is unconfined, andits thickness varies from 170 to 250 m (Wang 2010).

The sloping morphology and geological structures control re-charge, runoff, and discharge in the basin. Recharge to the aquiferof the basin is, mainly, from the precipitation in the area that runsoff from the mountainous regions onto the plains where the aquiferis located; percolation from excess irrigation water and glacialthawing also contribute to the recharge. According to Sun et al.(2011), precipitation only recharges the aquifer system in areasof the basin where groundwater depths are shallower than 5 m.The local economy of the basin area is mainly agricultural and de-pends a lot on groundwater resources since the peculiar climaticconditions of the basin limits the availability of surface waterresources. Thus, effective management of the groundwater resourcein the basin is very important to ensure its sustainability for con-tinuous development of the local economy.

Pumping Test Data Collection

The pumping test site was approximately within latitudes 41°20′15″to 41°20′31″ N and longitudes 80°35′21″ to 80°35′52″ E of the un-confined alluvial formation in the Tailan River basin. The test wasconducted for a total duration of 21 days (i.e., precisely 16 days ofpumping and 5 days for recovery) at a variable pumping rate usinga pumping well (F2) close to the edge of the alluvial fan and nineobservations wells (listed in Table 1), which were distributed atvarious radial distances around the pumping well (Fig. 1). The testwas conducted following standard procedure as outlined in litera-ture (e.g., Kruseman and de Ridder 1994; Fetter 2001).

Summarized data on the wells used in the test are presented inTable 1. The pumping well used in the test was a radial collectorwell comprising a 3.5 m diameter vertical caisson at 30 m deep intothe aquifer with eight small diameter lateral arms around it at 3.2 mfrom the bottom and at 1.9 m interval upward to a depth of 9.35 mfrom the bottom. The length and diameter of each lateral arm was30 m and 0.15 m, respectively. All the wells used in the test did not

penetrate through the full thickness of the aquifer formation, andthe diameter of each of the observation wells was 0.121 m.

During the test, the drawdown and recovery data were measuredin both the pumping and observation wells (except well G08 whereonly drawdowns were measured) using automatic loggers. The timeinterval for the measurements in wells F2, G03, and G05 were thesame (i.e., at 1 min) and differed slightly from those of the otherwells (i.e., 30 min) within the first 60 min of both the pumping andrecovery periods. Outside these periods, the measurements weremade at the same time interval in all the wells starting with a30 min time step and increasing gradually as the drawdown/recovery in the wells became smaller. The data from the loggerstogether with measurements of the pumping rates were collatedafter the test, processed for quality checks, and then, subsequently,used as input in the developed model of this study.

Plots of time–drawdown/recovery data from all the wells used inthe pumping test together with the pumping rate are shown in Fig. 2.Analyses of the plots indicate that with the exception of well G04,all the wells exhibited fairly continuous drawdown up till after5,730 min when they begun to fluctuate and the drawdown in-creased sharply owing to increased variability in the pumping rate.The cause of the sharp rise in well G04 earlier (i.e., at 340 min)could not be attributed to the pumping rate since it was fairly con-stant within that period (i.e., 0–5,730 min) and none of the otherobserved wells happen to have experienced a similar rise. Thegradual fall of the drawdown after the rise also takes out the pos-sibility of it being an error in measurement. Therefore, it is possiblethat the rise may be attributable to the flushing out of materials fromsome nonconnected pores or openings, which were blocking freeflow of a substantial amount of water around the well as a result ofthe pumping.

As shown in Fig. 2, the drawdown in the pumping well is sig-nificantly higher than those in all the observation wells, whichgradually decreased as its distance from the pumping well in-creases. Interestingly, wells of about the same radial distance fromthe pumping well (i.e., G01 and G06, G03 and G05, G07 and G10)produced almost the same curves in both the pumping and recoveryperiods. The recovery processes in all the observed wells weregradual while that for the pumping well was much quicker owingprobably to its nature, which facilitated it.

Modeling Methodology

In analyzing pumping test data from formations with dual per-meability structures characterized by interactions between highand less porous media, the exchange flow between the dual porouszones is needed. The exchange flow can simply be estimated by theuse of double continuum models based on the difference in hy-draulic heads between the dual pore zones via a linear exchange

Table 1. Location and Dimensional Data on the Wells Used for the Pumping Test

Well Distance from F2 (m) Longitude (E) Latitude (N) Ground elevation (m) Initial water level (m) Well depth (m) Saturated thickness (m)

F2 — 80°35′32.3″ 41°20′20.3″ 1,201.757 1,194.458 30.00 22.85G01 89.0 80°35′31.5″ 41°20′23.1″ 1,202.255 1,194.538 21.00 13.91G03 59.0 80°35′30.0″ 41°20′21.2″ 1,201.895 1,194.247 24.68 17.61G04 175.0 80°35′33.4″ 41°20′25.9″ 1,203.369 1,194.834 17.78 9.91G05 58.0 80°35′34.8″ 41°20′20.5″ 1,201.581 1,194.467 28.00 21.21G06 93.0 80°35′36.3″ 41°20′20.4″ 1,201.205 1,194.397 18.65 12.30G07 145.0 80°35′38.5″ 41°20′20.7″ 1,200.885 1,194.542 18.62 12.70G08 250.0 80°35′42.7″ 41°20′22.4″ 1,201.543 1,194.840 7.65 1.40G09 308.8 80°35′44.7″ 41°20′23.9″ 1,201.858 1,194.995 15.00 8.65G10 164.7 80°35′39.1″ 41°20′18.8″ 1,200.631 1,194.285 29.30 23.35

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term (Barenblatt et al. 1960; Teutsch 1989; Sauter 1992). This dou-ble continuum modelling approach has been used, successfully, toassess the hydraulic parameters of karst formations (e.g., Maréchalet al. 2008), which are similar to the pumping test design of thisstudy because the radial collector well used creates voids or open-ings in the conduit network surrounded by a porous media as inkarstic formations.

Therefore, a reservoir model based on the concept of doublecontinuum is developed for the analysis of the pumping test datafrom the study site. This model conceptualizes the pumping test siteas two interacting free-surface water reservoirs—i.e., a conduit res-ervoir and a porous reservoir—coupled by a linear flow exchangeand surrounded by a constant head flow boundary. The basicassumption underlying this concept is that the hydraulic headsin the reservoirs were virtually the same and that no lateral rechargeand discharge occurred in the entire reservoir system prior to thepumping. Fig. 3 shows a schematic drawing of the pumping test atthe study site in the “real world” field pumping situation and theconceptual inflows/outflows for the reservoir model.

Conduit Reservoir

The conduit reservoir represents the radial collector well used as thepumping well in the study. This reservoir is characterized by a voidmedium for quick flows and a low storage capacity. The initialsource of water pumped during the test comes from this reservoir.This, consequently, decreases the hydraulic head in the reservoirand leads to a hydraulic head difference between the two reservoirs,which causes groundwater in the porous reservoir to flow towardthe conduits at a higher rate than before pumping. Thus the con-duits act as a trench network draining the porous aquifer with par-allel flows.

This reservoir [Fig. 3(b)] is recharged by inflow from the porousmedium as a result of the hydraulic head difference in the two res-ervoirs while pumping from the well is the only output from thereservoir. The possibility of some amount of precipitation in thearea ending up as recharge to this reservoir is assumed to be neg-ligible owing to the small surface area of the conduits together withlow precipitation in the area. Thus from the principle of volumeconservation, the hydraulic head of this reservoir is estimated as

dhcdt

¼ Qmc − PScAc

(1)

where Qmc = exchange flow induced into the reservoir; Sc(dimensionless) = coefficient of storage of the conduit reservoir;

Fig. 2. Time–drawdown/recovery measurements from the observed wells with the pumping rate

Fig. 3. Schematic diagram of the conceptual modeling framework forthe pumping test at the study site: (a) pumping test setup at the studysite (not drawn to scale); (b) conceptual inflows and outflows of thereservoir model

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Ac ðL2Þ = free surface area of dewatering conduit reservoir;P ðL3=TÞ = pumping rate; and t ðTÞ = time.

Porous Reservoir

The porous reservoir corresponds to the porous aquifer beingdrained by the pumping well (i.e., the conduit reservoir). Comparedto the conduit reservoir, this is characterized by a less permeablemedium but with a high storage capacity. The hydraulic head in thisreservoir is initially assumed to be the same throughout the aquifer.However, the induced flow from this reservoir as a result of thepumping causes the hydraulic head in this reservoir to vary withtime. It is assumed that this variation occurs only within a specificarea within the regional aquifer of the study area after which thepumping has no effect to lower the hydraulic head of the aquifer.The areas of the aquifer not influenced by the pumping are referredto as the boundary medium while those areas induced by the pump-ing constitute the porous reservoir.

The porous reservoir [Fig. 3(b)] is recharged by infiltration fromprecipitation and exchange flow from the boundary medium.Therefore, the hydraulic head (hm) of this reservoir can be com-puted using the volume conservation given by

dhmdt

¼ RþQmm −Qmc

SyAm(2)

where Qmm = exchange flow from the boundary medium inducedinto the porous reservoir; Sy (dimensionless) = specific yield of theaquifer; Am ðL2Þ = free surface area of porous reservoir; andR ðL3=TÞ = recharge rate from precipitation.

Generally, every pumping well is supposed to have its influenceradius on groundwater flow in a formation that is being pumped.Therefore, in simple terms, the boundary medium represents theporous aquifer media outside the radius of influence in the con-ceptual model of this study. This medium is assumed to be aconstant head flow boundary surrounding the porous reservoirwith its hydraulic head (ho) given by Eq. (3). Since there wereno observation wells in the boundary medium, its initial hydraulichead is assumed to be the same as the initial head of the porousreservoir:

hoð0Þ ¼ hoð∞Þ ¼ hoðtÞ (3)

Exchange Flow

Naturally, flow is exchanged between two media when they areconnected hydraulically and there is a hydraulic head differencebetween them. This was more pronounced during the pumping testwhere the hydraulic heads in the conduits decreased very signifi-cantly in comparison to the aquifer matrix. To interpret the pump-ing test performed in the formation, the rate of flow exchangebetween the reservoirs together with that from the boundary mustbe identified. This was done using the linear exchange model(Barenblatt et al. 1960) given by

Q ¼ Cðh1 − h2Þ (4)

where Q ðL3=TÞ = exchange flow at any time; C ðL2=TÞ =coefficient of the exchange; and h1 ðLÞ and h2 ðLÞ = hydraulicheads in the two media.

Thus in the developed conceptual model, the exchange flowsbetween the conduit and porous reservoirs and, then, the porousreservoir and boundary medium were estimated using Eqs. (5)and (6), respectively:

QmcðtÞ ¼ Cmc½hmðtÞ − hcðtÞ� (5)

QmmðtÞ ¼ Cmm½hoðtÞ − hmðtÞ� (6)

where Cmc ðL2=TÞ = coefficient of exchange flow between theporous and conduit reservoirs; and Cmm ðL2=TÞ = coefficient ofexchange flow between the porous reservoir and the boundarymedium.

Numerical Solution

Eqs. (1), (2), (3), (5), and (6) of volume conservation in the reser-voirs and the calculation of exchange flows were converted todifference equations [like Eqs. (7) and (8) for (1) and (2), respec-tively] and solved using an iterative method through visual basicsimulation:

hcðiÞ ¼ hcði−1Þ þ fðti − ti−1Þ × ½ðQmcðiÞ − PiÞ=ðSc × AcÞ�g (7)

hmðiÞ ¼ hmði−1Þ þ fðti − ti−1Þ× ½ðRþQmmðiÞ −QmcðiÞÞ=ðSy × AmÞ�g (8)

The iteration considers the hydraulic head at each of the reser-voirs at the end of each time step h̄, the estimate of hydraulic headused for exchange flow calculations during the nth time step, to be acombination of the hydraulic head from the previous step (hn−1)and the unknown hydraulic head to be computed at the end ofthe present time step (hn). This is given by the semi-implicitformulation

h̄ ¼ ð1 − θÞhn−1 þ θhn (9)

where θ = user-specified weighting factor in the range 0 ≤ θ ≤ 1 butis set to be 0.5 in this study. If θ ¼ 0, this formulation reverts to theexplicit form. If θ ¼ 1, the hydraulic head from the previous timestep is ignored.

The hydraulic heads (h̄ and hn) converge to a solution whentheir difference for each reservoir is less than a predefined conver-gence criterion after enough iterations have been performed. Theiterations begin with specified initial heads for the reservoirs(i.e., pumping and observed wells) among the other inputs andare repeated for each updated head in the reservoirs for the entirepumping test duration. The various hydraulic heads and flow com-ponents at each time step in the reservoirs computed with the codeare then analyzed.

Results and Discussions

Model Calibration and Validation

The model was calibrated using a trial and error approach. This wasdone by simulating the hydraulic heads of the conduit reservoiragainst the heads in the pumping well and hydraulic heads ofthe porous reservoir against one each of the wells that had similardrawdown curves (i.e., wells G01, G03, and G07), discussed ear-lier, together with well G09 independently. Four parameters—surface area of porous reservoir (Am), specific yield of the matrix(Sy), coefficient of exchange flow from the porous reservoir to con-duit reservoir (Cmc), and the coefficient of exchange flow from theboundary medium to the porous reservoir (Cmm)—were adjustedduring the calibration process. It should be noted that Am is notan inherent parameter of the aquifer but a fundamental variablein the model equation, which can only be estimated through

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calibration unless the extent of the pumping influence is known.The coefficient of storage of the conduit reservoir (Sc) was assumedto be 1, and the surface area of the conduit network (Ac) was cal-culated from the dimensions of the radial collector well during thecalibration process.

The goal throughout the calibration process was to ensure thatthe model could simulate the observed hydraulic heads to anacceptable degree of accuracy with minimal deviation. Thus aftereach change in any of the model parameters, the model was run, thenormalized root mean square error (nRMSE) between the observedand simulated hydraulic heads was calculated, and then a plot of thesimulated heads was compared with the observed to check howwell they match. The model calibration was stopped when a goodmatch was achieved between the simulated and observed hydraulicheads at a minimum nRMSE. The calibrated model for each of thewells (i.e., G01, G03, and G07) was validated using each of theother corresponding wells at similar radial distances (i.e., G06,G05, and G10, respectively) to verify how representative the cali-brated parameters are of the pumping test.

The results of the model calibrated parameters together with theinitial and boundary conditions used for the calibration process are

presented in Table 2. Comparisons of the model simulated hy-draulic heads to the observed are shown in Fig. 4. In all, a reason-able overall match was obtained between the observed andsimulated hydraulic heads at each of the wells with an averagenRMSE value of 15.86% for the conduit reservoir and 8.49% atthe porous reservoir. The average fit of the model to the observedhydraulic heads in all the wells during pumping looked better(i.e., 10.99 and 8.06% for the conduit and porous reservoirs, re-spectively) than those during recovery, and all the porous reservoirsimulations were better than that in the conduit (Fig. 4). However,the early time simulations (i.e., before 675,000 s) of the conduitreservoir where the pumping rate was less varied produced a muchbetter simulation of the pumping well than in all the porous reser-voir calibrations. The conduit reservoir simulations at the latterstages of the pumping period look overestimated and may havebeen influenced by the varied pumping rate within that period.On the other hand, the head simulations in the porous reservoirwere better in the latter pumping period than the earlier. Generally,the simulated recoveries in both reservoirs appear to deviate signifi-cantly from the observed, although they follow the same trend asthe observed values in all the wells.

Table 2. Parameters, Initial and Boundary Conditions Used for the Model Calibration

Reservoir Well Initial conditions Boundary conditions Calibrated parameters

Conduit F2 hcð0Þ ¼ 1;194.458 m, measured P ðm3=sÞ ¼ series, measured during the test Sc ¼ 1, assumedAc ¼ 491 m2, estimated

Cmc ¼ 0.036 m2=sPorous G01 hmð0Þ ¼ 1;194.538 m, measured hoð0Þ ¼ hmð0Þ ¼ hoðtÞ, assumed Sy ¼ 0.150

Am ¼ 323;000 m2

Cmm ¼ 0.074 m2=sG03 hmð0Þ ¼ 1;194.247 m, measured hoð0Þ ¼ hmð0Þ ¼ hoðtÞ, assumed Sy ¼ 0.115

Am ¼ 323;000 m2

Cmm ¼ 0.062 m2=sG07 hmð0Þ ¼ 1;194.542 m, measured hoð0Þ ¼ hmð0Þ ¼ hoðtÞ, assumed Sy ¼ 0.230

Am ¼ 325;000 m2

Cmm ¼ 0.086 m2=sG09 hmð0Þ ¼ 1;194.995 m, measured hoð0Þ ¼ hmð0Þ ¼ hoðtÞ, assumed Sy ¼ 0.245

Am ¼ 328;000 m2

Cmm ¼ 0.098 m2=s

Fig. 4. Comparison of simulated and observed hydraulic heads for the model calibration

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Analyses of the model validation outputs show that there is asimilarly equal match between the simulated and observed heads(Fig. 5) for all the wells with an average nRMSE of 9.37% inthe porous reservoir. Like the calibration process, the pumping peri-ods were better simulated than the recoveries. This, therefore, in-dicates that the model can produce the observed hydraulic headsmuch better during the pumping period than in the recovery period.The ability of the model to produce the observed heads in the val-idation wells in a likely manner as the wells used in the calibrationimplies the estimated parameter values are representative of themodel for the conditions of the pumping test in the aquifer.

Studies by Sun et al. (2011) using groundwater pumping andmonitoring well data, hydrogeological maps, and cross-sectionmaps of the basin through modeling with the two-dimensionalFEFLOW software (Barlow and Brian 1996) estimated the speci-fic yield of the entire aquifer in the basin to be in the range of0.006–0.236. Comparatively, the estimated specific yield (Sy) ofthe porous reservoir by the model ranges from 0.115 to 0.245(at an average of 0.185), which is within the range obtained bySun et al. (2011) for the entire basin aquifer.

The exchange flow coefficients Cmm and Cmc were averagelyestimated to be 0.080 m2=s and 0.036 m2=s by the reservoirmodel, respectively. Interestingly, Cmc is about 55% lower thanCmm and may be due to the smaller size of the collector armdiameters in comparison to the extent and thickness of the aquifer.The Cmm and Cmc are, in simple terms, equivalent to transmissivityin the porous medium and conduits, respectively; thus the greaterthickness of the porous medium can effectively make its valuehigher than that of the conduits. The estimated Cmm and Sy appearto vary proportionally with an increase in distance of the observa-tion wells. As discussed previously, observed wells of almost thesame radial distance from the pumping well exhibit similar draw-down behavior (in Fig. 2) different from wells of varying distancesfrom the pumping well. Their nature suggests that within smalllocalized zones, the aquifer may seem homogeneous but across

it heterogeneity may be prevalent. Therefore, the variations inCmm and Sy may be due to possible heterogeneity across the aquiferformation.

The model estimates the free surface area of porous re-servoir (Am) to be approximately 325;000 m2 (on the average).Theoretically, the Am value was expected to be equal for the cal-ibration of all the wells since the pumping schedule was the same.However, they varied slightly (i.e., 323;000–328;000 m2) for someof the observed wells as their distance from the pumping well in-creased. This may be attributable to the slight differences in theboundary heads used in the calibration of the wells since they wereassumed equal to the initial heads of the wells, which differedslightly.

Flow Components

The results of exchange flow evolution in the reservoirs for eachwell used in the calibration process are shown in Fig. 6. Generally,the rate of flow induced from the porous aquifer to the conduit res-ervoir (i.e.,Qmc) during the pumping increased gradually with timefrom zero (no induced flow) at the beginning of pumping to about0.4 m3=s (i.e., maximum induced flow) at the end of the pumpingperiod. The induced flow follows the same trend as the pumpingrate from the conduit (Fig. 6) and indicates that a larger contributionof water from the porous medium makes up the volume of thepumped water. This fact is confirmed from the results of the waterbudget analysis of the conduit reservoir (Table 3), which also showsthat the porous medium contributes 98.6% of the pumped waterwith the rest coming from the conduits.

The influence of pumping on the induced flow from the boun-dary medium to porous reservoir is observed to decrease withincreasing distance of the observation wells away from the pump-ing well (Fig. 6). This indicates that the porous reservoir has morestorage as the observation well distance increases and leads to a lessdecrease of its hydraulic head since the pumping and induced flow

Fig. 5. Comparison of simulated and observed hydraulic heads for the model validation

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to the conduits remains the same. Therefore, the exchange flowreceived from the boundary medium will be much less for anobservation well with increasing distance away from the pum-ping well. The recovery of this flow in the porous medium is ob-served to decrease gradually while the induced flow from theporous medium to the conduits decreased rapidly when the pumpwas stopped.

Sensitivity Analysis

Sensitivity analysis is an integral part of any modeling process andis usually carried out to determine how each model input parameterinfluences the output. Thus a sensitivity analysis was performedusing the “one-at-a-time” sensitivity approach (Hamby 1994; Cricket al. 1987; Yu et al. 1991) to evaluate the effects of the calibratedmodel parameters (i.e., Am, Sy, Cmc, and Cmm) on the simulatedhydraulic heads by the reservoirs. Each of these model parameterswas varied equally (i.e., at 10, 20, and 30% increments) while keep-ing the others constant and, then, the model was run to observe andquantify how each parameter influenced the simulated hydraulicheads in the conduit and porous (i.e., using well G07 as an exam-ple) reservoirs. The influence of each parameter’s change on thereservoirs was quantified by estimating its percentage change onthe storage volume in the reservoirs.

The results of the sensitivity analyses are summarized in Table 4.They indicate that Cmm has a great influence on the simulated headsfrom the porous reservoir followed by the Sy and Am while the Cmchas a very low influence. However, the Cmc had more influence onthe simulated outputs from the conduit reservoir than both Sy andAm, which had minimal influence on the conduit reservoir. TheCmm, on the other hand, was still very sensitive to the simulatedhydraulic heads in the conduit reservoir and, therefore, the mostsensitive of all the model parameters.

Simulations for Groundwater Management

Sustainable abstraction of the groundwater resource of the aquiferis very important to the inhabitants of the basin who depend greatlyon the resource for irrigation and domestic water supply demands.Besides, the study area is in one of the provinces of China wheregroundwater overexploitation has made land subsidence verycommon (Ministry of Land Resources 2005; World Bank 1997);thus necessary planning is required to access the groundwater ofthe study site to not exacerbate this problem. The developed res-ervoir model was used to simulate two different pumping scenariosto obtain information on the exploitation potential of the aquifer todevelop the best possible way to manage the resource.

In the first scenario, the current pumping rate was increased at20, 40, 60, 80, and 100%, and simulations were done using thecalibrated model for each of these rates to determine the maximumsustainable water rates that can be withdrawn from the aquifer. Theresults of these scenario simulations are shown in Fig. 7. Since thedepth of the pumping well and the average ground elevation ofthe study site are 30 m and 1,202 m, respectively, the hydraulichead in the well should not be less than approximately 1,172 mfor sustainability of the pumping process. The results indicate thatgroundwater withdrawals of up to a 40% increase of the pumpingrate are sustainable for the entire pumping period while the incre-ments of 60, 80, and 100% become unsustainable after 840,000,690,000, and 390,000 s of pumping, respectively. The results alsoshow that the duration of pumping sustainability decreases with anincreasing pumping rate. In terms of the current pumping in theaquifer, increasing the pumping rate by 40% would be the maxi-mum increase to allow sustainable groundwater exploitation ofthe aquifer.

Fig. 6. Evolution of exchange flow components in each calibrated well during the pumping test

Table 3. Water Budget Calculations of the Reservoirs for Each CalibratedWell for the Pumping Period

Reservoir Well Outflow (m3) Inflow (m3) Storage (m3)

Conduit F2 4.64 × 105 4.57 × 105 7.13 × 103

Matrix G01 4.57 × 105 2.68 × 105 1.89 × 105

G03 4.57 × 105 2.69 × 105 1.88 × 105

G07 4.57 × 105 2.30 × 105 2.27 × 105

G09 4.57 × 105 1.84 × 105 2.73 × 105

Table 4. Summarized Results of the Sensitivity Analyses on the ModelParameters

ReservoirParameter

increments (%)

Change in reservoir storage (%)

Cmm Sy Am Cmc

Porous 10 −6.39 −3.28 −3.28 0.1920 −12.20 −6.53 −6.53 0.4330 −17.50 −9.68 −9.68 0.72

Conduit 10 −6.25 −3.46 −3.46 2.2220 −11.95 −6.85 −6.85 6.1330 −17.15 −10.11 −10.11 13.34

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Practically, it may be difficult to achieve the desired maxi-mum variable pumping for the sustainable exploitation discussedearlier. Therefore, the second scenario simulations involved usingconstant pumping values to determine the maximum possible sus-tainable withdrawal from the aquifer. The constant pumping ratesused (i.e., 0.31, 0.41, 0.51, 0.61, 0.71, and 0.81 m3=s) were incre-ments of the average of the variable pumping rate (i.e., 0.31 m3=s)of the field test. The hydraulic heads for these pumping simula-tions are shown in Fig. 8, and they indicate that a constant pumpingof 0.51 m3=s would be the maximum to achieve a sustain-able groundwater exploitation of the aquifer. This pumping ratewould yield 7.05 × 105 m3 of groundwater in comparison to6.57 × 105 m3 that can be produced from pumping at 40% ofthe field study rate discussed in the first scenario. Therefore,0.51 m3=s constant pumping rate exploitation of the aquifer isthe best option for abstracting maximum water volume under sus-tainable conditions.

Conclusions

This study has demonstrated a simple new approach, i.e., reservoirmodeling, for the analyses of pumping tests conducted with a radialcollector pumping well in an unconfined aquifer at Tailan Riverbasin, China. The developed model, based on the double con-tinuum concept, conceptualized the pumping test site as conduitand porous reservoirs coupled by a linear flow exchange and witha constant head boundary medium. A set of difference equationswere developed from the concept, mainly by volumetric balance,and solved by an iterative method through visual basic simulations.The conduit and matrix reservoirs represented the radial collectorpumping well and porous medium, respectively, and, thus, werecalibrated and validated using the observed time–drawdown pump-ing test data from the study site.

The developed reservoir model reasonably well simulated thehydraulic heads in the observation wells at average nRMSE of

Fig. 7. Hydraulic heads in the pumping well at variable percentage pumping increments

Fig. 8. Hydraulic heads in the pumping well at constant pumping rates

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15.86 and 8.49% by the conduit and matrix reservoirs, respectively,for the entire duration of the test. The simulated hydraulic heads ofall the wells in the pumping period were much better than thoseduring the recovery periods and suggest that the model is more suit-able to pumping conditions. The model estimated the specific yieldof the study site ranges from 0.115 to 0.245 and compares well withestimations by Sun et al. (2011) from modeling of groundwaterflow in the entire aquifer of the basin with a two-dimensionalnumerical model.

The developed model was applied, successfully, in simulatingscenarios of pumping in the study site for management of the aqui-fer resource and showed that pumping at a constant rate of0.51 m3=s is the possible maximum groundwater volume thatcan be withdrawn from the aquifer sustainably. Therefore, themodel provides a useful alternative for analyses of groundwaterabstraction with radial collector wells.

Acknowledgments

This research was supported by the special fund for “Key Techni-que for Groundwater Reservoir Construction in Arid Area(200901084)” of the Ministry of Water Resources, People’sRepublic of China.

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