Mercadeo a los servicios del eje de Educación Continua

The Hantush (1965)equation of groundwaterflow toa gravity well penetrating

a water-table aquifer near a stream with a semipervious bed was applied to the

semi-confined case (value of aquiferstorativity substituted for specific yield)andused

to quantify the effects of groundwaterpumping on lowerScotts Creek streamflows.

Aquifer andaquitardhydraulicproperties determinedby fieldandlaboratorymethods

were usedto solve theequation. The rateofstream depletionisgiven by theequation

(Hantush, 1965)

Qr=Q{erfc(U) − exp[−u2+ (U +w)2]erfc(U +w)}, (4.15)

where Qistheconstantdischarge ofthe well,erfc isthecomplimentaryerror function,

U =xo/(4αt)1/2 (where xo isthe effectivedistance from the wellto the streambank,

t istime since pumping began, andα =Kb/Sy (hydraulic diffusivity),where K isthe

hydraulicconductivityoftheaquifer, bistheweightedmeanofthedepthofsaturation,

and Sy is the specificyield of the aquifer), and w= (αt)1/2/a (a=K/(K0/b0) (where

K0 and b0 are thehydraulic conductivity and thickness of the semiperviouslayer of

the stream bed, respectively). The equation assumes that the semipervious layer has

insignificant storage.

Two scenarios were examined, the first (scenario 1) using averaged hydraulic

conductivity and thickness values for the aquitard, the second (scenario 2) using

hydraulic conductivity and thickness values for the aquitard that are exclusively

representative of the low-permeability material (silt and clay lenses) having the

greatest influenceongroundwater flowandneglectingthethinpermeablezoneswithin

the aquitard. The scenario 1 values used to calculate the rate of stream depletion

K0 = 4.00 × 10−7 _{m/s, and b}0 _{= 5 m. The scenario 2 values used were the same as}

for scenario 1, exceptthe hydraulic conductivity andthickness of the aquitardwere

adjustedto 6.00 × 10−8 _{m/s and 2 m, respectively. The rate of stream depletionwas}

calculated at various timessince pumpingbegan (2 to 24 hours) and at different well

discharge rates(100 to 300 gpm) forthe two scenarios. Figures4.50 and 4.51provide

graphical summaries of the estimated rates of stream depletion for the scenarios

described(see Appendix H forcalculated valuesin tabularform). Additionally, Table

4.10 provides a summary of the ratio of the rate of stream depletion to the well

discharge rate (Qr/Q) atvarious times since pumping began forthe two scenarios.

Figure 4.50: Scenario 1 estimated rates of stream depletion (Qr) at various times since pumping began (t) and atdifferent well dischargerates (Q) obtained using the Hantush (1965) solutionfor flow towells near streamswith semipervious beds.

Thecalculationssuggestthatundernormalpumpingconditions(8hoursofpumping

at a well discharge rateof 200gpm) the rateof streamflow depletionis 2.46 × 10−3

m3_{/s (8.68× 10}−2 _{cfs) or19%ofthepumping rateforscenario1and9.62 × 10}−4 _m3_/s

Figure 4.51: Scenario 2 estimated rates of stream depletion (Qr) at various times since pumping began (t) and atdifferent well dischargerates (Q) obtained using the Hantush (1965) solutionfor flow towells near streamswith semipervious beds.

Table 4.10: Estimated rate of stream depletion expressed as a fraction of the well discharge rate(Qr/Q)at various times (t)since pumping began forscenarios 1and 2.

Time(hrs) Scenario 1 Scenario 2

2 0.06 0.00 4 0.13 0.04 6 0.17 0.06 8 0.19 0.08 10 0.22 0.09 12 0.24 0.10 14 0.26 0.11 16 0.27 0.12 18 0.29 0.13 20 0.30 0.13 22 0.31 0.14 24 0.32 0.15

flowsduring the summer low-flow periodwould increaseby8.68 × 10−2 _{cfs (scenario}

1) or 3.40 × 10−2 _{cfs (scenario2) ifthere wereno groundwater pumping. Basedon the}

attenuatedanddelayed responsetopumping observedin theupper unconfined aquifer

(piezometers) andin ScottsCreek (instreampiezometers) duringthe24-hour pumping

tests,it may be concludedthat thescenario 1 calculated rateof stream depletion is

an overestimate. There areseveral reasonsforthis includingthefact thatthe solution

does not accountfor storage in eithertheaquitard or theupper unconfined aquifer,

andthatbyusing averagevaluesofK0,b0,andα,thecomplexityandvariabilityofthe

subsurface are oversimplified. The low-permeability silt andclay materials(K ≤ 10−8

m/s) have astrong influenceon groundwater movement. Regardless, the calculations

provide estimatesof theupper andlower bounds of therate of stream depletion at

varioustimessincepumpingbeganandatdifferentwelldischargerates. Toaccompany

the stream depletion rate estimates, asimple calculation of the maximum volume of

groundwater that can be abstracted before significantleakage occurs is performed.

Detailed analysis of drawdown data from pumping tests suggest that leakage

(possiblyfrom thetopunconfined aquiferandaquitard, orthrough bedrock),apparent

in time-drawdown data recorded in observationwells severalhundred metersfrom the

pumping well,starts to occur after ∼ 6 hours of continuous groundwaterwithdrawal

when the average well flow rate is260 gpm. Therefore, anestimate of the maximum

volume of groundwater that can be abstracted before significant leakage occurs is

94,000 gallons (0.3 AF) per day. The calculated rate of stream depletion for the

aforementioned pumping duration and well flow rate (scenario 2) is approximately

9.56 × 10−4 _m3_{/s or 3.37 × 10}−2 _{cfs. At present, pumping schedules during the}

driest summer months often exceed 94,000 gallons a day. Average flow rates are

approximately200gpmandpumpingdurationisaround4–10hours foratotal volume

recommended thatthecalculatedrates of streamflowdepletionbe usedin conjunction

with the estimated volume to adjust pumping schedules to avoid causing adverse

impactsto the lower Scotts Creek aquatic ecosystem.