Wells are used to control salt water intrusion, remove contaminated water, lower the water table for construction, relieve pressure under dams, and drain farmland

Drawdown Caused by a Pumping Well - Click here to download lecture equations in Word or PDF. Determine the drawdown or cone of depression if aquifer transmissivity and storativity are known

Assumptions - horizontal strata, radial flow, well is screened over entire thickness of aquifer, homogeneous, isotropic aquifer, and potentiometric surface is horizontal and not changing with time prior to pumping.

Transmissivity - effects the shape of the drawdown. If transmissivity is high, then the drawdown is broad and shallow. If transmissivity is low, then the drawdown is narrow and deep.

Storativity - effects primarily the amplitude of the drawdown. The lower the storativity, the deeper the drawdown.

Completely Confined Aquifer (Theis equation) - aquifer is confined both top and bottom, no source of recharge, aquifer is compressible (can store water), well pumps at constant rate. Drawdown depends on pumping rate, transmissivity, and a well function. The THEIS well function depends on transmissivity, storativity, distance from pumping well to observational well, and time.

Leaky, Confined Aquifer - aquifer bounded on top by aquitard and unconfined aquifer (source bed); water table in source bed initially horizontal and does not change during pumping; flow through aquitard is vertical; aquifer is compressible (stores water).

No storage in Aquitard (Hantush-Jacob formula) - most applicable for thin aquitards with low storativity or long pump tests. Drawdown depends on pumping rate, transmissivity, and a well function. The Hantush-Jacob well function depends on transmissivity, storativity, distance from pumping well to observational well, time, and a leakage factor, which depends on the thickness and hydraulic conductivity of the aquitard. Initial drawdown is the same as Theis equation but then drawdown slows towards a steady state where all of the pumped water is replaced by leakage across the aquitard.

Storage in Aquitard (Hantush formula) - most applicable for thick aquitards with high storativity or short pump tests. Drawdown depends on pumping rate, transmissivity, and a well function. The Hantush well function depends on transmissivity, storativity, distance from pumping well to observational well, time, and a leakage factor, which depends on the thickness and hydraulic conductivity of the aquitard as wall as the ratio of the storavity of the aquitard and aquifer. Initial drawdown is the same as Theis equation but then quickly slows as water is released from storage in the aquifer. Subsequently drawdown slows towards a steady state where all of the pumped water is replaced by leakage across the aquitard.

Unconfined Aquifer - water extracted by 2 mechanisms - elastic storage and specific yield

3 distinct phases of drawdown:

1) early - water released from elastic storage, follows Theis nonequilibrium curve, flow is horizontal

2) middle - water table begins to decline, water derived from gravity drainage, 3D flow, drawdown controlled by anisotropy of aquifer and thickness of aquifer

3) late - rate of drawdown decreases, flow is horizontal, and follows Theis curve with storativity equal to specific yield

Neuman's solution - unconfined aquifer, vadose zone not important; initial water comes from specific storage; eventually water comes from gravity drainage; drawdown small compared to saturated thickness; specific yield is at least ten times elastic storativity

Drawdown depends on pumping rate, transmissivity, and a well function. The Neuman well function depends on transmissivity, storativity, distance from pumping well to observational well, time, specific yield of the aquifer, anisotropy of the aquifer, and ratio of the thickness of the aquifer and the distance between the pumping and observation wells.

Aquifer Test Assumption - pumping well screened only in aquifer being tested, observation wells screened only in aquifer being tested, and all wells screened over entire thickness of aquifer

Steady State - If 2 observation wells, then can integrate and solve for transmissivity. For steady state conditions can not determine storativity of aquifer as hydraulic head does not change with time

Nonequilibrium Flow Conditions - Confined, Leaky Confined or Unconfined all use a curve matching technique. Transmissivity and storativity can be determined from how the drawdown changes with time. Confined aquifer has only one master curve. Leaky Confined and unconfined aquifers have multiple master curves depending on aquitard properties or specific yield, anisotropy of aquifer.

Curve Matching Procedure

Generate Well function versus u and leakage factor on log-log paper

Plot Drawdown versus time on log-log paper

Overlay the two plots and match the curves

Select match point and read Well function, function parameters (e.g., u), drawdown and time

Use these match values, plus pumping rate and distance to observation well to solve for transmissivity and storativity

Slug Tests - If only a single well is available or the aquifer is low permeability, then a slug test is used.

Cooper-Bredehoeft-Papadopulos Method - a slug of water is added to a well. Changes in water level with time are recorded. Head versus time is matched with type curves. Shape of the curve gives storativity. How long it takes for the water to drain from the bore hole gives transmissivity.

Hydrogeologic Boundaries - can be simulated by an imaginary well and superposition of solutions from the real well and the imaginary well.