Aquifer Paramater Estimation : Aquifer Paramater Estimation C. P. Kumar
Scientist ‘F’
National Institute of Hydrology
Roorkee (India)
Aquifer Parameters : Aquifer Parameters In order to assess groundwater potential in any area and to evaluate the impact of pumpage on groundwater regime, it is essential to know the aquifer parameters. These are Storage Coefficient (S) and Transmissivity (T).
Slide 3: Storage Coefficient (S) is the property of aquifer to store water in the soil/rock pores. The storage coefficient or storativity is defined as the volume of water released from storage per unit area of the aquifer per unit decline in hydraulic head.
Transmissivity (T) is the property of aquifer to transmit water. Transmissivity is defined as the rate at which water is transmitted through unit width and full saturated thickness of the aquifer under a unit hydraulic gradient.
Slide 4: Groundwater Assessment
Estimation of subsurface inflow/outflow – Change in groundwater storage –
S = h A S Groundwater Modelling
- Spatial variation of S and T required
Pumping Test : Pumping Test Pumping Test is the examination of aquifer response, under controlled conditions, to the abstraction of water. Pumping test can be well test (determine well yield) or aquifer test (determine aquifer parameters).
The principle of a pumping test involves applying a stress to an aquifer by extracting groundwater from a pumping well and measuring the aquifer response by monitoring drawdown in observation well(s) as a function of time.
These measurements are then incorporated into an appropriate well-flow equation to calculate the hydraulic parameters (S & T) of the aquifer.
Pumping Well Terminology : Pumping Well Terminology Static Water Level [SWL] (ho) is the equilibrium water level before pumping commences
Pumping Water Level [PWL] (h) is the water level during pumping
Drawdown (s = ho - h) is the difference between SWL and PWL
Well Yield (Q) is the volume of water pumped per unit time
Specific Capacity (Q/s) is the yield per unit drawdown
Slide 7: Pumping tests allow estimation of transmission and storage characteristics of aquifers (T & S).
Steady Radial Confined Flow : Steady Radial Confined Flow Assumptions
Isotropic, homogeneous, infinite aquifer, 2-D radial flow
Initial Conditions
h(r,0) = ho for all r
Boundary Conditions
h(R,t) = ho for all t Darcy’s Law Q = -2prbKh/r
Rearranging h = - Q r
2pKb r
Integrating h = - Q ln(r) + c
2pKb
BC specifies h = ho at r = R Using BC ho = - Q ln(R) + c
2pKb
Eliminating constant (c) gives
s = ho – h = Q ln(r/R)
2pKb
This is the Thiem Equation
Steady Unconfined Radial Flow : Steady Unconfined Radial Flow Assumptions
Isotropic, homogeneous, infinite aquifer, 2-D radial flow
Initial Conditions
h(r,0) = ho for all r
Boundary Conditions
h(R,t) = ho for all t Darcy’s Law Q = -2prhKh/r
Rearranging hh = - Q r
2pK r
Integrating h2 = - Q ln(r) + c
2 2pK
BC specifies h = ho at r = R Using BC ho2 = - Q ln(R) + c
pK
Eliminating constant (c) gives
ho2 – h2 = Q ln(r/R)
pK
This is the Thiem Equation
Unsteady Radial Confined Flow : Unsteady Radial Confined Flow Assumptions
Isotropic, homogeneous, infinite aquifer, 2-D radial flow
Initial Conditions
h(r,0) = ho for all r
Boundary Conditions
h(,t) = ho for all t PDE 1 (rh ) = S h
r r r T t
Solution is more complex than steady-state
Change the dependent variable by letting u = r2S
4Tt The ultimate solution is:
ho- h = Q exp(-u) du
4pT u u
where the integral is called the exponential integral written as the well function W(u)
This is the Theis Equation
Theis Plot : 1/u vs W(u) : Theis Plot : 1/u vs W(u)
Theis Plot : Log(t) vs Log(s) : Theis Plot : Log(t) vs Log(s)
Theis Plot : Log(t) vs Log(s) : Theis Plot : Log(t) vs Log(s) [1,1]
Type
Curve s=0.17m t=51s
Theis Analysis : Theis Analysis Overlay type-curve on data-curve keeping axes parallel
Select a point on the type-curve (any will do but [1,1] is simplest)
Read off the corresponding co-ordinates on the data-curve [td,sd]
For [1,1] on the type curve corresponding to [td,sd], T = Q/4psd and S = 4Ttd/r2 = Qtd/pr2sd
For the example, Q = 32 L/s or 0.032 m3/s; r = 120 m; td = 51 s and sd = 0.17 m
T = (0.032)/(12.56 x 0.17) = 0.015 m2/s = 1300 m2/d
S = (0.032 x 51)/(3.14 x 120 x 120 x 0.17) = 2.1 x 10-4
Cooper-Jacob : Cooper-Jacob Cooper and Jacob (1946) pointed out that the series expansion of the exponential integral W(u) is:
W(u) = – g - ln(u) + u - u2 + u3 - u4 + ..…
1.1! 2.2! 3.3! 4.4!
where g is Euler’s constant (0.5772)
For u<< 1 , say u < 0.05 the series can be truncated:
W(u) – ln(eg) - ln(u) = - ln(egu) = -ln(1.78u)
Thus: s = ho - h = - Q ln(1.78u) = - Q ln(1.78r2S) = Q ln( 4Tt )
4pT 4pT 4Tt 4pT 1.78r2S
s = ho - h = Q ln( 2.25Tt ) = 2.3 Q log( 2.25Tt )
4pT r2S 4pT r2S
The Cooper-Jacob simplification expresses drawdown (s) as a linear function of ln(t) or log(t).
Cooper-Jacob Plot : Log(t) vs s : Cooper-Jacob Plot : Log(t) vs s
Cooper-Jacob Plot : Log(t) vs s : Cooper-Jacob Plot : Log(t) vs s to = 84s Ds =0.39 m
Cooper-Jacob Analysis : Cooper-Jacob Analysis Fit straight-line to data (excluding early and late times if necessary):
– at early times the Cooper-Jacob approximation may not be valid
– at late times boundaries may significantly influence drawdown
Determine intercept on the time axis for s=0
Determine drawdown increment (Ds) for one log-cycle
For straight-line fit, T = 2.3Q/4pDs and S = 2.25Tto/r2 = 2.3Qto/1.78pr2Ds
For the example, Q = 32 L/s or 0.032 m3/s; r = 120 m; to = 84 s and Ds = 0.39 m
T = (2.3 x 0.032)/(12.56 x 0.39) = 0.015 m2/s = 1300 m2/d
S = (2.3 x 0.032 x 84)/(1.78 x 3.14 x 120 x 120 x 0.39) = 1.9 x 10-4
Theis-Cooper-Jacob Assumptions : Theis-Cooper-Jacob Assumptions Real aquifers rarely conform to the assumptions made for Theis-Cooper-Jacob non-equilibrium analysis
Isotropic, homogeneous, uniform thickness
Fully penetrating well
Laminar flow
Flat potentiometric surface
Infinite areal extent
No recharge
The failure of some or all of these assumptions leads to “non-ideal” behaviour and deviations from the Theis and Cooper-Jacob analytical solutions for radial unsteady flow
Slide 20: Other methods for determining aquifer parameters
Leaky - Hantush-Jacob (Walton)
Storage in Aquitard - Hantush
Unconfined, Isotropic - Theis with Jacob Correction
Unconfined, Anisotropic - Neuman, Boulton
Fracture Flow, Double Porosity - Warren Root
Large Diameter Wells with WellBore Storage - Papadopulos-Cooper
Pump Test Planning : Pump Test Planning Pump tests will not produce satisfactory estimates of either aquifer properties or well performance unless the data collection system is carefully addressed in the design.
Several preliminary estimates are needed to design a successful test:
Estimate the maximum drawdown at the pumped well
Estimate the maximum pumping rate
Evaluate the best method to measure the pumped volumes
Plan discharge of pumped volumes distant from the well
Estimate drawdowns at observation wells
Measure all initial heads several times to ensure that steady-conditions prevail
Survey elevations of all well measurement reference points
Number of Observation Wells : Number of Observation Wells Number of observation wells depends on test objectives and available resources for test program.
Single well can give aquifer characteristics (T and S). Reliability of estimates increases with additional observation points.
Pump Test Measurements : Pump Test Measurements The accuracy of drawdown data and the results of subsequent analysis depends on:
maintaining a constant pumping rate
measuring drawdown at several (>2) observation wells at different radial distances
taking drawdowns at appropriate time intervals at least every min (1-15 mins); (every 5 mins) 15-60 mins; (every 30 mins) 1-5 hrs; (every 60 mins) 5-12 hrs; (every 8 hrs) >12 hrs
measuring both pumping and recovery data
continuing tests for no less than 24 hours for a confined aquifers and 72 hours for unconfined aquifers in constant rate tests
AquiferTest Software : AquiferTest Software AquiferTest is a quick and easy-to-use software program, specifically designed for graphical analysis and reporting of pumping test data.
These include:
Confined aquifers
Unconfined aquifers
Leaky aquifers
Fractured rock aquifers
Pumping Test Analysis Methods : Pumping Test Analysis Methods Theis (confined)
Theis with Jacob Correction (unconfined)
Neuman (unconfined)
Boulton (unconfined)
Hantush-Jacob (Walton) (Leaky)
Hantush (Leaky, with storage in aquitard)
Warren-Root (Dual Porosity, Fractured Flow)
Moench (Fractured flow, with skin)
Cooper Papadopulos (Well bore storage)
Agarwal Recovery (recovery analysis)
Theis Recovery (confined)
Cooper Jacob 1: Time Drawdown (confined)
Cooper Jacob 2: Distance Drawdown (confined)
Cooper Jacob 3: Time Distance Drawdown (confined)
Graphical User Interface : Graphical User Interface The AquiferTest graphical user interface has six main tabs:
1. Pumping Test
The pumping test tab is the starting point for entering your project info, selecting standard units, managing pumping test information, aquifer properties, and creating/editing wells.
Slide 28: 2. Discharge
The Discharge tab is used to enter your constant or variable discharge data for one or more pumping wells.
Slide 30: 3. Water Levels
The Water Levels tab is where your time/drawdown data from observation wells is entered. Add barometric or trend correction factors to compensate for known variations in barometric pressure or water levels in your pumping or observation wells.
Slide 32: 4. Analysis
The Analysis tab is used to display diagnostic and type curve analysis graphs from your data. View drawdown derivative data values and derivatives of type curves on analysis graphs for manual or automatic curve fitting and parameter calculations.
Slide 34: 5. Site Plans
Use the Site Plan tab to graphically display your drawdown contours with dramatic colour shading over top of site maps.
Slide 36: 6. Reports
Use the Report tab to create professional looking output using a number of pre-defined report templates.
Tutorial Problem : Tutorial Problem A well penetrating a confined aquifer is pumped at a uniform rate of 2500 m3/day. Drawdowns during the pumping period are measured in an observation well 60 m away; Observation of time and drawdown are listed in the Table.
Determine the transmissivity and storativity by Theis method and Cooper-Jacob method using the AquiferTest software.
Slide 40: Answer -
T = 1110 m2/day, S = 0.000206
(ii) T = 1090 m2/day, S = 0.000184
Slide 41: Thank You !!!