Aquifer Parameter Estimation

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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).

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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.

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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

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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 = -2prbKh/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 = -2prhKh/r Rearranging hh = - 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  (rh ) = 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.

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2. Discharge The Discharge tab is used to enter your constant or variable discharge data for one or more pumping wells.

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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.

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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.

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5. Site Plans Use the Site Plan tab to graphically display your drawdown contours with dramatic colour shading over top of site maps.

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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

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Thank You !!!

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