Name: Problem 1. (30 points; 5 each)

Transcription

1 Hydrogeology - HWR/GEOS 431/531 Final exam Dr. Marek Zreda 16 December :00-1:00 Open books and notes There are 5 problems on 7 pages. Read entire test before starting! Name: Problem 1. (30 points; 5 each) North Dakota We are asked to design a study of recharge, residence time and flow velocities in the regional confined aquifer shown on the right. Assume aquifer thickness between 100 and 200 ft. Using the potentiometric data and making reasonable assumptions regarding the sediments and their porosity and hydraulic conductivity, discuss the following: ;; yy ;; yy Black Hills (a) Where is the recharge area? Nebraska miles Contours in feet (b) How much recharge is there? (c) What is a reasonable range of specific discharges? 1/7

2 (d) What are flow velocities? (e) Propose an explanation for the less-densely spaced equipotentials in the middle of the system (between 2000 and 1800 ft contours). (f) We want to confirm hydraulic data with isotopic dating. What isotopic systems are appropriate for groundwater dating in this aquifer? Why? 2/7

3 Problem 2. (20 points; 5 each) Consider a confined aquifer bounded on the sides and at the bottom by impermeable boundaries, and separated from a phreatic aquifer by a leaky aquitard. It is pumped by many wells distributed approximately uniformly over the entire area. All fluxes are due to pumping and leakage through the aquitard. H, h 0 Examine how the pumping will affect the hydraulic head and water quality in the confined aquifer. Assume that before development (t<0) b, K the confined and phreatic aquifer are in hydrodynamic equilibrium, and that because there are b, K, S, n many wells, the system response is uniform in space - the hydraulic head changes by the same amount everywhere. Therefore, we can use a lumped or volumetric approach. At time t=0 the pumps are turned on and the hydraulic head in the confined aquifer starts decreasing, which results in induced flow across the aquitard. After some time, new equilibrium is established, in which all the pumped water is balanced by the leakage across the aquitard (there is no change in storage in equilibrium). h A ;; ;; ;;; ;;; ;; System information: Surface area, A = 10x10 km = 100 km 2 Phreatic head, H = 1000 m (constant) Initial confined head, h 0 = 1000 m Aquitard thickness, h = 100 m Aquitard hydraulic conductivity, K = m/y Aquifer thickness, b = 100 m Aquifer porosity, n = 0.2 Aquifer storativity, S = Chemical concentration in phreatic aquifer, C 0 = 1000 ppm Total pumping rate from all wells, = 1000 m 3 /d (a) Determine the confined hydraulic head at the new equilibrium. 3/7

4 (b) Develop a volumetric expression for concentration buildup with time in confined aquifer. Assume that the pumped water has concentration 0 and flow across the aquitard has C 0. (c) How long will it take for the concentration to reach 5 ppm? (d) Evaluate our model. What is unrealistic in the model? Propose improvements. 4/7

5 Problem 3. (10 points) A horizontal, confined aquifer has a hydraulic conductivity K=10 m/d for water and a porosity changing linearly from n 1 =0.2 to n 2 =0.1 along a typical flow path. Two piezometers placed 100 m apart along the same flow path measure a head difference dh=1 m. (a) Derive a symbolic formula for travel time. Start with the usual t=l/v, then substitute an appropriate expression for v. Remember to integrate both sides to account for the variable n. Your formula should be a function of L, dh, K, n 1 and n 2. (b) Calculate travel time from one piezometer to the other. Is this value equal to the mean of travel times calculated using n 1 and n 2? Why or why not? (c) HWR/GEOS 531 only: Derive a symbolic formula for a case in which K varies linearly from K 1 to K 2. Keep constant porosity n=0.2. What is the difference between the formulas developed in (a) and (c)? Calculate travel time for K 1 =20 m/d and K 2 =10 m/d. 5/7

6 Problem 4. (20 points; 5 each) (a) Draw plan view of drawdown around a pumping well in an anisotropic aquifer. Assume the anisotropy ratio 1:3 (say, T x = 10 m 2 /d and T y = 30 m 2 /d). Also assume and state any other necessary values. (b) List three reasons for an upward inflection (that is, less drawdown) of a semi-log time-drawdown plot. List three reasons for a downward inflection of a semi-log time-drawdown plot. (c) List two hydrogeologic parameters (properties) that have the same units as the diffusion coefficient does. (d) Sketch distribution of concentration at the pumping well for the two cases below. Assume brief pulse input of concentration C 0 (shaded rectangle) and linear (straight line) flow from one well to the other. Justify. K K 1 5K 1 C C t t 6/7

7 Problem 5. (10 points) You conduct a step-drawdown pumping test (a test in which the pumping rate is increased periodically). Calculate and plot the resulting drawdown assuming the following conditions: 1 = 10 m 3 /hr for time from 0 to 1 hr 2 = 20 m 3 /hr for time from 1 to 2 hrs 3 = 30 m 3 /hr for time from 2 to 3 hrs T = 1 m 2 /hr S = r = 10 m 7/7