University of Arizona Department of Hydrology and Water Resources Dr. Marek Zreda

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1 University of Arizona Department of Hydrology and Water Resources Dr. Marek Zreda HWR431/531 - Hydrogeology Final exam - 12 May 1997 Open books and notes The test contains 8 problems on 7 pages. Read the entire exam first. PART I: Multiple choice questions. Problem 1. Circle the most appropriate answer (3 points each; total 30 points). (a) The assumptions incorporated in the Theis model do not include (1) uniform transmissivity (2) incompressible media and fluid (3) radial flow (4) infinite aquifer in lateral extent (5) essentially horizontal flow (6) none of the above (b) Diffusion coefficients for dissolved ions in a water saturated porous medium are (1) smaller than in water (2) larger than in water (3) smaller or larger than in water depending on the medium (4) smaller or larger than in water depending on the fluid (5) smaller or larger than in water depending on the ion (c) In a sandy confined aquifer transport of a non-reactive chemical is (1) always dominated by diffusion (2) always dominated by advection-dispersion (3) dominated by diffusion or advection-dispersion depending on the temperature (4) dominated by diffusion or advection-dispersion depending on the velocity (d) The equation (K h)=s s ( h/ t) [where h=h(x,y,z,t) is the hydraulic head, K is the hydraulic conductivity, S s is the specific storage coefficient, and t is the time] cannot be used to describe flow in (1) a confined aquifer (2) a phreatic aquifer (3) a leaky aquifer (4) the vadose zone (5) any of the above (e) Water solubility of a mineral does not depend on (1) temperature of the water (2) chemical composition of the mineral (3) chemical composition of the water (4) the presence in the water of ions that do not come from dissolution of the mineral (5) ph of the water (6) none of the above (f) The specific storage coefficient of an aquifer 1

2 (1) only depends on fluid properties (2) only depends on media properties (3) depends on both fluid and media properties (4) is only slightly smaller than the porosity (5) none of the above (g) Consider a fully penetrating well pumping from an infinite, homogeneous, isotropic confined aquifer of uniform thickness. Which of the following is not true of drawdown observed in an observation well? (1) drawdown increases with time since pumping started (2) drawdown increases with distance to the pumping well (3) the maximum rate of drawdown occurs when t=r 2 S/4T (4) drawdown can never drop the potentiometric surface below the top of the aquifer (5) drawdown is the same at all depths in the observation well (6) none of the above (7) all the above (h) An open monitoring well in a confined aquifer observes water level fluctuations due to barometric pressure changes. A nearby closed monitoring well, with a pressure transducer isolated (packed off) at the same depth will (1) observe the same fluctuations, with peaks corresponding to peaks, etc., and the same amplitude (2) observe "mirror image" fluctuations, with peaks corresponding to troughs, etc., but with lower amplitudes (3) have much larger amplitude fluctuations (4) not observe any fluctuations (i) Which of the following never controls groundwater circulation (1) geology (2) climate (3) topography (4) gravity (5) vegetation (6) geothermal gradient (7) none of the above (j) Dispersion coefficient does not depend on (1) molecular diffusion coefficient (2) groundwater velocity (3) hydraulic gradient (4) temperature (5) pore size distribution (6) any of the above 2

3 PART II: Short questions, short answers (use only the space provided). Problem 2. (5 points) Sketch a representative pore pressure - saturation (or pressure head - moisture content) curve for a sandy soil. On the same graph sketch a typical curve for a clayey soil. Label the curves and axes. On a separate graph sketch relative permeability - saturation (or hydraulic conductivity - moisture content) curves for the same two soils. The curves should be conceptually consistent. Problem 3. (5 points) Sketch a typical semi-log time - drawdown plot for drawdown in a confined aquifer that meets the conceptual demands of the Theis model. Contrast it to the following two situations by sketching their typical semi-log drawdown plots on the same graph. Label the axes and curves. (a) A leaky confines aquifer, with a leaky aquitard connecting to an overlying phreatic aquifer. storage in the aquitard and drawdown in the phreatic aquifer. Neglect (b) A confined aquifer fully penetrated by a nearby stream. (c) How many observation wells would it take to discriminate between these two situations, if either one or both may be important at a field site? 3

4 Problem 4. (5 points) The earth's rotation (Coriolis forces) plays a major role in atmospheric and oceanic circulation patterns. Why doesn't it play a similar role in very large groundwater systems? The Nubian aquifer of northeast Africa and the Great Artesian Basin of Australia are certainly large enough. If they were lakes, the Coriolis forces would be significant. In 25 words or less, explain why Coriolis forces are negligible in aquifers. Problem 6. (5 points) High-level radioactive waste is buried in a cavern in unfractured shale at a depth of 1000 m below the surface. The burial zone is separated from the overlying aquifer by 100 m of shale with hydraulic conductivity m/s and vertical hydraulic gradient of 10-2 upward. In the shale, nonreactive radionuclides have effective diffusion coefficients in the order of m 2 /s. It is expected that the wastes will become wet at some time during the next 1000 years and will then move slowly into the shale. Is it reasonable to expect that radionuclides will remain entirely within the shale during the next 100,000 years? Ignore the potential effects of faulting, glaciation, and so on, as a cause of radionuclide transfer through the shale. Consider only the influence of flow, mechanical dispersion, and molecular diffusion. 4

5 Problem 7. (5 points) [from Freeze & Cherry, problem 7, p. 459] A groundwater sample was submitted to a laboratory for isotopic dating by 14 C. The ground water came from a confined aquifer and is expected to be 10,000 to 20,000 years old, based on regional hydrodynamics. The lab reported 9 dpm/g (disintegrations per minute per gram) in the sample and the initial condition is 10 dpm/g. What is the apparent age of the sample? How does it compare with the expected age? Offer possible explanations, other than analytical error, for this result. What other isotope(s) would you measure to assess what processes affected the 14 C age? Problem 5. (5 points) Use the Thiem equation (below) to derive an expression for travel time to a pumping well as a function of distance r from the well. Plot your result for distances between R and 0.1R. Make necessary assumptions. Q h= H 0 + ln 2πT where h=h(r) is the hydraulic head, H 0 is the head at the boundary at the distance R from the pumping well, Q is the pumping rate, T is the transmissivity and r is the distance from the pumping well. r R 5

6 PART III: Problem solving. Write your answers on separate paper. Show all work. Be brief and neat. Read the questions carefully. Problem 8. (40 points) A power company plans on building a coal fired power plant in the lignite belt of Texas. The lignite will be strip mined. The lignite bed, which is to be mined, underlies a highly permeable sand and gravel deposit that is in hydraulic communication with the nearby Trinity River. This sand and gravel is thus a phreatic aquifer. The lignite bed forms the upper portion of the underlying aquiclude. The sand and gravel will have to be "dewatered" at the mine site in order for the mine to be worked. On the other hand, cost and environmental impact considerations make it desirable to minimize the amount of pumping needed to dewater the aquifer at the mine site, and to minimize induced infiltration from the river. A sketch of the site is shown below. The aquifer properties are estimated at K=10 m/d, saturated thickness b=15 m (before pumping), specific yield S y =0.25. There is no ambient flow in the aquifer. The stream is fully penetrating. The preliminary mine plan calls for dewatering via two wells located at the two western corners of the mine, as shown on the sketch. Evaluate this plan using a linearized well hydraulics analysis. Assume that the transmissivity is given in terms of the initial saturated thickness. Use the log drawdown (Jacob's approximation) model. Outline your answer. (a) In the area to be mined, where will the minimum dewatering (maximum heads) occur? Label this point A on your sketch of the mine. Is there another point that may deserve this designation? Label this point B. Show that s a >s b. (b) What minimum pumping rate will be necessary to lower the water table to the bottom of the mine at point A? This is the amount of water the mine will have to treat before discharging it to the river. (c) How long will it take to achieve the dewatering at this minimum pumping? (d) A the minimum pumping rate, what will the eventual rate of stream loss (induced infiltration) be? This loss will have to be "permitted" by the state engineer. (e) Sketch a rough flow net for this situation. (f) Suggest another possible groundwater control strategy, as an option to this two-well scheme. Justify your suggestion in terms of cost or lesser stream infiltration or both. (g) Describe (very briefly) the pump test you would design to verify the connection to the stream, the lack of vertical leakage, the aquifer properties, and the horizontal flow assumptions. (h) How long will it take the aquifer to recover after the mine is refilled and the pumps are turned off? Assume that the mine soil has the same transmissivity as the aquifer. 6

7 (i) You were asked to assume that the aquifer transmissivity remains constant. Explain why this is a very poor assumption in this case. (j) Consider the analogy of a fully penetrating pumping well in a phreatic aquifer. The linearized analysis assumes that drawdown and recovery behaviors are identical, with simply a change in sign. Actual well recovery in a phreatic aquifer can be quite different than drawdown. There are at least three physical reasons for this. Can you suggest what one or more of these may be? 7