ECS 621/489G Final Exam.

This is a take-home exam. It is due on Friday, Dec. 17, before 3:30pm

The following problems are all related to the dispute between two jurisdictions bordering a common river from which they withdraw water for domestic and industrial uses. Both jurisdictions use the method of river-bank filtration to pre-treat the water. Wells along the river are installed to pull water from the river before the water is treated and delivered to the residents of the jurisdictions. You are hired as a consultant to advise one of the jurisdictions to determine the maximum allowable pumping rates of their wells and to design wells with efficiencies meeting local designing codes. In order to accomplish this task, you will need to calculate the water budget of the area and determine the hydraulic properties of the aquifers and the specifics of the wells and pumping rates. Answer the following questions using the provided information.

  1. (15/50) The runoff in the river during a storm is recorded in the following table. Please estimate the amount of groundwater recharge. Use the recharge rate as the annual average recharge rate for the confined aquifer where the the well bores are located. The area of the watershed drained by the river is about 1.23 mi2. On average, storm of this size occurs every four weeks. Calculate the recharge rate and use it as the average and steady state groundwater recharge rate.
    Time (hr) Runoff (cfs)
    0.8 40.63
    4 34.28
    8 38.13
    12 71.88
    16 180.63
    18.8 208.13
    20 201.56
    24 135.63
    28 91.56
    32 63.13
    36 50
    40 36.56
    42 32.81
    44 28.13
    48 25
    52 23.44

  2. (15/50) Field data indicate that the confined aquifer is itself the composite of three different aquifers with different hydraulic properties. The three aquifers form three consecutive layers parallel to the general direction of the confined aquifer. Using existing rock cores of the wells, a technician in your company did a series of falling head permeameter experiments. The following table summarizes his results. Use the laboratory results to calculate the hydraulic conductivities of the rock layers. From the well drilling records, you found that the thickness of layers 1, 2 and 3 are 75 ft, 50 ft, and 25 ft, respectively. The radius of the rock core is 1 in and that of the standing pipe of the permeameter is 0.25 in. The specimens used for the permeameter experiments are 6 in long. Determine the equivalent hydraulic conductivity and transmissivity of the confined aquifer. Clearly state the assumption of your calculation.
    Rock layer of the rock core Initial pressure head above water level at the top of the specimen (ft) final pressure head above water level at the top of the specimen (ft) elapsed time (min)
    1 5.0 1.61 30
    2 5.0 4.14 30
    3 5.0 0.75 30

  3. (20/50) Water budget calculation indicates that 10% of the groundwater recharge calculated earlier is received by the confined aquifer. Previous field studies also suggest that the storativity of the confined aquifer is 2.4 x 10-4.  Local designing codes required that the well diameters to be either 24 in, 12 in, or 6 in and a well efficiency of at least 50% at the end of pumping period that is to last for 12 hr.  The well loss constants of the three type of wells are 0.00015, 0.0002, and 0.00025 hr2/ft5, respectively. The two jurisdictions have an agreement that, as a result of pumping from their wells, the water level in the river should not decrease at all. Design wells with an allowable maximum pumping rate, using the three well diameters, to meet the designing codes and jurisdiction agreements. Assume the well loss relation is sw = CQ2, where C is the well loss constant, Q is pumping rate and sw is well loss. Assume that there is only one well along the reach of the river and the well is to be 100 ft away from the river. What is the amount of water that the well will withdraw from the river every hour if the confined aquifer does not receive other recharge except from the 10% of groundwater recharge and the river?