ENGS 41. SUSTAINABILITY and NATURAL RESOURCE MANAGEMENT. Reservoir Dynamics

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1 ENG 41 UTAINABILITY and NATURAL REOURCE MANAGEMENT Reservoir Dynamics (Lynch book, Chapter 5, ection and following) (with added elements) Benoit Cushman Roisin 5 & 9February 2018 A reservoir is an artificial lake created by the building of a dam for the purpose of water storage and/or generation of hydroelectric power. Lake Mead is the largest reservoir in the UA. Its water capacity is million acre feet (32.22 km 3 ). It was formed by the 276 ft tall Hoover Dam on the Colorado. Lake Mead is situated about southeast 24 mi (39 km) from Las Vegas. The reservoir serves water to the states of Arizona, California, and Nevada, providing sustenance to nearly 20 million people and large areas of farmland. 1

2 The Las Vegas situation: (not in textbook) White & Meadowvalley Wash Wastewater Treatment Plants Colorado Loss to evaporation Wastewater collection Las Vegas Distribution Lake Mead Water Purification Intake Hoover Dam Pro s and con s of dams and reservoirs: PRO s Dams provide a range of economic, environmental, and social benefits, including water supply, flood control, hydroelectric power, wildlife habitat, waste management, river navigation, and recreation. CON s Blocking of flowing river water interferes with fish migration and reproduction. Very slow moving water promotes sedimentation, which decreases the fertility of the soil downstream. Quiet deep water promotes anoxic conditions (dissolved oxygen depletion). Human populations are displaced when a dam is constructed. ome cultural artifacts may be lost forever. Risk of catastrophic failure. 2

3 ince dams and reservoirs constitute large, strategic works, they have to be designed for certain performance criteria relative to water uses and hydropower. Once a reservoir is created, it needs to be monitored and operated in order to meet its objectives. The primary variable in reservoir management is the volume of water impounded ( for storage), easily monitored by the measure of the height H of the water level. For every reservoir, there exists a H() or (H) function. Also monitored are the total incoming water flow Q in. And the amount of precipitation (which can conveniently be added to Q in ). Q in W The main control parameter is the discharge Q out at the dam, which may be partitioned between a portion that passes through a turbine and the rest that by passes the turbine. Q out Other control parameters are the amounts withdrawn W for local uses. Geometric relations of a reservoir Oftentimes, a power law is adequate: V V k A A H a k H b a 1.5 b 3.0 a 1.5 b 3.0 3

4 Water budget for a reservoir: Q in Change in storage over time = inflows outflows W t ( dt) t ( ) Q Q WPrecipitation Evaporation dt in out In limit of a continuous description: Q out d Q Q W in out dt Discretization in a spreadsheet: k 1 k Qindt Qoutdt Wdt Consider the case of an alternation of a dry season followed by a wet season, each 6 month long (dt = 6 months). Q in alternates between Q low in the dry season and Q high is the wet season: Q dtq dtwdt 2 1 low out1 1 Q dtq dtw dt 3 2 high out to repeat the cycle The decisions are: When building the reservoir, what should be its maximum capacity? It must be so that max( 1, 2 ) max. During operations, what should be the values of the discharges Q out1 and Q out2 and the of the withdrawals W 1 and W 2? 4

5 In most places with a more gradual seasonal cycle, it makes sense to consider a 12 month cycle: Climatological precipitation over Hanover, NH Q dtq dtwdt in1 out1 1 Q dtq dtw dt 3 2 in2 out 2 2 Q dtq dtw dt in12 out The major design question is: What should max be? Example torageyield.xlsx Allowance may be made for: 1. Added capacity in case of anomalously high inflow during the wetter season (to avoid potentially damaging spillover) 2. Variation in withdrawals to meet seasonally varying needs of agriculture and municipal distribution (possible tourist season) 3. A minimum residual amount of water at all times, to avoid a dry basin. 5

6 Hydropower Generation: (Lynch, Page 165) POWER E gq H( ) turbine Power generated Efficiency Water density Gravity Flow through Water level drop (in Watts) (~80%) (1000 kg/m 3 ) (9.81 m/s 2 ) turbine (m 3 /s) (m) ENERGY H k 1 turbine, k k 2 E g dt Q ( ) H( ) k There is an unavoidable tradeoff between generation of hydropower and withdrawals: What is withdrawn from the reservoir can t pass through the turbine to generate power; To maximize hydropower, one would wish to keep the water level as high as possible at all times, but the reservoir exists to allow swings to even out water consumption while the inflow varies seasonally. imulation Example Hydro.xlsx 6

7 Case tudy: Wheelock Kemeny Basin (Lynch, ection 5.7) I b Kemeny Wheelock I a = Q 1 1 Rockefeller Dam Q 2 Q 3 Wheelock Upstream Rockefeller Dam Kemeny Downstream Berry Dam Time I a min max I b min max Rockefeller Berry Q 4 Berry Dam H H max max a max H min H max