The Nature of Subsurface Waters and Sources of Pollutants

Transcription

1 The Nature of Subsurface Waters ad Sources of Pollutats odule 3: Subsurface Waters, Lecture 1 Chemical Fate ad Trasport i the Eviromet, d editio. H.F. Hemod ad E.J. Fecher-Levy. Academic Press. Lodo Nature of the Subsurface Eviromet Subsurface varies with depth as well as by locatio. Aquifer: water yieldig formatio that may cotai sufficiet groudwater to be a practical source of potable water. Cofied aquifers are betwee aquicludes ad their flow is similar to pressure pipe flow (gravity alog the slope of the hydraulic gradiet is the drivig force). Ucofied aquifers are o top of aquicludes ad the slope of the water table defies the hydraulic gradiet ad the drivig force. I usaturated (vadose) zoe, water occurs as a thi film o the surface of grais of particles, the balace of the pore space is filled with air. I the saturated zoe, all pore space is filled with water. The water table is the depth where the pore water pressure equals the atmospheric pressure. 1

2 3.1. Sources of Pollutat Chemicals to the Subsurface Eviromet Plus other urba sources, such as de-icig salts ad stormwater ifiltratio. Darcy s Law Hydraulic head is a measure of the eergy per uit volume possessed by the water ad is described by Beroulli s equatio (sum of the physical height, the pressure head, ad the velocity head): h z + p ρg v + g The velocity head (kietic eergy term) approaches zero for slowig movig water (such as most groudwaters), ad the elevatio of the water i observatio wells describes the eergy gradiet. If the aquifer is cofied, the water may rise above the physical water level due to the pressure. If ucofied, the eergy gradiet is at the water level. Differeces i the hydraulic head are described by the head gradiet (dh/dx), the rate at which the hydraulic head (h) chages with distace (x). Darcy s law (from 1856) relates this gradiet to the specific discharge (q) ad the hydraulic coductivity (K): q v q K The specific discharge (Darcy flux) is equal to the amout of water flowig across a uit area perpedicular to the flow per uit time (Q/A). dh dx Typical aquifer porosities () are i the rage of 0. to 0.4. The rate at which a o-absorbig chemical moves i the groudwater is the seepage rate:

3 Aisotropy is whe the hydraulic characteristics are differet for differet directios. I this illustratio, the flat, elogated, grais provide better microscale chaelig compared to the radom, blocked, movemet i the vertical directio: Example Problem 3-1 moitorig wells are located 150 m apart i a ucofied sady aquifer. The hydraulic heads are at 0 m ad 19 m, ad the hydraulic coductivity is estimated to be 10-3 cm/sec. What is the specific discharge of the aquifer? Give that the porosity is 0., what is the rate at which osorbig dissolved chemicals will move betwee wells? 3

4 Darcy s law to estimate specific discharge betwee the wells: 3 dh 10 cm 19m 0m 6 q K 6.7 x10 cm/ sec dx sec 150m The correspodig seepage velocity: v q x10 cm/sec 3.3x10 0. cm/sec 3.. Flow Nets Flow ets are coveiet pictorial devices to visualize groudwater flow ad are powerful tools to perform graphical calculatios of specific discharge ad seepage velocity i locatios where groudwater flow is essetially steady ad predomiatly two dimesioal. ost easily applies to isotropic, homogeeous, porous media. Flow ets cosist of streamlies ad isopotetials. Streamlies are lies that follow the path of represetative parcels of water; water always flows parallel to streamlies. Isopotetials, draw perpedicular to streamlies, are lies alog which the hydraulic head is costat. Rules for Drawig a Flow Net Streamlies are always perpedicular to isopotetials i a isotropic aquifer. Flow boudaries (impermeable surfaces across which flow caot occur, such as surfaces of clay leses, cocrete, buried taks) should be thought of as streamlies because water flows parallel to them. Flow boudaries are perpedicular to isopotetials. Boudaries that ca act as either sources or siks (river ad lakes) sometimes ca be treated as lies of kow hydraulic head. A lie alog which a hydraulic head is costat (the shore of a lake) is by defiitio a isopotetial lie. 4

5 Flow ets are draw with a costat ratio of spacig betwee isopotetials to spacig betwee streamlies everywhere i the flow et (the ratio is usually 1, so the areas are approximately square; the size of the squares ca vary throughout the regio of water flow). Uder coditios of o recharge ad steady flow, the water table is a o-flow boudary ad is perpedicular to isopotetials Dispersio echaical dispersio chemicals dissolved i groudwater ted to spread out as the groudwater moves, similar to dispersio i lakes ad rivers. The mixig causes dilutio of the mass of the chemical ito a icreasigly larger volume of water. A chemical may appear dow gradiet earlier tha predicted based oly o groudwater velocity. I groudwater, mixig is ormally ot domiated by turbulece as it is i surface waters because the groudwater flow is much slower. echaical dispersio occurs due to the tortuous, widig, flow paths of the water. Some parcels of groudwater follow wide, direct routes, while others follow arrow paths that zigzag back ad forth at substatial agles to the average directio of flow. Groudwater dispersio ca be treated mathematically i the same way as turbulet dispersio i surface waters by applyig Flick s first law. I oe dimesio, the dispersio coefficiet, D, ca be represeted by: D α v D the mechaical dispersio coefficiet [L /T] α the dispersivity of the aquifer (approximately equal to the media grai diameter of the aquifer solids [L] v the seepage velocity [L/T] 5

6 Dispersio of a pulse of a tracer substace i a sad colum (similar to the dispersio of a tracer i a river, eve though mechaical dispersio predomiates here ad ot turbulet diffusio as i the river): The cocetratio for oe-dimesioal flow, as a fuctio of time ad distace is: C( x, t) C( x) 4παx e 4πD t L x vt) /(4 D t) ( The cocetratio at the ceter of mass: is the mass of tracer ijected per uit area of the colum is the porosity α is the dispersivity of the aquifer (approximated by grai size) x is the distace from the ijectio poit t is the time sice ijectio L Example Problem 3-5 A laboratory colum experimet uses sad with a mea grai size of approximately 0.5 mm. The packed colum is 1.5 m log ad 10 cm i diameter. Water flows with a seepage velocity of 1 m/hr ad the porosity is 0.3. A pulse ijectio of 5 mg salt is added. What will be the cocetratio of salt after oe hour at a distace of 0.9 m i the colum? What is the salt cocetratio i the ceter of mass whe cetered 1.3 m dow the colum? The mechaical dispersio coefficiet (D) i the logitudial directio ca be approximated by: D α v (0.5 mm)(1 m/1000 mm)(1 m/hr) 5x10-4 m /hr C( x, t) 180mg / m 3 e 4πD t L ( x vt) /(4 DLt ) (5mg /( π (0.05m) )) exp (0.9m 1m / hr 1hr) /(4 5x10 m / hr 1hr) C(0.9m1, hr) 4 (0.3) 4π(5x10 m / hr)(1 hr) 4 At 0.9 m, after 1 hr, C is 0.18 mg/l. The ceter of mass has passed the 0.9 m locatio. 6

7 C( x) 4παx (5mg /( π (0.05m) )) 3 C (1.3m) 3,000mg / m 3mg / L (0.3) (4π)(0.0005m)(1.3m) At 1.3 m, C is 3 mg/l at the ceter of mass. 7