esm223_07_Other_Reading_Capture_Zone_Curves

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Unformatted text preview: OCT-23-2UUU MON 10:39 HM BREN SCHOOL UCSB FAX N0. 805 893 7812 I P. 01‘ Capture-Zone Type Curves: A Tool for Aquifer Cleanup by Ira] Javandel and Chin-FL: Tsanga' ABSTRACT Currently a common method of aquifer cleanup is to extract the polluted ground water and, after reducing the concentratiou of contaminants in the water below a certain level. the treated water is either injected baclt into the aquifer, or if it is environmentally and economically feasible. released to a surfacevwater body. The proper design of such an operation is very important. both dramatically and environmentally. in this paper a method is developed Which can assist in the determination of the optimum number of pumping wells. their rates of discharge and locations. such that further degradation of the aquifer is avoided. The complex potential theory has been used to derive the equations for the streamlines separating the capture some of one. two, or more pumping wells from the rest of the aquifer. A. series of capture-zone type curves are presented which can be used as tools for the design of aquifer cleanup projects. The use of these type curves is shown by an hypothetical field case example. INTRODUCTION A recent publication by the Environmental Protection Agency (EPA. 1934) refers to the location of 7'36 hazardous waste sites. out of which 5 38 had met the criteria for inclusion in the National Priorities List (NFL) and another 248 sites had been proposed for addition to the NFL. aEatth Sciences Division. Lawrence Berkeley Laboratory, University of California, 1 Cyclotron, Road, Berkeley. California 94-720. Received July 1935. revised October 1935. accepted ncccmber 1935 , Discussion open until Match 1. 1987. 615 The NFL identifies the targets for long-term attics under the “Superfund” law (CERCLA, 1930). ~ " This list has been continuously growing since ’9 | October 1931 when EPA first published an interim priority lisr of 115 sites. In addition. as of October _ 1984, EPA has inventoried more than 19,000 ‘ uncontrolled hazardous waste sites. The ground | water beneath many of these sites is contaminated with various chemicals. Based on the Sec. 104.(a)(l; of FERCLA. the EPA has the primary responsibility for managing remedial actions at these sites unless it is determined that such actions will be done [ properly by the owner or operator of the facility. l or by any other responsible party. Once a plume of contaminants has been l identified in an aquifer and it has been established that remedial action should be undertaken, the l major task for the person in charge is to determint which remedial alternative is cost-effective. This is required by Sec. 105(7) of CERCLA (1980) and i Sec. 300.580) of the National Contingency Plan § (1 983). One alternative for remedial action is aquifer cleanup. Currently a common method of aquifer cleanup is to cxrract the polluted ground water and- , after reducing the concentration of contaminants ! in the water to a certain level. the treated water 15 either reinjected into the aquifer, or, if it is 136? mitted and feasible, it is released to a surface-watt! body. Given a contaminant plume in the ground _ water and its extent and concentration distribufl‘ln' and. further assuming the scum: of cont'amnation I has been eliminated. one has to choose the least expensive alternative for capturing the plurndi VOL 14, ND. S-GRO U-ND WATER-Sepmmber-Ocrobfl 1986 OCT-23-2UUU MON 10:40 All BREN SCHOOL UCSB “my questions to be answered for the design of “Ch projects include the following: ' 1, What is the optimum number of pumping “115 required? "1. Where should the wells be sited so that no out: "inated water can escape between the pumping Wells? i ' 3. What is the optimum pumping rate for each sell? 4, What is the optimum water treatment :icthod? 5. Where should one reinject the treated water mic into the aquifer? 'F'he purpose of this paper is to introduce a w 5:11an. method for answering four of the above :uestlons which are of hydraulic nature. I First, we shall develop the theory and give a series Of sample type curves which can he used as I zools for aquifer restoration. Then, the procedure {or application of the curves will be given in an action ‘80). answering the above questions. 71cc . n interim THEORY October 1 Lonsidet-a homogeneous and isotropic aquifer 300 with a uniform thickness 13. A uniform and steady :ound regional flow with a Darcy velocity U is parallel to minmd and in the direction of the negative x-axis. Let us 104(3)“; propose that a series of n. pumping wells penetrating must};an :hc full thickness of the aquifer and located on the :3 unless j-‘attis are used for extracting the contaminated _Dne :i l water, For n greater than one we want to find the facility.” I maximum distance between any two wells such ‘ -- > i'nat flow is permitted from the interval between the wells. Once such distances are determined we :en ablished i are interesred in separating the capture zone of _, thg i those wells from the rest of the aquifer. We shall gtgrminc 1 Start with n = 1 and expand the theory for larger .' This is I values of n. The following development is bated on 3) and linlllieation of the complex potential theory 'y Plan l Milne-Thomson, 1968). 1 is l Case 1, n = 1 for l in this case for the sake of simplicity and vater and. Without losing the generality, we shall assume that tinants the pumping well is located at the origin of the iflordinate system. The equation of the dividing water is 5 Per. ‘I. streamlines which separate the capture zone of this cwwam at” from the rear of the aquifer is "ind ‘ r=i Q — Q tan" 3’. <1) :rihution. ‘ ZBU erBU x math?" I Where a = aquifer thickness (or). Q = well diseharge 1‘35: ' lite (ma/sec), and U = regional flow velocity 1‘3- ‘l‘n/See). One may note that the only parameter in me. oher 019333 FAX N0. 805 893 7812 P. 02 SINGLE-WELL CAPTURE-ZUNE TYPE CURVES '1000. -500. 0. 500.1000.1500.EODO.EEDO. Meters Fig. 1. A set of type curves showing the capture zones of a single pumping well located at the origin for various values (If .l equation (1) is the ratio (QIBU) which has the dimension of length (m). Figure 1 illustrates a set a p of type curves for five Values of parameter (Q/BU). For each value of (Q/BU), all the water particles 3' within the corresponding type curve will eventually go .to the pumping well. Figure 2 illustrates the paths of some of the water particles within the capture zone with (Q/BU) = 2000. leading to the pumping well located at the origin. The intersection of each of the curves shown in Figure 1 and the ( ') x-axis is the position of the stagnation point whose distance from the well is equal to Q12 aBU. In fact, equation (1) may be written in nondimensional formas 1 1 - Yn =:_—_,,,_rt 1—— 2 YD 2 211 an xD () where yD = Elly/Q, dimensionless, and Me tors Cl- "500. “1000. '500. 0. 500. 1000. t500. 2000. 2500. Meters Fig. 2. The paths of some water particles within the capture I zone with (DIBUl I 2000, leading to the pumping well ~ located at the origin. 617 r OCT-23-2UUU MON 10:40 All BREN SCHOOL UCSEl l‘ 0.50 D . ES _ Pumping Well )9 0.00 x Regional Flew 3.0 4.0 Fig. 3. Nondimonsional-form of the capture-zone type curve for a single pumping well. XI) = BUx/Q, dimensionless. Figure 3 shows the nondimensional form of the captutevzone type 'curve for a single pumping well. Case 2, n = 2 Here, we shall consider two pumping wells located on the y-axis, each at a distance d from the origin. Each well is being pumped at a constant ratel‘Q. The complex potential representing the combination of flow toward these tWo wells and the ‘bniform regional flow is given by i. l W=Uz+ a 2,3 [his - id) +1n<z +id>1 + c (3) where z is a complex variable which is defined as x + iy and i = x/Tl'. ‘ The velocity potentian and stream function w for such flow system are the real and imaginary parts of W in equation (3) which can be written as p =Ux+4 Bfln[x2+(y-d)3]+111[X1+(y‘l'd):‘ll‘a"C Tn" ..... (4) — d o =Uy+ {tan“ y d-l-tan'l Y+ } (5) 2173 x x In general, when the distante between one wells is too large for a given diacharge rate Q, a stagnation point will be formed behind each pumping well. In this case some fluid particles are able to escape from the interval between the two Wells. When the distance between these two wells is reduced while keeping Q constant, eventually a position will be reached where only one stagnation point will ; appear and that would be on the negative xeaxis. In this case no fluid particles can escape from the space between the two wells. If we keep reducing 6133 FAX N0. 805 893 7812 P. 03 the distance between the two wells, again two . . . . $55 meiosis stagnation points Will appear on the negative 1;. - L of I: one moving toward the origin and the other away? in: r or from it, and still no fluid particles could escape :‘hE/fl from the space between the wells. The followingm’: I l'l by derivation gives the reaton for such behavior. ‘ Ta’stlLJ' To find the position of the stagnation points" ‘st 'JL one must set the derivative of W to zero: ‘3: e11 dw Q 1 1 i ' u— = U + w—vc , l = 0 dz zit-B ZHICl z+1d The roots of equation (6) are given by ' Th Q ,1. a. imit “'1' g _ m WT? I p 3 5“ wBU i [Q liwfiU) 1 4d l by “En. _ squat When 2d :5 Q/aBU, that is, the distance between»; ,Iugnat. the two wells is larger than Q/aBU, equation (7) p ‘ would give two complex roots. Each of these mi v +_ corresponds to the position of a stagnation point: ' " behind each pumping well. The coordinates of the“ . " 0' 'rgr‘ two stagnation points are . Lqumfl all ~ a Q i /"—"—‘—"—*2 a 2 {g of a P - l, identa.‘ Q “iii” lllulilil'flt d _ -1 W . an ( ZnBU ’ “é 4d {Q “T’Bm H lens at , tine ms Note that only when 2d at Q/aBU the Coordinatl‘fl“ mitten of these two stagnation points become approxi- _g;,j mately [~(Q/2nBU), d] and [*(QIZnBU), -d]. I 1 When 2d 2;- Q/nBU, contaminated water can escape l ’3' E from the space between the We pumping wells; at the larger the distance, the more fluid will escape. It is apparent from equation (7) that if the distant: between the We wells 2d is equal to Q/nBU, than both roots of equation (6) are equal and real such that ‘ ‘- — Q is) ' ZWBU where 3 \‘D = B 21222: in this case we shall have one stagnation point on the negative xvaxis whose distance from the origin is Q/erU. Under this condition no flow can pass betWeen the two pumping wells. Finally, if 2d s‘: Q/aBU, equation (6) would yield two real roots. The coordinates of the WW Ht! Lair" 5 -_;_..._._ —.—_..t— stagnation points corresponding to these two roots “50* are Q 2 I we: _ + 3.5 f 3 u. '2‘ O H: { zfiBU V [Q (nBU) ] ‘l-Cl l' I and Q r Fig. 4. C {— -- - vs V {Q3/(trBUlzl - 4612.0} 45 1° “'3‘” Walls. EtrBU OCT-23-2UUU MON 10:41 All BREN SCHOOL UCSB agam W0 mviously, when 2d becomes smaller and smaller, “game . km: Of these points tends to the origin and the e Other aw? ‘ ‘ I" he; one tends to the point with coordinates of mm fiscal?“ .flQh-rBU), 0] .When 2d re Q/rr BU, no flow can 1e foliflwmgi ‘ .5 between the two pumping wells. Therefore, it )ehavror. “ “3 3,. fimbiishEd that the condition for preventing the we of contaminated fluid between twn pump- .3! wells separated by a distance Ed is )= 0 Q 9 201 fi t—HBU ( 3 y The optimum condition is achieved at the 1.3.?) mi: when 2d = Q/cBU and the distance of the gagnarion point from the origin is (Q/ZNBU). The :quai'; . a of the streamlines passing through this use between mgriatiofl point is quation (7) g d of Fhese moo c 4- (tan‘1 y d + tan"1 y + ) = t Bu (10) iation Pomp; I - tnBU x' x no 1 line may note that again the only parameter in equation (10) is (Q/BU). Figure 4 shows the plot of a pair of these streamlines for (Q/BU) = 800; linates of D2] ) _ ‘ some H-‘eful distances on this figure are also ‘. identimd. Figure 5 gives a set of type curves m) i I din-strafing the capture zones for two pumping wells and for several values of parameter (CZ/BU). . ‘- i-I- (Jnc may note that equation (10) also can be : coordinates . on written in nondimensional form as e approxi- . 'BU3’“d]- iii 1 - to cum) _ yD +(1/21r) :er can escape ‘Fn +gltan 1-«——--:;---7--~+tan L T] :21 sing wells; I (11) will escape." f the distance where yD = BUy/Q, dimensionless; and l/nBU, then in = BUx/Q, dimensionless. nd real such I (53 * I 1000. In on Q/EU = T1 the origin i ow can pass i n . E D (6) would I - g If the two se two roots ] “500. l r H ‘1000. -9} sec. 0. see. 1000. 150d. 2000. secs. 2 Meters 3 -' HQ. 4. Capture tone of mo pumping wells properly located l i O} ‘9 Prevent any leakage from the space between the two WelIsv FAX N0. 805 893 7812 P. 04 DOUBLEHWELL CAPTURE-ZONE TYPE CURVES 1500. 1000. } EDD. {fl 5;, Re ionel Flow H 0 --—9—-———~—— g '500. “1000 '1500. Ih—- 'SOU. Cl. 500‘ 1000. 1500. 2000. 2500. 3000. Hetero Fig. 5. A set of type curves showing the capture zones of two pumping wells located on the y-exis for various values of (Cl/BU}. Case 3, n = 3 In this case we shall consider three pumping wells, one at the origin and two on the y-axis at (0, d) and (D, —d). The regional flow, as before, has a velocity of U and is parallel to and in the direction of the negative x-axis. The complex potential repre- senting flow toward these three Wells and the i uniform regional flow is given by WeUa+~2—9—Bv [1n a+ln(z-id)+ln(a+id)] +C (12) TI“ The velocity potential it and the stream function ill for this flow system are given by o=Ux+flg{ln(xi‘ +y2)+ 4n ln[x2 +(y—d)31+ln[x1 ‘+(y+d)‘i}+C (13) ‘ —d d W=Uy+B-(tan"z+tan"’Z—+tan“Z:-) (14) 21rB x x X I—Iere also, when d is large, fluid will escape between the wells and three stagnation points will be formed, one behind each well. Keeping the rate of discharge of each well constant and reducing the distance between each pair of wells, eventually a position will appear where no flow will pass in between the Wells. Again, to find the position of the stagnation points one must set the derivative of W in equation (12) equal to zero: } dW Q 1 1 1 —= +e—[—+ .+ . dz 21713 2 zflid z+id i=0 <15) 619 r— OCT-23-2UUU MON 10:41 All BREN SCHOOL UCSB Equation (15) may be written as 3 - m d2 w m- = 16) a + z A ( where A = *(ZnBUNQ. The disotiminant of equation (16) may be Written as d4 d1 1 D=d2('fi‘w+'A-T) It can be shown easily that D is positive, except for the limiting case when d = 0. In that case D vanishes, too. As a result, when d 9% 0 equation (16) has one real root and two other roots which ' are complex conjugates of each other. When d or Q/EW‘BU we obtain three stagnation points located at Q o O. _ O)Iz2‘( zflBuld)lz3'( ‘F—h ZnBU ’ .. ZnBU’ When d becomes smaller and smaller, that is, the distance between the wells decreases, the stagnation point on the x-axis moves away from the origin and the ether two tend to come closer to the ydaxis while appraoehing the x-axis. Such that for d = (2- 3x/El) Q/ZWBU the position of Stagnation points are 2;:(— ' Q Q Q z“(_l'54aaau’0)'z”‘l O'Hawau’l'gaweul' Q Q zi'l 0'73 aneu’ 9ai-riaul' The value of d = (2 3x72") Q/ZnBU is the maximum distance betWeen two pumping wells where no fluid could escape between the wells. One may note that this distance is approximately 1.2 times the optimum distance between two Wells for the ease of n = 2. Eventually, when d becomes zero, that is, when the outer two wells coineide with the middle one, three roots of equation (16) correspond to one stagnation point on the negative x-axis with a distance of SQ/EWBU from the origin and the other two collapse at the origin. At the optimum condi- tion, the equation for the streamlines passing through the stagnation point on the negative x-axis becomes -d +d 3 y+ zfilEUuan'hi-s- tan" yx +tan 1 a—w—yx )== TIPS-I (18) where d -~ 3 2 Q/(rBU). Since d is only a function of (QIBU), it is apparent that once again equation 620 on NO. 805 893 7512 g H P. 05 N i THREE-NEH. cantons-zone TVPE waves”, an 1500. . QIBU=|DODm Y 1000. 300 500 ‘ ‘ I 400 I fl, - 505 . A I I ' D V g o x Regional Flow l g 44 41—...»- ._._ ‘ I L. a w 2 '500. "1000. -1EDD. ‘ g -500. a. son. soon. 1500. anon. anon, 3gb. . Meters Q “#6, Fig. 5. A set of type curves showing the capture zones of \ + m l three wells all located on the y-axis for various values of”? i I (QIBU). ' I Hi where y: + } (13) is dependent on one parameter (Q/BU). Figigt we”, a _ a 6 shows a set of type Curves illustrating the capth ‘ : Md; zones for three pumping wells located on the deaccm p- y-axis for several values of parameter (Q/BU). N 1:; {our beam. that one of the pumping wells is located at the " indicates t origin and the other two are on the positive and J :he optimi negative y-axis with a distance of 3V3 Q/nBU front Dumping V the origin. 43%.; g is about tl' Here, one can also write equation (18) in a a}. Mug p131, nondimensional form as me - " ten 1 _ yo . Yo - (WE/t) sue- tan‘“ +tan1—---+ YD 2a [ xD X13 I _,_ a 2/ 3 l 1500. tan“1 M ] = i Er i x . D iooo. where x13, and yD are dimensionless coordinates as F defined before. =gg_ l General Case is , J | l | -soo. J i We shall now attempt to extend the solution. for a larger number of pumping wells. Table 1 55* shows some characteristic distances for the cases that we have already discussed. There are two generalizations that one can infer from Table 1. (1) The distance betWeen dividing Streamlines fa: upstream from the wells is equal to (nQ/BU) and” it is twice the distance between these streamlines at the line of wells. (2) The equation of the dividillfi streamlines for the case of n pumping wells can by; [ Fig.1 A . written down by comparing the corresponding ‘ equations for one, two, and three pumping wellsfig‘i IIo- "1000. OCT-23-2UUU MON 10:42 All BREN SCHOOL UCSB 1“ some Characteristic. Distances in Flow Regime FYF'E cu ‘ HVESJW ‘ Tabla 1- _ p in, One, Two, and Three Pumping Wells Under a ‘”“' _—‘--, l j”;- Uniform Regional Ground-Water Flow Optimum distance Distance between Distance between hetWetn each pair dividing streamlines streamlines of pumping wells at the line of fer upstream from #___._._ Q _ '— _ — : ture zonesqf I -,- + -—-—- {tan 1 y 1 + tan 1 Y . tut values of"" I Zflgu x x a _ “Q Han-1 3—15 } st (20) x ZBU r when: . ya, . . . yn are y-coordinates of pumping El/fhm' F1315“ I! wells 1, 2, . . . , and n. g ‘3 CaPtlii‘i Finding the optimum distance between two l as - ' on the dill: ‘ adjacent pumping wells when it gets larger than Egg/gag”: four becomes quite cumbersome. Our investigation mitive an .ndicates that for the case of four pumping Wells, I :he optimum distance between two adjacent QMBU {WP jumping wells is approximately 1.2 Q/(WBU) which ‘ :sabout the same as for the case of three pumping wells ' igure 7 shows a set of type curves for the i an o: four pumping wells for several values of FOUR-WELL CAPTURE-ZONE TYPE CURVES 1500. (Hi _ loco. lordinatcs as l D Rational Flow .he solution l g ' Table 1 r the cases '50“- are two - l Table 1. i '1000- amlines fat,” f ill/BU) andw "-"" . gtreamlines “Eco. u. see. loco. secs. acne. aeoo. seen. f the dwelth Meters wells can hi. i F; . ondfi J 9- 7. A set of type curves showrng capture zones of four P, 1 g Tl" “meme Wells, all leaned on the y-exis for several values of ping wells: lu/BuL 0‘ FAX N0. 805 893 7812 P. 08 parameter (Q/BU). Note that two of the wells are on the positive and the other two are on the negative y-axis. The distance between each pair of wells depends on the type curve (i.e., Q/BU value) chosen. Once the type curve is selected, the optimum disrance between each pair is d = 1.2 Q/(aBU). APPLICATION As was discussed earlier, presently a common method of aquifer cleanup is extracting the polluted ground water, removing from it the contaminants, and disposing or reinjecting the treated water. Naturally, the cost of such operation is a function of the exrent of cleanup. However, the important point is that once the maximum allowable contam- inant level of certain chemicals is given, the cleanup process should be designed such that (1) the cost is minimum, (2) the maximum concentration of a contaminant in the aquifer at the end of the operation does not exceed a given value, and (3) the operation time is minimized. To insure that the above conditions are satisfied, one has to answer those questions which were posed in the Introduction. The exact solution to this problem could be quite complex and site-specific. However, the following simple procedure could be useful for many cases and could avoid common errors. The criteria which we want to follow is that, to the extent which is possible, only those particles of contaminated water which are within the specified concontration contour line should fall in the captured zone of the pumping Wells. Suppose a plume of contaminants has been identified in an aquifer, the concentration distribu- tion of certain chemicals has been determined, and the direction and magnitude of the regional flow field is known. Further assume that the sources of contamination have been removed. The lasr assumption is not a requirement for this technique; hoWever, it is logical to remove the sources of contamination, if they are still active, before proceeding for cleanup. The following procedure leads to answers to the above questions. 1. Prepare a map using the same scale as the type curves given earlier in this paper. This map should indicate the direction of the regional flow at the site. Furthermore, the contour of the maxi- mum allowable concentration in the aquifer of a given contaminant should be indicated (from here on it will he called the contour line of the plume). 2. Superimpose this map on the set of type curves for one pumping well given in Figure 1. Make sure that the direction of the regional flow 621 F- \\ OCT-23-2UUU MON 10:42 All BREN SCHOOL 'UCSIB ‘ on the map matches the one in Figure 1. Move the contour line of the plume toward the tip of the capture curve and read the value of Q/BU from the particular curve which completely encompasses the contour line of the plume. 3. Calculate the value of Q by multiplying (Q/BU) obtained in step 2 by (EU), the product of the aquifer thickness, B, and the magnitude of regional velocity U. - i 4. If the well is able to produce the required discharge rate Q obtained in step 3, We have reached the answer. That is, one is the optimum number of pumping wells. Its optimum location is copied directly from the position of the well on the type curves to the contour map at the matching position. 5. If the Well is not able to produce at such a rate, then one has to follow the above procedure using the type curves for two pumping wells given in Figure 5. After identifying the appropriate type curve and calculating the rate of discharge for each well, one has to investigate the capability of the aquifer to deliver such discharges to both pumping wells. An important point to note is that because the zones of influence of two wells have some overlap, one may not be able to pump the same ‘ amount of flow rate from eachindividual well as one could from a single well, for the same allowable drawdown. If the aquifer is capable of delivering such flow rates to both pumping wells, then the optimum number of pumping wells is two, and their position can be traced directly from the type curves at the matching position. Note that the exact distance betvveen each pair of wells depends on the choice of the type curve and should be calculated from the equations given before. However, if the aquifer is not able to deliver that rate of discharge required for each well, then one has to use the type curves for the three-well case as given in Figure 6. This procedure could be carried out until the optimum number of wells are found. If one decides to reinject the treated Water baclt into the aquifer, then one strategy could be to do this at the upper end of the plume. This would substantially shorten the total cleanup time of the aquifer. To find the appropriate location for the reinjection well(s), one can use the same technique which we introduced for siting the entraction wells, neglecting the interference between the recharge and extraction wells. Here, one should match the way that the direction of regional flow on the 622 contour line of the plume with the type curves in a FAX NO. 8‘05seswr‘suigp H _I H 07 contour rnap becomes parallel and opposite tog; direction of regional flow on the type curves, doing, we ensure that all the particles of the WW water stay within the preSent position of the contour line of the plume and force the cent nated water toward the extraction wells. The a .: shortcoming of this technique is that a small ‘ volume of the contaminated water currently bag:- it at the tail of the plume will fall within a zone of" I wail. relatively very small velocity and may stay that; , for a long time. This also can be overcome by 11 of tilt moving the recharge weli(s) upstream as much as“ \ltl‘loug half of the distance between the calculated mes v location and the tail of the plume. .Jggc" ' til-€01- EXAMPLE would This example is designed to illustrate the use of this technique for aquifer cleanup. It is asaumed ‘ U = K'- that leakage from a faulty injection well has n ‘ contaminated a confined aquifer with trichloro a, “"3me ethylene (TCE). A thorough investigation of the sin “'6” is has identified the TCE concentration distribution as given in Figure 8. I-lydrologic studies have l revealed the following data: aquifer thickness, 10st ‘ i l = l .1 regional hydraulic gradient, 0.002;aquifer hydrauiit ’ (35 (M conductivity, 10“4 m/s; effective porosity, 0.2; in storage coefficient, 3 x HF; and permissible draw- _ 1 since c. . years, -c nay be ‘ noncoic 1 Ruth l l down at each well, 7 m, SuppDSe we want to clean the aquifer such that maximum remaining TCE concentration after the cleanup operation does not exceed 10 ppb. To optimize the aquifer cleanup operation cost we 1 want to minimize the ma of pumping the contam- inated water and treating it at the surface. Reinjec- tion of the treated water is an option which should not be ignored. The first step is to choose the optimum number of pumping wells, their location, and Where. Q = pu l :irityl :lapsec' | 7w 2 c‘ I £031 I :hct'ai ‘ 7w = 0 tion gi total d J the we TCE CONCENTRATION 9., ‘ drawd. OCT-23-2UUU MON 10:43 All BREN SCHOOL UCSB FAX N0. 805 893 7812 P re of discharge, using the procedure site m .3 their re irve5,' m above. Figure 8 includes the contour line of the in ‘ ,flppb ‘ :-_e area within this curve identifies the the j M where the TCE concentration is above 10 ppb )1“ should be captured and treated. Direction of The ‘ . ‘ [Cglflnfil flow is also shown in this figure. The mall .11: of this map is identical to that of Figure 1. ntly 1 .upflposition of this map on Figure 1 and match- Zoneo ii the direction of flow indicate that the size of 3y th 5'... ma within the 10 ppb contour is larger than “‘3 by - not" the type Curves presented in Figure 1. mUCh as. ‘ “than: . one could easily prepare other type “Ed ‘ ' met with larger values of (Cl/BU), extrapolation U = 2500 will t a type curve with QIB b contour line. How we lonai velocity U: ,uggcsts tha :arompass the 10 pp hould first calculate the reg U = Ki = (10" mls)(0.002) = 2.0 X 10'? misc: (21) therefore. the corresponding discharge rate of the In of well i: . ‘F'.’ l'lT-l 3- ) BU = :ltness, illit- BU Fer hydraili (2500 none m)(2 x 10"“ m/sec) = s x 10'3 musee 337‘. 0.2.; (22) :Sible dram ‘ ' ' ‘ ' n usually lasts for several lince cleanup operatio rawdown at the Well bore '0” .-l' fer such years. corresponding cl ation after i may --=-.1culated using either the equilibrium or LO ppb. To nonequilibrium equation for large values of time cos: we ‘uch as a year or so: :he contamr :e. Reinjet- Ah = 2'3Q log E'ZSKBt (23) hich should “KB riv 3 l where Ah = drawdown in the aquifer (m); mum [ “l = pumping rate (mifsec); K. = hydraulic conduc- 1. and ‘ :n-io- tin/sec); B = aquifer thickness (m)1 t = time ‘-‘ i claps. .. .ince the start of pumping (sec); "'-\' = effective Well radius (to); and S = storage Substituting for variables in equation (23), I 'he value of drawdown after one year and for -'w = 0.2 m becomes 9.85 m. Note that this calcula- iifln gives drawdown only in the aquifer. To obtain total drawdown in the well, one has to add to it l ills Well losses. These losses are a function of the I well tic-sign, and the best way to obtain the total . dl~'=1wdown in a well is to find the specific capacity I “l the well and its variation with the rate of dis- lmarge and time. In the above case, since the l_ dWWdown in the well is more than the permissible ‘lrawdown, we Will have to use more than one llumping well. Thus, we Superimpose the 10 ppb 1 inefficient l :enrnantm t ppb on. contour on the double curves given in Figure s. of the regional flow and mov the left, we see th QIBU = 1200 completely enc contour. The corresponding r each of the two wells now m3fscc. Wells, We should add t at the position of each we betWeen these two We equation (9): -well' Eaptureezone type ‘ Matching the direction ing the contour line to at the capture curve with ompasses the 1.0 ppb ate of discharge for becomes 0. ="0.0024- wdown at each of these two he drawdowns of both wells 11. The optimum distance 115 is obtained from To check the dra 2d = Q = 382 m (24) TTBU I and drawdown at each of these two wells is obtained from lit! 2 25KBt 2 25KBt Ah = l -—«—-H 2 417KB Mg its +103 (adrs l l 5) the drawdown after one year becomes 6.57 m. Generally, the well losses for small discharge rates such as 0.0024 mil/sec are small. However, if the amount of well losses together with the calculated drawdoWn 6.57 tn become larger than the assumed maximum allow— able drawdoWn of 7 meters, we haVe to examine the possibility of using three pumping wells. Superposition of the 10 ppb contour line with the three-well capturccone type curves (Figure 6) giVes a matching parameter of Q/BU : 800. Figure 9 shows the 10 ppb contour line of TCE on the Substituting for 2d, THREE-WELL CAPTURE-ZONE TYPE CURVES 1500. MOD. 44 500- (- E O elonul Flow \\\\\\\ “ \‘vr soa- _ _ “In”! - 500. O. Meier: Fig. 9. The 10-pph contour line of TCE at the matching position with the captur e-zone type curve of (Cl/Bill " 300. 62.3 93 7812 P. 09 OCT-23-2UUU MON 10:43 HM BREN SCHOOL UCSB FHX‘NO. F" W three-Well capturewzone type curves at the matching position. The area within the contour line has been assumption that no water with concentration ,3, below 10 ppb is extracted by the wells. Our imm crosshatehed for clarity. gation using RESSQ (Javandel M 611.. 1934) short}; Lem: The rate of discharge for each pumping well is that it takes about 48 years to extract the tow fluidi- _ volume of contaminated Water presently locate 1: at Q = somloflz X 10 it) = 0'0016 rug/sec within the 10 ppb Contour. This period eould digit. Drawdown in the middle well is the sum of the shortened substantially if we reinject the treatediliq qujfe. dravvdoWns of the two lateral wells in that well water back into the aquifer at an appropriate ,sn v plus its own drawdown, which amounts to 5.7 m. location upstream from the extraction wells. ll: ,3 {etc If we are convinced that the total drawdown is less To avoid mixing the highly contaminated Jr Sltll than 7 m or field tests indicate that, then our water with the surrounding water, it is often Jprurc optimum number of wells is three and the rate of beneficial to consider one or more extraction welfi grated discharge from each one is 0.0016 mil/sec. One of in the high concentration zone of the plume. The”, ,quit‘ev these wells is on the origin and the cther two are technique described here could be used to site at (O, 1320) as shown in Figure 9. these wells. u Extraction wells are assumed to penetrate and T1 DISCUSSION be open over the total thickness of the aquifer. If ~enral The method introduced in this paper is intended to provide guidance to proper siting of the wells are partially penetrating the aquifer, theli ; Enl’ll‘DT cleanup is effective at elevations corresponding tn” .n part 3 extraction wells and to determine their appropriate the screened zone and is subjecr to error in the “is .m' 895 rates of discharge for cleaning aquifers contaminated elevations corresponding to the nonpenetrared g is [1.5 with hazardous chemicals. It is important to note zone of the aquifer. in other words, contaminants .‘l'ldi-‘T F that the theory was developed based on the located in the nonpenetrated zone may not be "*1‘3- I iJE-.-\ assumption that the aquifer is confined, homoge— totally captured if the extraction wells are only :hsnl; _.- neous, and isotropic. Obviously, for aquifers partially penetrating. Obviously, if the plume is RSKER consisting of impermeable clay lenses and high con~ located only at the upper or lower part of the sent. a: ducting flow channels, this technique may give aquifers, highly permeable channels can easily carry away the contaminants at a much faster rate thanlthe general average regional flow. If the field investigation has clearly identified such a channel system, one can easily adapt this method to take it into consideration, However, these features can be missed during typical site investigations. Therefore, it is recommended that some array of monitoring wells be constructed downstream and beyond the capture zone of the extraction Wells. These wells should be continuously monitored during the cleanup operation to insure that such channeling does not exist. Although this technique minimizes the cost of aquifer cleanup, it does not necessarily minimize the operation time. Once we choose the minimum pumping rate, it takes a long time to extract all of the contaminated ground water. In the example described above, the total volume of contaminated water within the 10 ppb contour is about 5.15 million cubic meters (MGM). The rate of discharge from all three wells is 0.0048 m3/sec which is about 414.7 mil/day. Therefore, ignoring biodegradation and adsorption, the total period required to remove 5,16 MCM of contaminated water at the above rate is about 34 years. This is, of course, based on the 624- aquifer, then partially penetrating extracting wells he like are beneficial. :his mar The method is based on two~dimensional flow ' systems which implies that the aquifer is confined. I For unconfined aquifers the solution is more rump!“ complex. However, if the amount of drawdown relative to the total saturated thickness of the l ovironm aquifer is small, the error is not expected to be H“ large. SUMMARY Optimum design of the cleanup operation for a contaminated aquifer is an important task for the people in charge of such activities as well as for the i regulatory agencies responsible for enforcing the requirements set by law and the National Con- ringency Plan. An important part of such task is capturing the contaminated water and pumping it to surface. Rigorous analytical soltuions have been presented which give the position of stagnation points and optimum distances between pumping wells to avoid any escape of contaminated water between the wells. Equations for the dividing streamlines defining the capture zone of the pumping wells from the rest of the aquifer are 315° presented. A series of capture-zone type curves for one, two, three, and four pumping wells are given- ’ A procedure is recommended to facilitate seleeflf‘In i i l OCT-23-2UUU MON 10:44 HM BREN SCHOOL UCSB FAX N0. 805 893 7812 P. 10 J m optimum number, location,_and discharge 1:ch1’ the pumping wells. The criteria for such ‘ Qcomniendations include minimizing the cost, Acadia. legraelation of the water quality beyond .ge mooted zone, and achieving the goal that the . éuflmum concentration of a contaminant in the “gift: at the end of operation does not exceed a gran value. In case that the treated water needs to I '3 returned to the aquifer, a procedure is suggested for siting recharge wells. This is based on the A :thlll‘E-Zonc technique ‘which avoids mixing of the ‘action wan, - “and water with fresh water while reducing the alume. T115" l ,quifi- 1canup time. l to sue , I ACKNOWLEDGMENTS enetrate This work was supported by the U.S. Environ- aquifer. mental Protection Agency (EPA), Robert S. Kerr quifer, mg? 1 Environmental Research Laboratory (RSKERL), ponding (if; i 31 Part pursuant to lnteragcncy Agreement it in the ow 89930722-01-0 between the US. EPA and etrated :11: us. Department of Energy and in part itaminants' under " ii. Department of Energy Contract not be in? stains-reseoooss. The authors would like to are only thank Jack W. Keeley and Joseph F. Keely of slume is - RSKERL for their technical guidance, encouraged of the 7,4,3, ‘ neat, and review of this manuscript. We would oting wells ' , also like to thanlt Marcelo Lippmann for reviewing isional flow f" d l sconine: ‘ l l l l :his manuscript. REFERENCES {Time “3"” (innit ‘ *isive Environmental Response, Compensation, [Wdown .nic Liability Act of 1930. Public Law 96-510. The of 131-": Bureau of National Affairs, Inc. 5-632, 710701-0716. invironmental Protection Agency National Oil and Hazardous Substances Pollution Contingency Plan dto be erarion for :asl-c for the l as for the l ting the i .1 Con- ! 1 task is sniping it have been nation lumping 1 rd water ding "r. the at are also curves for ' are given. ': selection 1‘... au—FA Under the Comprehensiye Environmental Response, Compensation and Liability Act of 1930 40CFR300. Amended by 48 FR 4-0669, September 1933. The Bureau of National Affairs, lnc. S-fi72,101:1001«104~3. Javandel. 1.. C. Doughty, and C. F. Tsang. 1984. Ground water Transport: Handbook of Mathematical Models. American Geophysical Union, Water Resources Monograph 10, Washington, D.C. 223 pp. Milne‘Thornson, L. M. 1963; Theoretical Hydrodynamics. Macmillan Company, New York. 743 pp. , US. Environmental Protection Agency. 1934. National ‘ Priorities List, 736 Current and Proposed Sites in Order of Ranking and State, October 1934. Hill-7.2, 75 pp. II II I [raj Javandei received his PhD. in Civil Engineering, majoring in Geolrydrology, from the University of California, Berkeley, in 1963. In 1959 be joined the Pablcvi University faculty in Shiraz, Iran, where he was an Associate Professor and Cimirmon of the Civil Engineering Depart- rnent. He lens also taught courses in fluid mechanics and flora in porous media at the University of California, Berkeley. He has been a staff scientist in the Earth Sciences Division of the Lawrence Herkeley Laboratory since 1.980. His current principal interest is in hydraulics of wells, mathematical modeling ofgronndosater contamination. ‘ , aquifer restoration, and underground injection. Cbin-Fa-Tsang received his PhD. in Physics from the University of California, Berkeley in 1.969, and is currently ', a Senior StaffScientist and Deputy Group Leader of the Hydrogeology and Reservoir Engineering Group in the Earth Sciences Division of the Lawrence Berkeley Laboratory. His research interests range from advanced tori! test methods to flow offlnids and contaminant transport through porous and fractured media. He has been the Editor oftiJe Intetv national Seasonal Thermal Energy Storage Quarterly News- letter and was one of the Editors for the Journal of Environmental Geology. ...
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