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Unformatted text preview: OCT232UUU MON 10:39 HM BREN SCHOOL UCSB FAX N0. 805 893 7812 I P. 01‘ CaptureZone Type Curves:
A Tool for Aquifer Cleanup by Ira] Javandel and ChinFL: 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 capturezone 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 94720. Received July 1935. revised October 1935. accepted
ncccmber 1935 , Discussion open until Match 1. 1987. 615 The NFL identifies the targets for longterm 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 costeffective. 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 surfacewatt!
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. SGRO UND WATERSepmmberOcrobﬂ 1986 OCT232UUU 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 Lonsideta 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 xaxis. 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 MilneThomson, 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 SINGLEWELL CAPTUREZUNE 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 ( ')
xaxis 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 OCT232UUU 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. Nondimonsionalform of the capturezone 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 yaxis, 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+(yd)3]+111[X1+(y‘l'd):‘ll‘a"C
Tn"
..... (4)
— d
o =Uy+ {tan“ y dltan'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 zitB 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) ] ‘lCl l' I
and Q r Fig. 4. C
{—   vs V {Q3/(trBUlzl  4612.0} 45 1° “'3‘”
Walls. EtrBU OCT232UUU 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?“ .ﬂQhrBU), 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 dinstraﬁng the capture zones for two pumping
wells and for several values of parameter (CZ/BU).
. ‘ iI (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 CAPTUREZONE 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 yexis 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 yaxis 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 xaxis. 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(zid)+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— OCT232UUU 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+'AT) 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 xaxis moves away from the
origin and the ether two tend to come closer to the
ydaxis while appraoehing the xaxis. 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’ 9airiaul' 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 xaxis 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
xaxis becomes d +d 3
y+ zﬁlEUuan'his tan" yx +tan 1 a—w—yx )== TIPSI (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
THREENEH. cantonszone 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 yaxis 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
yaxis 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 yaxis 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. OCT232UUU 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 GroundWater 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
Han1 3—15 } st (20)
x ZBU
r when: . ya, . . . yn are ycoordinates 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 FOURWELL CAPTUREZONE 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 yexis 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 yaxis. 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 sitespecific. 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 \\ OCT232UUU 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 threewell 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. Ilydrologic 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. OCT232UUU 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'lTl 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 ‘ :nio 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 ticsign, 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 threewell 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, THREEWELL CAPTUREZONE TYPE CURVES 1500. MOD.
44 500 ( E O elonul Flow \\\\\\\ “ \‘vr soa _ _ “In”!  500. O. Meier: Fig. 9. The 10pph contour line of TCE at the matching position with the captur ezone type curve of (Cl/Bill " 300.
62.3 93 7812 P. 09
OCT232UUU MON 10:43 HM BREN SCHOOL UCSB FHX‘NO. F" W threeWell 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 capturezone type curves for one, two, three, and four pumping wells are given ’
A procedure is recommended to facilitate seleeﬂf‘In i i l OCT232UUU 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‘EZonc 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 89930722010 between the US. EPA and
etrated :11: us. Department of Energy and in part
itaminants' under " ii. Department of Energy Contract not be in? stainsreseoooss. 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 96510. The
of 131": Bureau of National Affairs, Inc. 5632, 7107010716. invironmental Protection Agency National Oil and
Hazardous Substances Pollution Contingency Plan dto be erarion for
:aslc 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 40669, September 1933. The
Bureau of National Affairs, lnc. Sﬁ72,101:1001«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. Hill7.2, 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. CbinFaTsang 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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This note was uploaded on 08/06/2008 for the course ESM 235 taught by Professor Dunne during the Winter '08 term at UCSB.
 Winter '08
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