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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,...
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 Winter '08
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 Aquifer, Water well, Type Curves

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