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= lunge and, conse-
<br />�- - and horizontal spreading of a p or ertrieable rocl.
<br /> ` fNpi1T pARAMETERS uentl the less tt is diluted) 1 p
<br /> { _ q
<br /> a the equations developed in this paper, two units where a ound water moves rather raptdl� , this
<br /> steal parameters are required as input
<br /> rranr Qhy p velott of the con- coefficient can be somewhat larger Ia to tnteres
<br /> desi�atcd mac. is the rY of conservatism for a worst case scenario for
<br /> first, a value of 10'' to 10-; cin=isec
<br /> �nant In the absence of chemical retardation, minimum dilution,
<br /> m ! the velocity of the ground water,Vw is adequate for poorly permeable materials (see, for
<br /> Th's is situp Y uate tsle---1959,p_718) The absolute «'orst
<br /> far cases where the partition'ng of the contaminant_ q a distribution
<br /> case is thus depicted as one having
<br /> fie described adequately through a distribution nt�f acro and a transverse dispersion
<br /> �tfiitienr i�d �fficae teal porous media
<br /> V„V coefficient in the range of a ryp P
<br /> " VC = 1 + (pb/n) Kd = p ` (I) diffusion coefficient It is empha5izcd hire that to
<br /> 12 t the alternative boundary analysis, we are not
<br /> a r01osin�, commonp�lr3ris the ratio of the dry density to the Interested in predicting exact e concentrationsuch a prediCe%elsl5
<br /> ly ranging between 4 and 1
<br /> (assumingfor the moment: that
<br /> rcr,i for mast b g even possible in the absence of a condeterm Hing
<br /> �eolo is materials and, as mentioned
<br /> aminatiorl
<br /> • history for model calibration),
<br /> ,,„e,the distribution coefficient
<br /> thego! nir►athre ins r imodel per
<br /> standards arc
<br /> poning between the liquid whether m
<br /> this partitioning is measured with achieved Hence, the worst case or upper bound
<br /> ne laboratory, P
<br /> column cxperimencs where prepared solutions calculations are useful to that they should demon-
<br /> ntaintng the contaminant are passed ite ametgme5 strate whether or not anievedtatthe ale pternati.e er limit f
<br /> �.,plogtc materials sampled at.the re not as accurate concentration will he a
<br /> latch experirnents are used, boundary
<br /> For fine-grained mater zlero anddistri103 0' mlfg ution coefficients
<br /> is AUEPr4AGE VALUE APPROXIMATIONS FOR
<br /> 1 rari�c in value betty
<br /> cons have a Kd of zero or near zero, the THE EFFECTS OF MIXING
<br /> t-iost comma SLS move wit move
<br /> the eloc ty of ground
<br /> e and tritium That is, Mixing is any process which causes one parcel
<br /> mese constituents lower relative of water to he mingled
<br /> dilution Processes atan caer
<br /> ,x-ater whereas most others will moves There are aL least thrporous media
<br /> } to the ground water In the absence of partitioning occur in contaminant transport in
<br /> (1) geometrical spreading of the contaminant
<br /> mcasurerrients, an upper bound f oc equals zero as
<br /> Incvelocity of ground water JKd 9 stream, assumed to be controlled by transverse
<br /> nc velocity
<br /> (L)3 5 ersitan processes, (2) continuous miain; of fresh
<br /> the latter a calculation that is well
<br /> e uatton (I) water along the cons din.L d schargTlearneOf the con
<br /> uc to arbe
<br /> K,thin the state of the art I?e � ebnt references for � I?
<br /> the retardation equation as givenand Freeze and from.,ecipitauan,
<br /> tic Grsak and Jackson (1978), taminant stream into some surface-water bol} , succi
<br /> Cherry (1979, p 405) as a stream The dilution effects of these processes
<br /> A second parameter requifed in the equations Will be examined in this section
<br /> � to follow is the transverse dispersion Coefficient,
<br /> ` designated DT i which is a rneasure of the spreading Geotsietstcal spreading
<br /> lace er colic- A scmiquantitativc, conservative estimate of
<br /> of a contaminant plume that takes p P p
<br /> j uiar to the flaw Imes Such dispersion
<br /> arises mtxtn due to transverse dispersion can be achiesume ved
<br /> between parallel flow elements due to
<br /> �iasie diffusion that through the following argument Let us endic lar `
<br /> ? �sid the tortuous pathways It is emphasized ransverMA!-Sp-sr—sion coefficient!DT, P P
<br /> to the flow lines The contaminant floN% pattern
<br /> this is not the commonly used "fitted longitudinal �-- thus be spread from the source as sho%y,n in
<br /> parameter of comple`t contaminant transport will t p ro\imate ly
<br /> Figure I(a) if the transit time t is a p
<br /> problems,referred to as the coeffiGtent of hydL°- where L is the distance from t3�e
<br /> ' di zamtc dispersion i�t its lower limit for a slowly equal to L/Vc,
<br /> mo%In fluid, DT approximated by a lis zrsion,
<br /> Ing can be apQ source andiVe is the contaminant �elocitS as eter-
<br /> diffusion coefficient for a porous medium, which mined by equation (1), then, Throughp
<br /> t - the contaminant front �4t11 Spread from �tiidih
<br /> is commonly taken as 10-s cm (Lerman, 1971, , t `: dere, the ditfusion lezJth
<br /> E v 32) Unger virtually no condirtons da we e�cpect L, to L, + 2(DT )
<br /> '�'��is taken as an appro�tmate measure of tine
<br /> � rhe transverse dispersion coefftcirnt to be less than
<br /> this so that 1Q_s CM /he can be taken as z conserva- 1��-
<br /> aP
<br /> the lower bound (the lower DT, th
<br /> e less the vertical sprea`l� as will he demonstrated liter in a boun ,05
<br /> f
<br />
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