A1_BTC Geodyna_3_TEXT_with Appendix and comma as English System Separator.doc

8/14/2019 A1_BTC Geodyna_3_TEXT_with Appendix and comma as English System Separator.doc

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Conjunctive Use of BTC and Batch Methods for Cd-Transport Casting in Coarse Sediment

Mohamed Fahmy Hussein and Hassan Khater

Cairo UniversityAbstract

Marginal sediments may e used as temporary retention repository to comat punctual pollution yheavy metals at the outlets of industrial !ones" This retention re#uires preliminary $no%ledge not only on theheavy-metal concentration in the discharged %aste%ater ut also needs information aout its reaction %ith thetarget sediment that may e used as a heavy metal trap" Modeling of atch e&periments and rea$throughcurves' (BTC)' provide pieces of information in that regard" Batch e&periments represented y Freundlichisotherms for CdCl* a#ueous solutions e#uilirium %ith a sandy loam sediment' and dynamic BTC runs forsaturated flo% of same solutions into the same sediment' %ere conducted in the laoratory using three Cd-concentrations in a limited case-study aiming at considering the conjugative use of these t%o procedures inorder to detect the positive and negative points of such conjunction and its applicaility for the local design of

ade#uate sand traps for Cadmium retention" +esults sho%ed deviations of the t%o laoratory techni#ues due todifferences in their theoretical concepts' mathematical formulation and their practice" Ho%ever' the atch resultssho%ed their utility to provide initial guess for the retardation factor' +' %hich can e inserted into ,-parameteranalytical solution (CfitM) used for (BTC) modeling" The iteratively otained K f ' S' and . values forFreundlich e#uation %ere used to generate the value of the distriution coefficient' k d' that %as' in turn'employed to get guess for the retardation factor' +' efore running (CfitM) code to get more insight into theoserved (BTC) data for saturated flo% comparale to that of sand traps that may e used for diminishing theimpact of presumed contaminated %aste%ater" Three concentrations (/' *0 and ,0 ppm) of Cd in the a#ueoussolutions %ere used and sho%ed distinctive adsorption and transport ehavior in the used sediment as mainlyrelated to the concentration of the input solution" The most dilute solution demonstrated largest Cd-adsorption'as reflected y sho%ing the highest k d and + values' %hereas some failure of the sediment as a potential trap %asdetected %hen Cd-concentration in the input solution increased to four and eight folds of that in the most dilutesolution used" This says that the sand trap is more successful %hen fed y the most dilute solution' and 1 or

successive traps should e used in line if high concentration is present" This %or$ presents a step for%ard in aset of local e&perimental %or$ that had general interest in modest and lo% cost %aste%ater treatment devices"

Key %ords2 BTC' Cadmium adsorption' +etardation factor' 3istriution coefficient' CfitM modeling

Introduction

3ynamic study of pollution in the field is a rather complicated and costly issue as itneeds lot of technical resources that are not availale to moderate laoratories" n order tosimplify the natural giving' the Brea$through Curves' (BTC)' and the atch runs' in the la'are preferentially admitted in a modest Cairo University la" Ho%ever' these e&periments areoutstanding procedures among the major tools currently in use in the much more advancedlaoratories for studying reactive and non-reactive solute transport in porous media" nterestin these t%o techni#ues has recently sensily increased as soil and ground%ater pollution isescalating %orld%ide" .onetheless' the (BTC) runs may still e less employed in many third%orld countries than the atch e&periments due to the complicated mathematics of the first"Conjunction of oth techni#ues may e profitale %hen oth may e accessed" This %or$deals %ith simple application of the assumed conjunctive use of oth methods"

The numerical solution of solute transport in porous media is an interesting alternativeto avoid the complicated and costly pollution field studies" Ho%ever' such codes re#uire a

priori $no%ing the values of code parameters as specific to a given particular case study" .onetheless' some of such parameters may e estimated from simple (BTC) and atch

e&periments at lo% costs as urgently needed in third %orld counties" For atch data' a specialiteration protocol can e run in order to otain est-fit adsorption curve (e"g" Freundlich



isotherm)" Moreover' special-purpose soft%are is often used to fit the non-linear (BTC) laoservations y the inverse solution of an analytical code (e"g" CfitM) in order to get thevalues of involved parameters"

4 given heavy metal can easily move %ith %aste%ater flo%ing out from an industrial!one and then may infiltrate and percolate to the local ground%ater via soil %hen the value of

the distriution coefficient' k d' for the surface sediment is small" 5n the contrary' the sameheavy metal may e shortly stopped' y adsorption and cation e&change' %ithin the topcentimeters of soil %hen the k d value is high" Thus' the fate of the pollutants in the discharged%aste%ater %ill largely differ according to the type of pollutant' its concentration in thea#ueous solution' and the type of sediment" Conse#uently' this parameter is needed for thedesign of ade#uate sand traps to punctually control pollution y heavy metals" The k d value ismainly regulated y solute concentration in the a#ueous solution' mineralogy of the solid-

phase' and type of the concerned solute" n addition' adsorption can ta$e place concurrentlyduring (BTC) and atch runs to different degrees" This depends primarily on the nature ofsolute' its concentration in %ater' and the minerals present in the porous-material' amongother factors (e"g" temperature' pH' etc6)"

The distriution coefficient' k d' can e considered as an assumed 7lin$8 et%een thee#uations used in curve fitting for the atch data' and that for the (BTC) data" n the (BTC)formulations' the k d parameter is just another %ay of e&pressing the retardation factor' +"Mean%hile' in atch run data processing y Freundlich isotherm' the capacity coefficient' K f 'and the sorption-intensity e&ponent' .' may e related to the k d and the + parameter" 9e maycall this' in the present %or$' 7conjunctive use of these t%o e&perimental techni#ues8"

Ho%ever' %e are a%are that solute-transport in a (BTC) run is an open-system time-dependent non-e#uilirium transient dynamic process that includes diffusion' even understeady-state saturated %ater-flo%' %hereas a atch run is oviously is a closed-systemdiffusion-free and time-independent e&periment deeming to $inetically attain an apparente#uilirium of the solute %ith the solid-phase' and its processing is usually done via Freundlich empirical e#uilirium-isotherm formula" 3espite this ig conceptual and practicaldifference et%een the atch isotherm and the (BTC) construct' they are considered in this%or$' in a first appro&imation' as a 7complementary set of methods8 in order to see %hat thisassumed complementarity may reveal to improve considerations needed for the design ofCadmium sand traps"

n this %or$' no geographic survey or a statistical presentation (e"g" uncertainty andreproduciility) or statistical trend for the otained data on the adsorption of Cadmium y thestudied sediment is attempted since three spi$ed concentrations %ere used" n fact' theseadditional items %ill e given in another %or$ that is under processing" The present %or$only deals %ith a preliminary and limited case-study that may promote the use of marginal

sediments (e"g" sand materials) as temporary depository for Cadmium retention in a desertarea %here increasing mining and industrial activities may menace the local preciousground%ater systems that are mostly fossil %ater resources" The major ojective of this studyto report an e&ample of the conjunctive use of the (BTC) and atch methods throughelucidating the %ea$ness and 1 or the po%er of such conjunction in the case of a limited casestudy that may lead' ho%ever' to %ider application in an ongoing %or$"

Theoretical background and literature

Solute transport in porous-media is an important ut over%helming hydrodynamic phenomenon" +egular reports on heavy metals in polluted soils near industrial !ones maygive 7snap-shots8 of their distriution at a particular time in given site(s) and depth(s)" nnature' ho%ever' solute transport and fate is a continuous transient process in oth space and

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time" The natural situation ma$es any complete study of that phenomenon so costly andcomple& tas$ that not all research %or$s may afford it" 3espite the difficulties' simplifiedstudies using modest $inetic and dynamic la approaches may provide precious informationon soil pollution prolems at much more less costs and technical re#uirements" 4mong thoseapproaches' atch and (BTC) methods stand distinguished" The conjunction of these t%o

$inetic and dynamic la procedures is appropriate %here the moility of heavy metals to localground%ater via soil is a serious ha!ard (9ang' *00:)" Many factors control the destiny ofsolutes in soils and a#uifers' including type of solute' its concentration in %ater and thenatural hydrogeochemical processes ta$ing place in the porous system" These processesinclude dispersion' convection in macro-pores' diffusion in micro-pores' adsorption' catione&change' dissolution' precipitation' redo& potential' and iological processes (;im<ne$ andvan =enuchten" *00: and ;im<ne$ et al' *00>)"

9hile it is almost impossile to ma$e full simulation of all aspects of the complicatedsolute transport phenomenon in natural soil and a#uifer systems' the analytical and numericalmodels provide some e&cellent tools for understanding solute ehavior in the porous systemsthrough the use of soil columns and sand tan$s (Siyal' *0?0 and Macintyre et al' ?>>?)"

+etention of a heavy metal %ith lo% moility at the soil surface (or in a sand o& trap)%ill prevent pollution of the local a#uifer' %hereas heavy metals %ith high moility representserious ris$ for ground%ater (Fig" ?)" Solute moility can operationally e e&pressed y thedistriution coefficient' k d" The magnitude of k d may e otained using the conjunctive use of

atch and rea$through runs in the laoratory"Kinetic studies carried out through atch e#uilirium have een long ago suggested that

ion e&change is an instantaneous process (Hissin$' ?>*,' Borland and +eitemeier' ?>/0' citedin .$edi-Ki!!a' ?>@>)" Batch data are usually modeled using the empirical Freundlichisotherm in its ra% form' or %ith certain modification (Coles and Aong' *00) in order toestimate the retardation factor' +' %hich is of particular interest for heavy metal transport in

porous media" .$edi-Ki!!a' ?>@>' %ith modification of our o%n' %rote' “This is expected

since ion exchange is a stochiometric process with change of enthalpy of about 2 kcal mol -1 ,

resembling dipole-dipole interactions (elfferich, 1!"2#$ %iffusion probably limits

instantaneous e&uilibrium, and thus determines an apparent exchange rate$ owever,

diffusion can be eliminated as a rate-limiting step in batch studies because of vigorous

shaking, but in 'T runs, particularly in aggregated soils, it cannot be eliminated since ion-

exchange can be damped by low ion diffusion to the exchange sites$) Several research%or$ers (e"g" Smith' ?>: .$edi-Ki!!a et al"' ?>:*) sho%ed that even if ion e&change isinstantaneous' the gloal $inetics can e influenced y fluid velocity and1or aggregate-si!e(that determine the diffusion path length) in (BTC) runs"

The (BTC) run is dealt %ith using operational e#uations applied to la oservations on

the relationship et%een dimensionless concentrations' C1C0' and the corresponding pore-volumes' DE' of the effluent flo%ing out from the soil column" The oserved (BTC)' %hich isvery often highly nonlinear' is modeled y certain codes in order to estimate the un$no%nvalues of the parameters involved in a given solute transport-model that is enhanced ycertain non-linear fitness protocol (;im<ne$' et al' *00:' and CFTM and CFTM codes'ig%mc' *00?)" The interest of such fitness is its relationship to field applications (Dorro and9ierenga' ?>>' and 9ang et al' *00:)" The use of the (BTC) method is also thought of hereas to e&tend its application under saturated %ater-flo% conditions to the use of marginalsediments as potential traps to restrain punctual pollution near industrial outlets"

n the simple models of solute transport there are t%o parameters2 the retardation factor'+' and the Declet numer' D' in the Convection-3ispersion G#uation' C3G (van =enuchten'

?>:?)" n more elaorated models' such as the Moile-mmoile' MM' models (van=enuchten and 9ierenga' ?>:) there are four parameters2 +' D' β ' ω ' Fig" * and " Here %e

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do not mention the parameter 7Dulse8 in oth types of models since %e consider that thesolute is applied continuously' rather than as rief contaminant pulse"

The retardation factor' +' is a ratio of pore-%ater velocity to solute velocity (in one porevolume for oth)" +? is otained %hen solute velocity is lo%er than %ater velocity duecation reaction %ith the solid-phase" 9hen %or$ing %ith anion tracers' + could e I?'

indicating anion e&clusion' other%ise it indicates the presence of stagnant moisture !ones"The + formula (G# ?) includes the distriution coefficient' k d' that accounts for soluteinteraction %ith the solid-phases" The + parameter is not scale-dependent"

The #uestion of %hether the oserved solute retention in soil column is due toadsorption or simply to cation e&change phenomenon' or oth' seems perple&" f cationretention %as to e merely attriuted to adsorption' %hat %ould e the electric alance in thesoil solution during any (BTC) runJ The so-called 7salt adsorption8 could e a good ans%erto that good #uestion in some cases" For e&ample' afo$u and Sumner (*00*) presentedevidence that simultaneous adsorption in e#uivalent amounts of cations and anions of anelectrolyte %ith no net release of other ions into soil solution (i"e" 7salt adsorption8 of an7indifferent electrolyte8) occurs in some acid tropical and sutropical soils in (BTC) runs that

those authors have conducted using dilute leaching solutions" afo$u and Sumner (*00?)have had previously reported that 7salt adsorption8 caused simultaneous depletion of Ca*L and

.5- from the leaching solution' %ith no other cations or anions %ere released in the leachate

in the first *"/ DE' and no inner-sphere comple&es of cations %ere formed %hen such 7saltadsorption8 occurred" Moreover' afo$u and Sumner (*00*) assumed that overlapping of thedoule layers around the positively charged Fe and 4l o&ides' and the negatively chargedsilicate minerals' is related to the 7salt adsorption8 of indifferent electrolytes caused ysimultaneous adsorption of their ions in oppositely charged diffuse layers as the late is eingcompressed in response to the increase in ionic strength in soil solution" This suggests that7salt adsorption8 occurs only %hen t%o oppositely charged solid phases are present" Theyconcluded that Cs and Cl they have used in their e&periments %ere most proaly7simultaneously adsored8 in the outer-spheres (diffuse layers) on oppositely charged soil

particles' %hereas the 7adsorption8 of such ions in the inner Stern layer %as not promotedunder their e&perimental conditions" The 7indifferent ions8 are those %hich are onlyasored through Coulom forces y surfaces of opposite sign' not asored on an unchargedsurface' and unale to reverse the sign of surface charge of the solid-phase particle ut onlycompress the electrical doule layer" 5n the contrary' the 7specifically asored ions8

possess a 7chemical8 affinity for the surface in addition to the Coulom interaction' %ith thisaffinity eing a) van der 9aals or hydrophoic onding' ) pi-electron e&change and c)comple& formation (http211%hat-%hen-ho%"com1nanoscience-and-nanotechnology1mineral-nanoparticles-electro$inetics-part-*-nanotechnology1)"

Materials and Methods

Mining and development of faulty industrial installations in the =reat Sahara may eaccompanied y contamination 1 pollution of vulnerale soils and precious ground%aterresources of local a#uifers on the long run y heavy metals through lea$age and depositionon surface sediments" The sediments used in this %or$ (and in other parts of our %or$ to ereported else%here) %ere collected as surface single-grain soil samples from four sites in themiddle of the * 000 $m* area and @00 thousand people oasis and the city of 74l-Kharj8(around latitude *,"?,:. and longitude ,@"0/G' i"e" *,:N/,O. ,@?:N?:OG)' (Fig 0)' atsome /0 to @@ $m to the south%est of the +iyadh city' the capital of the Kingdom of Saudi

4raia (KS4)' i"e" nearly at origin point of the central sandy plateau to the middle and theeast of the (KS4)' %ith height of at aout /00 m 4MSP' %here the local ut e&tended fossil

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ground%ater is one of the major %ater resources of the (KS4) and one of the $ingdomhistorical cultivated areas" Heavy pumping for domestic uses and for e&tensive agriculturale&pansion under pivot irrigation has greatly diminished the hydraulic head since ?>:0' andserious dra%do%n has ta$en place during last three decades eneath the #uart! eolian sandsand the #uart! and caronate #uaternary %adis of the 74l Kharj region8" This practice has

given rise to disappearance of the local up%ard flo%ing springs and their associated la$es"The 4l Kharj region is part of the major sedimentary asin of the (KS4)" The deposits of thislose sedimentary region has Calthiorthids QTorripsamments deep sandy soils' %ith 0-Rslopes' that are nearly level on smooth plains' and in the old alluvium of the closed %adi

ottoms' characteri!ed y very lo% soil salinity' and moderate to high permeaility"Ho%ever' small convoluted and and pattern areas have Calciorthides and =ypsiorthids soils%ith Calcic and =ypsic hori!ons (Saeed' ?>>/)" Unpleasantly' the +iyadh and 4l-Kharjagglomerations ecame' in addition' significantly menaced y industriali!ation-associatedris$s in the four recently-installed industrial comple&es in the outs$irts of these t%o cities'%ith heavy-metals eing the major pollutants (4l-Hamad et al' *0?*' and 4l-Shaye' *00*)"

5ne of the +oyal Saudi 4ir Forces ases' Drince Sultan 4ir Base' *,0N,:O. ,@,N/0OG' islocated in 74l-Kharj8 area' %hich is home for several fleets of F-?/s" 74l-Kharj8 %as hometo aout 0'000 coalition forces during the ?>>? =ulf 9ar ' e#uivalent of ?0R of the native

population"The sandy loam soil samples collected just outside the southeastern %adi ottoms

adjacent to 74l Kharj8 city (Fig" 0) have ul$ densities around ?00 $g1m and are mainlymade-up of #uart! particles" Ho%ever' the solid-phase caronates contriution is in the rangefrom > to /R" The four samples have lo% salinity (from 0"*0 to ?",0 dS1m)' very lo%organic matter content (from 0",0 to ?"*0R) and moderate saturated hydraulic conductivity(from to 0"0 to 0"/0 cm1min)" The present %or$ is concerned only %ith the sample from

location ? that has a sandy loam te&ture %ith :"@0R Calcite' 0",0R organic matter and ul$density of ?*:> $g1m" This particular soil sample %as selected for the present %or$ since ithas the lo%est solid-phase caronate content %hich may help to avoid potential effect of highcaronate content on Cadmium solution reaction %ith the solid-phase during atch and BTCruns" The pF-curves of samples from the four sampled locations %ere otained in thelaoratory using pressure-coc$er techni#ue' and then optimum representative pF smooth-curves %ere fitted to the θ(h) function oservations using the (+GTC) code (a special purposesoft%are regularly used for plotting soil moisture retention curves as the code is enhanced%ith a curve fitting optimi!ation method)" The corresponding pF curves are not sho%n heresince this issue %ill e dealt %ith in another %or$ on %ater flo% in the sampled soils' and theother three samples are also dealt %ith for other pollution-related issues else%here"

The e&perimental %or$ started %ith closed-system atch adsorption e&periments(4macher' et al' ?>::) using Cadmium Chloride on three su-samples from location ? inthree runs' each in duplicate' using three concentrations" The three Cd-solutions used for the

atch and the (BTC) e&periments had nominal concentrations of /' *0' and ,0 ppm Cd' utreal concentrations %ere slightly different' Tale ?" The soil material and Cd Cl* solution%ere mi&ed for the atch runs in ?2?0 ratio as fre#uently used (ualls' +' and Haines B"'?>>* and Een$ata et' *00@)' and e&posed to vigorous electric sha$ing during ?* hours' andthen the soil-particles %ere forced to settle-do%n y centrifugation (during *0 minute at 000rpm) in order to get a clear li#uid for chemical analysis of the residual solule Cadmiumassuming that e#uilirium adsorption has already ta$en place (4macher' ?>>? and 3aniel et

al' *00@)" 4tomic asorption apparatus %as used for Cd chemical analysis (Unicam >> 44Spectrometer' Dage ?>:*)" Batch data points %ere used in G&cel for non-linear iterative

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fitness for Freundlich' Pangmuir' and Freundlich-Pangmuir formulae y using S5PEG+function in the %or$space given in the follo%ing lin$(http211%%%"ars"usda"gov1services1soft%are1do%nload"htmJsoft%areVtrueWmodecodeV,-,/-00-00)"Ho%ever' only Freundlich e#uation %as considered in the rest of this %or$ as it is the mostformula in use y most %or$ers"

Brea$through curve' (BTC)' runs in open-system saturated flo% %ere posterior to the atch runs and %ere as conducted in the la using a locally made inflo%-outflo% setup (Fig",) %here the DEC soil columns %ere /0 cm in length and / cm in diameter" The sediment%as carefully pac$ed to an average fraction ul$-porosity' ρ ' of aout 0"/0' and its one pore-volume' DE' value %as aout /00 ml" Gffluent fractions %ere collected during ?* hours foreach run and stored at ,C for later chemical analysis" The oserved (BTC) data points of Cd-concentration in the effluent as corresponding to the oserved pore-volumes %ere used in theST4.M53 soft%are pac$age (CFTM and CFTM codes' ig%mc' *00?) in order to conductnon-linear est fit of the oserved (BTC) to otain the un$no%n values of code parameters(*-parameters' namely D and + in the case of (CfitM) code' and ,-parameters' namely D' +' β

and ω in the case of CfitM code)" Conjunction of the atch and the BTC results %as assumed postulated and studied as sho%n elo%' %ith the design of ade#uate sand traps for punctual pollution control in the local %or$shops of the 4l Kharj city in mind depending on the valuesof the otained parameters"

Results and Discussion

This %or$ is concerned %ith Cadmium adsorption on coarse-grained sediment for theestimation of transport parameters as a preliminary step for the design of ade#uate traps for

punctual pollution control using marginal sediments" This %or$ is a preparatory step in a%ider %or$ on five heavy metals (.i' Cu' Xn' D and Cd) and four sediments (ranging fromsandy to sandy loam' %ith different contents of calcium caronate in the range for > to /R)"BTC runs %ere conducted on sandy loam sediment collected from 4l $harj area' (KS4)' (Fig0)' using three aritrary spi$ed Cd concentrations of /' *0 and ,0 ppm in a#ueous solutions'(Figs , and @ and Tale )" Drolems %ith constant saturated flo% %ere encountered %ith theused do%n%ard flo% (Fig ,4) and repeated %or$ (reported else%here) %as carried out untilthe most stale discharge rate %as otained" n vie% of this situation' it %ill e much etter touse up%ard flo% in future %or$" 3ata of BTC is not sufficient in itself to get the re#uiredsolute transport parameters" The re#uired parameters are regularly derived from the nonlinear

est fit of (BTC) data using ade#uate computer code (Tale *)" Batch e&periments (Tale ?'Fig" / and Fig" ) %ere performed in order to use Freundlich constant K f otained from the

atch runs to get a first guess for + parameter via the k d coefficient" This conjunction of the

atch and the (BTC) runs is assumed ade#uate to ma$e %or$ing %ith the (CfitM) model lesstime-consuming" n fact' 7seeding8 value for good + input as affi&ed value in (CfitM) code%as otained from $ d via K f that is derived from iteration on atch data" The fi&ed + value%as delierately selected to e slightly lo%er than that otained via processing of the atchdata for each Cadmium solution" The results otained from the atch e&periments and the(BTC) data fitness in (CfitM) code (ST4.M53G soft%are pac$age' ;im<ne$ et al' *00:)should reduce the time needed to accomplish local pollution-control efforts"

3espite familiarity %ith (CfitM) code for the fitness of (BTC) data' the (CfitM) codefailed to optimi!e the oservations of Cd (BTC) runs that %ere carried out using the laapparatus sho%n in (Fig" ,)" Conse#uently' %e used (CfitM) code and otained the threecurves sho%n in (Fig" @4)" For the (CfitM) code' initial guesses for four parameters (the

retardation factor' +' Declet numer' D' Beta' β ' and 5mega' ω ) are needed' %hereas guesses

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for only t%o parameters (the retardation factor' +' and Declet numer' D) are re#uired toe&ecute the (CfitM) code"

4 rief account of the asic concept of this %or$ is given in Tale 4 and B" The idea%as ased on the conjunction of the results otained from Freundlich isotherm' namely its K f value (the capacity coefficient) transformed into a k d value (distriution coefficient)' that %as'

in turn' used to produce the retardation factor' +' and then inserted after%ards as initial guess(or much more etter as imposed 7fi&ed8 value) for + parameter in the input screen of the(CfitM) code' %hereas the other three parameters of the cod (namely' D' ' and ω) %ereintroduced as guess values to e freely fitted y the (CfitM) soft%are" The conjunction of

atch and the BTC methods that %e carried out is e&plained more in follo%ing paragraph"The fre#uent user prolem %ith (CfitM) code is that the user must introduce , guess-

parameters as free values to e optimi!ed y the soft%are and 1 or one or more of them to einserted as fi&ed value(s)" 9e may reduce the tas$ of getting good first guesses y otainingthe value of a given parameter from the data of another e&perimental %or$ (e"g"' to otain theDYcelt numer from another e&periment' since this parameters is 7soil material-dependent8not 7chemical dependent8 in particular %hen diffusion is negligile' and to process atch data%ith Freundlich isotherm iterative fit spreadsheet to get the value of k d and then that of + viaK f and . of Freundlich formula)" n fact' any linear isotherm for atch data %ill giveunrealistic k d values" n addition' in Freundlich isotherm processing %e have used the C0ZBTC (the initial concentration of the inflo% a#ueous solution) not the Ce#uilZatch (the finalconcentration of the solution after atch run)" This is so since the Ce#uil values proved to enot ade#uate for the lineari!ation needed for (CfitM) since it gives very high and unrealistick d and + values" Moreover' for each Cd solution in the BTC runs' %e tested a and of +values (that are all less than the + value otained y integration lineari!ation of atch results)'and among these + values %e pic$ed one + value that %e inserted as a fi&ed + in the CfitMscreen' and then the (BTC) est fit y CfitM %as finally e&ecuted" This procedure'

nonetheless' re#uired that %e e&ecute the (CfitM) code as many times as needed to get the est fit of the (BTC) run data"To illustrate the use of the first guess for the + parameter' a tale (not sho%n) %as

updated to revie% a try and error e&ecution of (CfitM) code %ith guess of + V ,0" n that particular case of + V ,0 inserted in (CfitM) as a free-to-fit guess value' the + otained fromthe non-e#uilirium (CfitM) code %as + V ,,"?, %hen the first-type oundary condition %asin use" 4nother guess (not sho%n) for + %as provided from the Freundlich isotherm as + V*@"/@ under the third-type oundary condition and the + value otained from that code %as:"?" This e&ample sho%s that (CfitM) code is highly sensitive for the value of the inserted+ guess" This code is also sensitive for the inserted guesses for the parameters Beta' β ' and5mega' ω ' ut there is no procedure $no%n to get initial guesses for those t%o parameters'

%hereas the conjunction of the atch and BTC runs provide an interesting %ay to get the est+ value to e introduced in (CfitM) screen as a fi&ed value that is not changed during thecode e&ecution" Ho%ever' for the DYclet numer' D' an independent estimation may e also

provided via an independent e&periment (BTC) ut this is possile only %hen diffusion isnegligile giving rise to D to e only depending on soil material' not also on chemical' in thisvery particular rare case and any (BTC) run"

The conjunction procedure used in this %or$ implies that %e consider the + value provided y the atch techni#ue the upper admitted ceiling (e&aggerated + values' since thek d value is asolutely e&aggerated in any atch run) for the + parameter values in theaccompanied (BTC) run' i"e" the value to e fi&ed in (CfitM) for + parameter should eslightly to moderately lo%er than + provided from lineari!ation y integration of Freundlichisotherm" This conjunction is in high conformity %ith the $no%n e&treme non-concordance

et%een the atch method and field conditions" Ho%ever' concordance gains some reproach

7



to field conditions in the case of the (BTC) techni#ue (To %hat e&tentJ .oody can saye&actly)" This upper limit for + values is used only in this conte&t as a nominal guide to selecta and of + values to e inserted in the (CfitM) screen' and %ith each ne% value in this andintroduced the code' soft%are e&ecution must e ane% run and the graphic and te&t taulationof the code are to e revie%ed to see ho% the est fit of the (BTC) is approached" The

statistical parameters of the code can also e used to finely judge the (BTC) curve fit" This isoviously much etter than using free +-value guesses %hich ma$e the (CfitM) code usevery time-consuming and may lead to no (BTC) curve est-fit at all" The e&aggeration of k d values' and suse#uently + value' in the atch run is inherent in this method due to itsconcept and to its practice" Ho%ever this e&aggeration may decrease or increase y thelineari!ation integration of Freundlich isotherm (Fig /4)"

3uring the (BTC) runs %e have oserved some irregularity of data points in early runs'and this situation has urged us to remove the last four data points of the ,0 ppm Cd-solution

efore fitting the curves sho%n in Fig" @ as %e could not interpret those last four data points"5ther irregularities %ere also detected" 4nomaly in the oserved data-points of the C1C0-Dorevolume relationship may e due to one or more events during the (BTC) run" These events

are proaly due to the changes of one or more of the follo%ing chemical and physicalfactors2 ?) pH' *) ionic strength y late desorption' ) redo& potential' ,) formation ofcomple&es %ith thin iron-o&ide coatings (cutans) on #uart! and on solid-phase caronates' /)

precipitation of Cd-caronate or hydro&ycaronate' ) change of %ater-regime that resulted innon-steady state' instead of steady-state saturated flo% conditions' @) change of temperature'that resulted in change of flo% rate and1or giving rise to some desorption' and :) poorcolumn-pac$ing (Huang' et al' ?>>)" 3espite this long list of theoretical reasons' %e mayrefer to our e&perience that says that the most ovious practical reason is' in fact' thedeviation from the saturated steady-state %ater flo% condition in the column during the(BTC) run in the la" +epeated runs on the same soil and chemical set are necessary" This%ill e sho%n in another %or$" mprovements of the analytical %or$ may include much moregood pac$ing and to tightly insure the dominance of the saturated steady-state flo%conditions efore the application of the chemical" The present BTC runs %ere done usingdo%n%ard %ater-flo% (Fig ,)" Ho%ever' up%ard %ater-flo% %ould e much etter to efollo%ed in the coming (BTC) e&periments in order to remove most amiguity on the C1C0-DE data points and shrin$ the numer of replicates"

.evertheless' the most ovious result of this limited e&perimentation is that it sho%sthe vast impact of the concentration of the pollutant in the position and shape of the BTCfitted curve on the C1C0-DE plot and the relationship of some parameters %ith Cdconcentration (Fig" @4 and B)"

The different positions and shapes of the three BTC curves for different Cd-

concentrations indicate the change of the metal adsorption ehavior on the soil material used%ith the change of concentration" The most dilute Cd solution sho%ed the highest adsorptionof Cadmium as sho%n y the highest k dZ.TP value (?0",*[?0- m solution1$g soil) for the /

ppm solution' (Tale ' at the intersection of ra% ?0 and column *)" 4dsorption consideralydecreased %ith the increase of Cadmium concentration in the input solution as seen at theintersection of ro%s ?? and ?* %ith column * in Tale *" This result is not astonishing as itmight loo$ at a first glance" n fact' .V0"@/' for the Freundlich isotherm reflects a fairsorption intensity' and the K f V ?"// sho% a fair capacity coefficient" Many authors havesho%n and + value increases %ith solute concentration decrease in the a#ueous phase (e"g"3avidson et al' ?>:0' page *)" The hydrodynamic parameters involved in (BTC) modelingdo not e&ist in Freundlich isotherm modeling of the atch run" The oserved increase of

sorption in the dilute Cd solution is in agreement %ith other authors (e"g" as far as the paper

8



of .$edi-Ki!!a ?>@>) %ho oserved' for aggregated 5&isol' that the adsorption of ,/Caincreased %ith a decrease in concentration at any given pH"

9e perceived that the (CfitM) output of the (BTC) runs sho%ed lo%er values for + parameter as compared to atch results (Tale ' in the ro%s ?0-?* intersection %ith thecolumn and ,)' i"e" atch runs generally overestimated the adsorption S value" t is

generally accepted that BTC run may give etter appreciation of cation adsorption than the atch-techni#ue" 3ynamic flo% in an open-system is prevailing in the (BTC) run' %hereas inthe atch e&periment the run is ased on a closed-system e#uilirium approach" n addition'the formulas and concepts of oth methods are largely different" Ho%ever' in the present%or$ %e %ere ale to sho% ho% these different techni#ues may e conjugated in order toemploy the CfitM code in an easier %ay"

.on-e#uilirium condition of solute-convey in the porous media in the BTC run is dueto2 (a) chemical non-e#uilirium due to $inetic adsorption %hich is dealt %ith in (CfitM)code through instantaneous adsorption and a first order $inetic formula' () physical non-e#uilirium caused y heterogeneous flo% regime %hich is dealt %ith in (CfitM) codethrough dual-porosity and solute mass-transfer et%een moile and immoile regions that is

governed y a first-order process (formulas are reported in the 4ppendi&)"

Conclusions and Recommendations

Conjunctive use of atch and (BTC) results is proposed to otain the retardation factor'+' in (BTC)' via the distriution coefficient' k d' derived from Freundlich constant K f eforeusing (CfitM) code in modeling heavy metal transport in soil" The approach seemsoperational since speculation on four-parameters in (CfitM) code (+' D' β ' and ω ) is e&posedto repeatedly introducing faulty guesses that may e tedious and ma$e the use of the codetime-consuming" The (CfitM) code is more involved than the (CfitM) code for simulatingtransport of chemically reactive solutes in soils since (CfitM) code accounts for non-

e#uilirium conditions and for partitioning of solute into moile and immoile moistureregions' and it considers convection transport as dominating in the moile region' %hereas itconsiders diffusion to the availale adsorption sites as dominant in the immoile region" 9e

propose the conjunction of BTC techni#ue (modeled y CfitM code) and atch method(modeled y Freundlich isotherm and integration lineari!ation) in order to save user time andeffort in applying (CfitM) code in studying contamination-related prolems" The value of +otained from the atch method should e used as an upper limit for + value to e fi&ed in(CfitM) code" Ho%ever' the user must e sure of the dominance of saturated steady-state%ater-flo% conditions during the BTC run in order to remove amiguities on the oserveddata and to improve the values fitted for the involved parameter" The + parameter forCadmium transport in the used sandy loam soil column in the BTC runs sho%ed lo%er valuesthan those otained from of Freundlich isotherm for same sediment and the same soluteconcentration in the a#ueous solution" This may indicate that the atch method overestimatesthese t%o parameters due to its conceptual asis' its formulation and its high %ater to soilratio" The values of the parameters k d and + have increased %ith the decrease of solutionconcentration sho%ing more adsorption of Cadmium from the more dilute a#ueous solution"Conse#uently' for the practical application of sand traps in the punctual control of Cadmiumat the industrial outlets' it is recommended to discharge the dilute %aste%ater into a singlerepository marginal sediment trap" Ho%ever' in case of discharging high Cd concentrations' itis recommended to use several traps in line" 3etails of traps design and regeneration must edeveloped %ith respect to' and in function of' the values of transport parameters and the si!e

of the %or$shop that discharges heavy metals to the environment"

9



References

4l-Hamed S" 4"' 9ahy M" F"' 4ou$arima 4" M"' and 4" 4" Sayedahmed' *?0*Classification of cultivated soils in 4l-Kharj' Saudi 4raia' ased on natural radionuclides using artificialneural net%or$s" nt" \ of Dhysical Sciences Eol" @(>)2 ?/?Q?/*/" http211%%%"academicjournals"org1\DS" 352 ?0"/:>@1\DS??"?@@/" SS. ?>>* - ?>/0 ]*0?* 4cademic \ournals

4l-Shaye S" M"' *00*Metals content in soils of the industrial cities and the industrial %or$shops in +iyadh' Saudi 4raia" 4sian \of Chem" ?, (-,)' ???-??@@

4l-Tur$i S"' ?>>/9ater resources in Saudi 4raia %ith particular to Tihama 4sir province" Dh" 3" Thesis in =eography'3urham G-Thesis' UK"

4macher M" C"' Selim H" M"' " K" s$andar' ?>::Kinetics of chromium (E) and cadmium retention in soils a nonlinear multi-reaction model" Soil Sci Soc4m \" /*(*)2>:Q,0:

4macher M"C"' ?>>?Methods of otaining and analy!ing $inetic data' in rates of soil chemical processes' Soil Sci" Soc" of4merica' SSS4' Special Dulication no" *@

CFTM and CFTM codes' ig%mc' *00?

Code for Gstimating G#uilirium Transport Darameters from Solute 3isplacement G&periments' ased onEan =enuchten' M" Th"' ?>:0 and *00?' n ST4.M53 (Studio for 4nalytical Models for Solving theConvection-3ispersion G#uation) (Simune$ \"'Ean =enuchten M" Th"' Peij F" \" and Sejna M"' ?>>)' C3-+5M 7HA3+US ?3 and HA3+US *3 ST4.M538' v *"0*' including soft%are and D3F reports'nternational =round%ater Modeling Center (=9MC)' Colorado School of Mines' Mines' Colorado' andUS Salinity Paoratory' US34' +iversides' California' *00?

Coles' C" 4"' and Aong' +" ."' *00Use of e#uilirium and initial metal concentrations in determining Freundlich isotherms for soils andsediments' Gngineering =eology' :/2?>-*/"

3aniel C" 9"Tsang' 9" Xhang and " M" C" Po' *00@Modeling cadmium transport in soils using se#uential e&traction' atch' and miscile displacemente&periments" Soil Sci" Soc" 4m' \" ?@?2 @,-:?

3avidson \" M' D" S" C" +ao' P" T"' 5u' 9" B" 9heeler' and 3" F" +oth%ell' ?>:0

4dsorption' movement' and iological degradation of large concentrations of selected pesticides in soils"GD4 +eport .o" 001*-:0-?*,' ??? p

3elegard C" H"' and =" S" Barney" ?>: *ffects of anford igh-+evel aste ompounds on orption of obalt, trontium, .eptunium, /lutonium,

and 0mericium of anford ediments$ +H5-+G-ST-? D' +oc$%ell Hanford 5perations' +ichland'9ashington

=ao ="' Feng Sh' Hongin Xhan H' Huang =" and ^" Mao" *00>Gvaluation of 4nomalous Solute Transport in a Parge Heterogeneous Soil Column %ith Moile-mmoileModel" \" Hydrologic Gngineering' 4SCG' >->@, - 352 ?0"?0?1(4SCG) HG"?>,-//:,"00000@?

\enne G" 4" ?>@@7Trace Glement Sorption y Sediments and Soils - Sites and Drocesses"8 n ymposium on olybdenum in

the *nvironment ' 9" Chappel and K" Detersen (eds")' pp" ,*/-//' M" 3e$$er' nc"' .e% Aor$' .e% Aor$ Huang K"' ." Toride' and M" TH" van =enuchten' ?>>/

G&perimental nvestigation of Solute Transport in Parge' Homogeneous and Heterogeneous' Saturated SoilColumns" Transport in Dorous Media ?:2 *:-0*

Hussein M" F" *00>BTC Solute-Transport Darameters for Three Sediments' in2 ,th Conference on +ecent Technologies in4griculture' *00>' Cairo Univ"' Fac" of 4gric' ,*?-,*

Kaplan 3" "' D" M" Bertsch' 3" C" 4driano' and K" 4" 5rlandini" ?>>,a74ctinide 4ssociation %ith =round%ater Colloids in a Coastal Dlain 4#uifer"8 adiochimica 0cta,

1@2?:?-?:@Kaplan' 3" "' and +" \" Serne" ?>>/

%istribution oefficient 3alues %escribing 4odine, .eptunium, elenium, Technetium, and 5ranium

orption to anford ediments" D.P-?0@>' Supplement ?' Dacific .orth%est Paoratory' +ichland'9ashington

Macintyre 9" ="' T" B" Stauffer' and C" D" 4nt%orth' ?>>?4 Comparison of Sorption Coefficients 3etermined y Batch' Column' and Bo& Methods on a Po% 5rganicCaron 4#uifer Material" =round 9ater' *>2 ' >0:->?

10

http://www.academicjournals.org/IJPS






.$edi-Ki!!a D"' ?>@>on e&change in aggregated porous media during miscile emplacement' Dh" 3" dissertation' 3ep" of Pand'4ir' and 9ater +esour"' Univ" of Calif"' 3avis

.$edi-Ki!!a D"' \" 9" Biggar' M" Th" van =enuchten' D" \" 9ierenga' H" M" Selim' \" M" 3avidson' and 3" +" .ielsen' ?>:Modeling tritium and chloride transport through an aggregated 5&isol' ater esour$ es$, 1!, >?-@00

Dage 4" l"' ?>:*Methods of Soil 4nalysis' part 2 Chemical and Microiological Droperties' *nd ed" 4rgon' 9isconson' US4Dorro " and D" \" 9ierenga' ?>>

Transient and steady-state solute transport through a large unsaturated soil column' =round 9ater' ?2 *'?>-*00

afo$u' ." D"' and M" G" Sumner' *00*4dsorption and desorption of indifferent ions in variale charge susoils2 The possile effect of particleinteractions on the counter-ion charge density" Soil Sci" Soc" 4m" \" 2?*?Q?*>"

afo$u' ." D"' and M" G" Sumner" *00?+etention and transport of calcium nitrate in variale charge susoils" Soil Sci" ?2*>@Q0@"

ualls' +' and Haines B"' ?>>*Measuring adsorption isotherms using continuous' unsaturated flo% through intact soil cores" Soil Sci" Soc"4m" \" /2,/-,0"

Selim H"M"' M"C" 4macher and "K" s$andar ?>>0Modeling the transport of heavy metals in Soils' *+ onograph 0d 6 0 22! 2!7, %T4, 5 0rmy

orps of *ngineers, old egions esearch and *ngineering +aboratory (*+#,18" p;im<ne$ \"' van =enuchten M"Th" and ;ejna M" *00:

3evelopment and applications of the HA3+US and ST4.M53 soft%are pac$ages' and related codes"Eadose Xone \" @ (Special ssue 7Eadose Xone Modeling8)2 /:@Q00

;im<ne$ \" and van =enuchten M"Th" *00:Modeling none#uilirium flo% and transport %ith HA3+US" Eadose Xone \" @ (Special ssue 7Eadose XoneModeling8)2 @:*Q@>@

;im<ne$ \"' \ac#ues 3"' T%ara$avi ." K" C"' and van =enuchten M" Th"' *00>Selected HA3+US modules for modeling susurface flo% and contaminant transport as influenced y

iological processes at various scales' Biologia ,12 ,/-,>Siyal 4" 4"' T"H" S$aggs and M"Th" van =enuchten' *0?0

+eclamation of Saline Soils y Dartial Donding2 Simulations for 3ifferent Soils" Eadose Xone \"' >2 ,:-,>/van =enuchten' M" Th"' and D" \" 9ierenga' ?>@

Mass transfer studies in soring porous media" 2 4nalytical solutions" Soil Sci" Soc" 4m" \"' ,0,' ,@Q,:0van =enuchten M" Th" and D" \" 9ierenga' ?>:

Solute 3ispersion coefficients and retardation factors" n2 Methods of Soil 4nalysis' Dart ?' Dhysical andMineralogical Methods-4gronomy Monograph no" > (*nd Gdition)' ?0*/-?0/,' 4merican Society of4gronomy-Soil Science Society of 4merica"

van =enuchten M" Th"' ?>:?3etermining Transport Darameters from Solute Miscile G&periments" US34' US Salinity Pa' +esearch"+eport .o" ??:' @ p

van =enuchten M" Th"' ?>:? .on-e#uilirium Transport Darameters from Miscile 3isplacement G&periments" US34' US Salinity Pa'+esearch" +eport .o" ??>' :: p

Een$ata S" M"' +ama$rishina M"' Shailaja S"' and D"." Sarma' *00@nfluence of soilQ%ater ratio on the performance of slurry phase ioreactor treating hericide contaminatedsoil" Bioresource Technology >: (*00@) */:,Q*/:>" doi2?0"?0?1j"iortech"*00"0>"0?:

9ang B"' \" Menggui \' \ohn +" .immo \" +"' Aang P" and 9ang 9"' *00:Gstimating ground%ater recharge in Heei Dlain' China under varying land use practices using tritium and

romide tracers" \" of Hydrology /' *0>Q ***http211%%%"ars"usda"gov1services1soft%are1do%nload"htmJsoft%areVtrueWmodecodeV,-,/-00-00http://www.epa.gov/radiation/docs/kdreport/vol1/402r99004a.pd!

http211%hat-%hen-ho%"com1nanoscience-and-nanotechnology1mineral-nanoparticles-electro$inetics- part-*-nanotechnology1

11


http://www.epa.gov/radiation/docs/kdreport/vol1/402-r-99-004a.pdf









Appendix

There are several methods to estimate the value of the k d parameter throughe&periments' ?) laoratory atch' *) in-situ atch') laoratory flo%-through (BTC) method',) field modeling' and /) k oc method' %ith the k d parameter included in the retardation factor'

+' http://www.epa.gov/radiation/docs/kdreport/vol1/402r99004a.pd! "+ V (?)

+ retardation factor' dimensionless (V pore-%ater velocity1solute velocity)k d distriution coefficient' m solution1$g soil ρ soil dry ul$ density' $g1m θ saturated ul$ moisture content' under saturated flo%' dimensionless fraction

For nonlinear e#uilirium adsorption' the Freundlich isotherm' S V Kf C.' and theHashimoto derivative' k dZH V ∂S1∂C' are used and + is e&pressed as + V ? L ( ρ 1θ) K f .C.-?"Freundlich turns into a linear isotherm %ith k d V K f only if . V ?

9hen k d V 0' (i"e" + V ?' G#" ?' this means that there is no reaction of the solute %ith the

sediment" High k d value' on the contrary' indicates high adsorption on the solid-phase" Gach porous-media and every given set of solution concentration imposes a particular value for k d parameter for the studied system" That is %hy detailed study should e conducted for eachcase" n fact' k d values that may e pic$ed from the literature can e misleading if generali!edto other sites1conditions" The values for k d do not only vary et%een solutes ut it %ill alsovary in function of the chemistry of the used a#ueous solution and the present solid-phases(3elegard and Barney' ?>:' Kaplan et al$, ?>>,a' and Kaplan and Serne' ?>>/)"

The assumptions associated %ith the thermodynamically-defined k d in the empiricallinear e#uilirium adsorption relationship are mostly violated in the computer codes used toestimate k d value http://www.epa.gov/radiation/docs/kdreport/vol1/402r99

004a.pd! "' i"e" the small difference et%een the 7thermodynamic k d parameter as derived

from ion-e&change8' and the 7empirical k d as used in solute transport codes8' is omitted inthese codes" Moreover' this reference indicates that a 7conditional k d8 (\enne' ?>@@) is used toidentify e&perimentally-derived distriution coefficient as a ratio et%een the adsored to thedissolved species' %ith the difference et%een the 7true thermodynamic k d8' and the7conditional k d8 also omitted' and the effect of pH and ionic strength change' duringe&perimental %or$' is dropped out' %hereas the so-called 7parametric k d8 and the7mechanistic k d8 are sparingly used in models since they need detailed information that iscostly or very comple& to otain and difficult to e installed in solute-transport models"

Declet numer' D' is a scale-dependent dimensionless e&pression of the ratio of thetransport y the relatively rapid convection (the mass-flo% y inertial forces %ith %ater inmacro-pores et%een large-si!e particles and et%een aggregates) to the transport ta$ing

place y the relatively slo% diffusion phenomenon (in micro-pores et%een fine-grained particles and inside fine aggregates)" 9hen diffusion is negligile (i"e" there is onlymechanical dispersion)' D %ill solely depend on the soil material' not the tracer"

Parge D values indicate supremacy of convection (product of average pore-%atervelocity' ν &' and column length' P) over effective hydrodynamic dispersion coefficient' 3P'%hich includes molecular diffusion and controlled y tortuosity (CFTM and CFTM codes'ig%mc' *00?' and van =enuchten and 9ierenga' ?>:)" The dominance of convection may

e seen y getting small values for longitudinal dispersivity (a scale-dependant length parameter that e&presses soil non-homogeneity %hich is referred to y the symol λ in thefour-parameter models or y the symol α in t%o-parameter models) since D _ P1α"

Dractically' the large D value means high moility from soil to ground%ater . Po% D values(i"e" high α values)' on the contrary' indicate dominance of solute transport y slo% diffusion

12









and reflect strong heterogeneity of solid-phase particle-si!es and arrangement (aggregation)on the microscopic level (Hussein' *00>)"

The parameter ω (dimensionless) is a rate constant $no%n as mass-transfer coefficientof solute e&change et%een the moile and immoile regions" t is e&pressed y dividing thehydrodynamic %ater residence-time' P1# ' hr' (3am$ohler numer) y the characteristic

time' hr' of e&change (?1α)" 5ther%ise' ω is otained y multiplying 3am$ohler numer ythe first-order $inetic rate coefficient' α' hr -?" The parameter β is instantaneous retardation'dimensionless' that has several e&pressions according to the appropriate su-model in use(van =enuchten' report .o ??> (?>:?' in his Tale ' p )"

Solute-transport phenomenon is ideali!ed through several conceptual models" Thesemodels may solve the second-order partial differential C3G e#uation y operational codesthat descrie solute transport %ith ion e&change or adsorption (%here adsorption includes ione&change) in a uni#ue moile %ater region (CfitM code) or may solve the C3G for moileand immoile %ater regions (CfitM code)" These codes are processed' under selected initialand oundary conditions' to yield specific analytical solution (that corresponds to a given

e&perimental run)" The values found y CfitM' or CfitM' for the uilt-in parameters may esuse#uently used in numerical simulation models for solving more elaorate prolems"The effective longitudinal hydrodynamic dispersion coefficient' 3P' (cm* hr -?) is uilt in

the Declet numer' D' (G#" *)" t is clear' in this e#uation' that short columns and fine-grainedsoil materials %ill produce small D values' and vice versa'D V V _ (*)

3P V ()

3P V (,)

3P _ λ ν & (/)

λ _ ()

%hereP V convective mass-flo% ν & P/hydrodynamic-dispersion coefficient ' 3P' dimensionless x mean effective pore-%ater velocity' cm1hour L column length' cm the product (ν & P) represents the advective solute-transportDL effective longitudinal hydrodynamic-dispersion coefficient' cm*1hour D molecular diffusion coefficient' cm*1hour (may e dropped since negligily small)d!" particle-si!e' cm' that is ?0R finer y %eight in semi-log cumulative dry-sieving plot# 3arcy velocity' cm1hour θ Bul$ moisture content' dimensionless fraction longitudinal dispersivity' cm (α in models %here all %ater is considered as moile)

The application of different analytical su-models' corresponding to different oundary

conditions' %ill produce some%hat different values for + and D (van =enuchten' ?>:?'+eport .o ??:) and this %ill result in some deviation of the otained values for 3 and k d

parameters" These deviations could e minimi!ed y using longer columns (0 to /0 cmlong)"

The convection-dispersion solute-transport process ta$ing place during ?-3 steady-state%ater flo% is e&pressed y a second-order partial differential e#uation (C3G) $no%n asFic$s *nd order la% (van =enuchten M" Th"' ?>:?' +eports .o" ??: and ??>)'

V (@)

9hen solute 7decay8 is also considered' a 7sin$-term8' $' is introduced to e&presschemical and1or iological 7$inetic reactions8 responsile for that 7decay8 (G#" :a to :e)"

V (:a)

This formula is used for reactive and non-reactive solute transport in the CfitM code"5ther forms of that e#uation may e reported as follo%ing'

13



V (:)

V (:c)

V (:d)

V (:e)

These forms are otained y manipulation of the retardation factor' +' formula'

+ V ? L ρ k d1θ + V ? L ρ (S1CP)1θ (+-?) V (S1CP) ρ 1θ ρ 1 θ V (+-?) (CP1S)%hereθ ul$ soil-moisture' dimensionless fraction ρ ul$ density' $ g m-9

CP solute concentration in solution' ppm' i"e" mg l -1

3P effective hydrodynamic-dispersion coefficient' cm2 :hour 't includes the (3[) term (the effective molecular diffusion coefficient' cm2 :hour )

! depth' negative do%n%ard' cm

# 3arcy velocity (flu&)' negative do%n%ard' cm:hour ν pore-%ater velocity' cm:hour

S adsored solute' g solute :kg soil

(S V K f C . in Freundlich isotherm , with K f capacity coefficient and . sorption intensity e&ponent)k or k d distriution coefficient' m9 soluion:kg soil (with k d ; . : P $ i$e$ k d ; K f V S1CP if . V? #P column length' cm

The *-parameter code CfitM code is used for transport of non-reactive and reactivesolutes assuming that all soil moisture content is moile' and all adsorption sites are freelyaccessile" Ho%ever' the ,-parameter MM codes (e"g" CfitM) %ere introduced (.$edi-Ki!!a' ?>@> and .$edi-Ki!!a' et al' ?>:) to consider more realistic prolems %ith moileand immoile soil moisture %here soil moisture is sudivided into `moile` (macro-porosity)and `immoile` (micro-porosity) %ater regions" Transport ta$es place y convection anddispersion mainly in the moile region %hereas in the immoile region it is presumed eingdiffusion-controlled (proportional to concentration differences et%een the t%o regions)" =aoet al' (*00>) stated that MM codes consist of a conventional C3G for solute transport in themoile region coupled %ith a term' ω' (G# >) descriing solute mass-transfer et%een themoile and the immoile regions %ith (G# ?0) e&pressing solute transfer flu& as proportionalto concentration difference et%een these t%o regions" The one-dimensional CfitM code forreactive solute transport (van =enuchten and 9ierenga ?>@' and van =enuchten' ?>:?'report no ??>) is e&pressed y G#" > and G#" ?0 (%ith . V ?)" G#" > is a reduced form of G#"?* in van =enuchten and 9ierenga (?>@) and it is the same as G#" */ in van =enuchten(?>:?) report .o ??>' page ?/" G#uations from G#" ?? to G#" *? sho% detailed terms and

parameters used in CfitM code"V (>)

V V (?0)# V ν m θ m (??)ν m V (?*)φm V (?)θ V θ m L θ im (?,)D V V (?/)ω V V (?)α V (?@)+ m V (?:)+ im V (?>)

+ V (*0)β 3imensionless variale V (*?)

14



S V f Sm L (? -f) Sim (**)%here# 3arcy velocity' cm:hour

ν m pore-%ater velocity in the moile %ater region' cm:hour

φm ratio of moile moisture' θm' to total moisture' θω mass-transfer coefficient of solute e&change et%een the moile and immoile regions e&pressed as a

rate constant' dimensionless

α first-order $inetic rate coefficient for solute e&change et%een the moile and immoile regions' hour -1

β dimensionless variale that has several e&pressions' Tale ' van =enuchten (?>:?)' page S total adsorption' g:kg soil

θ m moile moisture' dimensionless fractionθ im immoile moisture' dimensionless fractionf adsorption sites availale to moile moisture' e&pressed as mass fraction of solid-phase

The dimensionless form of G#s > and ?0 sho%ing the important parameters +' D' β and ω' areV (*)

V (*,)

The follo%ing dimensionless variales are used in the physical non-e#uilirium su-model(model B) in CfitM code (%ith T is pore-volume)"' ' '

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Pist of Figure Captions

%ig& "& The sandy loam sampling location' at 74l Kharj8 city' at some /0 $m to the southeast of +iyadh' theCapital of Saudi 4raia

%ig& !& S$etch sho%ing that lo% $ d value means lo%er adsorption (less retardation and higher ris$ to contaminateground%ater)" Source2 http://www.epa.gov/radiation/docs/kdreport/vol1/402r99004a.pd!

%ig& '& Conceptual physical none#uilirium models for %ater flo% and solute transport" mo and im in () and(c) V %ater content of moile and immoile regions M and F in (d) V %ater content of micro and macro-poreregions' M'mo' M'im' and F in (e) V %ater content of moile and immoile regions c V conc" ofcorresponding regions" S V total solute content of li#uid phase" Source2 Fig ? in ;im<ne$ and van =enuchten'*00: and Fig *"? in http211ig%mc"mines"edu1soft%are1ig%mcsoft1HA3+US?3Z,"pdf

%ig& (& Conceptual chemical none#uilirium models for reactive solute transport" mo and im in (d) V %atercontent of moile and immoile regions M and F in (e) V %ater content of micro and macro-pores c V conc" ofcorresponding regions' Se V adsored conc" in e#uilirium %ith li#uid concentration of corresponding region'and S$ V $inetically adsored solute conc" of corresponding region" Source2 Fig" " in ;im<ne$ and van=enuchten' *00: and Fig" "? in http211ig%mc"mines"edu1soft%are1ig%mcsoft1HA3+US?3Z,"pdf

%ig& )& 4" G&perimental setup %ith do%n%ard flo%" B" Setting for up%ard flo% from literaturehttp211%%%"epa"gov1radiation1docs1$dreport1vol?1,0*-r->>-00,a"pdf

%ig& *& .ormal and log-log atch oservations and Freundlich-Pangmuir isotherms for three Cd concentrations"

%ig& +& 4" Freundlich Cd-retention isotherms (Selim et al' ?>>0' figure *-?' page ??) for different soils" B"Superimposition of our log-log Fig /B on references figure" 5ur data points (et%een t%o old rang lines) havelo%er slope than most slopes in references figure proaly ecause of coarser te&ture of our sediment"

%ig& ,& 4" Three CfitM curves for three BTC runs %ith three concentrations (,">' *?": and ,0",: ppm) on thesame sandy loam sediment" B" The relationship of the +' k d and D parameters %ith the concentration of theinflo% solution" The values of the + and k d parameters otained from (CfitM) code sho% their largest values forthe most dilute solution (,"> ppm) indicating the highest adsorption for the most dilute inflo% solution"

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http://igwmc.mines.edu/software/igwmcsoft/HYDRUS1D_4.pdf









Documents

A1_BTC Geodyna_3_TEXT_with Appendix and comma as English System Separator.doc