Volume 1: Distribution and Recovery of Petroleum Hydrocarbon Liquids in Porous Media

Transcription

1 LNAPL Distibutio ad Recovey Model (LDRM) Volume 1: Distibutio ad Recovey of Petoleum Hydocabo Liquids i Poous Media Regulatoy ad Scietific Affais Depatmet API PUBLICATION 4760 JANUARY Satuatio, Relative Pemeability, ad Mobility Ratio Satuatio Elevatio [ft] Wate Relative Pemeability Mobility Ratio Elevatio (m) S (vg ) Wate Table h d[a] h d[w] h b

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3 LNAPL Distibutio ad Recovey Model (LDRM) Volume 1: Distibutio ad Recovey of Petoleum Hydocabo Liquids i Poous Media Regulatoy ad Scietific Affais Depatmet API PUBLICATION 4760 JANUARY 007 Pepaed by: Radall Chabeeau, Ph.D., P.E. The Uivesity of Texas at Austi Austi, Texas

4 SPECIAL NOTES API publicatios ecessaily addess poblems of a geeal atue. With espect to paticula cicumstaces, local, state, ad fedeal laws ad egulatios should be eviewed. Neithe API o ay of API's employees, subcotactos, cosultats, committees, o othe assigees make ay waaty o epesetatio, eithe expess o implied, with espect to the accuacy, completeess, o usefuless of the ifomatio cotaied heei, o assume ay liability o esposibility fo ay use, o the esults of such use, of ay ifomatio o pocess disclosed i this publicatio. Neithe API o ay of API's employees, subcotactos, cosultats, o othe assigees epeset that use of this publicatio would ot ifige upo pivately owed ights. API publicatios may be used by ayoe desiig to do so. Evey effot has bee made by the Istitute to assue the accuacy ad eliability of the data cotaied i them; howeve, the Istitute makes o epesetatio, waaty, o guaatee i coectio with this publicatio ad heeby expessly disclaims ay liability o esposibility fo loss o damage esultig fom its use o fo the violatio of ay authoities havig juisdictio with which this publicatio may coflict. API publicatios ae published to facilitate the boad availability of pove, soud egieeig ad opeatig pactices. These publicatios ae ot iteded to obviate the eed fo applyig soud egieeig judgmet egadig whe ad whee these publicatios should be utilized. The fomulatio ad publicatio of API publicatios is ot iteded i ay way to ihibit ayoe fom usig ay othe pactices. Ay maufactue makig equipmet o mateials i cofomace with the makig equiemets of a API stadad is solely esposible fo complyig with all the applicable equiemets of that stadad. API does ot epeset, waat, o guaatee that such poducts do i fact cofom to the applicable API stadad. All ights eseved. No pat of this wok may be epoduced, stoed i a etieval system, o tasmitted by ay meas, electoic, mechaical, photocopyig, ecodig, o othewise, without pio witte pemissio fom the publishe. Cotact the Publishe, API Publishig Sevices, 10 L Steet, N.W., Washigto, D.C Copyight 007 Ameica Petoleum Istitute

5 FOREWORD Nothig cotaied i ay API publicatio is to be costued as gatig ay ight, by implicatio o othewise, fo the maufactue, sale, o use of ay method, appaatus, o poduct coveed by lettes patet. Neithe should aythig cotaied i the publicatio be costued as isuig ayoe agaist liability fo ifigemet of lettes patet. Suggested evisios ae ivited ad should be submitted to the Diecto of Regulatoy ad Scietific Affais, API, 10 L Steet, NW, Washigto, D.C iii

6 PREFACE This mauscipt (Volume 1) povides backgoud ifomatio suppotig fomulatio of the Ameica Petoleum Istitute LNAPL Distibutio ad Recovey Model (LDRM), ad is peseted as a supplemet to API Publicatio Numbe 468, Fee-Poduct Recovey of Petoleum Hydocabo Liquids, which was published i Jue 1999, ad to API Publicatio Numbe 479, Models fo Desig of Fee-Poduct Recovey Systems fo Petoleum Hydocabo Liquids; A Use s Guide ad Model Documetatio, which was published i August 003 ad icluded i the API Iteactive LNAPL Guide, Vesio.0. Model sceaios ae descibed fo fee-poduct hydocabo liquid ecovey usig siglead dual-pump well systems, skimme wells, vacuum-ehaced well systems, ad teches. Ifomatio o LNAPL distibutio i poous media ad possible LNAPL movemet is discussed, ad the basic modelig equatios ae povided. Use of the LDRM softwae to compute LNAPL ecovey ates, volumes ad times is discussed, ad example applicatios ae povided i a compaio documet (Volume ), which also documets model testig ad evaluatio. The API LDRM softwae ca be dowloaded fom API's website at: goudwate.api.og/lapl. iv

7 TABLE OF CONTENTS Sectio Page 1 INTRODUCTION Backgoud ad Objectives Sceaios fo Fee-Poduct Hydocabo Liquid Recovey Sceaios fo Recovey Well Systems 1.. Sceaio fo LNAPL Recovey Usig Teches Oveview. 4 LNAPL DISTRIBUTION Capillaity i Poous Media Suface Tesio, Wettability ad Capillay Pessue Capillay Pessue Cuves Residual LNAPL Satuatio Speadig Coefficiets Leveett Assumptios. 11. Capillay Pessue Cuve Models Fittig Models to Capillay Pessue Cuve Data Poe-Size Distibutio Cuves Capillay Scalig Relatioships.15.3 Foces i Multiphase Fluid Systems LNAPL Distibutio ad Moitoig Wells Fluid Levels i Moitoig Wells Distibutio of Capillay Pessue LNAPL Satuatio Distibutios Iitial LNAPL Satuatio Values ad Residual LNAPL Satuatio LNAPL Capillay Rise..4.6 Calculatio of LNAPL Satuatio Distibutio fom Moitoig-Well LNAPL Thickess Fee-LNAPL ad Recoveable-LNAPL Specific Volume LNAPL MOVEMENT LNAPL Movemet ad Dacy s Law Dacy s Law NAPL Relative Pemeability: Budie ad Mualem Equatios Compaiso of Relative Pemeability Models LNAPL Vetical Migatio though Fie-Gai Soil Effect of Vetical Gadiets o LNAPL Satuatio Citical Dowwad Hydaulic Gadiet LNAPL Lateal Migatio ad Liquid Fee-Poduct Recovey Lateal Migatio of LNAPL to Pistie Soils LNAPL Mobility Ratio LNAPL-Laye Volume Flux Vacuum-Ehaced Recovey 41 v

8 3.3.5 LNAPL Recovey Usig Skimme Wells Recovey of LNAPL fom Beeath Fie-Gai Zoes Usig Skimme Wells LNAPL Recovey Usig Teches LNAPL CONTINUITY Cotiuity Equatios fo Regios of Captue Model Paameteizatio ad Itegatio REFERENCES...51 vi

9 LIST OF FIGURES Figue Page 1.1 Moitoig well LNAPL thickess, b.. 1. Recovey well system with 7 ecovey wells showig the adius of captue Simple Tech System fo LNAPL Recovey Itefacial eegy associated with molecula attactio i the liquid phase..5. Cotact agle ad wettability Soil capillay pessue cuve showig pimay daiage, imbibitio, ad scaig chaacteistic cuves LNAPL esidual satuatio ude omal field coditios 8.5 LNAPL esidual satuatio iceases with iitial LNAPL satuatio (afte Kuepe et al, 1993) LNAPL esidual satuatio depeds o iitial LNAPL satuatio (fom Johsto ad Adamski, 005) LNAPL dop located o a ai-wate iteface 10.8 Measued capillay pessue cuve Fitted capillay pessue cuve models (a) Budie ad (b) Mualem elatios Poe size distibutio cuves (a) fie-gai soil ad (b) fie sad soil Distibutio of fluid satuatio amog vaious poe sizes Fluid elevatios withi a LNAPL moitoig well Capillay pessue distibutio ea the wate table, icludig the capillay fige Capillay pessue distibutio i the pesece of LNAPL Calculated wate ad LNAPL satuatio distibutios based o two diffeet LNAPL-thickess values 4.16 LNAPL specific volume ad ecoveable volume cuves Two-phase NAPL elative pemeability fo Budie ad Mualem models LNAPL distibutio showig effect of vetical hydaulic gadiet Wate satuatio cuves pedicted by vg ad BC models LNAPL satuatio distibutio pedicted usig the Books ad Coey capillay pessue model with b > b [cit] Limitig LNAPL satuatio distibutio (oe) pedicted usig the Books ad Coey capillay pessue model with b > b [cit] LNAPL/wate mobility atio LNAPL ad goudwate flow to a well Ai flow to a vacuum-ehaced ecovey well with leakage fom the atmosphee acoss the shallow vadose zoe LNAPL ecovey usig a skimme well LNAPL tapped beeath FGZ ad skimme-well ecovey Radius of captue based o cotiuity fo the six wells o the left, ad based o adius of ifluece fo a sigle well o ight side of figue. 47 vii

10 LIST OF SYMBOLS A c A j aea extet of egio of captue fo well o tech pefomace coefficiet i LNAPL ecovey models b aquife thickess b a sceeed iteval fo ai flow above the wate table b moitoig well LNAPL thickess b W LNAPL thickess i well, costaied by fie-gai-zoe b w depth beeath the wate table of goudwate flow to a well o tech d mea gai-size diamete D LNAPL specific volume f a mass flux of ai i adial diectio f az mass flux of ai i vetical diectio f esidual LNAPL f-facto (factio of iitial LNAPL satuatio) f s esidual LNAPL f-facto (satuated zoe) f v esidual LNAPL f-facto (vadose zoe) g gavitatioal costat h fluid head h c capillay pessue head h d displacemet pessue head (ai-wate) h d[a] ai-lnapl displacemet pessue head h d[w] LNAPL-wate displacemet pessue head h [a] ai-lnapl capillay pessue head (equivalet wate head) h [w] LNAPL-wate capillay pessue head (equivalet wate head) J a ai-phase hydaulic gadiet J LNAPL hydaulic gadiet J w wate hydaulic gadiet J wz vetical wate hydaulic gadiet (positive upwad) k itisic pemeability K LNAPL hydaulic coductivity K s LNAPL satuated hydaulic coductivity k a ai elative pemeability k LNAPL elative pemeability K ws wate satuated hydaulic coductivity k w wate elative pemeability kˆ upwad uit vecto L T legth of LNAPL ecovey tech M va Geuchte M paamete m [w] LNAPL-wate mobility atio (= k /(k w μ )) m& a mass ate of flow of ai i adial diectio poosity N va Geuchte N paamete p fluid pessue p a ai pessue capillay pessue p c viii

11 p c[a] p c[w] p ai-lnapl capillay pessue LNAPL-wate capillay pessue LNAPL pessue p C LNAPL pessue at adius of captue (R C ) p W LNAPL pessue at adius of well (R W ) p w wate pessue p wi wate pessue at adius of ifluece (R I ) p ww wate pessue at adius of well (R W ) p( c ) factio of poes of size c q LNAPL volume flux (Dacy velocity) Q LNAPL dischage q z LNAPL vetical volume flux (positive upwad) q w wate volume flux (Dacy velocity) Q w wate dischage R c adius of captue R LNAPL ecoveable volume mea adius of cuvatue of iteface betwee fluid phases S e effective (educed) satuatio S e[t] effective total liquid satuatio S e[w] effective wate satuatio S LNAPL satuatio S i iitial LNAPL satuatio S LNAPL esidual satuatio S NW o-wettig phase esidual satuatio S /aw speadig coefficiet fo LNAPL acoss ai-wate iteface S w wate satuatio S W wettig phase satuatio S wi iitial wate satuatio S w ieducible wate satuatio S W wettig phase esidual satuatio T LNAPL-laye tasmissibility U LNAPL uit flux U w wate uit flux W T width of LNAPL les extedig away fom the ecovey tech z elevatio z a ai-lnapl iteface elevatio i moitoig well z aw wate table elevatio z FGZ elevatio of facies iteface with fie-gai-zoe z gs goud suface elevatio z max maximum elevatio of fee LNAPL (due to capillay ise) z w LNAPL-wate iteface elevatio i moitoig well z efeece elevatio z wt elevatio of wate table z 1 elevatio of iteface betwee soil layes 1 ad z 3 elevatio of iteface betwee soil layes ad 3 ix

12 α α a α [a] α w α [w] β η θ c λ μ μ a μ va Geuchte α paamete vg-α ai-lnapl scalig elatioship fo itefacial tesio plus buoyacy vg-α ai-lnapl scalig elatioship fo itefacial tesio vg-α LNAPL-wate scalig elatioship fo itefacial tesio plus buoyacy vg-α LNAPL-wate scalig elatioship fo itefacial tesio ecoveable volume slope paamete LNAPL tasmissibility slope paamete cotact agle Books ad Coey poe size distibutio idex dyamic viscosity ai dyamic viscosity LNAPL dyamic viscosity μ LNAPL-wate viscosity atio (μ = μ /μ w ) μ w wate dyamic viscosity ξ LNAPL tasmissibility itecept paamete ai desity ρ a ρ LNAPL desity ρ LNAPL-wate desity atio (ρ = ρ /ρ w ) wate desity ρ w σ a σ aw σ w χ ai-lnapl suface tesio ai-wate suface tesio LNAPL-wate itefacial tesio ecoveable volume itecept paamete x

13 EXECUTIVE SUMMARY This documet povides backgoud ifomatio ecessay to chaacteize the behavio of LNAPL i poous media with egad to pefomace of LNAPL liquid ecovey techologies. The scope of ifomatio is selected to suppot model assumptios ad developmet fo the API LNAPL Distibutio ad Recovey Model (LDRM) which simulates the pefomace of pove hydaulic techologies fo ecoveig fee-poduct petoleum liquid eleases to goudwate. This mauscipt (Volume 1) ad its compaio mauscipt (Volume ) supplemet API Publicatio Numbe 468 ad 479, ad documet the LDRM softwae models fo desig ad aalysis of liquid fee-poduct ecovey systems usig sigle- ad dual-pump wells, vacuum-ehaced wells, skimme wells, ad teches. The sceaio-based models fo ecovey wells ad teches ae descibed i Sectio 1. Sectio povides ecessay backgoud ifomatio fo chaacteizig the vetical distibutio of LNAPL located ea the wate table ude coditios of vetical equilibium. Capillaity, capillay pessue cuves, ad LNAPL esidual satuatio ae discussed. The capillay pessue cuve model peseted by va Geuchte is peseted, alog with scalig elatioships that allow the model epesetatio to be applied with diffeet multiphase fluid systems. Hubbet s elatioships fo foces i multiphase fluid systems ae peseted. These ae impotat i udestadig how wate-ehaced ad vacuum-ehaced ecovey systems ceate hydaulic gadiet withi the LNAPL phase causig its movemet to a well o tech. The elatioship betwee LNAPL thickess i a moitoig well ad fluid pessue ad capillay pessue withi a fomatio is discussed i some detail. This elatioship, whe combied with a capillay pessue cuve model, allow oe to estimate LNAPL accumulatios withi the poous medium fom moitoig well thickess measuemets. Sigificat paametes ae idetified. Calculatio of LNAPL specific volume ad LNAPL ecoveable volume as a fuctio of LNAPL thickess i a well is discussed. Sectio 3 coces possible LNAPL movemet. Dacy s law is peseted fo LNAPL flow, ad the Budie ad Mualem LNAPL elative pemeability models ae discussed. The effect of vetical hydaulic gadiet i fie-gai soil o LNAPL satuatio is descibed, ad the citical vetical gadiet at which LNAPL is displaced to accumulate beeath fiegai soil is idetified. Potetial lateal migatio of LNAPL is discussed. Fo lateal migatio ito pistie soils, capillay pessue cuve models that iclude a fiite displacemet pessue should be used, ad it is show that LNAPL plumes ae stable towads lateal speadig (a LNAPL plume will stop speadig eve though LNAPL has a positive head). The vetical distibutio of LNAPL mobility atio is examied to show LNAPL is much moe mobile i the uppe pat of the capillay fige tha goudwate. The LNAPL-laye tasmissibility is itoduced to calculate the LNAPL-laye volume flux. The lateal flow equatios fo LNAPL to wells ad teches ae developed fo wateehaced ad vacuum-ehaced systems, ad fo skimme wells. Sectio 4 shows how the cotiuity piciple applied with egios of captue ca be used, whe combied with the LNAPL ecoveable volume ad tasmissibility fuctios, to pedict pefomace of LNAPL liquid ecovey systems. Model paameteizatio ad itegatio ae discussed, ad the basic equatios of LDRM ae peseted. xi

14 1 INTRODUCTION 1.1 BACKGROUND AND OBJECTIVES The Ameica Petoleum Istitute (API) Publicatio Numbe 468, Fee-Poduct Recovey of Petoleum Hydocabo Liquids (Chabeeau et al., 1999), povides a oveview of ecovey techologies fo petoleum hydocabo liquids that ae eleased to the subsuface eviomet ad accumulate ea the wate table. The pimay ecovey techologies iclude skimme wells that poduce hydocabo liquids ad sigle- ad dual-pump wells that poduce both wate ad hydocabo liquids. Hydocabo liquid ecovey ates may also be ehaced by applyig a vacuum pessue to the well to icease the gadiet towads the well withi the hydocabo laye. API 468 descibes two (Excel speadsheet) models that may be used to chaacteize the subsuface distibutio of liquid hydocabo (lighte-tha-wate oaqueous phase liquids, LNAPL) i a sigle homogeous soil laye ad to calculate the potetial ecovey ate ad time usig sigle- ad dual-pump wells, ad vacuum-ehaced wells. API Publicatio Numbe 479, Models fo Desig of Fee-Poduct Recovey Systems fo Petoleum Hydocabo Liquids (Chabeeau, 003) descibes sceaio-based models fo LNAPL liquid ecovey usig skimme wells, wate ad vacuum ehaced ecovey wells, ad teches. Soil capillay pessue chaacteistics ae descibed usig the va Geuchte (1980) capillay pessue model (soil chaacteistics ad LNAPL distibutio ae descibed i API 468 usig the Books ad Coey (1964) capillay pessue model). Implemetatio of the models though use of fou sepaate speadsheets is peseted, based o sigle o two-laye heteogeeity, ad o selectio of elative pemeability model (Budie, 1953, o Mualem, 1976). The peset documetatio suppots elease of the LNAPL Distibutio ad Recovey Model (LDRM) by API which supesedes API 468 ad API 479 though developmet of a moe geeal modelig famewok with up to thee soil layes. The objective of the peset mauscipt (Volume 1) is to povide ecessay backgoud ifomatio to suppot modelig assumptios ad developmet of sceaio-based models descibig LNAPL liquid ecovey. The scope of the mateial peseted documets the quatitative famewok o which the LNAPL distibutio ad ecovey model is based. A moe geeal discussio of LNAPL topics is peseted i the API Iteactive LNAPL Guide (004). Hutley ad Beckett (00) discuss the effects of LNAPL ecovey o dissolved plumes. Model implemetatio though a sigle executable pogam ad model testig ae descibed i a compaio documet (Volume ). 1. SCENARIOS FOR FREE-PRODUCT HYDROCARBON LIQUID RECOVERY Pove techologies fo fee-poduct ecovey of petoleum hydocabo liquids ae descibed i API 468. Models to povide quatitative estimates of system pefomace must ecessaily be based o simplifyig assumptios that will ot be applicable to all field coditios. Nevetheless, the models povide isight ad guidace that should be helpful i techology selectio ad system desig, ad i aalysis of system pefomace. The model sceaios fo well systems ad teches ae discussed sepaately. 1

15 Fo this model fomulatio, the subsuface poous media is assumed to be lateally homogeeous, but ca have up to thee distict layes (umbeed with Laye 1 o top) with diffeet soil chaacteistic ad pemeability paametes. The vetical tasitio betwee layes is assumed to be abupt. A example two-laye soil system is show i Figue 1.1. This figue shows a moitoig well with a LNAPL laye located betwee the ai-napl iteface z a ad the NAPL-wate iteface z w. The total moitoig well LNAPL thickess is b. The elevatio of the abupt tasitio betwee the uppe ad lowe soil layes is desigated z 1. The elevatio of the wate table is desigated z aw. While the wate table is ot peset because of the LNAPL laye, its elevatio is easily detemied fom the elevatios z a ad z w, ad the LNAPL desity ρ (see Sectio ). Figue 1.1 Moitoig well LNAPL thickess, b The soil textue chaacteistics that must be defied fo each laye of the poous medium iclude the poosity ; the (wate phase) hydaulic coductivity K ws ; the va Geuchte paametes N ad α; ad the ieducible wate satuatio, S w. Selectio of esidual LNAPL satuatio values emais a elusive issue, ad vaious optios ae descibed i Sectio. Fluid popeties iclude the LNAPL desity, ρ (it is assumed that the wate desity is 1 g/cm 3 ), ad the wate ad LNAPL suface ad itefacial tesios, σ aw, σ a, ad σ w Sceaios fo Recovey Well Systems The basic sceaio fo fee-poduct ecovey usig well systems is the same fo sigle- ad dualpump wells, vacuum-ehaced wells, ad skimme wells. The pefomace of each well is chaacteized i tems of its adius of captue R c, with a typical sceaio show i Figue 1.. This figue depicts a pla view of a LNAPL les (i gay colo) with 7 ecovey wells located so that the patte of wells with thei adius of captue will cove most of the aea of the les. Fo sigle- ad dual-pump well systems, the adius of captue could exted out to the adius of ifluece (wate poductio) of the well. Fo vacuum-ehaced systems, the adius of ifluece of the vacuum extactio well (which, because of ai leakig fom the goud suface, is

16 typically o the ode of 30 feet 40 feet) limits the adius of captue. Fo skimme wells, the adius of captue is also limited to pobably 10 feet 30 feet, depedig o the soil chaacteistics. Figue 1. Recovey well system with 7 ecovey wells showig the adius of captue (modified fom Lefebve, 000) The data equied fo aalysis of ecovey-well-system pefomace icludes the adius of captue fo the well, the LNAPL-wate viscosity atio μ (the wate viscosity is assumed to be 1 cp), ad wate poductio ate fo a wate-ehaced system o wellhead vacuum pessue fo a vapo-ehaced system. Fo a wate-ehaced system, the effective depth of peetatio of the well ito the aquife must be specified, while fo a vacuum-ehaced system, the sceeed iteval of the vadose zoe must be give. The effective elative pemeability of the vadose zoe due to the pesece of esidual soil wate is assumed to be k a = 0.9. If zeo wate poductio ad wellhead pessue ae specified, the the well is assumed to fuctio as a skimme well. 1.. Sceaio fo LNAPL Recovey Usig Teches The modelig famewok may also be used to epeset a simple tech ecovey system, such as show i Figue 1.3. The tech has a legth L T tasvese to the diectio of goudwate flow. The LNAPL les is assumed to be of ectagula shape with legth L T ad width W T. The atual goudwate hydaulic gadiet J w is tasfeed to the LNAPL laye ad caies it ito the tech whee LNAPL is emoved by skimme wells o othe techology. The ate of LNAPL dischage ito the tech will deped o the effective les thickess as obseved i a moitoig well, soil textue, atual goudwate hydaulic gadiet, ad whethe goudwate is also poduced fom the tech i ode to icease the hydaulic gadiet. If the tech cuts acoss a LNAPL les, the the upsteam ad dowsteam sectios of the les must be aalyzed sepaately, with J w beig egative o the dowsteam side. 3

17 1.3 OVERVIEW Figue 1.3 Simple Tech System fo LNAPL Recovey The models fo well ad tech ecovey systems povide estimates of the ecovey volume ad ate as a fuctio of time. The mathematical models o which these estimates ae based use a simple epesetatio of the LNAPL laye effective satuatio ad tasmissibility. The epesetatio is cosistet with the actual fomatio distibutios of LNAPL satuatio ad elative pemeability ude coditios of vetical equilibium, ad withi the modelig famewok, balace of LNAPL volume (cotiuity) is maitaied betwee the ecoveed volume ad fomatio LNAPL volume withi the well adius of captue o les ectagula aea. Sectio discusses the effects of capillaity o LNAPL i poous media ad the elatioship betwee moitoig well LNAPL thickess ad fomatio LNAPL satuatio distibutio. The quatity of LNAPL is chaacteized though fuctios epesetig the LNAPL specific volume (itegal of the LNAPL volumetic cotet ove the les thickess) ad ecoveable specific volume, as a fuctio of moitoig well LNAPL thickess. A key to model simplicity is epesetatio of these elatioships though piecewise liea fuctios. Sectio 3 discusses LNAPL elative pemeability as a fuctio of multiphase satuatio. Both the Budie (1953) ad Mualem (1976) models ae used. Whe combied with the soil hydaulic coductivity, vetical itegatio of the LNAPL elative pemeability distibutio is used to chaacteize lateal movemet though the esultig tasmissibility fuctio. LNAPL tasmissibility is also epeseted as a piecewise liea fuctio of moitoig well LNAPL thickess. The mathematical models fo pedictig fee-poduct ecovey ae developed i Sectio 4. These models ae based o the fee-poduct thickess that oe would obseve i a moitoig well i good commuicatio with the fomatio fluids (wate, LNAPL, ai). The ate equatios fo sigle- ad dual-pump wells, vacuum-ehaced wells, skimme wells, ad tech ecovey systems deped o the moitoig well LNAPL thickess ad o the dischage of fomatio fluids (wate o ai). The piciple of cotiuity is applied to pedict how the moitoig well LNAPL thickess (ad ecovey ate) vaies as a fuctio of time. 4

18 LNAPL DISTRIBUTION The pupose of this sectio is to povide backgoud ifomatio o LNAPL behavio i the subsuface eviomet. This backgoud ifomatio is ecessay fo udestadig the distibutio of LNAPL liquids ude coditios of vetical equilibium. It icludes the effects of capillay foces o the distibutio of immiscible fluids i poous media ad methods fo pedictig the fomatio LNAPL satuatio distibutio as a fuctio of moitoig well LNAPL thickess. Repesetatio of LNAPL esidual satuatio is also discussed. Additioal ifomatio o the effects of capillaity o the behavio of multiphase fluids i poous media may be foud i Bea (197), Coey (1986), ad Dullie (199)..1 CAPILLARITY IN POROUS MEDIA.1.1 Suface Tesio, Wettability ad Capillay Pessue Whe the poe space of a poous medium is occupied by two o moe immiscible fluids, the iteface sepaatig fluid phases is the most sigificat featue. Molecules ea this iteface have geate eegy tha molecules withi the bulk phase, ad the excess itefacial eegy makes the iteface act as a membae ude tesio; the total eegy i the system is miimized though miimizig the itefacial aea (Hillel, 1980). The souce of the itefacial eegy (o suface tesio) is associated with the attactive foces that exist betwee molecules i the liquid phase. Fo molecule A withi the bulk liquid phase-β show i Figue.1, it is attacted equally by eighboig molecules o all sides, esultig i o et foce o the molecule associated with molecula attactio. Now coside the molecule at locatio B show i this figue. It is attacted by eighboig molecules withi the bulk phase but ot by those i the phase-α [if molecules i phase-α also attacted the molecule fom phase-β, the the iteface would ot exist ad the phases would be miscible]. Thee is a et foce o the molecule located at B. I ode fo molecules at locatios A ad B to chage places, the molecule fom A would have to move agaist this foce field, thus gaiig eegy. Likewise, the molecule fom B would move i the diectio of the et foce, loosig eegy. Thus molecules ea the iteface must have geate eegy tha molecules withi the bulk phase. This itefacial eegy (pe uit aea, eg/cm ) is the same as the suface tesio (dye/cm), ad esults i capillay pheomea tyig to miimize the itefacial aea (miimize the fee eegy of the system at equilibium). Figue.1 Itefacial eegy associated with molecula attactio i the liquid phase 5

19 Alog lies of cotact of the iteface with a solid phase, the iteface will make a cotact agle, θ c. The phase with the smalle cotact agle pefeetially coves the suface, ad is called the wettig phase. The cotact agle is the agle measue betwee the solid suface ad the iteface though the wettig phase, as show i Figue.. Fo usual field coditios of iteest i eviometal ivestigatios, the wettability sequece mieal based soil is wate NAPL ai, with wate beig the most wettig phase fo mieal poous media. Figue. Cotact agle ad wettability If the iteface sepaatig two fluid phases is cuved, the thee will be a pessue diffeece acoss the iteface betwee the phases o eithe side. This pessue diffeece is called the capillay pessue, ad it depeds o the itefacial eegy (suface tesio), cotact agle, ad mea adius of cuvatue. The capillay pessue is the excess pessue i the owettig phase ove the wettig phase, ad it may be calculated usig the equatio of Youg (1805) ad Laplace (1806) as follows (Adamso, 198): p c ( θ ) σ cos c = (.1) I equatio (.1), p c is the capillay pessue, σ is the suface tesio (itefacial eegy), ad is the mea adius of cuvatue of the iteface. I a wate-wet poous medium, excess pessue must be applied to the owettig phase (ai o NAPL) to displace wate fom the medium, ad the capillay pessue is positive. It is assumed that the adius of the poe cotaiig the iteface betwee wettig ad owettig fluid is the same as the mea adius of cuvatue..1. Capillay Pessue Cuves A impotat chaacteistic of a poous medium is the elatioship betwee the capillay pessue ad wettig fluid satuatio (Hillel, 1980). This chaacteistic is called the capillay pessue cuve (ad it is so impotat, it is ofte simply called the chaacteistic cuve fo the soil). Iceases i capillay pessue will foce the itefaces betwee the owettig ad wettig phase ito smalle poe spaces (equatio -1), ad esult i a coespodig icease i owettig phase satuatio ad decease i wettig phase satuatio. Likewise, deceases i capillay pessue will allow the iteface to move ito lage poe spaces, with a icease i wettig phase satuatio ad decease i owettig phase satuatio. Because of the complex system of poe spaces, the sequece upo daiage of poe space is ot the same as that upo efillig, ad the capillay pessue cuve shows hysteesis. This meas that the elatioship betwee capillay pessue ad satuatio is ot a sigle fuctio, but will also deped o the wettig ad daiage histoy of the soil. 6

20 The capillay pessue cuve is usually measued by statig with a soil that is fully satuated with wettig phase fluid. A owettig fluid is itoduced at iceasig capillay pessues. Time is povided fo the fluids to equilibate withi the poe space, ad the esultig satuatio values ae ecoded. The capillay pessue is iceased util o futhe eductio i wettig phase satuatio is measued. The ed-poit value is the wettig-phase esidual satuatio, S W, ad epesets the wettig phase fluid that is held tightly at gai cotacts ad as fluid skis, so that the wettig phase is o loge cotiuous fo flow. The esultig capillay pessue vesus satuatio cuve is called the daiage cuve. It povides a measue of iitial displacemet of wettig phase by owettig phase. The daiage cuve is usually used to chaacteize the soil. If the expeimet descibed i the pecedig paagaph is cotiued, with the capillay pessue beig loweed statig with wettig-phase esidual satuatio, the the esultig satuatio vesus capillay pessue values follow the imbibitio cuve. Whe the capillay pessue is loweed to zeo, the soil will ot be fully satuated with the wettig phase fluid. This ed-poit owettig phase satuatio is sometimes called the owettig-phase esidual satuatio, S NW (though this cocept equies futhe discussio fo pactical field applicatios, see below). Figue.3 shows a gaphical epesetatio of the expeimet that has bee descibed. Both the pimay daiage ad wettig cuves ae show. If the daiage-imbibitio cycle is stopped ad evesed befoe the esidual edpoits ae eached, the a scaig cuve esults. Two such cuves ae also show i Figue.3. Figue.3 Soil capillay pessue cuve showig pimay daiage, imbibitio, ad scaig chaacteistic cuves.1.3 Residual LNAPL Satuatio The owettig phase esidual satuatio show i Figue.3 is a epoducible measue of the capacity of a poous medium to etai owettig fluid duig e-fillig with the wettig phase fo a two-phase fluid system. Howeve, such values have little elevace to issues associated with LNAPL i the goudwate eviomet (Adamski et al., 003). Typical LNAPL eleases esult i LNAPL-wate capillay pessues which ae vey much smalle tha those equied to 7

21 poduce ieducible wate satuatios alog the pimay daiage cuve. Most ofte, maximum LNAPL satuatio values obseved i the field ae less tha LNAPL esidual values suggested usig the expeimetal pocedue suggested by Figue.3. Thus may of the liteatue-epoted tabulated values of esidual LNAPL satuatio ae of limited use i eviometal emediatio applicatios. Fo example, a ofte cited efeece is Mece ad Cohe (1990) who epot esidual LNAPL satuatio values agig fom 0.15 to 0.50 fo the satuated zoe, ad 0.10 to 0.0 fo the vadose zoe. These values ae much lage tha the maximum LNAPL satuatio values measued at idustial facilities with appeciable LNAPL cotamiatio issues (Mak Adamski, BP Ameica, pesoel commuicatio, 004). To be useful, estimates of LNAPL esidual satuatio must coside the atue of the LNAPL elease ad the maximum LNAPL satuatio values that exist ude field coditios. A typical field situatio of a LNAPL elease is outlied i Figue.4. The locatio is assumed to be ea the wate table, ad the poous medium is iitially satuated with wate. As eleased LNAPL accumulates ea the wate table, it will develop a pessue geate tha that of the eighboig goudwate (positive capillay pessue) ad displace wate fom the medium followig the daiage cuve. Poit A i Figue.4 coespods to the maximum capillay pessue developed by the LNAPL elease ad esults i a iitial LNAPL satuatio S i = 1 S wi. Hee, the tem iitial efes to the begiig of the ecovey peiod whee wate displaces LNAPL fom the medium, with capillay pessue-satuatio followig a scaig cuve. Duig LNAPL ecovey, at poit B i the figue, the capillay pessue has bee educed to zeo ad LNAPL will o loge move ito a ecovey well due to a capillay pessue divig foce. The emaiig LNAPL satuatio, desigated S, caot be ecoveed usig covetioal LNAPL hydaulic ecovey techologies. The factio S epesets the LNAPL emaiig tapped withi the fomatio. Figue.4 LNAPL esidual satuatio ude omal field coditios While limited theoy exists to pedict esidual LNAPL satuatio values, S, fom iitial satuatio values (1 S wi ) = S i, thee is sufficiet empiical data to develop useful pedictive models. Data fom laboatoy colum expeimets, show i Figue.5, suggests that esidual 8

22 LNAPL satuatio values icease with iitial LNAPL satuatio. These expeimetal esults fom Kuepe et al. (1973) wee fo TCE (DNAPL) i a sad-packed colum. Figue.5 LNAPL esidual satuatio iceases with iitial LNAPL satuatio (afte Kuepe et al., 1993) Figue.6 fom Johsto ad Adamski (005) shows expeimetal data fom laboatoy etetio cell studies with capillay pessue cycled to iceasig values ad the etued to zeo. The Safety Bay Sad data is fom Steffy et al. (1997). The othe data is fom moe ecet studies caied out i CSIRO laboatoies i 004 ad 005. Figue.6 LNAPL esidual satuatio depeds o iitial LNAPL (fom Johsto ad Adamski, 005) Data fom these ad othe expeimets suggests that LNAPL esidual satuatio values icease liealy with iceasig iitial LNAPL satuatio. This meas that egios that accumulate geate LNAPL satuatios duig a elease will etai geate LNAPL esidual satuatios duig subsequet migatio ad ecovey. 9

23 The suggested mathematical model elatig iitial ad esidual satuatios is ( Swi ) f Si S = f 1 = (.) The esidual f-facto appeas to vay with soil textue, ad may also vay fo the satuated (twophase) ad vadose (thee-phase) zoes. Figue.5, fo a two-phase system with Ottawa sad, gives f = Fo the Safety Bay Sad (fie-to-medium sad), the data show i Figue.6 give f = 0.3. Fo the Texas City soils show i this figue, which ae a fie-sad (SP-SC) ad loamy sad (SC), the laboatoy expeimets give f = 0.39 ad 0.43, espectively. Fo the Swa Valley clay loam (CL), f = A pedictive model fom simila to equatio (.) is suggested by Waddill ad Pake (1997), whee they itepet S wi as the quasi-static esidual satuatio accoutig fo small but esidual wate movemet i the usatuated zoe. Fo the vadose zoe thei model pedicts that the f- facto is smalle by a amout also depedet o the iitial LNAPL satuatio [f v = f s (1 S i )]. Waddill ad Pake suggest empiical f-facto values agig betwee 0. ad 0.5, ad ecommed a media value of Speadig Coefficiets With LNAPL peset at the iteface betwee ai ad wate, the speadig coefficiet measues the tedecy of fo LNAPL to spead o wate (Adamso, 198; Dullie, 199). The speadig coefficiet S /aw may be defied by (see Figue.7) S aw aw ( σ σ ) = σ + (.3) The sigificace of the speadig coefficiet may be appeciated if oe cosides the suface ad itefacial tesio values as suface eegy. As oted ealie, molecules ea the suface of a liquid have excess eegy compaed with molecules withi the bulk liquid phase. At equilibium, the poous medium (fluid phases plus solid) will achieve a state of least (fee) eegy. This implies that if the speadig coefficiet is egative (S /aw < 0), the the LNAPL dop will emai stable o the ai-wate iteface, fomig a bead such as show i Figue.7. This distibutio would miimize the total suface eegy. O the othe had, if the speadig coefficiet is positive, the the dop will spead ove the iteface esultig i a laye (film) of LNAPL existig betwee the wate ad ai phase. This coditio will also esult i a state of miimum fee eegy fo a positive speadig coefficiet. a w AIR LNAPL σ a σ aw WATER σ w Figue.7 LNAPL dop located o a ai-wate iteface 10

24 Fo most LNAPL systems the speadig coefficiet is positive, ad withi the vadose zoe, LNAPL is i diect cotact with the ai phase. This leads to Leveett s assumptio (discussed below). Thee is questio as to whethe the speadig coefficiet will ifluece the esidual LNAPL satuatio i the vadose zoe. It is possible that a speadig LNAPL phase will allow dowwad migatio of LNAPL though film-flow, esultig i lowe LNAPL-esidual satuatio values. Zhow ad Blut (1997) povide expeimetal data suggestig that thee-phase LNAPL esidual satuatio values ca be vey low (less tha 0.1%) fo fluid systems with positive speadig coefficiets..1.5 Leveett Assumptios Based o esults fom his eseach o capillaity i poous media, Leveett (194) suggests that withi a thee-phase fluid system, 1) the capillay pessue betwee the wate ad NAPL phase depeds oly o the wate satuatio, while ) the capillay pessue betwee the NAPL ad ai phase depeds o the total liquid satuatio (wate plus NAPL). The basis fo this assumptio may be appeciated though cosideatio of Figue -11, which is discussed below. Leveett specifically states that the oil must spead o the wate fo this assumptio to be completely valid (positive speadig coefficiet).. CAPILLARY PRESSURE CURVE MODELS Capillay pessue cuve measuemets ae most ofte fit to mathematical models that ae used fo quatitative aalysis. Fo this pupose the pimay daiage cuve is aalyzed. At peset, the most popula model fo eviometal ivestigatios was developed by va Geuchte (1980). This model takes the mathematical fom (vg model) N ( + ( ) ) M S e = 1 αh c (.4) I equatio (.3), S e is the effective (wettig-phase) satuatio that is scaled to age fom 0 1 ad h c is the capillay pessue head. The model paametes ae α, N ad M. While N ad M ca be teated idepedetly, they ae most ofte elated based o the selected model fo elative pemeability. If the Budie (1953) elative pemeability model is selected, the the elatioship is Budie: M = 1 /N ; N > (.5) If the Mualem (1976) model fomulatio is used, the elatioship is Mualem: M = 1 1/N ; N > 1 (.6) Relative pemeability fuctios ae discussed i Sectio Fo the pimay daiage cuve of Figue.3, the effective satuatio would be defied by S S S W W e = (.7) 1 SW Othe scalig factos fo the effective satuatio ae itoduced below fo the imbibitio cuve. The paametes α ad N may be used to chaacteize soil textue. Smalle values of α, which has uits of legth -1, coespod to smalle poe sizes. Smalle values of N coespod to wide ages i poe sizes. Togethe, the paametes α ad N attempt to descibe the poe size 11

25 distibutio fo the medium. The model fit (Mualem) fo a fie-gai plastic clay soil with ai displacig wate gives α = 0.17 ft -1 = cm -1, N = 1.46, ad S w = 0.69 is show i Figue.8. Eve at oe-atmosphee capillay pessue (~30 ft), this soil still has moe tha 80% wettigphase (wate) satuatio. 100 Capillay Pessue Head (ft) Wate Satuatio Figue.8 Measued capillay pessue cuve..1 Fittig Models to Capillay Pessue Cuve Data Data povided though measuemet of capillay pessue cuves is fudametal to pedictio of LNAPL behavio. Alteative methods fo paamete estimatio ae available. A widely used, publicly available model is RETC, developed by the U.S. Saliity Laboatoy (va Geuchte et al., 1991). This model is available though the web site: Alteatively, simple speadsheet models ca be witte to estimate capillay pessue cuve paametes fom measued data. A impotat poit is that estimated values of the vgpaametes α ad N will deped ot oly o the measued data, but also o the elative pemeability model selected, equatios (.5) ad (.6). Fo example, Figue.9 shows the fitted cuves ad model paametes fo the same data set with the Budie ad Mualem models. 1

26 1.0 Capillay Pessue Head, h (m) Budie Model α = 0.67 m -1 N = 3.75 S w = 0.36 (M = 0.477) Wate Satuatio, S w 1.0 (a) Capillay Pessue Head, h (m) Mualem Model α = 0.57 m -1 N = 3.7 S w = (M = 0.694) Wate Satuatio, S w (b) Figue.9 Fitted capillay pessue cuve models usig (a) Budie ad (b) Mualem elatios.. Poe-Size Distibutio Cuves Capillay pessue models such as equatio (.4) ae ideally suited fo chaacteizig the age of daiable poe sizes of a poous medium. Usig equatio (.1) to elate the poe size to the capillay pessue, the the factio of poes of a give size may be specified by p ( ) c ds M N N + 1 e = = M + 1 dc α β y N ( 1+ y ) I equatio (.8), p( c ) is the factio (pobability) of poes of size c, c is assumed to equal the mea adius of cuvatue i equatio (.1), ad y = αβ/ c whee β = σ cos(θ c )/(Δρg). A equivalet expessio to equatio (.8) was itoduced by Dake ad Ritte (1945). Gaphs of p( c ) fo two diffeet soils ae show i Figue.10 (the aea ude each cuve is oe). The (.8) 13

27 media poe size vaies fom a few micos to moe tha 100 micos fo these two examples. I geeal, oe fids that iceasig the value of α shifts the cuves to lage poe sizes (icludig the size of the lagest poes). If the value of the paamete N is iceased, the age i poe sizes deceases (the distibutio becomes aowe). Thus the paamete α is associated (diectly) with the size of poes while the paamete N is associated (ivesely) with the age i poe size Fequecy E-06 1E-05 1E Poe Radius (μm) (a) Fequecy Poe Radius (μm) (b) Figue.10 Poe size distibutio cuves fom equatio (.8) fo (a) fie-gai soil with α = 0.15 ft -1 (0.005 cm -1 ), N = 1.5; ad (b) fie sad soil with α =3.8 ft -1 (0.15 cm -1 ) N =.5 Whe combied with the cocept of wettability, the otio of distibutio of poe sizes allows oe to udestad a umbe of sigificat chaacteistics of multiphase poous media behavio. Accodig to the cocept of wettability, the wettig phase will occupy the smallest poe sizes while the owettig phase will occupy the lagest. This distibutio is show schematically i Figue.11. Chaacteistics such as pemeability may be associated with poe size. Thus whe associatig elative pemeability with fluid satuatio, oe should associate the lage poe sizes fo the owettig phase ad the smalle poe sizes fo the wettig phase. 14

28 Figue.11 Distibutio of fluid satuatio amog vaious poe sizes..3 Capillay Scalig Relatioships Measuemets of capillay pessue cuves ae made fo a sigle fluid-pai system, usually the ai-wate system fo eviometal applicatios. A impotat questio is how to scale paametes that have bee detemied fo oe fluid system to a diffeet fluid combiatio. I this egad, itepetatio of the physical sigificace of paametes is impotat. With egad to the vg-model of equatio (.), the paamete α is associated diectly with the capillay pessue head. Usig equatio (.1) fo guidace, it appeas that scalig elatioships should iclude the suface tesio ad cotact agle atios. The paamete N is associated with the poe size distibutio. It is assumed that the distibutio of poe sizes does ot chage fo diffeet fluid systems; that is, thee is eithe sigificat shikage o swellig of the poous medium fo diffeet fluid systems. Fo this case, the paamete N will ot chage fo diffeet fluid combiatios. Thus the capillay scalig elatioships must coside oly the paamete α. Assumig that the α value was obtaied fo a ai-wate system, the appopiate scalig elatioships fo the NAPL-wate ad ai-napl system ae σ aw α[ w ] = α (.9) σ w σ aw α[ a ] = α (.10) σ a Use of these scalig paametes alog with the appopiate capillay pessue heads fo the diffeet fluid systems will assue that capillay pessue-fluid satuatio elatio is coseved fo diffeet fluid pais. With egad to the poe size distibutio cuve, this meas that the iteface betwee wettig ad owettig fluids would be located withi appopiate poe size based o capillay pessue, egadless of the fluid-pai combiatio..3 FORCES IN MULTIPHASE FLUID SYSTEMS Newtoia fluids (wate, NAPL, ai) will ot move uless thee is foce actig o them. The piciple foces causig fluid movemet ae pessue gadiets ad gavity. If thee is a balace betwee the vetical pessue gadiet ad gavity i each fluid phase, the a coditio of hydostatics (vetical equilibium) exists, ad thee will be o motio i the vetical diectio. 15

29 Eve ude coditios of vetical equilibium, thee ca be lateal gadiets esultig i (pimaily) hoizotal fluid movemet. The foce pe uit weight actig withi each phase is called the hydaulic gadiet (dimesioless). Fo the wate ad NAPL phases, both pessue gadiets ad gavity ae impotat. Howeve, fo ai, because of its small desity, gavity foces ae small ad ae eglected i calculatio of the hydaulic gadiet (J). Fo the thee phases, the hydaulic gadiets ae specified by J J w J pw = kˆ ρ g w p = kˆ ρ g a pa = ρ g a (.11) (.1) (.13) Equatios (.11) ad (.1) may be combied usig the defiitio of the capillay pessue betwee LNAPL ad wate (p c[w] = p p w ) to give (Hubbet, 1953) J p c[ w] w = + kˆ ρ g ρ ρ ρ w 1 + J w (.14) ρ Similaly, equatios (.1) ad (.13) may be combied usig the defiitio of the capillay pessue betwee the ai ad LNAPL (p c[a] = p a p ) to give J p [ a] ρ c a = kˆ + J a (.15) ρ g ρ Equatios (.14) ad (.15) state that the fluid foces actig o the NAPL phase cosist of 1) foces due to capillay pessue gadiets, which i tu deped o the soil textue distibutio ad the fluid satuatios, ) buoyacy, which acts upwad whe NAPL desity is less tha the wate desity, ad 3) foces associated with wate o ai phase movemet. Whe the fist two tems balace (cacel), thee is o vetical fluid movemet. I this case LNAPL ca oly move lateally iduced by the flow of wate o ai. This is oe of the pimay assumptios of the LNAPL ecovey model. If oly the vetical compoets of the hydaulic gadiets vaish, the the LNAPL-wate ad ai- LNAPL capillay pessue distibutios satisfy the followig equatios: p [ w] = ( w ρ ) g( z z1) c p ρ (.16) [ a] g( z z ) c = ρ (.17) I equatios (.16) ad (.17) the elevatios z 1 ad z ae efeece elevatios at which the espective capillay pessue is zeo (the pessues i the owettig ad wettig phases ae the same). 16

30 .4 LNAPL DISTRIBUTION AND MONITORING WELLS.4.1 Fluid Levels i Moitoig Wells If LNAPL is peset withi the subsuface eviomet i sufficiet quatify, the it may appea i moitoig wells that ae sceeed acoss the wate table elevatio. The levels of NAPL ad wate i the well will adjust though time util the fluids i the well ae i equilibium (same eegy) with those i the fomatio; diffeeces i eegy levels would cause flow ito o out of the well. Figue.1 povides a schematic view of LNAPL i a moitoig well. The elevatio z gs is the elevatio of the goud suface. The elevatios z a ad z w ae the elevatios of the ai- NAPL ad NAPL-wate iteface i the well, espectively. z aw coespods to the elevatio of the wate table if o NAPL wee peset. b is the thickess of the NAPL laye i the moitoig well. Ude equilibium coditios betwee fluids i the well ad those withi the fomatio, all of the vaiable values show i Figue.1 ae detemied by the fomatio LNAPL distibutio. Figue.1 Fluid elevatios withi a LNAPL moitoig well 17

31 .4. Distibutio of Capillay Pessues Ude hydostatic coditios, the fluid pessue i each phase chages i the vetical diectio i accodace with the hydostatic pessue equatio, which expesses a balace betwee pessue ad gavity foces. Fo eithe wate o LNAPL this may be witte dp dz = ρg (.18) Fo the ai phase, gavity foces ae small ad the equivalet equatio would ead p a = p atm = costat, i.e. ai pessue emais costat at atmospheic pessue ude equilibium coditios. The equilibium (hydostatic) pessue distibutio fo a ai-wate system is show i Figue.13. At the elevatio of the wate table (z aw ) the wate pessue is atmospheic (gage pessue is zeo). It is assumed that the ai pessue emais atmospheic thoughout. The height of the capillay fige is detemied by the displacemet pessue head, h d, of the soil. Smalle poe sizes esult i a geate height of the capillay fige. I a egio that has ot bee impacted by LNAPL, the capillay fige emais ealy wate-satuated with egative wate pessue. Figue.13 Capillay pessue distibutio ea the wate table, icludig the capillay fige Figue.14 shows the capillay pessue distibutio fo a egio impacted by LNAPL. The gage wate pessue is still zeo at the wate table. The LNAPL pessue is zeo at the elevatio z a. This would be the elevatio of the ai-lnapl iteface i a moitoig well, if oe wee peset. Thus z = z a i equatio (.17). The wate ad LNAPL pessues ae the same at the elevatio z w, at which the LNAPL-wate capillay pessue vaishes. This would be the elevatio of the LNAPL-wate iteface i a moitoig well, ad z 1 = z w i equatio (.16). The elevatio z max is the maximum elevatio of fee LNAPL due to capillay ise. Above this elevatio, ay LNAPL is peset at esidual satuatio ad is ot mobile. 18

32 Figue.14 Capillay pessue distibutio i the pesece of LNAPL With equilibium coditios betwee the well ad fomatio fluids, the moitoig well LNAPL thickess ca be used to assess coespodig eegy coditios withi the fomatio (i geeal, the fluid head is specified by h = p/ρg + z). This is based o kowledge of the LNAPL ad wate desity. The followig coditios ae based o hydostatic coditios withi the well: z a z aw ( ρ ) b z = 1 (.19) aw z = ρ b (.0) w h w aw a ( ρ ) z w = z = ρ z + 1 (.1) h a w ( ρ ) b = z = h + 1 (.) I these equatios the desity atio, ρ, is defied by ρ = ρ /ρ w. Equatio (.) is especially impotat because it elates LNAPL head to wate head plus equilibium LNAPL-laye thickess i a well..4.3 LNAPL Satuatio Distibutios Fluid level elevatios i moitoig wells povide the basis, whe combied with capillay pessue cuves, fo calculatio of fomatio LNAPL satuatio distibutios (Fa et al., 1990; Lehad ad Pake, 1990). Ude equilibium coditios, the fluid eegy withi the well is the same as that withi the fomatio. At the elevatio z w i the well, the pessue is the same withi the wate ad NAPL phases, ad thus the capillay pessue p c[w] = 0 at this elevatio. The elevatio z w seves as the efeece datum fo calculatio of the NAPL-wate capillay pessue head distibutio. Accodig to equatio (.14) the LNAPL-wate capillay pessue head distibutio is give by h [ w] p [ w] = ( )( z z ) c = ρ ρw g 1 (.3) w 19

33 Usig equatios (.3) ad (.8) i equatio (.3) gives fo the effective wate satuatio distibutio i the fomatio This is moe coveietly witte i the fom S S ( ( ) ) N 1 + h M [ w]( ) [ w] [ w] e z = α N ( ) M [ w]( z) = + ( α w( z zw )) e 1 (.4) Equatio (.4) itoduces a ew scalig facto that takes ito accout both suface tesio ad buoyacy effects: α w σ aw = ( 1 ρ ) α (.5) σ w The effective satuatio i equatio (.4) accouts fo the pesece of esidual NAPL. Thus S [ w] e S S S S w w = (.6) 1 I equatio (.6) S is the esidual NAPL satuatio. With this scalig, whe S e[w] = 1, S w = 1 S sice pat of the poe space is occupied by esidual NAPL. The wate satuatio distibutio is give by S w w ( z) S + ( S S ) S [ ]( z) w w = 1 (.7) I equatio (.7) both the esidual wate ad LNAPL satuatio may also vay with elevatio. Fo elevatios z < z a, the poe space ot occupied by wate will be filled with LNAPL. Thus fo z < z a, S ( z) S ( z) w e w = 1 (.8) I equatio (.8) the wate satuatio is give by equatio (.7). I a simila fashio, oe may use Leveett s assumptios ad calculate the total liquid satuatio above the elevatio z a. Usig equatio (.17) the ai-napl capillay pessue head distibutio satisfies h [ a] p [ a] = ( z z ) c = ρ ρwg a (.9) 0