DESIGN EQUATIONS FOR IN SITU THERMAL DESORPTION. by G. L. Stegemeier

Transcription

1 DESIGN EQUATIONS FOR IN SITU THERMAL DESORPTION by G. L. Segemeier Cmpuains ha are required fr design f ISTD presses uilize a large number f fundamenal equains, bh fr perain f surfae equipmen and fr design f he in siu press. The in siu presses are desribed by he fundamenal fluid fl and hea fl equains. Alhugh he aual mpuains are arried u in mplex numerial simulars, he simplified analyial expressins ill be used illusrae he press mehanisms. FLUID FLOW (Seady Sae) Fl f fluids is desribed by a Dary equain fr eah f he fling phases. In ms in siu presses, e need aun fr fl f aqueus and lei liquid phases and f a gas phase mpsed f air, aer vapr, and lesser amuns f lei vaprs. The linear frm f Dary s equain, as given in Equain (), generally desribes fl in he hermal blanke press. The radial frm, as given in Equain (), desribes fl in he hermal ell press. In he Dary equains, he rk prperies (abslue permeabiliy and prsiy) are differeniaed frm fluid prperies (vissiy and densiy). The inerferene f dissimilar fluids in muliphase fl is desribed by a relaive permeabiliy rrein ha is a funin f he saurains f eah f he phases. All prperies may vary ih emperaure, and in his ay he fl f visus il, aer, and vaprs is prperly desribed hrughu he enire press. HEAT FLOW Cnduin (Seady Sae) Hea fl by nduin in prus media is desribed by he emperaure hea fl equains ha are similar in frm he pressure fluid fl equains. Fr seady-sae, linear, nduive hea fl, Furier s equain, given in Equain (3), is appliable. The Furier equain fr seady-sae, radial, nduive hea fl, is given in Equain (4). Cnduin (Transien) Beause hea fl is s muh sler han fluid fl, ransien sluins are needed desribe he press. Fr linear fl, he rise in emperaure as a funin f ime and disane frm a plane heaer blanke is given by Equain (5). This equain inrpraes he bulk hermal prperies f sil and he hea inpu rae per uni area f he heaer. Fr pure nduin ihu nvein, he emperaure fall-ff ih disane is desribed by he mplemenary errr funin given in Equain (6) and Figure. The line sure sluin given in Equain (7) is a gd apprximain fr radial nduin hea fl frm a hermal ell. The shape f he resuling emperaure prfile ih radial disane frm he line sure is defined by he expnenial inegral funin given in Equains (8) and (9) and Figure. When an array f heaer ells is insalled in a vlume f sil, he emperaure rise a any inerell lain is he superpsiin sum f eah f he heaers in he paern, as shn in Equain (0) and Figure 3. Alhugh he nribuin he emperaure rise frm disan ells is less han frm lser nes, eah ell in he array nribues he emperaure rise. The effes f his superpsiin beme ms impran afer lng heaing imes.

2 Radiain Radiain heaing is impran nly in he very high emperaure regin near he heaers. Typially, a heaer emperaures less han 000 F, radiain hea ransfer bemes insuffiien fr praial heaing raes frm blankes r ells. The Sephan Blzmann equain shs radiain hea ransfer have a furh-per dependene n he abslue emperaures. This is given in Equain (). VAPORIZATION Daln s La A mderae levels f heaing, ms in siu liquids ill vaprize by biling, evaprain in air, r seam disillain. Fr immisible liquids, he frains f individual mpnens in he gaseus phase are desribed by Daln s La, hih saes ha he al pressure f a gaseus mixure is he sum f he parial pressures f he mpnens. See Equain (). Beause he liquids are immisible, eah mpnen vaprizes independenly f he hers, as deermined by is single-mpnen vapr pressure, hih is a funin nly f he emperaure. The mle frain f a mpnen is direly relaed he parial pressure as shn in Equains (3) and (4). Raul s La If he liquids are misible, he parial pressure f a mpnen is redued by is mle frain in he liquid phase. See Equain (5). Fr example, he sligh slubiliy f benzene in aer ill redue he parial pressure f benzene in he vapr phase, prvided here is n exess liquid benzene presen. This ill reard vaprizain f he las rae f benzene unil all f he liquids are vaprized. Seam Disillain/Air Evaprain The eigh frain f an lei naminan ha an be arried in a sream f air r f seam is given in Equains (6) and (7). This frmulain assumes ha a liquid naminan residue is being evapraed in a sream eiher f air r f aer vapr. Equain (7) shs ha he eigh frain f naminan in he vapr sream is dependen n he mleular eighs and he pure mpnen vapr pressures. (Subsrip refers he naminan and subsrip refers eiher air r seam.) In he in siu hermal desrpin presses, he al pressure f he vapr sream is slighly bel ne amsphere. Therefre, fr high biling pin naminans, he parial pressure f he air r seam is very nearly equal he al pressure. Beause seam has a ler mleular eigh han air, i is a mre effeive disilling medium han air. The large amun f aer vapr presen in he subsurfae als makes seam disillain an impran mehanism fr revery f naminans a emperaures ell bel heir biling pins. CHEMICAL REACTION KINETICS When high emperaures are generaed in siu and suffiien air is presen, ms f he naminans are desryed in he subsurfae. The lng residene ime f reaans a elevaed emperaures in he ISTD press favrs mplein f hemial reains. Assuming firs-rder reains, e may represen he kinei behavir as shn in Equains (8) and (9). These equains, hen mbined ih Arrhenius Equain (0), prvide a mbined expressin fr mplein f a hemial reain, as a funin f ime and emperaure. See Equain (). Our experiene in field prjes has shn ha 90 99% f he hemial reains ake plae in he subsurfae sil. The remaining unreaed mpunds are reaed in a high-emperaure hermal xidizer, ahieving as muh as % desruin effiieny fr he mbined press. The resuling prdus are arbn dixide, aer, and hydrhlri aid, all f hih are readily vaprized a even mderae effluen emperaures.

3 3 A generalized sihimeri equain fr reain f hlrinaed hydrarbns ih air is given in Equain (). This frmulain assumes he air sream be mpsed f 0% xygen by vlume. By mniring he effluen sream fr arbn dixide, he amun f remediaed hydrarbn remved frm he sil an be alulaed. See Equain (3). Similarly, by mniring he effluen sream fr hydrhlri aid, he amun f remediaed hlrinaed hydrarbn an be deermined. See Equain (4). Maerial balanes f fluid mpnens in he ISTD press are arried u a a pariular sie ih he flling ndiins and assumpins:. The sysem vlume is ha bunded by he periphery f he reaed vlume f subsurfae sil and he surfae reamen equipmen u he effluen sak... The simple balane nsiss f (he mass f a mpnen iniially presen in he sil) + (he mass f mpnen fling in he reaed vlume frm adjaen sil) ( he mass f mpnen prdued during he reamen) + ( mass f mpnen remaining in he reaed sil a he end f he press). 3. Individual mpnens inlude (a) he lei naminan, Equain (5), (b) aer, Equain (6), and () air, Equain (7). 4. The iniial mass f lei naminan in he sil is bained by analysis f sil samples. Depending n he frequeny f his sampling a he sie, he al naminan arge an be readily bained by nsruin f is-nenrain maps and mparing he iniial amun in plae ih he prdued amun as deermined by Equain (3) r (4). In a ell-designed prje, essenially n naminan is released he amsphere, n naminan is alled resaurae he leaned vlume, and alms n residual naminan ill be lef in he heaed vlume. 5. The iniial amun f aer in he arge zne may als be deermined frm re sampling. Generally, here is muh mre aer han lei naminan. In addiin, he mvemen f grundaer exerir he arge regin is prevalen a many sies and in sme ases may even exeed he amun f aer iniially presen in he arge regin. All f his aer mus be vaprized if i is n remved by deaering ells. Typially, he amun f aer in he prdu sream is 0 50% by vlume. A he end f a suessful prje, all f he liquid aer ill have been vaprized. The mass f aer vapr remaining in he arge zne is negligible. 6. The mass f air iniially in he sil is negligible, even in dry sils, beause f he l densiy f air mpared he liquid mpnens. Beause f he high mbiliy f air, e nrmally expe dra in a large vlume frm uside he heaed regin. Thus, he prdued air alms enirely riginaes frm uside he reamen area. An energy balane fr he press is mre easily bained han he mass balane f mpnens. Sine he sil emperaures are a gd measure f he mpleeness f remediain, he energy balane, hih akes in aun elerial and hermal energies, prvides an independen means f mniring prgress f he perains. This is amplished by using he hea apaiy f he sil and he hermal prperies f he liquids and gas esimae he average emperaure aained frm injein f a quaniy f elerial energy. Equain (8) is a simple energy balane ha des n ake in aun nduive hea lsses frm he surfaes f he heaed regin r aer ha riginaes frm uside he reaed vlume. In summary, he design f an in siu hermal remediain prje uses a ide range f ehnial neps ha are applied mplex gelgial mdels. The use f mprehensive numerial simulars ha inrprae all f he frmulains given abve is essenial fr he suessful design f a prje. January 9, 998

4 4 EQUATIONS USED IN CALCULATION OF IN SITU THERMAL DESORPTION FLUID FLOW (Seady Sae) Linear q L kkr A p µ l () Radial q R π k k h p µ ln r () ( r r ) e HEAT FLOW (Seady Sae) Linear Radial q hl T λ A (3) L q hr π λ h T ln ( r r ) e (4) HEAT FLOW Cnduin (Transien) Linear F α T ( x, ) e λ π x 4α x erf x α (5) erf ( X ) π X 0 e d e π X + k k X ( k + ) k 0!! (6) here ( k + )!! 3 5 ( k + ) and X x α

5 5 Radial T F r ( r, ) Ei 4π λ 4α ( ) ln ( γ ) Ei X X + n ( X ) n n n! (7) (8) here X r 4α and e e lnγ d d (9) 0 lnγ + n n + ln n (9a) Well Paerns T ( x, y, ) F 4 π λ m n Ei ( x x ) + ( y y ) n 4α n (0) HEAT FLOW Radiain (Seady Sae) Linear 4 4 ( ) F S T T + e e f ()

6 6 VAPORIZATION Daln s La p p + p Κ () p n f f + Κ f (3) + n f p (4) p + p + Κ p n Raul s La p n n x p + x p + Κ x p (5) Seam Disillain f + (6) f (7) M p + M p KINETICS s -Order Reains d d k (8) k e (9) Arrhenius Equain ln k E k (0) RT Cmbined Equain e k e E RT ()

7 7 STOICHIOMETRIC REACTION OF CHLORINATED HYDROCARBONS 4 C x H y Cl z + (4x + y z) O + 4 (4x + y z) N 4x CO + (y z) H O + 4z HCl + 4 (4x + y z) N HCl CHC z M M HCl CHC CHC ( 36.5 z) ( x + y + z 35.5) () CHC M VM STP M x M CHC CO 0 CO q p d (3) CHC M VM STP M z M CHC HCl 0 HCl q p d (4) MATERIAL BALANCE Cnaminan Waer Air m + ρ i d ρ q d + r 0 0 m + ρ i d ρ q d + r 0 0 (5) (6) i d a 0 0 q d (7) a l h ENERGY BALANCE l h {[ ρ C ( φ) + ρ C φ S ]( T T ) + ρ h φ S } + q ρ C ( T T ) F R R f i a a a f i A (8)

8 8 NOMENCLATURE Fluid Fl q L,R fl rae [ l 3 ] k abslue permeabiliy [ l ] k r relaive permeabiliy [ ] A area [ l ] p pressure drp [ m l ] l fl pah lengh [ l ] µ vissiy [ m l ] r e uer radius [ l ] r ell radius [ l ] h lengh f ell [ l ] Cnduive Hea Fl T emperaure hange [ T ] x linear disane [ l ] ime [ ] F hea injein rae / uni area [ m 3 ] λ hermal nduiviy [ m l 3 T ] α hermal diffusiviy [ l / ] F hea injein rae / uni lengh [ m l 3 ] q hl linear hea fl rae [ m l / ] q hr radial hea fl rae [ m l / ] r radial disane [ l ] x,y ell disanes N S and E W [ l ] m al ell un [ ] X argumen f erf and Ei funins [ ] k, n inegers [ ] ln γ Euler s nsan [ ]

9 9 Radian Hea Fl S Sephan Blzmann nsan [ m 3 T 4 ] e emissiviies [ ] f shape far T emiing emperaure [ T ] T absrbing emperaure [ T ] Vaprizain Daln s La p al pressure [ m l ] p,, Κ n vapr pressure f pure mpnens [ m l ] f,, Κ n mle frain f pure mpnens in vapr [ ] Raul s La x,, Κ n mle frain f misible pure mpnens in liquid [ ] p,, Κ n parial pressure f mpnen in vapr [ m l ] Seam Disillain/Air Evaprain eigh f high biling pin lei naminan in vapr [ m ] eigh f aer r air in vapr [ m ] f eigh frain f lei naminan in vapr [ ] M mleular eigh f lei naminan [ m mle ] M mleular eigh f aer r air [ m mle ]

10 0 Kineis nenrain [ eq m ] base nenrain [ eq m ] k kinei nsan [ ] k referene kinei nsan [ ] E aivain energy [ m l mle ] R gas nsan [ m l T mle ] T emperaure [ T ] Sihimery CHC eigh f hlrinaed hydrarbn prdued [ m ] HCl eigh f HCl prdued [ m ] M CO mleular eigh f CO [ m mle ] M CHC mleular eigh f hlrinaed hydrarbn [ m mle ] M HCl mleular eigh f hydrgen hlride [ m mle ] V M@STP mlar vlume f a gas [ l 3 mle ] x number f C ams / mleule z number f Cl ams / mleule CO frainal nenrain f CO in prdu sreams [ ] HCl frainal nenrain f HCl in prdu sreams [ ] q p al fl rae f gas in prdu sream [ l 3 ] Maerial Balane m mass f naminan [ m ] ρ densiy f naminan [ m l 3 ] i infl rae [ l 3 ] q prduin rae [ l 3 ] r residual naminan [ m ]

11 Energy Balane l lengh f sie [ l ] idh f sie [ l ] h heigh f sie [ l ] ρ densiy f aer [ m l 3 ] ρ R densiy f mineral grains [m l 3 ] C R hea apaiy f mineral [ l T ] φ prsiy [ ] ρ densiy f aer [ m l 3 ] C hea apaiy f aer [ l T ] S aer saurain [ ] q a fl rae f air [ l 3 ] ρ a densiy f air [ m l 3 ] C a hea apaiy f air [ l T ] T f final emperaure [ T ] T i iniial emperaure [ T ] h hea f vaprizain f aer [ l ] F ell hea injein rae / uni lengh [ m l 3 ] ime f heaing [ ] A area / injein ell [ l ]

12 T/T erf (X) X x/(a) /

13 Figure EXPONENTIAL INTEGRAL FUNCTION 3.5 T / T - Ei (- X ) X r / 4 a

14 Figure 3 - SUPERPOSITION f EXPONENTIAL INTERGAL FUNCTIONS 4