MODEL DEVELOPMENT AND SIMULA- TION OF IN SITU STABILIZATION IN LEAD-CONTAMINATED SOILS

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Maurice Brent Lindsey
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1 MODEL DEVELOPMENT ND SIMUL- TION OF IN SITU STBILIZTION IN LED-CONTMINTED SOILS 1 Z. Shi and 2 L.E. Eikson 1,2 105 Duland Hall, Depatment of Chemial Engineeing, Kansas State Univesity, Manhattan, KS 66506; 1 Phone: (785) 52-42, 1 shiza@ksu.edu; 2 Phone: (785) 52-41, 2 leik@ksu.edu BSTRCT Stabilization and emediation of lead-ontaminated soils have eeived onsideable attention eently. mending Pb-ontaminated soils with phosphate as an in situ emediation option has been poposed as an altenative to othe emediation options suh as soil emoval. Reseah shows that hydoxyapatite (H) [Ca 5 (PO 4 ) OH] an edue the bioavailability of Pb effiiently and thus is onsideed as an ideal phosphate soue fo fomation of lead pyomophite. Envionmental models ae ineasingly being elied upon to help identify the limiting fatos in suh kind of in situ emediation. In the pesent wok, models whih inlude adsoption, diffusion, and eation have been developed to desibe the tansfomation of lead ontaminants to pyomophite in single patiles, aggegates, and soil beds, espetively. Pinipal fatos ontolling the time of emediation have been identified. The ontaminated aggegates emediation model has been developed and simulated to desibe the effet of initial ontaminant onentation, diffusion oeffiient, and aggegate diamete on the time of emediation. Key wods: modeling, stabilization, emediation, hydoxyapatite, lead pyomophite, bioavailability INTRODUCTION In situ stabilization of soil lead by the addition of phosphate mineals has been onsideed a ost-effetive and envionmentally benign altenative emediation tehnology fo Pbontaminated soils. This method tansfoms the eative and bioavailable Pb into hemial foms that ae stable and have extemely low solubility, mobility, and bioavailability unde typial envionmental onditions. Lead pyomophite is one of the most stable Pb foms in soils unde a wide vaiety of envionmental onditions. (Lindsay,1979). Ma et al.(199) showed that hydoxyapatite (Ca 5 (PO 4 ) OH) has the potential of immobilizing Pb in solution by foming hydoxypyomophite. Fomation of pyomophites upon addition of apatite o soluble inogani P amendments has been obseved in Pb-ontaminated soil mateials. (Cotte- Howells and Capon, 1996). Howeve, little attention has been paid to modeling the fomation of pyomophite using mathematial methods. In this study, models ae developed fo both single-patile and soil aggegates. Futhemoe, two ases, stagnant suoundings and flowing suoundings, ae onsideed with espet to the single patile. MODEL DEVELOPMENT FOR SINGLE PRTICLE Fist, onside the ase whee all lead in the patile is in the poess of being ompletely onveted to pyomophite. (hydoxyapatite) must diffuse to the sufae to eat with solid B (lead ompound) at the liquid-solid sufae. Reations of this type ae typially zeo ode in B and fist ode in ( = -k when C B >0 and 70 Poeedings of the 2000 Confeene on Hazadous Waste Reseah

2 = 0 when C B = 0 ). The ate of the mass tansfe to the sufae is equal to the ate of sufae eation. The following assumptions ae imposed while deiving the model: (1) Patiles ae in spheial fom. (2) Reation only takes plae at the solidliquid sufae. () The podut does not fom a laye on the patile. The uneated pat of the patiles is always aessible to the hydoxyapatite. (4) The onentation of the hydoxyapatite is kept onstant. The ate of onsumption of hydoxyapatite is W = k ( ) = = k (1) s s Eliminating the sufae onentation of, s, gives kk W = = (2) k + k We onside two ases: (1) The patile is immesed in a stagnant fluid, in whih ase the Shewood numbe is Sh = = 2 () D (2) The fluid flows aound the patile, in whih ase 12 1 Sh = Re S (4) whee DU Re = v v S = D Case 1: Stagnant Fluid Fom Equation(), the mass tansfe oeffiient is 2D k = (5) D Equation (2) may be witten as kk k = = k + k k k (6) Substituting Equation (5) into the above equation gives k k = = (7) 1 + DD* 2 D whee D*=2D /k lead mole balane on the solid patiles yields In Out + Geneation = umulation ( ) d ρπ D Bπ D = (8) dt oding to the stoihiometi elation of and B, lead pyomophite an be fomed with eithe hloide o hydoxyl ions: + ( ) ( ) 2 2 ( ) ( ) 5 5 ( ) ( ) ( ) ( ) ( ) 5 5 ( ) ( ) 5 ( ) ( ) ( ) 5 5 Ca PO OH s + Cl + H > Pb PO Cl s Ca SO H O Ca PO OH s + 5PbS s + Cl + H + 10O Pb PO Cl s Ca SO H O > Ca PO OH s + PbCO s > Pb PO OH s + Ca + CO (9) Fo all ases, we have: -5 =- B Equations (7), (8) and (9) an be used to obtain dd 10( ) 10k 1 = = dt ρ ρ 1 + D D* dd 1 = α (10) dt 1 + D D* whee 10k α = (11) ρ Poeedings of the 2000 Confeene on Hazadous Waste Reseah 71

3 Figue 1. Convesion time fo lead fo the ase of a stati aqueous phase. t t=0, D= Equation (11) an be integated to obtain Di D+ ( Di D ) =αt 2 D * The time fo omplete onvesion is found by letting D = 0; that is, t 2 1 D i = Di + α 2 D* Conside fou diffeent speies of B : (1) Pb ρ = 5.48 * 10 4 mol/m (2) PbSO 4 ρ = 2.10 * 10 4 mol/m () PbCO ρ = 2.45 * 10 4 mol/m (4) PbS ρ =.17 * 10 4 mol/m Thee diffeent onentation of hydoxyapatite: = 5.18 mol/m = mol/m = mol/m Fou diffeent initial patile diametes: = m = m = m = 0.01 m Let k = 10-4 m/s, D = 10-9 m 2 /s. The esults fo this ase ae shown on Figues 1-4. (12) Figue 2. Convesion time fo PbSO 4 fo the ase of a stati aqueous phase. Case 2: Flowing Fluid In this ase 12 1 Sh = Re S () in whih 6 2 v 10 m / s S = = = D 10 m / s DU D * Um / s 6 Re = = = 10 DU 6 2 v 10 m / s (take fluid veloity as U m/s) 6 Sh = = * 10 DU 1000 D = DU Then k Fom (6) ( ) ( ) * D = (1) D k = 1 + k k Substituting Equation (1) into Equation (6) we have k = = k k gain dd 10( ) 10k = = dt ρ ρ k * D 72 Poeedings of the 2000 Confeene on Hazadous Waste Reseah

4 Figue. Convesion time fo PbCO fo the ase of a stati aqueous phase. ( )* Numeial methods ae used to solve this diffeential equation. The esults fo this ase ae given by Figues 5-8. DISCUSSION OF RESULTS * D = α whee, 10k α = ρ * D dd * D = α dt (14) + DU D + k D Simulation fo lead patile in stagnant fluid The esults of simulation fo the ase of a single lead patile suounded by a stagnant fluid ae pesented in Figues 1 though 4. In Figue 1, thee diffeent onentations of the applied hydoxyapatite and patiles with fou diffeent diametes ae onsideed. The esults indiate that the onentation of hydoxyapatite affets the time of emediation signifiantly. t Figue 4. Convesion time fo PbS fo the ase of a stati aqueous phase. lage hydoxyapatite onentations, the emediation poess takes plae muh faste ompaed with small hydoxyapatite onentations, beause the eation ate is fist ode with espet to the onentation of hydoxyapatite. lso Figue 1 eveals the effet of patile diamete on the ate of emediation. Fo patiles with small diametes, the hydoxyapatite diffuses moe apidly inside the patile. The hydoxyapatite moves extemely slow in lage patiles, theeby polonging substantially the time fo emediation. Figues 1 though 4 show that the initial lead onentation also has an effet on the emediation time. small initial ontaminant onentation equies a small hydoxyapatite supply. Thus less time is equied fo ompletion of the fomation of pyomophite. Simulation of lead patile in flowing fluid The esults of simulation fo the ase of a single lead patile suounded by a flowing fluid ae shown in Figues 5 though 8. Figue 5 indiates that the flow ate of the suounding fluid has an effet on the emediation time. With lage flow ate, the mass tansfe oeffiient is geatly enlaged, whih signifiantly enhanes the emediation poess. Compaison of Figue 1 with Figue 6 eveals that at the same ondi- Poeedings of the 2000 Confeene on Hazadous Waste Reseah 7

5 Figue 5. Convesion time fo lead with flowing suoundings at diffeent flow veloities (D=10-9 m 2 /s, k =10-4 m/s, =5.15 mmol/l). tion, flowing suoundings will effetively edue the emediation time, even at a low flow ate of U = 10-4 m/s. Figues 6 and 8 also indiate that the onentation of hydoxyapatite has a geat effet on the emediation poess in the ases with flowing suoundings. Lage patiles take moe time to omplete the poess. CONTMINTED GGREGTE REMEDITION MODEL The ontaminated aggegate emediation model onsides that the lead ontaminants ae initially unifomly deposited in soil aggegates. The following assumptions ae made in deiving the model: a. ggegates ae in spheial shape; b. ggegates ae satuated, homogeneous, and isotopi and ae made up of solid patiles and stagnant wate;. The tempeatue is onstant in the aggegate; d. Lead ontaminants ae unifomly deposited within the aggegate; e. Reation takes plae at solid sufaes within the aggegate; f. The eation is of 1 st ode with espet to H and 0 ode with espet to lead ompound; Figue 6. Convesion time fo Pb at diffeent values of (D =10-9 m 2 /s, k =10-4 m/s, U=10-4 m/s). g. Tanspot in the aggegate is by diffusion only; h. The tanspot esistane of H to the solid patile sufae is negligible; i. The H onentation at the aggegate sufae is onstant; j. The initial amount of H in solid phase is negligible; k. The lead ompound exists in phase equilibium with liquid and solid phases; the diffusion of dissolved lead ompound onentation an be negleted; l. No podut laye will be fomed on the solid patile. The mass balane of H in a spheial aggegate gives D 2 = 2 + t τ = k if thee is uneated lead pesent = 0 if thee is no uneated lead I.C. t = 0, = 0 fo all B.C. = a =R, fo all t 0 If the diffusion of lead is negleted, B = 5 = 5k db 6 = 5 ε ρ*10 dt 74 Poeedings of the 2000 Confeene on Hazadous Waste Reseah

6 Figue 7. Convesion time fo PbCO (D =10-9 m 2 /s,k =10-4 m/s, = mmol/l). 0 I.C. t = 0, B = B Fo pyomophite, P = = k dp 6 = ε ρ*10 dt I.C. t = 0, = 0 Numeial esults ae shown on Figues DISCUSSION OF RESULTS The esults of simulation fo emediation of soil aggegates ae pesented in Figues 9 though 14. Figue 9 shows the effet of diffusion oeffiient and initial ontaminant onentation on the emediation time. Ineasing the diffusion oeffiient enhanes tanspot of hydoxyapatite inside the aggegate whih edues emediation time geatly. Lage initial onentations of ontaminant need moe hydoxyapatite, whih esults in lage emediation time. The effet of diffusion oeffiient is moe signifiant at high initial ontaminant onentation. Figue 10 indiates that eation onstant is also an impotant fato that affets the emediation poess. Figues 9 and 10 show that the ate of onvesion depends on the values of the ate onstant, as well as the diffusivity. Substantial ineases in onvesion time ou when eithe value is edued. The P Figue 8. Convesion time fo PbCO fo diffeent values of (D =10-9 m 2 /s, k =10-4 m/s, U=10-4 m/s). effet of eation ate onstant is also moe signifiant at high initial ontaminant onentation. Figue 11 eveals the effet of aggegate size on the ate of emediation. Fo aggegates with small diamete, the hydoxyapatite diffuses moe apidly inside the aggegates. The hydoxyapatite moves extemely slowly in lage aggegates, whih auses longe emediation time. Figue 12 indiates that the onentation of hydoxyapatite affets signifiantly the time of emediation. Lage hydoxyapatite onentations make hydoxyapatite moe aessible to eat with lead ontaminants, whih leads to shote emediation times ompaed with small hydoxyapatite onentations. Figue 1 shows that at the same ondition, PbS is the most diffiult to emediate beause of its lage density among the thee lead ontaminants examined. Figue 14 pesents a onentation pofile at the ente of the aggegate as a funtion of eation time. The emediation time is defined as the time needed fo the onentation of lead ontaminant to dop below 1 ppb. CONCLUSION Mathematial models have been developed to analyze lead stabilization in a single-soil patile and aggegated soil. In a single-soil Poeedings of the 2000 Confeene on Hazadous Waste Reseah 75

7 Figue 9. Total onvesion time fo PbCO fo diffeent values of D (D=0.02 m, 0 =2.6 g/l, k =10-4 1/s). patile model, only the diffusion esistane at the patile sufae is onsideed. While in a soil-aggegate model, the diffusion esistane within the aggegate alone is taken into aount. In the eal system, both esistanes ae impotant and should be onsideed simultaneously, whih may esult in longe emediation time fo the system. CKNOWLEDGEMENTS The authos gatefully aknowledge suppot though the U.S. EP EPSCoR pogam and KTEC. REFERENCES Cotte-Howells, J., and S. Capon, Remediation of ontaminated land by fomation of heavy metal phosphate. ppl. Geohem. 11:5-42. Fogle, H. Sott, Elements of hemial eation engineeing. Pentie Hall. Englewood Cliffs, NJ. Hettiaahhi, G., In situ stabilization of soil lead. Ph.D. Dissetation. Kansas State Univesity. Lambet, M., G. Piezynski, L. Eikson, and J. Shnoo,1997 Remediation of lead-, zin- and admium-ontaminated soils. Figue 10. Total onvesion time fo PbCO at diffeent value of eation ate onstant (D=0.02 m, 0 =2.6 g/l, D =10-9 m 2 /s). Issues in Envionmental Siene and Tehnology. 7: Levenspiel, O., Chemial eation engineeing. John Wiley&Sons, New Yok, NY. Lindsay, W.L., Chemial equilibia in soils. John Wiley &Sons. NY Ma,Q.Y., S.J. Taina, T.J. Logan, and J.. Ryan, 199. In situ lead immobilization by apatite. Evion. Si. Tehnol. 27: Van Riemsdijk, W.H., L.J.M. Boumans, and F..M. De Haan,1984. Phosphate soption by soils: I. model fo phosphate eation with metal-oxides in soil. Soil Si. So. m. J., Vol.48: NOTTION k mass tansfe oeffiient (m/s) k eation ate onstant (m/s) ate of eation of (mol/m 2 s) D effetive diffusion oeffiient (m 2 /s) initial diamete of the patile (m) ρ density of the solid patile o aggegate (kg/m ) ε volumeti fation of liquid in the aggegate 76 Poeedings of the 2000 Confeene on Hazadous Waste Reseah

8 Figue 11. Total onvesion time fo PbCO at diffeent diametes of aggegate (k =10-4 1/s, 0 =2.6 g/l, D =10-9 m 2 /s). Figue 12. Total onvesion time fo PbCO at diffeent initial H onentations (k =10-4 1/s, D=0.02 m, D =10-9 m 2 /s). Figue 1. Total onvesion time fo thee lead ompounds ( = 2.6 g/l, k =10-4 1/s, D=0.02 m, D =10-9 m 2 /s). Figue 14. Conentation pofile at the ente of the aggegate ( = 2.6 g/l, D =10-9 m 2 /s, k =10-4 1/s, B =100 mg/kg, D=0.02 m, ). B onentation of lead ompound in solid τ totuosity of poes in the aggegate phase (mg/kg) U veloity of flowing fluid (m/s) P onentation of pyomophite in the v visosity of the fluid (m 2 /s) solid phase (mg/kg) onentation of H in the liquid phase (kg/m ) Poeedings of the 2000 Confeene on Hazadous Waste Reseah 77

Investigation of a Dual-Bed Autothermal Reforming of Methane for Hydrogen Production

Investigation of a Dual-Bed Autothemal Refoming of Methane fo Hydogen Poduction Amonchai Aponwichanop *, Manatsanan Wasuleewan, Yaneepon Patchaavoachot, and Suttichai Assabumungat Depatment of Chemical