Boundary Conditions for the Convective-dispersive Solute Transport in Soils

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1 J. Jpn. Soc. Soil Phys. No. +*., p.1/2.,**0 * *** Boundary Conditions for the Convective-dispersive Solute Transport in Soils Nobuo TORIDE*, Masaru SAKAI* and Hirotaka SAITO** + + CDE boundary condition, BC initial condition, IC Danckwerts, +3/- ; Wehner and Wilhelm, +3/0 +32* van Genchten and Parker, +32. convective-dispersive equation, CDE CDE CXTFIT Toride et al., +33/ STANMOD SÀimůnek et al., +333 HYDRUS- + D SÀimůnek et al.,,**/, c r t D, c r cr, v z z D L, T + v L T + c r ML - t T z L z* van Genchten and Parker +32. c r c f flux-averaged concentration resident concentration r CDE,+ z* z * J w LT + c * J wc * q L - L - J wqv vc * D cr z vcr vc * z* - third-type BC,. - * /+.2/*1 +/11 ** :

2 76 +*.,**0 z c r z t* c rz** CDE van Genuchten and Alves, +32, c rzt + c *, erfc exp zvt,.dt + vz +, D v, t D exp vz D erfc erfc z erfcz expx, dx CDE Jury and Roth,**/ p. -+ CDE L Z z L T vt Jwt L Lq J wt Lq L + c * C rc rc * CDE Jury and Horton,,**0, pp.,/.,// C r T + P, C r Cr, Z Z P P vl D P L, D L D Lv L v P + a b P+* /* third-type Z T P L/* cm, v+* cm d + D/* cm, d +, +* cm, d + c * z* P t I s qvc *t van Genchten and Parker, +32. I sqvc *t qc rztdz c *,, + first-type BC c r* tc * CDE van Genuchten and Alves, +32, c rzt c * +, erfc +, exp vz D erfc Jury and Roth,**/ pp c d first-type P c * c *

3 : 77 + P third-type first-type I s z* I st qd cr* t qvc * dt z qd cr*t dtqvc *t z I s van Genuchten and Parker +32. E Et + qvc *t qc rztdzqvc *t + qd cr*t qvc *t dt z exp ẓ + z +, + z erfc zv, tdpt qvc * t,, P E T P E + c d c * Farlow, +330 van Genuchten and Parker +32. E

4 78 +*.,**0, P E. Cl third-type first-type D+ cm, d + v+./ cm d + -,- + a b - c * c * t d c * t. q*.3/ Na / cm c **.+ mol c L + CaCl, Cl +33+ Cl +./ cm d + q + cm, d + c * c * c * t c r * t c * D cr z vcr z* vc* tkc *c r* t k LT + D s kd sd - c * t c r * t

5 : 79 c * - / Cl k D+ cm, d + v+./ cm d + k*.+1/ cm d + Bird et al., +30* ; van Genuchten and Parker, +33. D cr z kc *c r* z* t + c r * t c * /. Cl k*.+1/ cm d +. D+ cm, d +, v+./ cm d + HYDRUS-+D k d. -+, Kreft and Zuber +312 J w J s c f c f Js J w c r D v c r z c r resident concentration Jury and Roth,,**/, pp.,3.. TDR. EC Toride et al.,,**- t z c r c f t D, c f cf, v z z c f*tc * c f z D v, c r z, z *

6 80 +*.,**0 z c r, c f z t* c rz* z* c fz** c f CDE c r CDE Parker and van Genuchten, +32. c r Nielsen and Bigger, +30, c rz*z* Toride et al., , Parlange et al. +33, c r z Lt* CDE Brenner +30, Brenner +30, 0 P T *.0 - P, + zl*.- P+* 0 T*.0 c f c r

7 : 81 1 P c f c r zl zl*.3 1 P zl - BTC P/ P/ +* P/* - P D l Dlv PLl l mm, cm / cm,* cm Jury and Roth,,**/, p.,,0 CDE L l Jury and Roth,,**/, pp.,,/,,0 CDE L+*l CDE P+* P+* P 1 P BTC v D L P 1 L BTC t L 1 T L CDE. zz + +, Leij et al., +33+ c r q +D + z q+v+cr zz + c r q,d, z q,v,cr zz +

8 82 +*.,**0 q +v +q,v, D q c * + a b - 2 q*.0 D,* cm, d + v,* cm d + q*.. D+,/** cm, d + v-* cm d + c * HYDRUS D q / CDE 2 : q *.0 D,* cm, d + v,* cm d + : q*.. D+,/** cm, d + v-* cm d + Bird, R.B., Stewart, W.E. and Lightfoot. E.N. (+30*) : Transport phenomena. John Wiley & Sons, New York. Brenner, H. (+30,) : The di#usion model of longitudinal mixing in beds of finite length. Numerical values. Chem. Eng. Sci., +1 :,,3,.-. Danckwerts, P.V. (+3/-) : Continuous flow systems. Chem. Eng. Sci.,, : ++-. Farlow, S. J : Jury, W.A. and Roth, K.,**/ :

9 : 83 Jury, W.A. and Horton, R.,**0 : pp.,,-,10 Kreft, A. and Zuber, A. (+312) : On the physical meaning of the dispersion equation and its solutions for di#erent initial and boundary conditions. Chem. Eng. Sci. -- : *. Leij, F.J., Dane, J.H. and van Genuchten, M. Th. (+33+) : Mathematical analysis of one-dimensional solute transport in a layered soil profile. Soil Sci. Soc. Am. J., // : 3..3/-. Nielsen, D.R. and Biggar, J.W. (+30,) : Miscible displacement : III. Theoretical considerations. Soil Sci. Soc. Am. Pro.,,0 :,+0,,+. Parker, J.C. and van Genuchten, M. Th. (+32.) : Fluxaveraged and volume-averaged concentrations in continuum approaches to solute transport. Water Resour. Res.,,* : 20021,. Parlange, J.-Y., Starr, J.L., van Genuchten, M. Th. Barry, D.A. and Parker. J.C. (+33,) : Exit condition for miscible displacement experiments. Soil Sci., +/- : +0/+1+. SÀimůnek, J., van Genuchten, M. Th. and Sejna, M. (,**/) : The HYDRUS-+D software package for simulating the movement of water, heat, and multiple solutes in variably saturated media. Version -.*. HYDRUS Software Series +, Dep. of Environmental Sciences, Univ. of California Riverside, Riverside, CA. SÀimůnek, J., van Genuchten, M. Th., Sejna, M., Toride and Leij, F. J. (+333) : The STANMOD computer software for evaluating solute transport in porous media using analytical solutions of convection-dispersion equation. Versions,.*, International Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado :Ca, Na 0, : -++. Toride, N., Leij, F.J. and van Genuchten, M. Th. (+33-) : Flux-averaged concentrations for transport in soils having nonuniform initial solute distributions, Soil Sci. Soc. Am. J., /1 : +.*0+.*3. Toride, N., Leij, F.J. and van Genuchten, M. Th. (+33/) : The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. U.S. Salinity Laboratory Research Report +-1, ++,+, Riverside CA. Toride, N., Inoue, M. and. Leij, F. J. (,**-) : Hydrodynamic dispersion in an unsaturated dune sand, Soil Sci. Soc. Am. J., 01 : 1*-1+,. van Genuchten, M. Th. and Alves, W. J. (+32,) : Analytical solutions of the one-dimensional convective-dispersive solute transport equation. USDA Tech. Bull U.S. Gov. Print. O$ce, Washington, DC. van Genuchten, M. Th., and Parker, J.C. (+32.) : Boundary conditions for displacement experiments through short laboratory soil columns. Soil Sci. Soc. Am. J.,.2 : 1*-1*2. van Genuchten, M. Th. and Parker, J.C. (+33.) : Reply to Comments on Boundary conditions for displacement experiments through short laboratory soil columns. Soil Sci. Soc. Am. J., /2 : Wehner, J.F. and Wilhelm, R.H. (+3/0) : Boundary conditions of flow reactor. Chem. Eng. Sci., 0 : 233-.

10 84 +*.,**0 CDE :,**0 2 -* :,**0 3 +/

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