Analytical Solution for Multi-Species ContaminantTransport in Finite Media with Time-Varying Boundary

Conditions

報 告 者：林 建 文指導教授：陳 瑞 昇 博士

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Jesús S. Pérez Guerrero · Todd H. Skaggs ·M. Th. van Genuchten

{Transp Porous Med (2010) 85:171–188.}

OUTLINE INTRODUCTION OBJECTIVES METHODS CONCLUSIONS FUTURE WORK

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TAIPOWER, 2009)

INTRODUCTION

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how to deal with …?

examples of common international

INTRODUCTION

4(USEPA, 2010)

Pu-238

Th-230

Ra-226

U-234

+DAY

Radioactive decay often involves a sequence of steps (decay chain). For example, Pu-238 decays to U-234 which decays to Th-230 which decays, and so on, to Ra-226.

Decay products are important in understanding radioactive decay and the management of radioactive waste.

INTRODUCTION

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Analytical solutions for transport problems involving sequential decay reactions have been developed mostly for steady-state boundary conditions and for infinite or semi-infinite spatial domains.

Relatively very little literature is available about analytical solutions for multispecies

transport problems for either finite media or time-dependent boundary conditions.

OBJECTIVES

The objective of this study is to extend the CITT procedure to obtain an analytical solution for a sequential decay reaction transport problem with time-varying boundary conditions and a finite domain.

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METHODS

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( j =1,2,3,…; )

𝑅1

𝜕𝐶1

𝜕𝑇=𝐷

𝜕2𝐶1

𝜕 𝑋 2 −U𝜕𝐶1

𝜕 𝑋− 𝜆1𝑅1𝐶1

𝑅2

𝜕𝐶2

𝜕𝑇=𝐷

𝜕2𝐶2

𝜕 𝑋 2 −U𝜕𝐶2

𝜕 𝑋−𝜆2𝑅2𝐶2+𝜆1𝑅1𝐶1

First-order sequentially decaying species

Homogeneous finite porous media

Subject to linear equilibrium adsorption processes

Constant advective velocity

[L2T -

1]

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CONCLUSIONS

Using the CITT in combination with a filter function with separable space and time-dependencies, the superposition principle, and a classic algebraic substitution

The analytical solution is general and permits different values for the retardation coefficients of each species.

Establish the initial and boundary conditions, derivation of two-dimensional advection dispersion equation

Variables and equations dimensionless

FINITE HANKEL transform

General integral transform technique (GITT)

Solve the particular solution for differential equation

Inverse transform, Analytical solution obtained 9

FUTURE WORK

𝜕𝐶𝜕𝑋

=0

𝜕𝐶𝜕𝑌

=0𝐿

𝐶0

f

𝑍

( j =1,2,3,…; )

initial and boundary conditionsAnalytical solutions

HYDROGEOCH

EM5.0

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FUTURE WORK

Transport safety assessment of nuclear substances

Risk assess-ment

Geochemical transfer mode (HYDROGEOCHEM)

Biogeo chemica

l Transfer

Groundwater Flow

Numerical solutions

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Thanks for your attention

𝜕𝐶𝜕𝑋

=0

𝜕𝐶𝜕𝑌

=0𝐿

𝐶0

f

𝑍

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FUTURE WORK ( j =1,2,3,…; )

initial and boundary conditions

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METHODS