P1258791372wcEQp

1
Numerical evaluation of multicomponent cation
exchange reactive transport in heterogeneous
media
School of Civil Engineering University of La
Coruña A Coruña, Spain Now at Utah State
Univ. USA
2
(No Transcript)
3
Outline

• Introduction why cation exchange?
• Mathematical formulation of cation exchange RT
• Montecarlo simulation of multicomponent cation
  exchange
• Setup
• Model simulations
• Analysis of temporal and spatial moments
• Arrival time
• Second order
• Apparent retardation coefficients
• Conclusions

4
Introduction
Background

• Some radionuclides (Cs) sorb by cation exchange
• Mass transfer by cation exchange is highly
  nonlinear
• A few analytical solutions for particular cases
  are reported in the literature (Charbeneau, 1988,
  Dou et al., 1996)
• Most of these analytical solutions are for simple
  cases and often neglect hydrodynamic dispersion
• Semianalytical analytical solutions using a
  first-order Taylor expansion of exchange
  equations (Samper Yang, 2007)
• There is a need to extend current analytical
  solutions

5
Stochastic analysis for heterogeneous media
Background

• Natural aquifers are heterogeneous in different
  scales
• K, Kd and CEC can be treated as spatial random
  functions
• A lot of research has been done for a single
  sorbing species in heterogeneous systems (K Kd)
• Less attention has been paid to cation exchange
  reactive transport in heterogeneous aquifers
• Possible approaches
• Use existing stochastic analytical solutions
• valid for trace concentrations (Yang Samper,
  2006)
• Perform Montecarlo simulations

6
Cation exchange

• Dissolved free cations exchange with interlayer
  cations
• It can be described as an equilibrium reaction
  between a dissolved cation and an exchange site
• The equilibrium constant is the selectivity
  coefficient

7
Analytical solution for cation exchange RT
Mathematical formulation

• Transport equations of dissolved cations

• Cation exchange mass action law

(Gaines-Thomas)

• Constraint on equivalent fractions

8
Analytical solution for cation exchange RT
Mathematical formulation

• Cation exchange reactions

(Gaines-Thomas)
9
Stochastic analysis for heterogeneous media
Case description
Numerical simulation

• Vertical cross-section
• Mean longitudinal hydraulic gradient-0.1
• Initial water 1 mM NaNO3 and 0.2 mM KNO3
• Boundary water 0.6 mM CaCl2.
• Selectivity coefficients kNa/K0.2, kNa/Ca0.4
• Simulations performed with CORE (Samper et al.,
  2003 2007)

10
Breakthrough curves of Cl, K, Ca and Na
11
Stochastic analysis for heterogeneous media
Numerical simulation
Spatial moments calculation

• Continuous injection
• Depth averaged concentrations
• Single realization
• Moments are computed from spatial derivatives of
  concentrations qi(x,t)

First-order spatial moment
Second-order spatial moment
Cation apparent velocity
Apparent retardation coefficient
12
Stochastic analysis for heterogeneous media
Numerical simulation
Monte-Carlo simulation
Groups
A Only Log-K is random B Only Log-CEC is
random C Uncorrelated log K and log CEC D
Positive correlation E Negative correlation
GCOSIM3D (Gómez-Hernández, 1993)
Log-K and Log-CEC are random Gaussian functions
with isotropic spherical semivariograms small
correlation length
13
(No Transcript)
14
Breakthrough curves of Cl, K, Ca and Na
15
Stochastic analysis for heterogeneous media
Numerical simulation
Spatial distribution
Homogeneous K CEC
16
Stochastic analysis for heterogeneous media
Numerical simulation
Spatial distribution
Only Log-K is random
Variance of Log-K1.0
Variance of Log-K0.1
17
Stochastic analysis for heterogeneous media
Numerical simulation
Spatial distribution
Only Log-CEC is random
Variance of Log-CEC1.0
Variance of Log-CEC0.1
18
Stochastic analysis for heterogeneous media
Numerical simulation
Spatial distribution
Both Log-K and Log-CEC are random Variances are
0.5 and 1 for Log-K and Log-CEC
Positive correlation
Negative correlation
19
Stochastic analysis for heterogeneous media
Random Log-K and Log-CEC with spherical
variograms of range 10
20
Stochastic analysis for heterogeneous media
Simulations results for negatively correlated
logK and log CEC
21
Breakthrough curves of Cl, K, Ca and Na
22
Spatial moments 1st moments
Displacement of center of mass Xi(t)

• Different Var of logK
• The greater the variance of log K, the larger the
  displacement of plume fronts

23
Spatial moments 1st moments
Displacement of center of mass Xi(t)

• Different Variance of CEC
• The greater the variance of log CEC, the smaller
  the displacement of plume fronts of Na and Ca

24
Spatial moments 1st moments
Displacement of center of mass Xi(t)

• Different correlation structures of log K and log
  CEC
• Displacements of plume fronts for negative
  correlation are larger than those for positive
  correlation

25
Spatial moments 2nd moments

• Different variance of log K
• The greater the variance of log K, the larger the
  2nd order moments

26
Spatial moments 2nd moments

• Different variance of CEC
• The greater the variance of log CEC, the larger
  the 2nd order moments

27
Spatial moments 2nd moments

• Different correlations of log K and log CEC
• Larger spreading for negative correlation for Ca
• Larger spreading for negative correlation for Na

28
Apparent retardation coefficients

• Different variance of log K
• R(t) does not change a lot when variance of log K
  increases from 0.1 to 0.5

29
Apparent retardation coefficients

• Different variance of log CEC
• R(t) increases with the variance of log CEC

30
Apparent retardation coefficients

• Different correlation structures of log K and
  log CEC
• R(t) is largest for uncorrelated log K and log
  CEC

31
Conclusions

• Spatial moments and apparent velocity of Na are
  significantly different from those of Ca2
• First order spatial moment and apparent velocity
  
• Increase with increasing variance of log-K, but
  decrease with increasing variance of log-CEC.
  They also depend on correlation structures of
  (log-K log-CEC)
• Second-order spatial moments
• Increase with time
• Depend on variances of Log-K Log-CEC and their
  correlation structure
• Apparent retardation factors
• Depend on variance of log CEC and correlation
  structure, but much les on variance of log K

32
Acknowledgments

• ENRESA
• Universidad
• de A Coruña

33
(No Transcript)