(Z&B)

Steps in Transport Modeling

Calibration step(calibrate flow & transport model)

Adjust parameter valuesDesign conceptualmodel

Assess uncertainty

Designing a Transport Model

Conceptual model of the flow system

Input parameters

Governing equation 1D, 2D, or 3D steady-state or transient flows steady-state or transient transport

Boundary conditions

Initial conditions

Design the grid

Time step

TMR(telescopic mesh refinement)

From Zheng and Bennett

TMR is used to cut outand define boundaryconditions around a local area within aregional flow model.

GWV option forTelescopic Mesh Refinement

Input Parameters for Transport Simulation

Transport

hydraulic conductivity (Kx, Ky, Kz)storage coefficient (Ss, S, Sy)

porosity ()dispersivity (L, TH, TV)retardation factor or distribution coefficient1st order decay coefficient or half life

recharge ratepumping rates

source term (mass flux)

All of these parameterspotentially could be estimatedduring calibration. That is,they are potentially calibrationparameters.

Transport

v = K I / D = v L + Dd

We need to introduce a “law” to describedispersion, to account for the deviation ofvelocities from the average linear velocitycalculated by Darcy’s law.

Average linear velocity True velocities

Figure from Freeze & Cherry (1979)

Microscopic or local scale dispersion

Macroscopic Dispersion (caused by the presence of heterogeneities)

Homogeneous aquifer

Heterogeneousaquifers

Figure from Freeze & Cherry (1979)

Dispersivity () is a measure of the heterogeneity present in the aquifer.

A very heterogeneous porous mediumhas a higher dispersivity than a slightlyheterogeneous porous medium.

Z&B Fig. 3.24

Option 1: Assume an averageuniform K value and simulatedispersion by using large valuesof dispersivity.

Field (Macro) Dispersivities

Gelhar et al. 1992WRR 28(7)

Also see Appendix DIn book bySpitz and Moreno (1996)

A scale effect is observed.

Schulze-Makuch, 2005 Ground Water 43(3)

Unconsolidated material

Tompson and Gelhar (1990)WRR 26(10)

Theoretical “ideal” plume

Tompson and Gelhar (1990), WRR 26(10)

Hydraulic conductivityfield created usinga random field generator

Option 2: Simulate thevariablity in hydraulicconductivity and usesmall (micro) dispersivityvalues.

See Section 14.4.2 (p. 429) in Z&B

Model Application: The MADE-2 Tracer Test

Injection occurshalfway betweenthe water tableand the bottomof the aquifer.

Injection Site

Theoretical “ideal” plume

MADE-2 Tracer Test

Generating the hydraulic conductivity field

Kriging

Random field generator

Anderson et al. (1999), Sedimentary Geology

Incorporating the geology

Anderson et al. (1999)Sedimentary Geology

Synthetic depositof glacial outwash

Weissmann et al. (2002), WRR 38 (10)

Weissmann et al. (1999), WRR 36(6)

4 Facies

LLNL Site (LaBolle and Fogg, 2001)

Instantaneous sourceNote the complex shape of the plume.

Option 1: Assume an averageuniform K value and simulatedispersion by using large valuesof dispersivity.

Option 2: Simulate the variablity in hydraulicconductivity and use small (micro) dispersivity values.

Summary

Option 2 requires detailed geological characterizationthat may not be feasible except for research problems.

Transport

v = K I / D = v L + Dd

“…the longitudinal macrodispersivity of a reactive solute can be enhanced relative to that of a nonreactive one.”

Burr et al., 1994, WRR 30(3)

At the Borden Site, Burr et al. found that the value of L

needed to calibrate a transport model was 2-3 times larger when simulating a chemically reactive plume. Theyspeculated that this additional dispersion is caused byadditional spatial variability in the distribution coefficient.Research by Allen-King (NGWA Distinguished Lecturer)shows similar effects.

Transport

v = K I / D = v L + Dd

Borden Plume

Simulated: double-peakedsource concentration(best calibration)

Simulated: smoothsource concentration(best calibration)

Z&B, Ch. 14

Goode and Konikow (1990), WRR 26(10) from Z&B

Transient flow field affectscalibrated (apparent) dispersivity value

Calibrated values of dispersivity are dependent on:

• Heterogeneity in hydraulic conductivity (K)

• Heterogeneity in chemical reaction parameters (Kd and )

• Temporal variability in the source term

• Transience in the flow field

Transport

v = K I / D = v L + Dd

Common organic contaminants

Source: EPA circular

Spitz and Moreno (1996)

fraction of organic carbon

Spitz and Moreno ( 1996)

(Z&B)

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