11 Advances in Computational Models of Subsurface Media: Past, Present, and Future Gour-Tsyh Yeh ( ...

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Advances in Computational Models of Subsurface Media:

Past, Present, and FutureGour-Tsyh Yeh ([email protected])

Graduate Institute of Applied GeologyNational Central University

Jhongli, Taoyuan 32001TAIWAN

Presented atEarth Science-2015: 4th International Conference on Earth

Science and Climate ChangeHotel Melia Alicante, Alicante, Spain, June 16-18,

2015

mailto:[email protected]

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Media Simple homogeneous isotropic to complicated

heterogeneous, anisotropic media Processes

Flow: Simple saturated to variably saturated, multiphase Chemical Transport: Single species to multi-species,

multi-component Bio-geochemistry: Simple ad hoc to reaction-based

approach Thermal: Simple isothermal to non-isothermal approach Geomechnaics: Elastic, viso-elastic, plastic, viso-elastic-

plastic materials Computation

Exact Solution: Analytical to semi-analytical solutions Numerical Approaches: FEM, FDM, FVM, special methods

Introduction

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Advances In the Past1. 1960’s and Earlier: Analytical Flow and Solute

Transport Models in Saturated Zones or Unsaturated Zones.

2. 1970’s: Single Phase Flow and Solute Transport Models in Saturated Zones or Vdose Zones.

3. 1980’s: Variably Saturated Flow, Two or Three Phase Flow. Coupled Flow and Solute Transport in Saturated Zone or Vadose Zone. Reactive Transport in Saturated Zone or Variably Saturated Media.

4. 1990’s: Coupled Flow and Solute Transport in Variably Saturated Media. Coupled Single Phase Flow, Thermal Transport, and Reactive Transport in Saturated Zones, Unsaturated Zones, or Variably Saturated Media.

5. 2000’s: Coupled Two or Three Phase Flow, Thermal Transport, and Reactive Transport.

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Over 100 groundwater models have been developed

Subsurface Flow Chemical ReactionsSolute Transport

FEMWATER (1981,1987)

3DFEMWATER (1987)

FEMWASTE (1981)/LEWASTE (1991)

3DFEMWASTE (1987)/3DLEWASTE (1991)

EQMOD (1990)

KEMOD (1995)

HYDROGEOCHEM (1991)

2DFEMFAT (1993)

3DFEMFAT (1994)

2DHYDROGEOCHEM/3DHYDROGEOCHEM (1995)

BIOKEMOD (1998)

MicrobiologicalReactions

HYDROBIOGEOCHEM 1.0 (1998)

LEWASTE (1991)

LEHGC1.0 (1995)LEHGC2.0 (1998)

BIOGEOCHEM (2003)

HYDROBIOGEOCHEM 2.0/3.0 (2003, 2006)

New Paradigm

3DSALT (1996)

1997 GMS-FEMWATER

3DMGZM (1998)

AT123D (1981)3DFEWA (1994)

FEWA (1983)

3DLEMA (1994)

FEMA (1985)/LEMA

2DFATMIC/3DFATMIC (1995)

HYDROGEOCHEM3.1 (2002)



MPS2D/MPS3D (2003)

Renamed


BIOGEOCHEM (2003)

HBGC123D (2000)

2DFEMFAT (1993)


LEHGC1.1 (1995)

3DWATMAS (1995)

WATMAS (1995)

MURF, MURT,3DMURF, 3DMURT

(1992)

HYDROGEOCHEM4.0-5.0 and 4.5/4.6-5.5/5.6 (2004 and 2015)

ThermalTransport

GMECH (2012)

Geomechanics

THMC 6.0-7.0 and6.1-7.1 (2013 and 2015)

FEMWATER2.0 - 7.0

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Only three models stand out

AT123D: Analytical Transient One , Two , and Three Dimensional Simulations of Waste Transport in the Aquifer System.

GMS-FEMWATER: A Three-Dimensional Finite Element Model for Simulating Density-Dependent WATER Flow and Transport in Variably Saturated Media.

HYDROGEOCHEM: A Coupled Model of Fluid Flow, Thermal Transport, and HYDROGEOCHEMical Transport through Saturated Unsaturated Media.

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One of the most general and widely used analytical models. It has been marketed by many consulting companies and many training courses have been conducted by these companies.

Use Google Search “AT123D New Jersey”, you find: Guidance for Using the SESOIL and AT123D Models to Develop Site Specific Impact to Ground Water Soil Remediation Standards ...

In fact, EPA, API, and more than 20 states in USA have the similar guidelines to use AT123D in conjunction with SESOIL

Five dollars make you rich ($5 x 1,000 x 365 x 24 = $44 Millions)

AT123D: One of the most widely used analytical models for groundwater plume delineation

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How AT123D has been used for regulation

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FEMWATER: Used Worldwide Among the very first well-documented subsurface

models to integrate vadose and groundwater zones

Interception

Snow

Infiltration

Burst Seepage Runoff

Prompt Subsurface Runoff

Groundwater Runoff

Delayed Subsurface Runoff

Trickled Seepage Runoff

Transpiration

Evapotranspiration

Evaporation

Soil Evaporation

Precipitation

Precipitation Excess

Surface runoff

Overland flow

Groundwater Runoff

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Environmental setting where FEMWATER can be employed

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1:Aquifer storage and recovery (ASR) using FEMWATER

STORAGE RECOVERY

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Animation of Total Head: totalhead_unsym.avi

Largest ASR system in the SFWMD7 wells, 9 MGD capacity, since 1997Arsenic not a problem1.7 billion gallons currently storedPump treated surface water to ~750’ deep – sandy portion at top of Floridan aquifer

Marco Island SystemBob Verrastro, 2012 Lower East Coast, Water Supply Plan Update, Workshop #3, June 19, 2012

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Animation of Concentration: Concentration.avi

Marco Island SystemBob Verrastro, 2012 Lower East Coast, Water Supply Plan Update, Workshop #3, June 19, 2012

Largest ASR system in the SFWMD7 wells, 9 MGD capacity, since 1997Arsenic not a problem1.7 billion gallons currently storedPump treated surface water to ~750’ deep – sandy portion at top of Floridan aquifer

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2. Application of FEMWATER to Mitigating a Dredging Site

Model domain (left) and subsurface data point location (right)

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Simulated contour of 0.001 ppt salinity (blue lines) at various times

Proper mitigations (e.g., slurry walls in combination with pumping) could contain the salt with the disposal facility, DA2

Motsu_con.avi

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3: Model of Injection Gallery

Legend

Slurry Wall Location

Surface of Bad Trash

Water TableSurface

Trash (Kh = 1.0 ft/day Kv = 0.5 ft/day)Backfill (Kh = 0.5 ft/day Kv = 0.1 ft/day)Revised Blanket ConfigurationInjection in Blanket Only (80 gpm)No Extraction

Location of Unsaturated Trash

BlanketI_New.avi

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HYDROGEOCHEM: Widely used by government agencies and academia

Aqueous complexation and precipitation-dissolution models (Westall et al., 1976)

Adsorption-desorption processes and models (Davis and Leckie, 1978)

Ion-Exchange (Al Valocchi, et al., 1981) Among the first generic reactive chemical

transport models to include aqueous complexation, precipitation-dissolution, adsorption-desorption, ion-exchange, redox, and acid-base reactions – Dawn of HYDROGEOCHEM Era (Yeh and Tripathi, 1990)

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Environmental setting for HYDROGEOCHEM Simulations

Reaction

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Applications with HYDROGEOCHEM 5.0 (A THC Process Model)

Variably Saturated Flow (H) Thermal Transport (T) Reactive Transport of N reactions among M

Species [C(R)]

T, H, or C Modeling TH, TC, or HC Modeling THC Modeling

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Variably Saturated Flow Problem Description

KKxx xx = K= Kyyyy = K = Kzz zz = 1 dm/day = 1 dm/day

KKxy xy = K= Kxz xz = K= Kyz yz = 0 dm/day. = 0 dm/day.

Initial and Boundary Conditions for Variably Saturated FlowInitial and Boundary Conditions for Variably Saturated Flow

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Steady-stateSteady-statepressure headpressure head

Velocity fields alongVelocity fields alongcross-section x = 0cross-section x = 0

Pressure Field and Flow Animation

Velocity.avi

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Thermal Transport Description

T=308T=308ooKK

T=298T=298ooKK

T=298T=298ooKK

T=298T=298ooKKInitial Condition:

Specific Heat:Specific Heat:CCw w = 1.0E20 dm= 1.0E20 dm22/day/day22//ooK K CCm m = 1.0E19 dm= 1.0E19 dm22/day/day22//ooKK

Thermal conductivity: Thermal conductivity: = 1.0E19 dm= 1.0E19 dm22/day/day22//ooKK

Initial and Boundary Conditions for Thermal TransportInitial and Boundary Conditions for Thermal Transport

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Animation of Temperature Contours for Thermal TransportAnimation of Temperature Contours for Thermal Transport

0

25

50

75

100

Z

050

100150

200

X0

50

100

150

200

Y

XY

Z

TIME: 50 days

0

25

50

75

100

Z

050

100150

200

X0

50

100

150200

YX

Z

T: 298 299 300 301 302 303 304 305 306 307 308

Animation of Temperature

Temperature.avi

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Reaction Network of Various Types (33 reactions, 41 Species)

Reaction No parameterMineral Dissolution and Surface Site Formation Reactions

Fe(OH)3(s) ↔ Fe3+ - 3 H+ (R1) k1f = 0.05

Fe(OH)3(s) ↔ FeOH (R2) *

Aqueous Complexation Reactions

CoEDTA2- ↔ Co2+ + EDTA4- (R3) Logk3f= 2.03, Log k3

b = 20.00

Ca2+ + EDTA4- ↔ CaEDTA2 (R4) Log K4e = 12.32

H+ + EDTA4- + Ca2+ ↔ CaHEDTA- (R5) Log K5e = 15.93

Ca2+ ↔ H+ + Ca(OH)+ (R6) LogK6e= -12.60

Fe(OH)3(s) + EDTA4- ↔ FeEDTA- (R7) Log k7f = 25., Log k7

b = -2.57

Fe3+ + H+ + EDTA4- ↔ FeHEDTA (R8) Log K8e = 29.08

---- -- ---

4H+ + EDTA4 - ↔ H4EDTA (R23) LogK23e= 23.10

H+ + OH- ↔ H2O& (R24) LogK24e= 14.00

Reactive Transport Description (1)

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Adsorption-Desorption Reactions

FeOH ↔ FeO- + H+ (R25) LogK25e=-11.60

--- -- ---

FeOH - H+ + Co2+ ↔ FeO-Co+ (R30) Logk30f = -0.99, Log k30

b = 1.70

FeOH + H+ + Ca2+ + EDTA4- ↔ FeOH2-CaEDTA-

(R31) Log k31f = 25.0, Log k31

b = 1.19

Ion-Exchange Reactions

Mg2+ + 2 ↔ + 2Na+ (R32) Logk32f = -0.75, Log k32

b = -0.5

Ca2+ + 2 ↔ + 2Na+ (R33) Log k33e = 0.6

* This users’ specified equation is modified fromStumm and Morgan, 1996, in which SA is the unit surface area (m2 g-1) of mineral, NS isthe surface site density (mol sites m-2), NA is Avogadro’s number (mol sites per mol),Mmineral is the molecular weight of mineral&The species H2O can be decoupled from the system if its activity is assumed 1.0.

Na 2Mg

2Ca Na

]S[ + ]S[ + ]S[ + ]S[ + ]S[ + ]S[ + ]S[ + ]S[ = [M]MN

NS87654321mineral

A

sA

Reaction Network of Various Types (33 reactions, 41 Species)


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Initial and Boundary Conditions for Reactive TransportInitial and Boundary Conditions for Reactive Transport

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Reactive Transport Description (4)Initial ConditionsInitial Conditions

Species High Concentration Region

Low Concentration Region

C6 (Ca2+) 1.00E-05 1.00E-05C1 (Fe3+) 1.00E-07 1.00E-07C4 (Co2+) 1.00E-05 1.00E-05C2 (H+) 3.00E-05 1.00E-05

C5 (EDTA4-) 1.00E-05 1.00E-05C28 (H2O) 5.56E+01 5.56E+01

C10 (FeEDTA-) 1.00E-05 1.00E-05M (FeO3(s)) 2.00E-05 1.00E-07

C3 (CoEDTA2-) 1.00E-06 1.00E-07

C29 (Mg2+) 1.00E-05 1.00E-05C30 (Na+) 1.00E-04 1.00E-05Site-C29 1.40E-04 1.00E-05Site-C30 7.00E-04 1.00E-05Site-C6 1.50E-04 1.00E-05

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Species Dirichlet B.C Variable B.C-I Variable B.C-IIC6 (Ca2+) 1.00E-03 1.00E-05 0C1 (Fe3+) 1.00E-07 1.00E-07 0C4 (Co2+) 1.00E-05 1.00E-05 0C2 (H+) 1.00E-05 1.00E-05 0

C5 (EDTA4-) 1.00E-03 1.00E-05 0

C28 (H2O) 5.56E+01 5.56E+01 55.56C10 (FeEDTA-) 1.00E-05 1.00E-05 0C3 (CoEDTA2-) 1.00E-03 1.00E-07 0

C29 (Mg2+) 1.00E-05 1.00E-05 0C30 (Na+) 1.00E-04 1.00E-05 0


Boundary ConditionsBoundary Conditions

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Animation of Species S1: S1.avi

M (Fe(OH)3(s)) S1 (FeOH) (R2); Fe(OH)3(s) ↔ Fe3+ - 3 H+ (R1)

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Animation of Species C10: C10.avi

C1 + C5 C10 ; Log k7f = 25.00, Log k7

b = -2.57 (R7)

Fe3+ + EDTA4- ↔ FeEDTA-

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Further Advances: Present and Future

Multiphase flow (aqueous phase, gaseous phase, and super liquid phase, NAPL, etc.)

Thermal Transport (temperature changes induced by fluid injection, associated phase changes and chemical reactions)

Geo-Mechanics (how faults and fractures affect fluid pressure and chemical migration, and the converse of fluid pressure inducing rock deformation and fault displacement)

Reactive Transport (subsurface biogeochemical reactions among chemicals, groundwater/brine, and rock) [aqueous complexation, adsorption-desorption, ion-exchange, precipitation-dissolution, redox, acid-base reactions, microbial-mediated redox, nutrient cycle, carbon cycle, biota kinetics, metal cycle, etc.]

THMC: Thermal-Hydraulic (Hydrology)-Mechanic-Chemical Processes

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Environmental setting for Multiphase Flow System

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Example:Heterogeneous Media,Pumping, and injecting wells

1

2

3

Initial condition0.10.10.8

SSS

Finite element discretization Fluid properties

Material properties

0 31

0 32

0 3 33

1

2

3

21 2

21 2

21 2S

19 2 2

1.0 g/cm

1.4 g/cm

1.0 10 g/cm841.0828 g/cm/day690.0828 g/cm/day15.81 g/cm/day

6.162 10 cm day / g

4.086 10 cm day / g

2.057 10 cm day / g

1.557 10 day / cm

1

2

β

β

MRT

8 2

-131

-132

-121

4.27 10 cm0.25

0.044 cm

0.099 cm

0.11 cm2.2

0ir

nS

k

Total number of nodes = 1485Total number of elements = 1408

165 cm

65 cm

GRAVEL

CLAY

SILT

6 2

12 2

10 2

GRAVEL

4.27 10 cm 0.25CLAY

4.27 10 cm 0.40SILT

4.27 10 cm 0.35

k

k

k

11.2

5 cm

67.50 cm78.75 12.1

875

cm

15 0 21 1

15 0 22 1

15 0 23 1

Boundary condition 1

7.2335 10 - gh g/cm/day

7.3356 10 - gh g/cm/day

7.6113 10 - gh g/cm/day

P

P

P



h

Well position

(63.75, 32.5)(63.75, 30.46875)(63.75, 28.4375)

(67.5, 32.5)(67.5, 30.46875)(67.5, 28.4375)(71.25, 32.5)(71.25, 30.46875)(71.25, 28.4375)


Pumping well

Pumping rate

3

3

0 0.5 days

Pumping rate = 0 cm /day0.5 3 days

Pumping rate = 50 cm /day

Injection well

Injection of water

3

3

0 0.5 days

Injection Rate = 10 cm /day0.5 3 days

Injection Rate = 50 cm /day


1

2

3

Boundary condition 30.10.10.8

SSS

(105, 32.5)(105, 30.46875)(105, 28.4375)

15 0 21 1

15 0 22 1

15 0 23 1


7.0872 10 - gh g/cm/day

7.1893 10 - gh g/cm/day

7.6079 10 - gh g/cm/day

P

P

P

Multiphase Flow Module

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Animation: Case3_Sw.avi, Case3_Sn.avi, Case3_Sa.avi

Time= 0~ 3 day

S2 S3

S1

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Example: instability of a two layered solid body – well known as salt diapirism.

= 22

Material2

= 5x106 S1= 0 S2= -0.2

= -1.0 1= 15 2= 0 3= 0

= 30 = 1x106 S1= 2.5 S2= -7.5

= 0 1= 0 2= 0 3= 0

Material1

g

200

100

1,200

Geomechanical Module

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Deformation initially and at equilibrium for the viscous problem

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Animation for the viscous problem : Viscous.avi

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A THMC Model – HYDROGEOCHEM 6.0, 6.1, 7.0 and 7.1

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A THMC Model – HYDROGEOCHEM 6.0

Any Number of Phase FlowThermal TransportReactive Transport of Any

Number of Reactions among Species

Geo-Mechanical Deformation of Visco-Elastic Materials

All Four Modules Are Explicitly Coupled via Storage Coefficients and/or Capillary Pressure Induced Diffusion

L

M N

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3 Phase FlowThermal TransportGeo-mechanical Deformation

Due to Multi-phase Flow and Reactive transport

Reactive Transport of 40 Species Subject to 28 Reactions

Coupled Processes Modeling with HYDROGEOCHEM 6.0 – Problem Description (1)

40

1. Radioactive wastewater containing high concentration of NpO2+

is injected into a three fluid phase (water, NAPL, and air) system.2. Thermal effects are included.3. Injection effects on geo-mechanics (porosity change and

deformation) are considered.4. Media contain high adsorption sites in Region A.5. Chemistry includes intra phase (homogeneous) reactions and

inter phase (heterogeneous) reactions


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Reaction Network: 28 reaction, 40 species

Water phase reaction No Reaction Constants + -

2 (l)H O H + OH R1 1Log K 14.00

2+ 2-

3 3Ca + CO CaCO l R2 2Log K 3.22 2+ + 2- +

3 3Ca + H + CO CaHCO R3 3Log K 11.43 2+ + +

Ca H + CaOH R4 4Log K 12.85 + 2- -

3 3H + CO HCO R5 5Log K 10.32 + 2-

3 2 32H + CO H CO R6 6Log K 16.67

+ +2 2 2lNpO + H O H NpO OH R7 7Log K 8.85

+ 2-2 3 2 3NpO + CO NpO CO

R8 8Log K 5.60

3+ 2-2 3 2 3 2

NpO + 2CO NpO CO

R9 9Log K 3.5

Air phase reaction No Reaction Constants (g) 4(g) (g) 3(g)O + CH OH + CH R10 10Log K 0.45

(g) (g) (g) (g)O + HCO OH + CO R11 11Log K 21.41

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Inter phase reaction No S = Kd C

+ +2 2l NAPLNpO NpO R12 d, 12K 0.2

+ +2 2lNpO NpO g R13 d, 13K 0.3

2 2 NPALH O H O R14 d, 14K 0.001

2 2 gH O H O R15 d, 15K 0.01

lNAPL NAPL R16 d, 16K 0.01

gNAPL NAPL R17 d, 17K 0.001

lAir Air R18 d, 18K 0.0001

NPALAir Air R19 d, 19K 0.0001

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Inter-phase reaction (Kinetic reaction) No Reaction rates

2 2 k NPALH O H O R20 -5 -220 2 2 k(NAPL)R =10 H O 10 H O

2 2 k gH O H O R21 -5 -321 2 2 k(g)R =10 H O 10 H O

k lNAPL NAPL R22 -5 -222 k(l)R =10 NAPL 10 NAPL

k gNAPL NAPL R23 -5 -223 k(g)R =10 NAPL 10 NAPL

k lAir Air R24 -5 -124 k(l)R =10 Air 10 Air

k NPALAir Air R25 -5 -125 k(NAPL)R =10 Air 10 Air

Adsorption-desorption reaction No Reaction Constants -=SOH H + =SO R26 26Log K 10.30 +2=SOH + H =SOH R27 27Log K 5.40

-2 2 2NpO + H O + =SOH H + = NpO OH SOH R28 28Log K 3.5

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Initial and Boundary Conditions for Multiphase Flow

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Initial and Boundary Conditions for Thermal Transport

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Initial and Boundary Conditions for Reactive Chemical Transport

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Initial and Boundary Conditions for Geo-mechanics Simulation

4848

Mesh and Numerical Parameters


1. A uniform mesh of 1,485 nodes and 1,408 elements2. Total simulation time: 2.985 days3. Initial time step size = 0.0001 day4. Maximum time step size = 0.001 day5. Total time steps: 3,000

49Water coming to the simulated region displaces other two phases.

Contour of degree of saturation for the aqueous phase


50NAPL is displaced by the injection water and moves downward

Contour of degree of saturation for the NAPL phase


51Air is displaced by the injected water and moves upward.

Contour of degree of saturation for the gaseous phase


52

Animation for Degree of Saturation S1_ana.avi

S2_ana.avi S3_ana.avi


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Contour of temperature distribution


54

Animation for Temperature Temperature_ana.avi


55NpO2

+ is transported away from the injected well and is retarded when it reaches the adsorption region.

Contour of Total Dissolved NpO2+


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Animation for Total NpO2+ in each phase D1_ana.avi

D2_ana.avi D3_ana.avi


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Animation for Dissolved Species NpO2+ Naptinum_ana.avi


58NpO2+ is adsorbed when the front of plume reaches the

adsorption site

Contour of total adsorbed NpO2+


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Total Adsorbed_ana.aviAnimation for total adsorbed NpO2+


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The distribution of pH is in the range of 10.50~10.711. pH is relatively low in the region A compared to region B.2. pH is increasing with the coming of the injected NpO2

+. (NpO2+ and H+ are

competing for the site)

Contour of pH


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pH_ana.aviAnimation for pH


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1. Total concentration of CH4 in air phase

Contour of CH4(g)


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Contour of Change of Porosity

1. Porosity change due to the drainage and injection of wastewater 0

0

100%

2. The ration of the change of porosity


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FI_ana.aviAnimation for Porosity Change


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Summaries and Conclusions(1)

The development of groundwater models and their applications to real-world problems has evolved significantly since the late 1970’s.

The coupling groundwater processes include multiphase flow, thermal transport, geo-mechanics, reactive transport, and propagation of electro-magnetic waves (bases of geophysical methods).

The advances of numerical models center around their increasing design capability to foster these coupling processes: from the simplest one-phase groundwater flow to the most complete aforementioned processes.

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Summaries and Conclusions(2)

It is gratifying to involve in the advances of groundwater model development in my career.

We have developed over 100 groundwater models, only a few stands out as de facto standard.

The state of modeling capability is still incomplete to handle complete groundwater processes.

We are fortunate enough to involve in the development of next generation numerical models

We are pleased that our development stands among the forefronts in the world.

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The End

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11 Advances in Computational Models of Subsurface Media: Past, Present, and Future Gour-Tsyh Yeh ( ...

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