Carl Steefel1, Sergi Molins1, Hang Deng1, Christophe Tournassat2, Lauren

Beckingham3, Li Yang1, Jennifer Druhan4, David Trebotich1

1 Energy Geosciences Division, Lawrence Berkeley National Laboratory 2 BGRM, French Geological Survey Orléans, France 3 Auburn University, Alabama 4 University of Illinois, Champaign

Multi-Scale Reactive Transport Modeling

October 25, 2016

Bureau de Recherches Géologiques et Minières

Orleans, France

Acknowledgments

• This work was supported by the U.S. Department of

Energy, Office of Science, Basic Energy Sciences, Chemical

Sciences, Geosciences, and Biosciences Division.

• This work was also supported as part of the Center for

Nanoscale Control of Geologic CO2, an Energy Frontier

Research Center funded by the U.S. Department of

Energy, Office of Science, Basic Energy Sciences.

Work to date has covered a range of scales, but

scales have not been coupled

Multiscale Problem

Coupled processes in reactive transport

Steefel, DePaolo, & Lichtner, 2005

Pore to Continuum Scale

• Pore scale models

• Solid, gas, and liquid interfaces

resolved

• Gradients in concentration and

reaction rate can develop

• Continuum models

• Solid, liquid, and gas all coexist in

space within REV

• Reactions treated as if taking place

throughout control volume

• Fluid phase is well mixed (no

gradients in concentration or rate)

Li et al, 2008

Equations: Pore to Continuum Scale

Pore Scale Continuum or Darcy Scale

Flow

𝜕𝒖

𝜕𝑡+ 𝒖 ⋅ 𝛻 𝒖 + 𝛻𝑝 = 𝜈Δ𝒖

𝛻 ⋅ 𝒖 = 0

𝒒 = −𝒌

𝜇𝛻𝑝

𝛻 ⋅ 𝒌𝛻𝑝 = 0

Transport 𝜕𝑐

𝜕𝑡= 𝛻 ⋅ 𝐷𝛻𝑐 − 𝛻 ⋅ 𝒖𝑐

𝜽𝜕𝑐

𝜕𝑡= 𝛻 ⋅ 𝒟𝛻𝑐 − 𝛻 ⋅ 𝒒𝑐

where 𝒟 = 𝜽𝝉𝐷 + 𝜶𝑳 𝒖

Reaction

−𝐷𝛻𝑐 ⋅ 𝒏 = 𝑘 𝑓(𝒄) 𝑟 = 𝑘 𝑨 𝑓(𝒄)

From Experiment to Characterization to High-

Resolution Simulation

Molins et al, ES&T 2014

Capillary tube experiment on

calcite

Microtomography

at the ALS

Digital image of CaCO3

packed capillary tube for

simulation

Pore-scale reactive transport simulation with 3

billion degrees of freedom

Comparison with

experiment

Fracture Evolution

The formation of an altered layer caused

by preferential dissolution of calcite is

also evident in the µCT images.

The µCT images and

aperture maps showed the

formation of a preferential

flow channel in the

fracture, i.e. wormholing or

channeling

Duperow Experimental Results

Ajo-Franklin et al., 2016

Ajo-Franklin et al., 2016

Movie courtesy Dave Trebotich, Berkeley

Lab

Initial data for simulation from Beamline

8.3.2, Advanced Light Source, Berkeley Lab

Fracture Evolution in Duperow Dolomite

scCO2 saturated brine injected into fracture from left side

High resolution pore scale model showing mineral

dissolution and wormholing

Subsurface Exascale Computing

Exascale Computing: 1018 floating point operations/sec

High resolution pore scale simulations of topology of a single fracture in dolomite using Chombo-Crunch.

Top: Initial geometry of fracture. Bottom: Modified geometry after 18 hours.

2.5D Micro-Continuum Model for

Fracture Evolution

• Each grid is represented as a

continuum

o Porosity: 𝜙𝑖,𝑗 = 𝑏𝑖,𝑗/𝐷𝑍

o Permeability: 𝑘𝑖,𝑗 = 𝑏𝑖,𝑗3 /(12𝐷𝑍)

o Aperture (𝑏) changes as a result of

mineral reactions.

• The fracture is discretized in

two dimensions parallel to

the fracture plane

o Aperture map of the initial

fracture geometry derived

from the µCT images

Deng et al, 2016

The temporal changes cannot be captured, regardless of the parameters used.

A diffusion coefficient on the order of 10-10 m2/s was used for the altered layer.

The simulation results demonstrate that the diffusion limitation caused by the altered layer is the mechanism for decreasing calcite dissolution over time.

2.5D Modeling Results: Effluent Chemistry

Without diffusion limitation With diffusion limitation

Deng et al, 2016

The model captures the spatial pattern of fracture aperture increase.

Without diffusion

limitation With diffusion

limitation Experiment

Ap

ertu

re c

ha

ng

e [m

m]

2D maps of aperture change

2.5D Modeling Results: Aperture Change

Deng et al, 2016

Glass Corrosion

Resolution of Nanoscale Reaction Fronts

A: High resolution atom probe tomography (APT) profile across glass alteration front.

B: Schematic representation of distribution of fronts for 25 year altered glass shown on left.

Gin et al. (2013)

Application to nanoscale reaction fronts resulting from

borosilicate glass corrosion/weathering over 25 years

mKC Model for Glass Corrosion

Diffusion of water through the pristine glass and its alteration products;

Ion exchange between water and the cations in the glass;

Kinetically controlled hydrolysis reactions resulting in breaking of glass

network bonds (Si, B, Al);

Multicomponent diffusion of ions through the glass corrosion products;

Precipitation reactions for amorphous and/or crystalline phases of variable

composition that are kinetically and thermodynamically controlled;

Kinetically controlled ripening and/or densification reactions that can reduce

the porosity and/or pore connectivity (and thus the diffusivity) of the

corrosion products;

Kinetically and thermodynamically controlled formation of new crystalline

phases (e.g., smectite, zeolite), with possible consequences for the transport

properties of the corrosion layer;

Flow and diffusion in the aqueous phase adjacent to the glass surface.

Steefel et al, 2015

Simulation of Nanoscale Reaction Front

𝑅𝑐𝑜𝑟𝑟 = 𝑘𝑎𝐻−ℎ𝑦𝑑𝑟𝑎𝑡𝑒𝑑10 1 −

𝑄𝑎𝑚−𝑠𝑖𝑙𝑖𝑐𝑎

𝐾𝑎𝑚−𝑠𝑖𝑙𝑖𝑐𝑎

3

Corrosion rate law used in modeling

Front Position over Time Simulated Elemental Profiles

• Overall corrosion rate is controlled

by diffusion through pristine glass

• Relatively rapid glass corrosion

once glass is hydrated via diffusion-

cation exchange

• Nonlinear dependence on glass

hydration to capture front

separation

Modeling Coupled Nucleation

and Growth

Modeling classical and non-classical nucleation

and crystal growth/transformation

ACC ACC r

calcite ACC ACC calcite r

calcite calcite calcite r

R k G

R A k G

R A k G

Approach based on Crystal Size Distributions (Steefel & Van Cappellen, 1990)

Approach based on mineral “pools”, Li, Jun, & Steefel, in prep.

Nucleation of Amorphous Calcium

Carbonate (ACC) followed by

“aging” to more stable calcite

Coupled Flow-Diffusion Experiments in

Micro-Capillary Tubes

Steefel & Yang, in prep.

Dif

fusi

on

-Con

troll

ed

Dirichlet

boundary condition No flux

boundary condition

Flow

Forsterite

0.000 0.005 0.010 0.015 0.020 0.025 0.030

0.00E+000

2.00E-009

4.00E-009

6.00E-009

8.00E-009

1.00E-008

1.20E-008

1.40E-008

1.60E-008

1.80E-008

Mag

ne

site m

ass (

mo

le)

dist_x (m)

Mass of magnesite precipitation observed

Maximum amount of magnesite that could have formed from corresponding forsterite dissolution

Secondary Magnesite Precipitation vs

Primary Forsterite Dissolution

~ 56% all Mg2+ released via forsterite dissolution has been precipitated as magnesite

Magnesite mapped by

Raman spectroscopy

Secondary Magnesite Precipitation

Rprecipitation is the overall precipitation;

Aforsterite, the surface area of forsterite for heterogeneous

nucleation of magnesite;

Amagnesite : surface area of neoformed magnesite

Nucleation Crystal Growth

3 2

0 23 3exp

3 lnprecipitation forsterite magnesite growth magnesite

B

R J A A k fk T

06/29/2016 Goldschmidt2016

Conceptual Model for Formation of

Secondary Magnesite Pattern

NUCLEATION OF MAGNESITE: Where the pore fluids are supersaturated with respect to

magnesite as a result of forsterite dissolution, the exponential function of the heterogeneous

nucleation rates produces a peak-shaped distribution of initial magnesite nuclei

EPITAXIAL GROWTH OF MAGNESITE: These initial magnesite seeds quickly catalyze

growth of magnesite on magnesite and the peak grows

SUPPRESSION OF SUBSEQUENT NUCLEATION: The growth of the magnesite peaks

reduces supersaturation locally within some diffusion distance of the peak

time

Suppression of

nucleation Suppression of

nucleation

Transition to Crystal Growth Initial Nucleation Zone

Modeling Coupled Nucleation and

Growth of Magnesite with CrunchTope

σ = 150 mJ/m2

• Forsterite rate constant:

10-9 mol/m2/s

• Magnesite rate constant:

10-8 mol/m2/s

• D = 10-9 m2/s

Modeling with CrunchTope:

Steefel et al, 2015, Reactive transport

codes for subsurface environmental

simulation, Computational Geosciences

19

Effects of nucleation and

crystal growth on pore structure

Sc1 Sc2 Sc3 Sc4

Sc1 Sc2 Sc3 Sc4

Sc2 Sc3 Sc4

a)

b)

c)

Sc1

Solid 2

Solid 1

C. Noiriel et al, 2015

Flow velocity fields for

various crystal growth

scenarios

Scenarios for precipitation

in porous grain pack

Modeling Isotopic Fractionation

Calcite Precipitation with Kinetic Isotope

Fractionation

Solid Fluid  

Rf = kf [Ca][CO3]

 

Rb = kb[CaCO3]

Gebrehiwet et al., 2012 20 mm

2 233( )net f b f f eq CaCO sCa CO

R R R k a a k K a

Based on Principle of Detailed Balancing

Lasaga, 1981; DePaolo, 2011

Calcite Precipitation with Isotopic

Re-Equilibration

4444 3

44

3

[ ]

[ ]Ca

CaCOa X

CaCO

44RN =44kb

44 X[44Ca][CO3]

Ksp

44 X-1

æ

è ç ç

ö

ø ÷ ÷

40RN =40kb

40X[40Ca][CO3]

Ksp

40X-1

æ

è ç ç

ö

ø ÷ ÷

Druhan et al., 2013; Steefel et al. 2014

δ44C

a (

‰)

fluid

bulk mineral

days

δ44C

a (

‰)

fluid

bulk mineral

days

δ44C

a (

‰)

fluid

bulk mineral

days

Druhan et al., 2013; Steefel et al. 2014

Isotopic Equilibration of Calcium in Calcite

Isotopically irreversible In equilibrium with bulk In equilibrium with surface

Kinetic Fractionation as a Function of

Growth Rate

Isotopic ratio at boundary

DePaolo, 2011

Calcite Precipitation at

Low Damköhler Number

Fractionation at Variable Damköhler Number

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 20 40 60 80 100

Log Q/Keq

Su

pers

atu

rati

on

(L

og

Q/K

eq

)

Distance (cm)

Approach to chemical

equilibrium, so

kinetic fractionation

is reduced

Rayleigh distillation produces is linear log

Concentration d44Ca space

New Frontiers

Watershed Concentration-Discharge Relations: Linear or Nonlinear?

Distribution of residence times

in a high elevation watershed,

Colorado (Engdahl and

Maxwell, 2015)

Hypothetical distribution of

residence time and reaction rates

(Damköhler number) in a

mountainous catchment

• Fukushima Daiichi Nuclear Power

Plant accident occurred in March

2011, spreading airborne

contamination out to sea and to

northwest over a large tract of land

• Need to understand behavior of

individual “compartments” (farmland,

forest soils, water bodies, and

groundwater systems) and their

interactions.

• Predictive modeling based on high

resolution characterization is needed

to evaluate effectiveness of active

and passive remediation options.

Fukushima Nuclear Accident

35

Exascale Computing Trajectory

Pore-scale soil processes (Molins et al, 2014)

Extreme resolution terrestrial modeling Nested hierarchical scale terrestrial modeling

Watershed-scale water and

geochemical cycling is a

problem that will require

Exascale Computation

Summary Points

• Multi-scale nature of reactive transport in earth and

environmental systems remains a challenge

• Improved estimates of reactivity are possible when physical

and chemical heterogeneity are taken into account

• Mineral nucleation, mostly neglected in reactive transport

models, may have a dramatic effect on evolution of both

physical (permeability) and geochemical properties

• Rock or sediment texture still poorly captured in reactive

transport models (needs to be focus of next 10 years of

software development)

• Impermeable, clay-rich materials will require treatment of

electrostatic effects on transport and sorption

• Fully coupled corrosion models may provide insight into

waste form durability

Reactivity in Subsurface

Formations

Reactivity of Sediments, Nagaoka Japan

Haizume Formation Predominantly sandstone

Thin layers of shales

(siltstone to mudstone)

interbedded within

sandstone layers

Mineralogy (XRD)

Abundant quartz,

plagioclase, K-feldspar,

smectite and pyroxene

Injection depth = 1100

m

T = 48°C

P = 108 bars

40 t CO2/day, total of 10 kt CO2 stored

CO2 injection period: 7/2003 –1/2005

k = 6 mD

Thickness = 60 m

Characterization Approach for Nagaoka Sediment

Beckingham et al, 2016, Geochimica

2-D SEM-BSE & QEMSCAN of Nagaoka

Sediment

Beckingham et al, 2016

Sediment dominated by smectite, plagioclase, pyroxene +

volcanic glass

Beckingham et al, 2016, Geochimica et Cosmochimica Acta

Surface Area Approximations

1. Disaggregated sediment experiments in

well-stirred reactor

2. Compare with intact coreflood experiments

(pore structure intact)

Nagaoka Experimental Approach

46

Cation leaching (Ca+Na+K >

SiO2) in glass phase over first 300

hours

Fit with mineral volume

percentages from QEMSCAM

Mapping—All grains accessible

Disaggregated Sediment Experiment

With and without glass phase Grain Size Distribution

Including Grain Size Distribution and Glass

48

Best Fit with Image Analysis Surface Area

Simulation of Coreflood Experiment using

Disaggregated Sediment Experiment RSA

Overprediction: EPIC FAIL!

10x to 20x lower SSA than Disaggregated Sediment experiment values

Second glass with cation leaching required to match results

Core Modeling with Pore-Accessible RSA

Contaminant Migration

53

Multi-Site Cation Exchange Models

• Multi-site formulation may

expand range of chemical

conditions over which

sorption can be described

• For example, the case of Cs+,

an important contaminant at

Hanford

Binary exchange

data from Zachara

et al. (2002)

Retardation of Radionuclides

1

porosity

bulk density of soil or sediment

distribution coefficient (ml/g)

B d

f

B

d

KR

K

f

C v C

t R x

Advection Equation with Retardation

Modeling of Cs breakthrough using

column experiment-derived parameters

Using column-derived data,

an improved parameterization is possible

(Steefel et al., 2003)

Cesium Kd from Ion Exchange Model

Cesium Kd in Hanford

Sediments

S-SX Tank Farm Leaks at Hanford,

Washington

Investigate 216,000 liter leak which occurred over

1 week in 1965 at the SX-115 tank

Flow and Heat Transport Modeling of

SX-115 Leak

Steefel, 2004

3D Reactive Transport Modeling of

SX-115 Leak

Steefel, 2004

Match of Field Data with Column

Parameters

Steefel, 2004

Cs Migration below Hanford SX-108 Tank

Steefel et al., 2005

Greatest mobility of 137Cs was below the

Hanford SX-108 tanks

Abject failure of Kd models spawned a major

Science and Technology Program at Hanford

funded by the U.S. Department of Energy