The role of magnesite spatial distribution patterns in

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Geochimica et Cosmochimica Acta 155 (2015) 107–121
www.elsevier.com/locate/gca
The role of magnesite spatial distribution patterns in
determining dissolution rates: When do they matter?
Fatemeh Salehikhoo a, Li Li a,b,c,⇑
a
John and Willie Leone Department of Energy and Mineral Engineering, The Pennsylvania State University, University Park, PA 16802,
United States
b
Earth and Environmental Systems Institute, The Pennsylvania State University, University Park, PA 16802, United States
c
EMS Energy Institute, The Pennsylvania State University, University Park, PA 16802, United States
Received 1 July 2014; accepted in revised form 27 January 2015; Available online 7 February 2015
Abstract
We systematically explore the role of magnesite distribution patterns in dictating its dissolution rates under an array of flow
velocity and permeability contrast conditions using flow-through column experiments and reactive transport modeling.
Columns were packed with magnesite distributed within quartz matrix in different spatial patterns: the Mixed column has
uniformly distributed magnesite while the zonation columns contain magnesite in different number of zones parallel to the main
flow. Dissolution rates are highest under conditions that maximize water flowing through the magnesite zone. This occurs under
fast flow and high-permeability or uniformly distributed magnesite zones. Under high flow and low permeability magnesite conditions, dissolution only occurs at the magnesite–quartz interface, leading to rates an order of magnitude lower in the One-zone
columns than those in the Mixed columns. Spatial patterns do not make a difference under low flow conditions when the system
approaches equilibrium (v < 0.36 m/d) or under conditions where magnesite zones have higher permeability than quartz zone.
The bulk column-scale rate depends on Ae through RMgCO3 ;B ðmol=sÞ ¼ 109:60 Ae , where Ae is the surface area that effectively
dissolves with IAP/Keq < 0.1. The rate constant of 109.60 is very close to 1010.0 mol/m2/s under well-mixed conditions,
suggesting the potential resolution of laboratory-field rate discrepancy when Ae, instead of the total BET surface area AT, is
used. The Ae values are 1–3 orders of magnitude lower than AT. The effectively-dissolving magnesite–quartz interface areas vary
between 60% and 100% of Ae, pointing the importance of “reactive interfaces” in heterogeneous porous media. This work
quantifies the significance of magnesite spatial distribution patterns. It has important implications in understanding biogeochemical processes in the Critical Zone and in the deep subsurface, where spatial variations in mineral properties prevail.
Ó 2015 Elsevier Ltd. All rights reserved.
1. INTRODUCTION
Mineral dissolution reactions occur ubiquitously and are
important in understanding earth system formation and
functioning in applications relevant to water, energy, and
environment. Different minerals exhibits orders of magnitude variations in permeability and are distributed in
⇑ Corresponding author at: John and Willie Leone Department
of Energy and Mineral Engineering, The Pennsylvania State
University, University Park, PA 16802, United States.
http://dx.doi.org/10.1016/j.gca.2015.01.035
0016-7037/Ó 2015 Elsevier Ltd. All rights reserved.
patterns varying from uniform distribution in one extreme
to layered or clustered patterns at the other end of the spectrum. For example, clays typically are present as low permeability “lenses”, while carbonates are commonly distributed
as scattered cementation in sandstones of much higher permeability (Koltermann and Gorelick, 1996; Peters, 2009).
Preferential flow paths and interfaces abound in the
Critical Zone, defined as the zone from the top of the tree
canopy to the top of the bedrock (Brantley and Lebedeva,
2011; Chorover et al., 2011), due to the presence of roots,
macro pores, and different soil horizons (Beven and
108
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
Germann, 1982; Zhang et al., 2014). Spatial heterogeneities
in conductive properties regulate water distribution and local
flow velocities, while those in geochemical properties and
mineral reactivity determine where and how much reactions
occur. The combination of the two types of heterogeneities
controls the extent and rates of water–rock interactions.
The role of spatial variations in porosity and permeability has been studied for decades (Sudicky, 1986;
Adams and Gelhar, 1992; Fiori et al., 2010; Sudicky
et al., 2010; Dagan et al., 2013; Pedretti et al., 2013) and
has been known to be pivotal in determining flow and
non-reactive solute transport (Zinn et al., 2004;
Willingham et al., 2008; Willmann et al., 2008; Rolle
et al., 2009; Heidari and Li, 2014). Extensive work has been
done to capture the anomalous, non-Fickian solute transport commonly observed in heterogeneous porous media
using effective models including the dual porosity model
(Gerke and Vangenuchten, 1993), multi-rate mass transfer
model (Haggerty and Gorelick, 1995), as well as non-local
methods such as Continuous Time Random Walk
(Berkowitz et al., 2006) and Fractional Advection
Dispersion Equation (fADE) (Benson et al., 2000a, b).
The collective wisdoms on physical heterogeneities,
however, have not been incorporated in understanding
the role of spatial patterns in determining mineral reactions.
Chemical weathering rates inferred from soil profiles measured in field studies are a natural result of spatial heterogeneities and have been extensively documented to be 2–6
orders of magnitude lower than laboratory-derived rates
(Swoboda-Colberg and Drever, 1993; White and Brantley,
2003; Maher et al., 2006; Zhu et al., 2010). Water chemistry
and organic carbon content have exhibited close tie to the
spatial distribution of different zones with distinct physical
and biogeochemical characteristics (Andrews et al., 2011;
Jin et al., 2011). Quantification of the effects of mineral spatial patterns, however, is challenging due to the complex
process coupling.
The effects of physico-chemical heterogeneities on biogeochemical reactions have started to be addressed for
microbe-mediated redox reactions (Zhang et al., 2010b; Li
et al., 2011; Scheibe et al., 2011; Bao et al., 2014), adsorption–desorption (Liu et al., 2008, 2013; Deng et al., 2012;
Sassen et al., 2012; Wang and Li, 2015), and mineral dissolution and precipitation (Willingham et al., 2008; Werth
et al., 2010; Zhang et al., 2010a; Navarre-Sitchler et al.,
2013; Atchley et al., 2014; Salehikhoo et al., 2013).
Mineral spatial distribution has been observed to cause
unstable dissolution fronts and wormhole development
(Smith et al., 2013). Liu et al. (2013) concluded that spatial
patterns of sediment grains that led to preferential flow
paths result in much slower uranium desorption compared
to those in relatively homogeneous columns. Existing work
mostly documents the observation of impacts through
numerical experiments and to a lesser degree, flow-through
pore-scale or column experiments.
Despite of recent advances, there is a significant lack of
data and mechanistic understanding on the role of spatial
heterogeneities in determining mineral reaction rates. As a
result, predicting (bio)geochemical processes in heterogeneous porous media, whether they are shallow Critical
Zone or deep subsurface, has continued to present a major
challenge for earth and environmental systems. The objective here is to understand and quantify how and to what
extent the spatial patterns of magnesite, a representative
carbonate mineral, in controlling its dissolution under an
array of flow velocity and permeability contrast conditions.
Using columns packed with the same total amount of magnesite however distributed in different spatial patterns, this
work expands Li et al. (2014) by investigating a large variable space, with the ultimate goal of understanding general
principles that underlie the dependence of mineral dissolution on spatial patterns. All measured data, including those
from this work and those from our previous work
(Salehikhoo et al., 2013; Li et al., 2014), are available in
Fig. 1. (A) Schematic figures of columns with four spatial patterns of magnesite (white) and sand (sand color): Mixed, Three-zone, Two-zone,
and One-zone. A total of seven columns were packed into two sets of columns with different permeability contrasts. The MgHigh columns
were packed with the same grain sizes of magnesite and quartz (354–500 lm) and have higher permeability magnesite zone with a jratio,Mg/Qtz
of 1.2. The MgLow columns have smaller magnesite grains (297–354 lm) and lower permeability magnesite zone with a jratio,Mg/Qtz of 0.74.
(B) A 3D schematic of the One-zone column and its radial cross-section representation. The symbol qi and ci represent the flow rates and
concentrations from the annulus between radius ri and ri1.
Table 1
Physical and geochemical properties of columns*.
MgLow Columns (jratio,Mg/Qtz = 0.74)
jratio,Mg/Qtz
/ave
/Mg,one-zone
/Qtz,one-zone
7
VFMg,Mg,one-zone
8
VFQtz,Mg,one-zone
6
Two-zone
297–354 lm, 2.04 m2/g
354–500 lm, 0.10(± 0.028) m2/g
11.59
10.48
83.53
76.47
10.60
10.48
–
0.74
0.05
–
–
–
0.05
0.30
3.40
14.00
(±0.05)
(±2.09)
–
–
0.347
0.403
–
–
–
–
–
–
–
–
One-zone
Mixed
Three-zone
Two-zone
One-zone
11.27
74.58
10.99
0.74
–
–
0.20
7.80
(±0.12)
–
0.422
–
–
–
–
11.90
78.04
12.00
1.10
0.07
0.004–0.008
0.15
10.74
(±0.03)
1.20
0.395
0.38
0.54
0.80
0.20
354–500 lm, 1.87(±0.54) m2/g
10.45
75.58
10.57
1.10
0.07
0.003–0.008
0.25
6.69
(±0.04)
0.74
0.410
0.37
0.56
0.74
0.26
11.47
76.49
11.37
–
0.05
–
0.05
8.26
(±0.06)
–
0.410
–
–
–
–
11.25
76.86
11.12
0.60
–
–
0.10
12.30
(±0.004)
–
0.407
–
–
–
–
*
A total of 7 columns were packed as listed here. All 7 columns were carried out under the flow velocities of 0.03, 0.36, 3.60, 7.20, and 18.00 m/d. In addition, the Mixed and One-zone MgHigh
and MgLow columns were run at 0.015 m/d. This adds up to a total of 39 experiments. Calculation has shown that the amount of dissolved magnesite is less than 0.1% of the overall packed
magnesite. As such, we assume that the Mg zone properties remain constant during experiments.
1
The percentage of the magnesite grain volume per total volume of the solid phase (magnesite and sand).
2,3
aL and aT are the longitudinal and transverse dispersivity defined in Eqs. (2) and (3), respectively. They were obtained by 2D reactive and non-reactive transport simulations. Note that there are
no aL and aT values for the Two-zone and Three-zone columns because these columns were not simulated in 2D domain. For the Mixed columns, aT does not have impact on tracer and Mg(II)
breakthrough so no values were obtained. For the One-zone column, the aT values were 0.008, 0.008, 0.008, 0008, 0.004, 0.003, and 0.003 cm for the flow velocities of 0.015, 0.03, 0.36, 3.60, 7.20,
and 18.00 m/d, respectively.
4
aL0 are the longitudinal dispersivity obtained using 1D non-reactive transport simulation without considering details of spatial heterogeneity.
5
Effective permeability calculated based on Darcy’s law using measured flow rates and pressure gradient.
6
/ave, /Mg,one-zone, and /Qtz,one-zone are average porosity, porosity of the Mg zone, and porosity of Qtz zone in the One-zone columns, respectively.
7,8
VFMg,Mg,one-zone and VFQtz,Mg,one-zone are magnesite and quartz volume fractions in the Mg zone in the One-zone columns, respectively.
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
Mixed
Magnesite (Mg) grains
Quartz (Qtz) grains
Mg (gram)
Qtz (gram)
1
VFMg (Solids)
Diameter of Mg zone (cm)
2
aL (cm)
3
aT (cm)
4 0
aL (cm)
5
jeff (1013 m2)
MgHigh Columns (jratio,Mg/Qtz = 1.20)
109
110
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
Earth Chem data library (http://www.earthchem.org/)
(Salehikhoo and Li, 2015).
2. METHODOLOGY
This work uses column experiments and reactive transport modeling approach similar to our previous work (Li
et al., 2014). Here we briefly highlight parts of the methodology necessary for understanding the rest of the paper.
Columns were packed with mixed and zoned patterns,
where magnesite was distributed in different number of
zones in parallel to the main flow (Fig. 1). All column properties are listed in Table 1. Reactive transport modeling was
used with constraints from data to understand physical and
geochemical heterogeneity coupling under a wide range of
permeability contrast ratios between 0.01 and 12.0.
Mineral volume fraction, mineral preparation procedure,
and inlet solution were kept the same as in Li et al.
(2014) for easy comparison.
2.1. Column experiments
2.1.1. MgHigh and MgLow column sets
Two sets of plexiglass columns with a diameter of
2.56 cm and a length of 10.5 cm were packed. The
MgHigh columns have a higher permeability ratio of magnesite over quartz, jratio,Mg/Qtz, of 1.2 than that of the
MgLow columns (0.74). Each column set has a Mixed column and zonation columns with different numbers of magnesite zones (Fig. 1A). The difference in permeability ratios
was achieved by using different magnesite grain sizes, with
354–500 lm and 297–354 lm in the MgHigh and MgLow
columns, respectively. Their corresponding BET surface
areas are 1.87 and 2.04 m2/g, respectively. The surface areas
are in the high end of literature values for grounded
magnesite (0.0662–0.224 m2/g) (Pokrovsky et al., 2005;
Saldi et al., 2012) and are similar to those of chalk cores
from carbonate reservoirs around 2.0 m2/g (Austad et al.,
2012). The quartz BET surface area of 0.10 m2/g is similar
to literature values between 0.06 and 0.10 m2/g (Colon
et al., 2004; Nishiyama and Yokoyama, 2013). The magnesite volume percentages in all columns are 11.02 ± 0.20%
and 10.55 ± 0.06% of the total solid volume for the
MgHigh and MgLow columns, respectively.
2.1.2. Column properties
The average porosity was determined by the mineral
weight, density, and total column volume. For the zonation
columns, the packing resulted in different porosities for the
magnesite and sand zones. For the One-zone column, the
porosity and mineral volume fraction of individual zones
were calculated based on the mass and volume conservation
of the columns, as detailed in Li et al. (2014). The effective
permeability was determined by measuring pressure gradients and by using Darcy’s law. The permeability ratio
between the individual zones of the One-zone columns were
quantified by reproducing the tracer experimental data, as
will be detailed later.
2.1.3. Surface areas
We defined three surface areas and two surface area
ratios. The total BET surface area AT was calculated as
the product of the total magnesite mass (g) and the measured BET surface area (m2/g) for the whole column. It is
constant across all columns within each column set. The
effective surface area Ae is the magnesite surface area bathed
in far from equilibrium fluids with IAP/Keq lower than 0.1
and contributes significantly to the overall column-scale
rates. The choice of 0.1 was made based on the analysis
of the 2D simulation outputs, which indicate that the
local rates with IAP/Keq < 0.1 dominates the overall
column-scale rates. The ratio Ae/AT quantifies the portion
of the effectively-dissolving surface area.
The interface surface area AI is the Ae at the immediate
vicinity (within 2 mm) of the Mg–Qtz interface. For the
Mixed column, all magnesite and sand grains are assumed
to be in contact with each other so that AI equals to Ae.
For the One-zone columns, the 2 mm thickness at the Mg–
Qtz interface encompasses the boundary grid blocks that
have orders of magnitude higher rates than their counterparts at the same distance from the inlet. The ratio AI/Ae
defines the contribution of the dissolving surface area at
the Mg–Qtz interface to Ae.
2.1.4. Non-reactive tracer test for dispersivity determination
During the tracer tests, effluent samples of sodium bromide were collected every 0.2 residence time and were analyzed using Dionex ICS2500 Ion Chromatography (IC).
Bromide transport in the Mixed and One-zone columns
Table 2
Initial and boundary conditions.
Species
Initial concentrations (mol/L, except pH)
Inlet concentrations (mol//L, except
pH)
pH
Total Inorganic Carbon
(TIC)
Mg(II)
8.80
3.43E3 (Approximate, close to equilibrium with magnesite)
4.00
1.07E5 (in equilibrium with CO2
gas)
0.00
Na(I)
Varies between 0.52E5 to 1.20E5, depending on experimental
conditions
1.00E3
Cl(-I)
Br(-I)
1.00E3
0.00
SiO2(aq)
1.00E5
1.00E3 (in dissolution experiment)
1.12E3 (in tracer experiments)
1.00E3
0.00 (in dissolution experiments)
1.20E4 (in tracer experiments)
1.00E5
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
dispersion coefficients DL (m2/s) and DT (m2/s) are calculated as follows:
was simulated using advection and dispersion equation
(ADE, shown later in Eq. (1) however without the reaction
term) in a 2D domain using the reactive transport code
CrunchFlow. The measured porosity and flow rate were used
as input while the local longitudinal dispersivity (aL) and permeability ratios were determined by the best fit to the bromide breakthrough data. The global dispersivity value (a0 L)
was obtained by running 1D ADE simulation using the average properties without explicitly considering spatial
heterogeneities.
DL ¼ D þ aL vz
DT ¼ D þ aT vx
ð2Þ
ð3Þ
Here aL and aT are the longitudinal and transverse dispersivity (m). The dispersion coefficients vary spatially due to
the non-uniform permeability distribution.
Magnesite dissolves through three parallel reactions
(Plummer and Wigley, 1976; Chou et al., 1989) (Table 3).
Under acidic conditions (pH < 6.0), reaction (1) dominates;
under higher pH conditions, reaction (3) dominates.
Reaction (2) is important under CO2-rich conditions. The
overall rate follows the Transition State Theory (TST)
based rate law:
IAP
ð4Þ
rMgCO3 ¼ k 1 aHþ þ k 2 aH2 CO3 þ k 3 A 1 K eq
2.1.5. Flow-through dissolution experiments
The dissolution experiments were run with flow velocities at 0.015, 0.03, 0.36, 3.60, 7.20, and 18.00 meters/day
(abbreviated as m/d) with corresponding average residence
times from 3,956.40 to 3.36 minutes. The flow velocities
from 0.015 to 0.36 m/d are typical for groundwater in
natural porous media (Knapp, 1989; Newell et al., 1990),
while those from 3.60 to 18.00 m/d are typical for fractures
and engineered systems. The inlet and initial solution
compositions are listed in Table 2. Before each experiment,
each column was flushed with a solution at the pH of 8.8
and flow velocity of 18.00 m/d to ensure similar initial
conditions. Effluent samples were analyzed for cation concentrations using a Perkin-Elmer Optima 5300 Inductively
Coupled Plasma Atomic Emission Spectrometry (ICPAES).
where k 1 , k 2 , and k 3 are the rate constants (mol/m2/s) for
their corresponding reactions, aHþ and aH2 CO3 are the activities of the hydrogen ion and carbonic acid, A is surface
area of magnesite (m2/m3 pore volume), IAP is the ion
activity product defined as aMg2þ aCO2 , and Keq is the equi3
librium constant. The ratio IAP/Keq quantifies the distance
from equilibrium. The magnesite kinetic and thermodynamic values were the same as those from Salehikhoo
et al. (2013).
The 2D simulation domain is 25 100 mm in width and
length with the resolution of 1 mm. For the One-zone column, the middle 11 100 grids are for the Mg zone and
the two 7 100 grids at the sides are for the Qtz zone.
The heterogeneous mineral distribution results in spatially
variable concentration and flow velocities. To take that into
account, average effluent concentrations were calculated as
the local flow rate-weighted average concentration (Fig. 1B
and Li et al. (2014)).
2.2. Reactive transport modeling
Two-dimensional simulation was carried out for a thin
slice of the 3D Mixed and One-zone columns (Fig. 1B)
using the extensively used reactive transport code
CrunchFlow. Mass conservation equations were solved
for the concentrations of primary species. The concentrations of secondary species were calculated through the mass
action laws and the primary species. As an example, the
reactive transport equation for Mg(II) is as follows:
@ðC MgðIIÞ Þ
þ r DrC MgðIIÞ þ vC MgðIIÞ þ rMgCO3 ¼ 0
@t
111
2.3. Dissolution rates at different scales
2.3.1. Local dissolution rates
The local dissolution rate rMgCO3 ;i is the rate in the grid
block i based on Eq. (4) and is from the modeling outputs.
ð1Þ
Here CMg(II) is the total Mg2+ concentration (mol/m3 pore
volume), t is time (s), D is the combined dispersion–diffusion tensor (m2/s), v (m/s) is the flow velocity that can be
decomposed into vz and vx in the directions longitudinal
and transverse to the main flow, rMgCO3 is the magnesite dissolution rate (mol/m3 pore volume/s).
The dispersion–diffusion tensor D is defined as the sum
of the mechanical dispersion coefficient and the effective
diffusion coefficient in porous media D*(m2/s). At any particular location (grid block), their corresponding diffusion/
2.3.2. Column-scale dissolution rates
The column-scale bulk rate RMgCO3 ;B ðmol=sÞ was
calculated based on the column mass balance:
RMgCO3 ;B ¼ QT C MgðIIÞ;out C MgðIIÞ;in
ð5Þ
Here QT is the total flow rate (L/s), C MgðIIÞ;out and C MgðIIÞ;in
are the effluent and influent Mg(II) concentrations, respectively (mol/L). The area-normalized rates RMgCO3 can be
Table 3
Magnesite dissolution reactions, and thermodynamic and kinetic parameters.
Reactions
þ
2þ
þ HCO
3
2þ
MgCO3 ðsÞ þ H () Mg
MgCO3 ðsÞ þ H2 CO03 () Mg þ 2HCO
3
MgCO3 ðsÞ () Mg2þ þ CO2
3
(1)
(2)
(3)
Log Keq
k (mol/m2/s)
2.50
3.85
7.83
6.20 105
5.25 106
1.00 1010
112
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
obtained by dividing RMgCO3 ;B with total BET surface
area AT. The difference between the zoned columns
RMgCO3 ;B;Z and the corresponding Mixed column
RMgCO3 ;B;M is quantified below:
bZ=M
RMgCO3 ;B;Z
¼
RMgCO3 ;B;M
ð6Þ
A rate ratio of one means the same rates from the zonation
column and Mixed column. Large deviation from 1.0
indicates significant effects of spatial patterns.
3. RESULTS
3.1. Column properties
3.1.1. Porosity and permeability
The two column sets have different porosity, permeability, and dispersivity values (Table 1). The porosity of
the Mixed MgLow column (0.35) is the lowest among all
columns, likely because smaller magnesite grains fill in the
pore space between large grains. This is further confirmed
by its lowest permeability among all 7 columns. Similar
observation has been made in other studies (Heidari and
Li, 2014; Wang and Li, 2015). The effective permeability
values vary from 3.4 1013 to 14.0 1013 m2. The
Two-dimensional flow fields for the Mixed and One-zone
MgHigh and MgLow columns at the average flow velocity
of 7.2 m/d are shown in Fig. 2A. For the Mixed column,
flow rates are homogeneously distributed. For the One-zone
columns, the flow fields are dictated by the jratio,Mg/Qtz of 1.2
and 0.74. With the same overall flow rate, the flow velocity
in the magnesite zone is higher than that in the sand zone by
a factor of 1.2 in the One-zone MgHigh column.
3.1.2. Dispersivity
The bromide breakthrough curves (BTC) of the MgHigh
columns almost overlap, with the zonation columns having
slight tails (Fig. 2C). For the MgLow columns, the BTC of
the Mixed column follows the standard ADE curve while
those of the zonation columns show much longer tails than
their MgHigh counterparts, indicating larger effects of spatial heterogeneities. The 2D ADE reproduced the tracer
BTCs for the Mixed and the MgHigh columns relatively well.
For the One-zone MgLow columns, the 2D ADE equation
reproduced the longer tail however also earlier breakthrough
than the data, indicating its inadequacy in capturing solute
transport in heterogeneous porous media (Bijeljic et al.,
2011; Pedretti et al., 2013). The column-scale (global) longitudinal dispersivity values (aL0 ) of the Mixed columns are
lower than that of the zonation columns and are the same
as their local longitudinal dispersivity aL because of their
homogeneous distribution. The aL0 values for the MgLow
columns are higher than that of their corresponding
MgHigh column. The global aL0 values are larger than the
local aL values, because dispersivity increases with spatial
scale, one of the major findings in subsurface stochastic
hydrology (Gelhar et al., 1992; Hochstetler et al., 2013).
Simulation results show that the transverse dispersivity
aT values have negligible impacts on the tracer breakthrough, a similar observation to those in literature
(Ballarini et al., 2014). However, it is critical in reproducing
Fig. 2. (A) Predicted spatial profiles of local flow velocities at 7.2 m/d. With the same flow rates, water is distributed according to the
permeability ratio and therefore flows more through the higher permeability magnesite zone in the One-zone MgHigh column than that in the
One-zone MgLow column. (B) Global (a0 L) and local (aL) dispersivity values in different columns. The zonation columns of both sets have
higher a0 L than that of the corresponding Mixed columns. (C) and (D) Experimental (symbols) and 2D transport modeling output (lines) of
the Br BTC for the MgHigh (C) and MgLow (D) columns. The C/C0 is the ratio of the effluent and inlet concentrations. Compared to the
MgHigh columns, the BTC tails are more significant for the zoned MgLow columns.
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
113
the Mg(II) breakthrough for the One-zone column. The aT
values of 0.008, 0.008, 0.008, 0.008, 0.004, 0.003, and
0.003 cm were obtained for the flow velocities of 0.015,
0.03, 0.36, 3.60, 7.20, and 18.00 m/d, respectively. These
values are comparable to literature values in 2D tank
experiments under similar flow conditions (Rolle et al.,
2009; Hochstetler et al., 2013). They are relatively constant
at slow flow regimes however decreases as flow velocity
increases.
3.2. Effects of permeability contrasts
For all columns, effluent Mg(II) concentrations reach
steady state after about three residence times (Fig. 3A).
The steady state concentrations are highest in the two
Mixed columns and are lowest in the One-zone MgLow column. All other columns fall between these two extremes.
The steady state concentrations from the zonation
MgHigh columns almost overlap while those from the
MgLow set are distinct. For the MgHigh columns, bZ/M
values vary between 0.55 and 0.58, indicating rates from
the zonation columns about half of that of the Mixed column. For the MgLow columns, the bZ/M value of One-zone
MgLow column is 0.37, indicating approximately 2.7 times
lower rates compared to the Mixed column.
Fig. 4 shows bZ/M values for MgHigh and MgLow columns under different flow conditions calculated from
experimental data. All bZ/M values are lower than unity,
with those of the MgHigh set closer to unity, indicating less
significant role of spatial distribution compared to the
MgLow columns. Within the same column set, under each
flow velocity, the ratio decreases with decreasing number of
zones. The bZ/M values are closer to unity under slow flow
velocities and decrease with increasing flow velocities. As
discussed in Li et al. (2014), in the low flow regime, the
longer residence time leads to equilibrium condition and
the dominance of diffusion, which reduces the effects of
Fig. 4. Ratios of the measured column-scale rates of zonation
columns to their corresponding Mixed column, bZ/M, as a function
of flow velocity. The rate ratios are close to 1 at slower flow
velocities and decrease with increasing flow velocity. The effects of
spatial patterns are most significant under conditions with fast flow
and low permeability magnesite zone.
spatial distribution. The effects of spatial distribution patterns are most significant under fast flow and low permeability magnesite conditions.
The permeability ratios in the experiments were limited
by the smallest magnesite grain size that can be packed.
In the natural subsurface, permeability contrasts between
different zones often vary by orders of magnitude. To further explore rates under larger permeability contrast conditions, the parameters (rate constants, porosity, dispersivity)
obtained by reproducing the BTC data was used to simulate
the One-zone columns with different magnesite permeability
however the same quartz permeability. Fig. 5A compares
Fig. 3. (A) Experimental and modeling output of Mg(II) breakthrough for the MgLow (open symbols) and MgHigh (filled symbols) columns
at 7.20 m/d. Lower permeability Mg zone (MgLow column) results in lower steady state Mg(II) concentrations, indicating the role of
permeability contrast in affecting column-scale rates. (B) Ratios of column-scale bulk rates bZ/M between the zonation and Mixed column.
Spatial pattern has the largest effect with the low permeability One-zone column, with its rate about 0.37 of the Mixed column.
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F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
the BTC of the Mixed and One-zone columns with jratio,Mg/
Qtz of 0.07, 0.74, and 12.00 at 7.20 m/d. Fig. 5A shows that
the Mg(II) concentration increases with increasing magnesite permeability, approaching that of the Mixed column
at the jratio,Mg/Qtz of 12.00.
Although not shown here, the One-zone column with
jratio,Mg/Qtz of 0.07 is characterized by more than an order
of magnitude lower flow velocity in the Mg zone than that
in the Qtz zone. The low flow in the Mg zone and limited
mass transport between the two zones leads to high pH,
high IAP/Keq, and therefore low dissolution rates
(Fig. 5B). In fact, only the magnesite grains at the immediate vicinity of the inlet and at the Mg–Qtz interface effectively dissolve under far from equilibrium conditions. In
contrast, with the jratio,Mg/Qtz of 12.00, the flow velocity
in the Mg zone is more than one order of magnitude higher
than that in the Qtz zone. The fast flow rapidly flushes out
the reaction products, resulting in relatively low local pH,
IAP/Keq, and high dissolution rates. The entire Mg zone
is far from equilibrium and all magnesite grains dissolve
under far from equilibrium conditions, leading to similar
overall dissolution rate to that of the Mixed column. As
such, with the reactive zone having high permeability zone,
the column-scale dissolution rates are not limited by mass
transport between zones. It is important to note that here
under all permeability ratio conditions, pH values quickly
rise to above 6.0 within a few millimeters from the inlet,
indicating the dominance of reaction (3) in the overall dissolution rate, instead of reaction (1) in Table 3.
Fig. 6A shows the spatial profiles of IAP/Keq to illustrate
effective (Ae) and interface (AI) surface areas and their ratios
for the One-zone columns with jratio,Mg/Qtz of 0.07 and 12.00.
With jratio,Mg/Qtz = 0.07, only the grains at the very Mg–Qtz
interface and at the inlet are in dilute solution. Both Ae and
AI are small (approximately 2.0 m2); the contribution of inlet
effective region is relatively small compared to that of the
magnesite boundary annulus of 2 mm thickness. As such,
the AI/Ae is approximately 90%, indicating most Ae is at
the Mg–Qtz interface. With jratio,Mg/Qtz = 12.00, water
primarily flows through the high permeability Mg zone, all
magnesite grains are in dilute solution and effectively
dissolve. The AI/Ae is about 60%, essentially the magnesite
volume ratio of the 2.0 mm interface annulus over the whole
2
2
ÞL
magnesite zone. This can be calculated by pðRpRr
¼ 59:5%,
2L
where R and r are 5.5 and 3.5 mm, respectively, and L is
the column length. In this case, the interface grains are less
important compared to the column with jratio,Mg/
Qtz = 0.07. As shown in Fig. 6B, both AI and Ae increase with
jratio,Mg/Qtz with Ae increases faster. As a result, AI/Ae
decreases with jratio,Mg/Qtz until it reaches about 60% at the
jratio,Mg/Qtz of 12.00, beyond which Ae, AI, and AI/Ae remain
constant (Fig. 6C). The continuum-scale rates increase from
9.03 1010 to 5.44 109 mol/s with jratio,Mg/Qtz increase
by about 3 orders of magnitude (Fig. 6D).
Simulations were carried out for the One-zone column
with a permeability contrast range between 0.01 and
12.00. Fig. 7A shows that RMgCO3 ;B vary by more than 2
orders of magnitude with 3 orders of magnitude variation
Fig. 5. (A) The Mg(II) breakthrough curves at 7.20 m/d for the Mixed column and One-zone MgLow columns under the jratio,Mg/Qtz of 0.07,
0.74, and 12.00. (B) Predicted spatial profiles of pH (first row), IAP/Keq (second row), and local dissolution rates (third row) in the Mixed
column (the first left one in each row) and in the One-zone column with different jratio,Mg/Qtz. Higher permeability magnesite zone (jratio,Mg/Qtz
of 12.00) facilitates water flow through the reactive zone, leading to far from equilibrium conditions and more effectively-dissolving magnesite
grains. In contrast, low permeability magnesite zone limits the amount of water flowing through the reactive zone and leads to significant mass
transport limitation, where only magnesite grains at the Mg–Qtz interface dissolve effectively.
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
115
Fig. 6. (A) Illustration of effective (Ae) and interface (AI) surface area in the One-zone column with jratio,Mg/Qtz = 0.07 and 12.00 at 7.20 m/d.
Note that Ae is the surface area of ANY magnesite grains in dilute solution with IAP/Keq < 0.1 (within solid white lines). In contrast, AI is the
magnesite surface area that (1) is in dilute solution AND (2) sits within 2 mm from the Mg–Qtz interface (area within the dashed white lines).
With jratio,Mg/Qtz = 0.07 (left), only the magnesite grains at the immediate vicinity of the Mg–Qtz interface and at the inlet effectively dissolve
in dilute dissolution and contribute to Ae because the water that flows through the magnesite zone is a small proportion (7% of overall flow).
The AI is 90% of the overall Ae. With jratio,Mg/Qtz = 12.0 (right), all magnesite grains are in dilute solution because most water rapidly flushes
through the Mg zone. The interface grains AI approximates 60% of Ae (close to the volume fraction of the interface annulus of 2 mm thickness
to the overall magnesite volume) and is less important. (B) Calculated surface areas as a function of jratio,Mg/Qtz. The dashed line is the
constant AT (22.5 m2). (C) Surface area ratios (Ae/AT and AI/Ae) versus jratio,Mg/Qtz. (D) Bulk dissolution rates as a function of jratio, Mg/Qtz.
Fig. 7. (A) Calculated column scale bulk rates (RMgCO3 ;B ; mol=s), (B) bZ/M, (C) Ae/AT, (D) AI/Ae, and (E) AI/AT of the One-zone column under
different jratio,Mg/Qtz and flow velocity conditions. The permeability of the Mg zone was varied while permeability of the Qtz zone and other
parameters were maintained constant. Column-scale rates reach their maximum under high flow velocity and high permeability magnesite
conditions (top right), where the difference between the Mixed and One-zone column is at its minimum and the interface surface area is the
least important. The spatial pattern matters most under fast flow and low magnesite permeability conditions (bottom right), where only the
interface magnesite grains effectively dissolve. The “NA” means “Not Applicable” where values cannot be obtained due to equilibrium
conditions.
in flow velocities and permeability contrasts. Under low
flow conditions (v < 100.4 m/d), RMgCO3 ;B values are low
and do not depend on jratio,Mg/Qtz because of equilibrium
conditions. As a result, all bZ/M values are close to unity
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F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
(Fig. 7B). Under these conditions, neither physical heterogeneity (permeability ratio) nor geochemical heterogeneity
(mineral reactivity difference) is important; both Ae and
AI are close to zero because of the thermodynamic
control. Under higher flow conditions (v > 100.4 m/d),
RMgCO3 ;B increase with flow velocity and permeability contrast, reaching their maximum at the top right with the
highest flow velocity and jratio,Mg/Qtz. The bZ/M values are
close to unity, suggesting negligible differences from the
corresponding Mixed columns. The bZ/M values decrease
with increasing flow velocity and decreasing jratio,Mg/Qtz,
reaching its minimum and therefore maximum effects of
spatial patterns under the fastest flow and lowest magnesite
permeability conditions (bottom right) with bZ/M
approaching 0.1. This means an order of magnitude lower
rate in the One-zone column than that in the corresponding
Mixed column. In general, flow conditions have a larger
control over dissolution rates than permeability ratio.
The Ae/AT map follows similar patterns as that of
RMgCO3 ;B . Interestingly, only under the highest flow velocities
and highest jratio,Mg/Qtz conditions at the top right of the
map, Ae/AT is close to unity. Under most conditions, Ae is
1–3 orders of magnitude lower than AT. Values of AI/Ae
cover a relative narrow range of 0.60–1.0 compared to that
of Ae/AT values (Fig. 7D). The lowest 60% occur at the right
top corner under high flow and high magnesite permeability
conditions and is essentially the mass and volume percentage
of the magnesite grains in the 2 outermost millimeters of the
magnesite zone, as discussed previously. Values of AI/Ae
reach a maximum of 100% under fastest flow and lowest magnesite permeability conditions where only magnesite at the
interface effectively dissolves. Fig. 7E shows that the AI/AT
values are all below 60%, meaning that the interface effective
surface area AI is much lower than the total BET surface area
under most conditions (Fig. 7E).
3.3. Dependence of column-scale rates on effective surface
area Ae
Here we combine the data from this work and those from
our previous work (Salehikhoo et al., 2013; Li et al., 2014)
and calculate the effective surface area under each experimental condition. The effective surface areas increase with flow
velocity at a slope of 100.26 m2/(m/d), until it equals AT at
Fig. 8. (A) Effective surface area as a function of flow velocity under different spatial patterns, permeability contrast, and column length
conditions. (B) The column-scale bulk rates as a function of effective surface area. The data includes those from this work and our previous
work (Salehikhoo et al., 2013; Li et al., 2014). The diamonds are for the Mixed and flow-transverse columns from (Salehikhoo et al., 2013).
Other symbols (circle, triangle, star, and square) are for the flow-parallel One-zone columns (Mixed, Three-zone, Two-zone, and One-zone).
The regression line RMgCO3 ;B ðmol=sÞ ¼ 109:60 Ae runs through data with an R2 of 0.91. The slope of 109.60 is very close to the rate constant
(1010 mol/m2/s) of reaction (3) in Table 3, indicating that rate constants measured under well-mixed conditions can be used to infer reaction
rates under conditions with mass transport limitation if Ae is used.
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
high flow velocities (Fig. 8A). The 5, 10, and 22 cm Mixed
and flow-transverse One-zone columns (Salehikhoo et al.,
2013) reach their respective AT at approximately 2.0, 5.0,
and 18.0 m/d. Under each flow velocity, the Mixed and the
One-zone flow transverse columns have the highest Ae, followed by flow-parallel MgHigh columns, and by flow-parallel
MgLow columns. The column-scale bulk rates increase with
Ae instead of the total BET surface area AT (Fig. 8B). The
regression line RMgCO3 ;B ðmol=sÞ ¼ 109:60 Ae fits through
most experimental data with a square of correlation coefficient R2 being 0.91. The slope of 109.60 mol/m2/s is very
close to the k3 value of 1010 mol/m2/s of reaction (3) in
Table 3 that represents the rate constant in each grid block
under well-mixed conditions. This indicates that the rate constants under well mixed conditions can be used directly to
infer the reaction rates under natural subsurface conditions
if we use Ae instead of AT, potentially resolving the longstanding laboratory-field rate discrepancy.
A few exceptions (within the dashed circle) occur at flow
velocities higher than those critical flow velocities where Ae
values reach their corresponding AT. Under these conditions, the fast flow velocities lead to short residence times
and lower pH conditions closer to the inlet pH. As a result,
the dissolution rates of reaction (1) in Table 3 dominate and
depend on pH conditions, instead of reaction (3) without
pH dependence. As such, although all magnesite grains
are effectively dissolving (Ae = AT), RMgCO3 ;B increase with
flow velocity because the average pH in the column decreases with increasing flow velocity.
3.4. Column-scale rates and modified Damkohler number
In Salehikhoo et al. (2013), we defined a Damkohler
number (DaI) that compares the relative magnitude of
117
advection and reaction using their characteristic time scales
(sadv/sr). The DaI values group rates from Mixed and Flowtransverse One-zone columns under different flow and column length conditions. Rates from flow-parallel columns
however deviate from the RMgCO3 –DaI relationship (Li
et al., 2014). Here we define DaI0 using a modified sr0 :
Da0I ¼
sadv
sadv
¼ Ae;Z ¼ Ae;Z
0
sr
s
Ae;M r
Ae;M
L
v
V p C eq;Mg
RMgCO3 ;B
¼
Ae;M
DaI
Ae;Z
ð7Þ
The DaI0 compares sadv , the fluid residence time (column
length L/the average actual flow velocity v, or the total pore
volume Vp divided by the flow rate Q), with s0r , the characteristic time scale to reach equilibrium. The s0r modifies the original sr with Ae,Z/Ae,M, where sr was calculated by the total
Mg(II) mass at equilibrium (Vp, the total pore volume of
the column (m3), multiplied by Mg(II) concentration at
equilibrium Ceq,Mg, approximately 3.0 104 mol/L in
this work), divided by the column-scale bulk rate
RMgCO3 ;B ðmol=sÞ. The ratio Ae,Z/Ae,M is a correction factor
for the mass transport limitation caused by spatial patterns.
The Mixed column is used as a reference. This value is one
for Mixed columns and smaller than one for zonation columns. For Three-zone and Two-zone columns that the
effective surface areas are not available, the Ae,Z/Ae,M was
approximated by the bulk rate ratio RMgCO3 ;B;Z =RMgCO3 ;B;M ,
based on the linear relationship between the bulk rates
and the Ae shown in Fig. 8B.
All measured column-scale rates are plotted as a function
of DaI0 in Fig. 9. Note that here RMgCO3 ðmol=m2 =sÞ was calculated by normalizing the RMgCO3 ;B ðmol=sÞ by the total
BET surface area AT (m2) to eliminate the original difference
in AT in different columns. Replotting RMgCO3 as a function of
DaI0 moved the data points of the zonation columns closer to
Fig. 9. Column-scale rates RMgCO3 ðmol=m2 =sÞ as a function of the modified Damkohler number (DaI0 ) using Eq. (7). Here RMgCO3 was
obtained by dividing column-scale bull rate RMgCO3 ;B with AT. The Da0I groups column-scale rates under different spatial patterns, flow
velocity, and column length conditions. The diamonds are the rates from Salehikhoo et al. (2013) for the Mixed and flow-transverse One-zone
columns of 22, 10, and 5 cm. All other symbols are for Mixed, and flow-parallel zonation columns. The insert shows RMgCO3 ðmol=m2 =sÞ as a
function of DaI (without the modification by Ae,Z/Ae,M), where the rates from zonation columns deviate from the regression line.
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F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
the regression line. Under fast flow regime, DaI0 values are
small (<0.25) and column-scale rates are high. Under low
flow regime, DaI0 values are large (>1), column-scale rates
are low and the dissolution is close to equilibrium. At
medium flow velocities, advection and reaction rates are
comparable and the dissolution is transport-controlled.
4. DISCUSSION AND CONCLUSIONS
The effects of physical heterogeneities on flow and nonreactive solute transport have been studied extensively in
the past four decades. The effects of mineral spatial distribution patterns on geochemical processes, however, have
remained largely unexplored (Li et al., 2007a, b; Molins
et al., 2012). Here we provide the first series of experimental
data that quantify the effects of magnesite spatial distribution on its dissolution rates. A total of 79 flow-through
experiments were carried out using Mixed and zonation columns (One-zone, Two-zone, Three-zone) with flow velocities from 0.015 to 18.00 m/d and permeability ratios
(jratio,Mg/Qtz) of 1.20 and 0.74. All Mixed and One-zone columns were simulated using reactive transport modeling to
quantify the effective and interface surface area. An additional 36 numerical experiments were carried out to expand
to a larger range of jratio,Mg/Qtz from 0.01 to 12.00.
Column-scale dissolution rates depend on three key variables: spatial pattern, flow velocity, and permeability contrast between different zones. As a general principle, the
rates are highest when the conditions maximize the water
flow through the reactive zone. The effective surface area
Ae is lower than AT by 1–3 orders of magnitude under most
conditions. The column-scale dissolution rates relates to Ae
through RMgCO3 ;B ðmol=sÞ ¼ 109:60 Ae , where the slope
109.60 (mol/m2/s) is close to the rate constant 1010 mol/
m2/s used under well-mixed conditions. This indicates that
if Ae, instead of AT, is used, the rate laws and rate constants
measured in well-mixed laboratory systems can be used to
infer rates in natural systems where flow, transport, and reactions are coupled. This can explain why the surface area
often needs to be readjusted to be orders of magnitude lower
than lab-measured values to reproduce field data (Moore
et al., 2012). This can help resolve the observed laboratoryfield rate discrepancy – the two to six orders of magnitude
higher measured rates in laboratory systems than those
observed in the field (Swoboda-Colberg and Drever, 1993;
Velbel, 1993; Arvidson et al., 2003; Maher, 2010; Reeves
and Rothman, 2013) – a major puzzle in the geochemical
community. Although a large body of literature has
documented possible reasons for this discrepancy
(Alekseyev et al., 1997; Nugent et al., 1998; Maher, 2010),
this discrepancy has not been examined from the perspective
of spatial heterogeneities.
The interface surface area, AI, is a measure of the effective-dissolving magnesite surface area at the Mg–Qtz interface. Under conditions where the effects of spatial patterns
are significant (fast flow, low permeability Mg zone, flowparallel), AI is more than 90% of Ae, suggesting the direct
use of AI to approximate Ae. If the geometry of mineral
spatial structure is known, AI can be a convenient
approximation because Ae is much more challenging to
obtain. The fact that AI and Ae are typically orders of
magnitude lower than the measured BET surface areas
challenges our traditional thinking of reactive surface area
and has important implications. Similar to biogeochemical
processes (McClain et al., 2003), geochemical processes also
occur mostly at the “reactive interface” or “hot spots” with
the sharpest contrasts in conditions and properties. These
reactive interfaces represent the true effectively-dissolving
surfaces in heterogeneous porous media. The rates at these
interfaces are typically orders of magnitude higher than the
rest of the domain.
This work shows that spatial patterns make a significant
difference under conditions where flow velocity is sufficiently
high (v > 0.36 m/d) and where mass transport from the
magnesite zone is limited. This includes conditions where
magnesite is distributed in the direction parallel to the main
flow, in low permeability zones, and under fast flow conditions. A measured maximum rate difference by a bZ/M value
of 0.37 occurs between the flow-parallel One-zone and Mixed
columns at 18.00 m/d and jratio,Mg/Qtz of 0.74. A maximum
difference by an order of magnitude (a bZ/M value of 0.11)
was observed in the numerical experiments at 18.00 m/d with
jratio,Mg/Qtz of 0.01. The mass transport limitation imposed
by the low permeability magnesite zone results in dissolution
only at the Mg–Qtz interface while the rest of Mg zone is at
equilibrium. In natural systems, distinct zones of mineralogy
and reactivity often have permeability contrasts by orders of
magnitude and are distributed in widely different spatial
patterns (Koltermann and Gorelick, 1996). This indicates
that effects of spatial heterogeneities are likely to be
significant in natural subsurface systems.
The effects of spatial patterns are not significant under
three conditions: (1) when magnesite is in higher permeability zone (jratio,Mg/Qtz > 10) where most water flows
through; (2) when the magnesite zone is oriented in the direction transverse to the main flow where water easily flushes
out reaction products; (3) when the flow velocities are sufficiently low (<0.36 m/d) that the reactions are at equilibrium.
The significance of spatial patterns increases with flow
velocity, with negligible effects at flow velocity lower than
0.36 m/d and most predominant at 18.00 m/d. It is important to note that these “threshold” flow velocities depend
on the reactivity of specific minerals. Magnesite is among
the fast dissolving minerals and its dissolution reaches equilibrium under relatively high flow conditions. For minerals
that dissolve at order of magnitude lower rates, for example, silicates (Blum and Stillings, 1995), we expect the role
of spatial heterogeneity is important at threshold flow velocities that are orders of magnitude lower. In addition, silicates often dissolve incongruently with secondary mineral
precipitation. The role of spatial patterns can potentially
be more significant because they also control where and
how much precipitation occurs.
The control of spatial patterns on mineral dissolution
rates has broad implications for understanding and forecasting earth systems. For example, preferential flow paths
abounds in the Critical Zone (CZ) representing themselves
in various forms, including macro pores, soil horizons and
layers of different properties that dictate the distribution of
water flow (Beven and Germann, 1982; Luo et al., 2008,
F. Salehikhoo, L. Li / Geochimica et Cosmochimica Acta 155 (2015) 107–121
2010; Zhang et al., 2014). The characteristics of mineral distribution patterns and the associated properties ultimately
determine the extent water–rock interactions. Pore water
chemistry has been shown to differ dramatically following
the physical distribution of soil horizons (Jin et al., 2011).
Over geological time scales, the initial physical structure
can have significant impacts on chemical weathering and
CZ formation. The spatial patterns of mineralogical/geochemical compositions and hydrologic properties also regulate the functioning of microbial activities in engineered
biogeochemical systems (Li et al., 2010, 2011; Bao et al.,
2014). A recent study documented the strong correlation
between bedrock composition and vegetation (Hahm
et al., 2014) the spatial patterns of bedrock type govern
the release of phosphorus, therefore determining the distribution of forest cover in Sierra Nevada Batholith,
California under otherwise similar climatic and elevation
conditions. These studies point to the significance of spatial
patterns not only in controlling mineral reaction and chemical weathering rates, but also in regulating landscape formation and evolution, ecosystem functioning, and
elemental cycling at larger scales.
ACKNOWLEDGEMENTS
This work was supported by the Penn State Institutes of Energy
and the Environment (PSIEE) and by the DOE Subsurface
Biogeochemistry Research program DE-SC0007056. The Penn
State Laboratory for Isotopes and Minerals in the Environment,
and the Penn State Earth and Environmental Systems Institute
provided valuable support for sample analysis. We acknowledge
the associate editor Dr. Bjorn Jamtveit and two anonymous reviewers for their constructive comments that have improved this paper.
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Associate editor: Bjorn Jamtveit