Lauren E. Beckingham*1, Catherine A. Peters*, Wooyong Um+, Keith W. Jones ++, and W. Brent Lindquist+++ *Princeton University, +Pacific Northwest National Laboratory, ++Brookhaven National Laboratory,+++Stony Brook University

1formerly known as Lauren E. Crandell and currently at Lawrence Berkeley National Laboratory

Cai, R., Lindquist, W.B., Um, W., and K. Jones. 2009. Adv Water Resour, 37:1396-1403. Crandell, L.E., Peters, C.A., Um, W., Jones, K., and W.B. Lindquist. 2012. J Contam Hydrol, 131:89-99. Kim, D., Peters, C.A., and W.B. Lindquist. 2011. Water Resour Res, 47:W01505. Li, L., Peters, C.A., Celia, M.A. 2006. Adv Water Resour, 29:1351-1370. Peters, C.A. 2009. Chem Geol, 265:198-208.

References

b.) c.)

Acknowledgement: This material is based upon work supported by the Department of Energy under Award Numbers DE-FG02-09ER64747 (SUNY Stony Brook); DE-FG02-09ER64748 (Princeton University); and KP1702030-54908 (Pacific Northwest National Laboratory). The information does not necessarily reflect the opinion or policy of the federal government and no official endorsement should be inferred. We also acknowledge the use of PRISM Imaging and Analysis Center which is supported in part by the NSF MRSEC program through the Princeton Center for Complex Materials (grant DMR-0819860).

Sedimentary Rock, Alberta Basin Overview. Advancements in 3D imaging techniques and analysis methods, and easier access to benchtop 3D X-ray microscopes, have led to a proliferation of 3D imaging studies of chemical alterations within porous media. However, 2D imaging methods continue to offer complementary insights into processes controlling sub-grain scale variations in mineralogy and intragranular porosity that are often difficult to observe with 3D methods. For example 2D imaging studies of mineral precipitation-induced changes in the pore network structure including detailed observations of distributions of secondary mineral precipitates can be coupled with 3D image analysis of a pore network to determine the pore properties required to infer permeability.

Methods. In this work, the combined advantages of 2D and 3D imaging methods are highlighted through 3D X-ray Computed Microtomography (X-ray CT) and 2D Scanning Electron Microscopy (SEM) imaging of a reacted column experiment in the context of the Hanford, WA site and a sedimentary rock sample from the Alberta basin. Both samples were imaged using 3D X-ray CT imaging at a voxel resolution of 4 µm and analyzed using 3DMA Rock to determine pore and throat size distributions as well as pore coordination numbers. Polished sections were then created from each sample and imaged using 2D SEM imaging with resolutions of 0.4 µm for the reacted column and an order of magnitude larger for the sedimentary rock. 2D images were analyzed using an erosion dilation method to determine pore and throat size distributions that were then corrected using sample-specific bias correction factors. The permeability of each sample was predicted from pore network models informed with the 2D or 3D pore and throat size distributions and the coordination numbers determined from the 3D analysis.

Major findings. Differences in 2D and 3D image resolutions resulted in over- or under- estimating small pore throats and led to predicted permeabilities that differed by orders of magnitude. For both samples, higher resolution images resulted in over-estimating small pore throats and under-estimating expected permeability. While higher resolution images are generally favored, they may not improve predictions of permeability as they require additional processing to distinguish small flow-conducting pore throats from surface roughness features. While 3D imaging is required to determine the network coordination, 2D imaging is necessary to understand where secondary minerals precipitate within the pore network and to quantify sub-grain scale variations. These advantages are demonstrated through SEM imaging of polished sections from the reacted column experiment. 2D images revealed that secondary mineral precipitates occurred as a relatively uniform coating on grain surfaces, unrelated to mineralogy, pore size, or other factors. SEM images also revealed new observations of sub-grain scale variations that showed that Hanford sand grains have a high amount of intragranular porosity and mineral precipitates formed in intragranular regions. These observations, which are important to understanding the reactive system, could not have been made if 3D imaging was used exclusively.

Reacted Sediment Column, Hanford, WA

3-4 µm resolution 1.8 µm resolution

Advantages of 2D Imaging

Pore Space Analysis

Permeability Modeling

Permeability Modeling

Pore Space Analysis 1.  3D X-ray CT analysis at 4 µm voxel resolution

Distributions were determined using 3DMA rock in Kim et al. 2011.

2. 2D SEM BSE images of thin sections (Peters et al. 2009)

3. 2D analysis of pore and throat size distributions Distributions were computed using an erosion-dilation image analysis method with sample

specific bias correction factor following Crandell et al. 2012. 104

103

102

101

100 101 102

Throat sizes 2D 1.8 µm resolution

2D 3-4 µm resolution

r (µm)

104

103

102

101

100 101 102

frequ

ency

Pore sizes 2D 1.8 µm resolution

2D 3-4 µm resolution

r (µm) Higher resolutions capture a greater number of small pores

and throats and fewer large pore throats

4. Pore network modeling to predict permeability Pore network models were created by randomly sampling pores and throats to create a

10x10x10 network of pores. At the pore scale, the network is solved for the pressure, P, in each node using Poiseuilles law for throat conductance. At the continuum scale, Darcy’s law is used to predict the network permeability, Κ, from total flow, QT, viscosity, v, and the network x-sectional area, Λ, and length, L, (Li et al. 2006). Permeability was experimentally measured with a probe permeameter by Core Labs.

where Pi and Pj are fluid pressures in pore i and j,respectively. The inflows and outflows must balancefor each pore i:

Xnc

j!1

Qij ! 0. "22#

Combination of Eqs. (21) and (22) results in a linearalgebraic system for the unknown pressure field. Giventhe boundary pressures, this system is solved for thepressure in each pore, from which the steady-state flowfield is calculated.

At the continuum scale, the total flow rate followsDarcy!s law:

QT !jmK

DPL; "23#

where QT (cm3 s$1) denotes the total flow rate throughthe network in the main flow direction, z; j is the intrin-sic permeability of the network (cm2); K represents thecross-sectional area of the network in the directionorthogonal to the main flow (cm2); DP symbolizes thepressure di!erence between the two boundaries in z-direction; and L is the length of the network in z-direc-tion (cm). By rearrangement of the above equation, thepermeability of the network can be calculated. The per-meability is thus a function of the mean and variance ofthe conductance field, lX and r2

X , and the correlationwith local volumes. As mentioned previously, theseparameters were chosen so that the permeability corre-sponds to a typical value for sandstone. An iterative ap-proach was used whereby the statistical parameters werevaried until a flow field was generated that resulted inthe desired permeability.

4. Continuum-scale reaction rates

4.1. The rates from the network model: RN

For a porous medium, the ‘‘true’’ reaction rate at thecontinuum scale is the total mass change rate due toreactions at every reactive surface, normalized by thetotal amount of surface area of reactive minerals. Thenetwork model allows us to estimate such a ‘‘true’’ reac-tion rate at the continuum scale. The pore-scale massbalance equations are used to simulate changes in aque-ous concentration over time in each pore. At each timestep, the sum of the mass change rates due to mineralreactions for the entire network, divided by the total sur-face area of reactive minerals, gives the ‘‘true’’ reactionrate for the network. For example, for anorthite, thee!ective continuum-scale reaction rate for the networkmodel is as follows:

RN;A !Pn

i!1AA;irA;iPni!1AA;i

; "24#

where n is the total number of pores. Expressed inmol cm$2 s$1, this rate is equivalent to the rate calcu-lated by summing the mass change rate of Ca2+ due toanorthite reaction across the network, and then dividingby the total anorthite surface area. An equation analo-gous to Eq. (24) is used to calculate the continuum-scalerate for kaolinite. The continuum-scale rates, RN,A andRN,K, depend on local reaction rates (rA,i and rK,i,respectively), as well as the coupling between the localrates and local surface area of reactive minerals. Fornon-reactive pores, as values of AA;i are zero, the termAA;irA;i is not counted in the calculation of RN. As such,concentrations in non-reactive pores are irrelevant to thereaction rates, although they enter indirectly via thetransport equations. The continuum-scale reaction ratesare dependent only on the concentrations in reactivepores.

4.2. The rates from the continuum model: RC

This section presents the methodology for calculat-ing continuum-scale reaction rates using a continuummodel, which is the fundamental building block of tradi-tional forward modeling. Forward modeling generallyemploys a continuum approach [63,64,78], in which por-ous media are characterized by spatially-averaged prop-erties at the scale of the grid block, thereby ignoringdetails at the sub-grid scale. It is common practice toapply reaction rate laws determined from well-mixedlaboratory systems to calculate the reaction rates forthe porous medium in an entire grid block. Further-more,the mathematical forms and parameters of theserate laws are assumed to hold at the grid block scaledespite possible nonlinearities in upscaling.

In a similar manner, the continuum model uses spa-tially-averaged values to represent system properties,assumes uniform concentrations in the aqueous phase,and applies lab-measured reaction rates directly at thecontinuum scale. In so doing, it ignores pore-scale heter-ogeneities a priori, and assumes no mass transport lim-itation from pore to pore. In the calculation thatfollows, the continuum model is constrained to havethe same hydrodynamic properties, total surface areaof reactive minerals, initial conditions and boundaryconditions as the network model.

Because the reactions and the species involved arethe same as in the network model, we follow thesame systematic formulation to develop mass balanceequations for the five components: Ca2+, CT, SiT, AlT,and HT. For each key component, the mass balanceequations take the following general form, appliedover the entire volume of the pore network definedearlier:

V Td%&'dt! QT%&'in $ QT%&'C ( SC;&; "25#

1358 L. Li et al. / Advances in Water Resources 29 (2006) 1351–1370

Freq

uenc

y

k (cm2)

k (m2)

10-11 10-10 10-9 10-8 10-7

10-15 10-14 10-13 10-12 10-11

10

0

20

30

40

50

60

70

80

90

resolution 2D 1.8 µm

resolution

resolution 3D 4 µm

2D 3-4 µm

measured experimentally

2D and 3D methods predict comparable permeability values

Higher resolutions may underestimate predicted permeability

Resolutions between 3 to 4 µm should provide accurate predictions of permeability

1.  3D X-ray CT analysis at 4 µm voxel resolution before, during, and after reaction Computed in Cai et al. 2009 using 3DMA rock.

We define the tortuosity of each path as the path length dividedby the plane separation distance h. Fig. 4d displays the distributionof tortuosities measured for these spanning paths; Table 2 presentsthe average tortuosity values. In spite of the significant decrease inthe number of pathways connecting the section ends, there wasonly a slight shift to higher path tortuosities, specifically averagetortuosity increased by only 2.3% (C1) and 2.7% (C2). Since tortuos-ity, s, must be unity or larger, this percent increase was computedas !sfinal " sinitial#=!sinitial " 1#.

3.5. Discussion and conclusions

Our results – dissolution dominating in the larger pores, precip-itation filling in small pores, and clogging small throats – are notqualitatively unexpected. (In fact this qualitative agreement lendsfurther support for the results.) Certainly precipitation processesneed quiescent conditions for nucleation. Such conditions are ex-pected to occur in regions of slow fluid flow associated with (i)angular corners in pores at multi-grain junctions, (ii) small pores,and (iii) throats. The significance of our work is the demonstrationof the ability to quantify such changes over a microscale pore-net-work volume, in a non-destructive manner, allowing for repeatedmeasurements over repeated flow conditions and providing basicconcepts for predicting contaminant transport in a larger scale.The specific quantitative findings presented in Sections 3.1–3.4are, of course, based upon a small volume from a single column.Careful experiments under controlled conditions with a largernumber of samples are clearly required to extract significant quan-titative results for specific reaction processes. This caution not-withstanding, our results do provide some tantalizing insights. Inaddition to the expected loss of pore-to-pore connectivity accom-panying throat clogging, we recorded a significant decrease inthe number of network pathways. In spite of this decrease, therewas not a significant increase, on average, in the tortuosity of theremaining pathways. While there was an increase in the numberof large pores due to dissolution processes, there was not a corre-sponding increase in the number of large throats, suggesting thatall throating areas are dominated by precipitation processes.

There are specific issues that still need to be addressed regard-ing the use of CMT imaging on flow-column experiments.

The first is the question of the size of the volume to be exam-ined in order to produce representative results. In earlier work[15], we have demonstrated that microgeometrical measurementsbased on CMT images of 14:8 mm3 volume are locally representa-tive (produce statistically reproducible results in a core sample) inFontainebleau sandstones ranging from 7.5% to 22% porosity.While the 17:9 mm3 images examined here are comparable in size,the REV requirements to capture the effects of reactive flow remainto be addressed.

The region of the flow-column imaged was close to the mid-length of the column. It would be interesting to compare imagestaken from the inlet and outlet ends of the column to see if reactivechanges are different.

Sealing the column for extensive time periods between runswhile waiting for imaging time certainly complicates reactioninterpretation. Clearly tight management between the flow-col-umn runs and availability of beam time is required. Experimentallyit would be attractive to have the flow column experiment run in abeam line hutch, allowing for the possibility to swing the columninto the beam periodically for imaging, without having to haltthe flow for any significant amount of time.

Acknowledgements

This work was supported, in part, by: the US Department of En-ergy under contract nos. DE-FG02-06ER64190 (WU); DE-FG02-92ER14261 (WBL); and the Research Foundation of SUNY (RC).

Appendix. Image analysis detail

We utilize section C2 to illustrate implementation of points 1–5of the image analysis.

Segmentation (identification of grain and void voxels) of anyimage by the method of indicator kriging used in the 3DMA-Rocksoftware [19] requires setting two CT values, T0 and T1, that definea window. (Voxels having CT value below T0 are defined as void

1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1Pore volume (mm )

0

100

200

300

400

500

Num

ber

of p

ores

3100 1000 10000 100000

Throat area ( m )

0

500

1000

1500

Num

ber

of th

roat

s

day 0day 86day 106

µ 2

1.5 1.6 1.7 1.8Tortuosity

0

2

4

6

8

Pro

babi

lity

dens

ity C1 only

0 50 100 150Effective pore radius ( m)

0

5

10

15

20

25

Ave

rage

coo

rdin

atio

n nu

mbe

r

day 0day 86day 106

µ

a b

c d

Fig. 4. Distributions of (a) pore volume and (b) throat area as well as (c) average pore coordination number vs. effective pore radius determined from sections C1 and C2 after0, 86 and 106 days of exposure to simulated caustic waste flow. (d) Distribution of pathway tortuosities (section C1 only).

R. Cai et al. / Advances in Water Resources 32 (2009) 1396–1403 1401

We define the tortuosity of each path as the path length dividedby the plane separation distance h. Fig. 4d displays the distributionof tortuosities measured for these spanning paths; Table 2 presentsthe average tortuosity values. In spite of the significant decrease inthe number of pathways connecting the section ends, there wasonly a slight shift to higher path tortuosities, specifically averagetortuosity increased by only 2.3% (C1) and 2.7% (C2). Since tortuos-ity, s, must be unity or larger, this percent increase was computedas !sfinal " sinitial#=!sinitial " 1#.

3.5. Discussion and conclusions

Our results – dissolution dominating in the larger pores, precip-itation filling in small pores, and clogging small throats – are notqualitatively unexpected. (In fact this qualitative agreement lendsfurther support for the results.) Certainly precipitation processesneed quiescent conditions for nucleation. Such conditions are ex-pected to occur in regions of slow fluid flow associated with (i)angular corners in pores at multi-grain junctions, (ii) small pores,and (iii) throats. The significance of our work is the demonstrationof the ability to quantify such changes over a microscale pore-net-work volume, in a non-destructive manner, allowing for repeatedmeasurements over repeated flow conditions and providing basicconcepts for predicting contaminant transport in a larger scale.The specific quantitative findings presented in Sections 3.1–3.4are, of course, based upon a small volume from a single column.Careful experiments under controlled conditions with a largernumber of samples are clearly required to extract significant quan-titative results for specific reaction processes. This caution not-withstanding, our results do provide some tantalizing insights. Inaddition to the expected loss of pore-to-pore connectivity accom-panying throat clogging, we recorded a significant decrease inthe number of network pathways. In spite of this decrease, therewas not a significant increase, on average, in the tortuosity of theremaining pathways. While there was an increase in the numberof large pores due to dissolution processes, there was not a corre-sponding increase in the number of large throats, suggesting thatall throating areas are dominated by precipitation processes.

There are specific issues that still need to be addressed regard-ing the use of CMT imaging on flow-column experiments.

The first is the question of the size of the volume to be exam-ined in order to produce representative results. In earlier work[15], we have demonstrated that microgeometrical measurementsbased on CMT images of 14:8 mm3 volume are locally representa-tive (produce statistically reproducible results in a core sample) inFontainebleau sandstones ranging from 7.5% to 22% porosity.While the 17:9 mm3 images examined here are comparable in size,the REV requirements to capture the effects of reactive flow remainto be addressed.

The region of the flow-column imaged was close to the mid-length of the column. It would be interesting to compare imagestaken from the inlet and outlet ends of the column to see if reactivechanges are different.

Sealing the column for extensive time periods between runswhile waiting for imaging time certainly complicates reactioninterpretation. Clearly tight management between the flow-col-umn runs and availability of beam time is required. Experimentallyit would be attractive to have the flow column experiment run in abeam line hutch, allowing for the possibility to swing the columninto the beam periodically for imaging, without having to haltthe flow for any significant amount of time.

Acknowledgements

This work was supported, in part, by: the US Department of En-ergy under contract nos. DE-FG02-06ER64190 (WU); DE-FG02-92ER14261 (WBL); and the Research Foundation of SUNY (RC).

Appendix. Image analysis detail

We utilize section C2 to illustrate implementation of points 1–5of the image analysis.

Segmentation (identification of grain and void voxels) of anyimage by the method of indicator kriging used in the 3DMA-Rocksoftware [19] requires setting two CT values, T0 and T1, that definea window. (Voxels having CT value below T0 are defined as void

1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1Pore volume (mm )

0

100

200

300

400

500

Num

ber

of p

ores

3100 1000 10000 100000

Throat area ( m )

0

500

1000

1500

Num

ber

of th

roat

s

day 0day 86day 106

µ 2

1.5 1.6 1.7 1.8Tortuosity

0

2

4

6

8

Pro

babi

lity

dens

ity C1 only

0 50 100 150Effective pore radius ( m)

0

5

10

15

20

25

Ave

rage

coo

rdin

atio

n nu

mbe

r

day 0day 86day 106

µ

a b

c d

Fig. 4. Distributions of (a) pore volume and (b) throat area as well as (c) average pore coordination number vs. effective pore radius determined from sections C1 and C2 after0, 86 and 106 days of exposure to simulated caustic waste flow. (d) Distribution of pathway tortuosities (section C1 only).

R. Cai et al. / Advances in Water Resources 32 (2009) 1396–1403 1401

We define the tortuosity of each path as the path length dividedby the plane separation distance h. Fig. 4d displays the distributionof tortuosities measured for these spanning paths; Table 2 presentsthe average tortuosity values. In spite of the significant decrease inthe number of pathways connecting the section ends, there wasonly a slight shift to higher path tortuosities, specifically averagetortuosity increased by only 2.3% (C1) and 2.7% (C2). Since tortuos-ity, s, must be unity or larger, this percent increase was computedas !sfinal " sinitial#=!sinitial " 1#.

3.5. Discussion and conclusions

Our results – dissolution dominating in the larger pores, precip-itation filling in small pores, and clogging small throats – are notqualitatively unexpected. (In fact this qualitative agreement lendsfurther support for the results.) Certainly precipitation processesneed quiescent conditions for nucleation. Such conditions are ex-pected to occur in regions of slow fluid flow associated with (i)angular corners in pores at multi-grain junctions, (ii) small pores,and (iii) throats. The significance of our work is the demonstrationof the ability to quantify such changes over a microscale pore-net-work volume, in a non-destructive manner, allowing for repeatedmeasurements over repeated flow conditions and providing basicconcepts for predicting contaminant transport in a larger scale.The specific quantitative findings presented in Sections 3.1–3.4are, of course, based upon a small volume from a single column.Careful experiments under controlled conditions with a largernumber of samples are clearly required to extract significant quan-titative results for specific reaction processes. This caution not-withstanding, our results do provide some tantalizing insights. Inaddition to the expected loss of pore-to-pore connectivity accom-panying throat clogging, we recorded a significant decrease inthe number of network pathways. In spite of this decrease, therewas not a significant increase, on average, in the tortuosity of theremaining pathways. While there was an increase in the numberof large pores due to dissolution processes, there was not a corre-sponding increase in the number of large throats, suggesting thatall throating areas are dominated by precipitation processes.

There are specific issues that still need to be addressed regard-ing the use of CMT imaging on flow-column experiments.

The first is the question of the size of the volume to be exam-ined in order to produce representative results. In earlier work[15], we have demonstrated that microgeometrical measurementsbased on CMT images of 14:8 mm3 volume are locally representa-tive (produce statistically reproducible results in a core sample) inFontainebleau sandstones ranging from 7.5% to 22% porosity.While the 17:9 mm3 images examined here are comparable in size,the REV requirements to capture the effects of reactive flow remainto be addressed.

The region of the flow-column imaged was close to the mid-length of the column. It would be interesting to compare imagestaken from the inlet and outlet ends of the column to see if reactivechanges are different.

Sealing the column for extensive time periods between runswhile waiting for imaging time certainly complicates reactioninterpretation. Clearly tight management between the flow-col-umn runs and availability of beam time is required. Experimentallyit would be attractive to have the flow column experiment run in abeam line hutch, allowing for the possibility to swing the columninto the beam periodically for imaging, without having to haltthe flow for any significant amount of time.

Acknowledgements

This work was supported, in part, by: the US Department of En-ergy under contract nos. DE-FG02-06ER64190 (WU); DE-FG02-92ER14261 (WBL); and the Research Foundation of SUNY (RC).

Appendix. Image analysis detail

We utilize section C2 to illustrate implementation of points 1–5of the image analysis.

Segmentation (identification of grain and void voxels) of anyimage by the method of indicator kriging used in the 3DMA-Rocksoftware [19] requires setting two CT values, T0 and T1, that definea window. (Voxels having CT value below T0 are defined as void

1e-07 1e-06 1e-05 1e-04 0.001 0.01 0.1Pore volume (mm )

0

100

200

300

400

500

Num

ber

of p

ores

3100 1000 10000 100000

Throat area ( m )

0

500

1000

1500

Num

ber

of th

roat

s

day 0day 86day 106

µ 2

1.5 1.6 1.7 1.8Tortuosity

0

2

4

6

8

Pro

babi

lity

dens

ity C1 only

0 50 100 150Effective pore radius ( m)

0

5

10

15

20

25

Ave

rage

coo

rdin

atio

n nu

mbe

r

day 0day 86day 106

µ

a b

c d

Fig. 4. Distributions of (a) pore volume and (b) throat area as well as (c) average pore coordination number vs. effective pore radius determined from sections C1 and C2 after0, 86 and 106 days of exposure to simulated caustic waste flow. (d) Distribution of pathway tortuosities (section C1 only).

R. Cai et al. / Advances in Water Resources 32 (2009) 1396–1403 1401

2. 2D SEM BSE images of thin sections at 0.4 µm resolution After reaction, the column was impregnated with epoxy and segmented for 2D imaging (in Crandell

et al. 2012). BSE images were also digitally altered to remove secondary mineral coatings for “simulated before reaction” scenario in Crandell et al. 2012.

103

102

101

100 102 101 100

r (µm)

103

102

101

100 102 101 100

r (µm)

frequ

ency

4. Pore network modeling to predict permeability Pore network models were created in the same fashion as the sandstone sample. Additional

network models were created varying the size of the smallest pore throat included, effectively varying the roughness threshold. The permeability change due to mineral precipitation was evaluated by creating a network model informed by the digitally altered images with secondary precipitates removed.

3. 2D analysis of pore and throat size distributions

A roughness threshold of 15 µm will improve permeability predictions from 0.4 µm resolution 2D images

0

100

10-11 10-10 10-9 10-8 10-7 10-12 10-13 k (cm2)

10

20 30

40 50

60

70

80 90

Freq

uenc

y

Simulated before reaction

After reaction After reaction

with 15 µm roughness threshold

Simulated before reaction with 15 µm roughness threshold

10-15 10-14 10-13 10-12 10-11 10-16 10-17 k (m2)

10

20

30

40

50

60

70

80

90 100

Freq

uenc

y

2D 0.4 µm resolution

2 µm 1 µm 3 µm

4 µm

5 µm

10 µm 15 µm

20 µm

3D 4 µm resolution

Small variations in the smallest pore throat size result in huge differences in permeability predictions

0

The change in predicted permeability diminishes with use of a constant roughness threshold

Column permeability is predicted to decrease due to mineral precipitation

Rapid identification of sub-grain scale variations in mineralogy and porosity

Clay coatings

Alberta Basin sandstone sample 3w4

An unreacted Hanford column

300µm

Reacted Hanford column

Precipitation on grain surface

100µm

Precipitation in porous grain

Pore throats closed off

100µm

Easy observation and classification of clay or secondary minerals on grain surfaces

Direct evidence of changes in pore network structure due to secondary mineral precipitates

Pore throats closed off

Quartz

Basaltic lithic clasts

microfractures

micro voids in clasts

macro voids

with cancrinite

macro voids with banded palagonite

Reacted Hanford column

sizes, has greater porosity and permeability than 10W4,though it has the smallest number of pores and channels.The clay phase occupies between 48% and 65% of the totalpore surface area in these networks, while less than 1.3%of the total pore surface is contacted by the AG phase. Thepercentage of pores containing anorthite is 46% or less,while more than 99% of the pores in all three networks con-tain kaolinite. (This is a significantly different mineral dis-tribution from that used in the hypothetical networks of Liet al. [2006, 2007a, 2007b], where percent occupancies ofthe clay and anorthite phases were chosen to be identical.)The prevalence of the clay mineral category in the pore net-works is consistent with other observations of clay mineralcoating on grains in the Viking samples [Peters, 2009].

[37] Figure 2 shows measured distributions of pore vol-ume, coordination number, throat area, and channel lengthin the three network models. The distinctness of the distri-butions for 14W5 follows from its composition of ill-sortedgrains. The pore volume distributions of 3W4 and 10W4are reasonably lognormal in shape, while the distributionfor 14W5 is much broader, consisting of a larger fraction oflarge size pores. Similarly, 14W5 has a wider range ofthroat areas comprising a greater fraction of large sizethroats. The coordination number distributions of 3W4 and10W4 are similar. In comparison, 14W5 has more poreswith coordination numbers of 1 or 2 and fewer pores ofhigher coordination numbers. It also has fewer short-lengthchannels and a greater percentage of longer-length channelsthan the other two rock samples.

[38] Figure 3 shows measured distributions for the clayand AG surface areas SCV and SMV. As clays are confinedto pores and tend to coat grain surfaces, values for SCV arehighly correlated with pore grain surface areas. However,

as AG grains are uncorrelated with pore space, values forSMV are independently distributed. In this case the SMV dis-tribution for 10W4 appears to differentiate itself from thatof 3W4 and 14W5.

3.2. Network Reaction Rates[39] Figure 4 shows the time evolution of the core-scale

reaction rates from the network flow simulation in 3W4using models (2a) and (2b). Similar plots for 10W4 and14W5 are not shown. For anorthite, RC and R overestimatethe dissolution rate, RN, with RC generally providing betteragreement to RN than does R. (There is an exception; RC

does worse than R for 14W5 at the faster flow rate.) Thus,for the anorthite reaction under these acidic conditions, het-erogeneity in local fluid residence times, reactant concen-trations, and mineral surface areas produces a smallerreaction rate than that which would be predicted if thesequantities are uniform throughout the network of pores. Forkaolinite, RN predicts steady state precipitation, while RC

and R predict less negative values; that is, the precipitationrate is underestimated using uniform properties. In fact, atthe higher flow rate for 3W4, both RC and R predict bulkkaolinite dissolution. (The same statements hold for 14W5.For 10W5, RC and R erroneously predict bulk kaolinite dis-solution at both flow rates.)

[40] In discussing the results, we concentrate on threefeatures of the upscaled rates : the time to reach steadystate, the relative magnitudes of the steady state values, andwhether the steady state rate indicates net dissolution orprecipitation. We characterize the time to reach steady stateby the values t95 and t99: t95 indicates the time value atwhich a reaction rate is within 5% of its steady state value;t99 is defined analogously. Since the steady state values are

Figure 2. Measured distributions of (a) pore volume, (b) coordination number, (c) throat area, and (d)channel length for the three pore networks.

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sizes, has greater porosity and permeability than 10W4,though it has the smallest number of pores and channels.The clay phase occupies between 48% and 65% of the totalpore surface area in these networks, while less than 1.3%of the total pore surface is contacted by the AG phase. Thepercentage of pores containing anorthite is 46% or less,while more than 99% of the pores in all three networks con-tain kaolinite. (This is a significantly different mineral dis-tribution from that used in the hypothetical networks of Liet al. [2006, 2007a, 2007b], where percent occupancies ofthe clay and anorthite phases were chosen to be identical.)The prevalence of the clay mineral category in the pore net-works is consistent with other observations of clay mineralcoating on grains in the Viking samples [Peters, 2009].

[37] Figure 2 shows measured distributions of pore vol-ume, coordination number, throat area, and channel lengthin the three network models. The distinctness of the distri-butions for 14W5 follows from its composition of ill-sortedgrains. The pore volume distributions of 3W4 and 10W4are reasonably lognormal in shape, while the distributionfor 14W5 is much broader, consisting of a larger fraction oflarge size pores. Similarly, 14W5 has a wider range ofthroat areas comprising a greater fraction of large sizethroats. The coordination number distributions of 3W4 and10W4 are similar. In comparison, 14W5 has more poreswith coordination numbers of 1 or 2 and fewer pores ofhigher coordination numbers. It also has fewer short-lengthchannels and a greater percentage of longer-length channelsthan the other two rock samples.

[38] Figure 3 shows measured distributions for the clayand AG surface areas SCV and SMV. As clays are confinedto pores and tend to coat grain surfaces, values for SCV arehighly correlated with pore grain surface areas. However,

as AG grains are uncorrelated with pore space, values forSMV are independently distributed. In this case the SMV dis-tribution for 10W4 appears to differentiate itself from thatof 3W4 and 14W5.

3.2. Network Reaction Rates[39] Figure 4 shows the time evolution of the core-scale

reaction rates from the network flow simulation in 3W4using models (2a) and (2b). Similar plots for 10W4 and14W5 are not shown. For anorthite, RC and R overestimatethe dissolution rate, RN, with RC generally providing betteragreement to RN than does R. (There is an exception; RC

does worse than R for 14W5 at the faster flow rate.) Thus,for the anorthite reaction under these acidic conditions, het-erogeneity in local fluid residence times, reactant concen-trations, and mineral surface areas produces a smallerreaction rate than that which would be predicted if thesequantities are uniform throughout the network of pores. Forkaolinite, RN predicts steady state precipitation, while RC

and R predict less negative values; that is, the precipitationrate is underestimated using uniform properties. In fact, atthe higher flow rate for 3W4, both RC and R predict bulkkaolinite dissolution. (The same statements hold for 14W5.For 10W5, RC and R erroneously predict bulk kaolinite dis-solution at both flow rates.)

[40] In discussing the results, we concentrate on threefeatures of the upscaled rates : the time to reach steadystate, the relative magnitudes of the steady state values, andwhether the steady state rate indicates net dissolution orprecipitation. We characterize the time to reach steady stateby the values t95 and t99: t95 indicates the time value atwhich a reaction rate is within 5% of its steady state value;t99 is defined analogously. Since the steady state values are

Figure 2. Measured distributions of (a) pore volume, (b) coordination number, (c) throat area, and (d)channel length for the three pore networks.

W01505 KIM ET AL.: UPSCALING GEOCHEMICAL REACTION RATES W01505

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sizes, has greater porosity and permeability than 10W4,though it has the smallest number of pores and channels.The clay phase occupies between 48% and 65% of the totalpore surface area in these networks, while less than 1.3%of the total pore surface is contacted by the AG phase. Thepercentage of pores containing anorthite is 46% or less,while more than 99% of the pores in all three networks con-tain kaolinite. (This is a significantly different mineral dis-tribution from that used in the hypothetical networks of Liet al. [2006, 2007a, 2007b], where percent occupancies ofthe clay and anorthite phases were chosen to be identical.)The prevalence of the clay mineral category in the pore net-works is consistent with other observations of clay mineralcoating on grains in the Viking samples [Peters, 2009].

[37] Figure 2 shows measured distributions of pore vol-ume, coordination number, throat area, and channel lengthin the three network models. The distinctness of the distri-butions for 14W5 follows from its composition of ill-sortedgrains. The pore volume distributions of 3W4 and 10W4are reasonably lognormal in shape, while the distributionfor 14W5 is much broader, consisting of a larger fraction oflarge size pores. Similarly, 14W5 has a wider range ofthroat areas comprising a greater fraction of large sizethroats. The coordination number distributions of 3W4 and10W4 are similar. In comparison, 14W5 has more poreswith coordination numbers of 1 or 2 and fewer pores ofhigher coordination numbers. It also has fewer short-lengthchannels and a greater percentage of longer-length channelsthan the other two rock samples.

[38] Figure 3 shows measured distributions for the clayand AG surface areas SCV and SMV. As clays are confinedto pores and tend to coat grain surfaces, values for SCV arehighly correlated with pore grain surface areas. However,

as AG grains are uncorrelated with pore space, values forSMV are independently distributed. In this case the SMV dis-tribution for 10W4 appears to differentiate itself from thatof 3W4 and 14W5.

3.2. Network Reaction Rates[39] Figure 4 shows the time evolution of the core-scale

reaction rates from the network flow simulation in 3W4using models (2a) and (2b). Similar plots for 10W4 and14W5 are not shown. For anorthite, RC and R overestimatethe dissolution rate, RN, with RC generally providing betteragreement to RN than does R. (There is an exception; RC

does worse than R for 14W5 at the faster flow rate.) Thus,for the anorthite reaction under these acidic conditions, het-erogeneity in local fluid residence times, reactant concen-trations, and mineral surface areas produces a smallerreaction rate than that which would be predicted if thesequantities are uniform throughout the network of pores. Forkaolinite, RN predicts steady state precipitation, while RC

and R predict less negative values; that is, the precipitationrate is underestimated using uniform properties. In fact, atthe higher flow rate for 3W4, both RC and R predict bulkkaolinite dissolution. (The same statements hold for 14W5.For 10W5, RC and R erroneously predict bulk kaolinite dis-solution at both flow rates.)

[40] In discussing the results, we concentrate on threefeatures of the upscaled rates : the time to reach steadystate, the relative magnitudes of the steady state values, andwhether the steady state rate indicates net dissolution orprecipitation. We characterize the time to reach steady stateby the values t95 and t99: t95 indicates the time value atwhich a reaction rate is within 5% of its steady state value;t99 is defined analogously. Since the steady state values are

Figure 2. Measured distributions of (a) pore volume, (b) coordination number, (c) throat area, and (d)channel length for the three pore networks.

W01505 KIM ET AL.: UPSCALING GEOCHEMICAL REACTION RATES W01505

7 of 16