Appendix Contents
1. Hantush Analytical Solution …………………………………………………………………………..2
2. Model Benchmark Exercises ………………………………………………………………………....3
2.1 MODFLOW ………………………………………………...…….……………………………...3
2.1 TOUGH2 ………………………………………………...…….………………………………....4
3. Verification of Hantush Analytic Model Assumptions ………………………………….….5
4. References ……………………………………………………………………………………………………6
Tables
Table S1. Parameters used in MODFLOW benchmark study……………………………….7
Table S2. Parameters used in TOUGH2 benchmark exercise……………………………....7
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
1. Hantush Analytic Solution
Hantush (1960) found an analytical solution to equation (2-3). The solution is given by: s

Q
4

T
 
( S 1) where s is head change, Q is the reservoir injection rate, T is transmissivity (T = Kb; where b is reservoir thickness and K is hydraulic conductivity), and u and  are the arguments
Hantush’s well function. The Hantush (1960) well function is defined as follows:
  
 
 u
 e
 erfc


 
  u



( S 2)
 where erfc [ ] is the complementary error function and  is the variable of integration. The variables  , and u are defined as follows: u

  r
2
S
4 Tt
4 r b



K
1
S s
'
KS s

K
2
S s
''
KS s



( S 3)
( S 4) where r is the radius from the pumping well; S s
is the reservoir specific storage; t is time, b
 is the reservoir thickness, K
1
and K
2
are the vertical hydraulic conductivities of the upper
S S of the upper and lower confining units, respectively. A plot of 1/u verses H[u,b] is shown if
Figure S1.  
2

2. Model Benchmark Exercises
2.1 MODFLOW
We compared our hybrid numeric-analytic model’s ability to predict the downward propagation of pore pressures into the crystalline basement beneath a basal injection reservoir to MODFLOW (). We used a 10 km x 10 km x 4.255 km grid comprised of a 400 m thick reservoir underlain by a 3855 m thick bedrock unit. The grid was discretization was
101 x 101 x 47 layers. The top layer was comprised of one layer 400m thick. A total of 46 layers were used to discretize the crystalline basement. Below the top layer the grid using a telescoped grid in the vertical dimension with a layer thickness that varied between about 1 m and 538 m between the crystalline basement-reservoir interface and the base of the domain (0 < z < 3855; Fig. S2A). A single injection well within the upper reservoir layer was placed at the origin of the model domain in the reservoir. The layers thicknesses were refined at the bedrock-reservoir interface. A lateral cell spacing of 100 m was used in the x and y directions. Figure S2B below compares MODFLOW model results to our hybrid analytical-numerical model. We used the parameter listed in Table A1 in this benchmark study. Our model produced similar thought not identical head distributions within the reservoir and crystalline basement (Fig. S2B). We compare results after 10 years of continuous pumping at an injection rate of 4162 m 3 /day. The two models produced similar depths of penetration into the bedrock beneath the injection well. Computed heads for the
MODFLOW model extended further out into the reservoir than what was predicted using our analytical solution. In fact, the MODFLOW computed heads for the 10m and 1 m contours extended beyond the Theis solution (Theis, 1934) and must be due to grid dispersion. Our computed reservoir heads from the Hantush analytic solution do not extend
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out beyond the Theis solution which makes physical sense. Leakage into the bedrock should reduce the heads within the resevoir.
2.2 TOUGH2
We present a second benchmark study in which we compare our single-phase, constantdensity, hybrid analytic-numerical model to TOUGH2. We attempted to reproduce published pressure changes for a multi-layered reservoir system composed of 8 reservoirs and 7 confining units. Injection was into the lowest reservoir. Birkholzer et al.
(2009) performed a sensitivity study to assess the effects of confining unit permeability variation on the distribution of deviatoric fluid pressure in response injection of 1.52 MT/yr of supercritical CO
2 into the basal reservoir (Table S1). One specific goal of this benchmark exercise was to assess whether or not a single-phase models can be used to approximate the far field pressure response associated with CO2 injection. In our single-phase model, we assumed an equivalent water mass by dividing the CO
2
mass by freshwater density (1000 kg/m 3 ). The reservoir permeability was fixed at 10 -13 m 2 (100 mD). Birkholzer et al. (2009) used a radial grid with a single injection well (Figure S3A). The grid had lateral dimensions of 200 km and a thickness of 1180 m. The increased pore pressures computed using
TOUGH2 after 30 years of continuous injection are shown in Figures S3B-S3E (solid black lines) for confining unit permeability ranging from 10 -17 to
10 -20 m 2 . Computed pore pressure increases from our hybrid analytic-numerical model are shown by the dashed red lines in Figures S3B-S3E. There is a reasonably good match between the two models. As with the MOFLOW results, the TOUGH2 computed pressures extend out further into the injection reservoir than predicted using the Hantush (1960) analytical solution. Differences in computed fluid pressure increases above hydrostatic
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levels between the two models is likely due numerical grid dispersion in the reservoir layer as well as two-phase flow effects such as the effects of permeability. CO
2 fluid compressibility was not accounted for in our analytic-numeric model. More compressible
CO
2
would potentially lower the heads near the injection well. Relative permeability effects would effectively make the confining units less permeable for CO
2
migration.
3. Verification of Hantush Analytic Model Assumptions
The Hantush (1960) analytical solution assumes that hydrostatic conditions occur above the upper confining unit. In addition, either a no flux condition at the base of the lower confining unit (for lower reservoir injection) or a hydrostatic head condition in the reservoir below the lower confining unit is assumed (for middle reservoir injection). In all cases, we found that these conditions were largely meet in our simulations. For middle reservoir injection, heads never increased above about 0.3% of the deviatoric head values within the reservoir. For lower reservoir injection, it was important to confirm that we could neglect the effects of fault leakage on predicted reservoir heads. This condition is met if leakage across the confining units is much larger than leakage down the faults. For the case of highest fault leakage (Figure 4C), we found that leakage volume down the fault after
10 years of injection is relatively small (19.4 m 3 /day, assuming a fault 1 km long and 2 m wide) compared to the diffusive leakage volume across the Eau Claire Formation/Mount
Simon interface (984.7 m 3 /day). Finally, Hantush’s analytical solution applies when: t

S
' b
'
10 K
1
; and t

S
'' b
''
10 K
2
( S 5)

5

where t is time, S’ and S’’ is the storativity of the upper and lower confining layers, respectively; b’ and b’’ is the thickness of the upper and lower confining layers, respectively.
Applying the values of the crystalline basement and shale properties (Table S1, S2) to equation (S5) yields critical times between 10 5 to 10 8 days which is about equal to or greater than the 3650 days (10 years) of simulation time used in this study.
4. References
Birkholzer, J. T., Q. Zhou, and C.-F. Tsang. "Large-Scale Impact of CO
Greenhouse Gas Control 3(2009): 181-94.
2
Storage in Deep Saline
Aquifers: A Sensitivity Study on Pressure Response in Stratified Systems." Int. J.
Hantush, M. S. "Modification of the Theory of Leaky Aquifers." J. Geophys. Res. 65.11 (1960):
3713-32.
McDonald, M.G. and Harbaugh, A. W. A “Modular Three-Dimensional Finite-Difference
Groundwater Flow Model.” Techniques of Water – Resources Investigations, USGS,
(1988): Book6, ChA1.
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Table S1.
Parameters used in MODFLOW benchmark study.
Variable Value
Reservoir Hydraulic Conductivity
Crystalline Basement
Reservoir Specific Storage
Crystalline Basement Specific Storage
Reservoir Thickness (b)
Crystalline Basement Thickness (Q)
Injection Rate (Q)
Total Simulation Time
Time Step Size
3.1E-03 (m/day)
3.1E-07 (m/day)
10 -5 (m -1 )
10 -6 (m -1 )
400 m
3800 m
4162 m 3 /day
10 years
1 day
Table S2. Parameters used in TOUGH2 benchmark exercise.
Variable
Reservoir Permeability (k)
Confining unit permeability (k)
Reservoir Compressibility (  s
)
Confining Unit Compressibility ( 
Reservoir Thickness (b)
Confining Unit Thickness (b’) s
)
Injection Rate (Q)
Total Simulation Time
Time Step Size
Value
10 -13 m 2
10 -17 m 2 to 10 -20 m 2
9.0 x 10 -10 m -1
4.5 x 10 -10 m -1
60 m
100m
4162 m 3 /day
10 years
1 day
7