Paper No.
5623
Study of Siderite Solubility under Extreme High Temperature and Pressure in 1 M NaCl
Solution
Chao Yan, Paula Guraieb, Jin Huang and Ross C. Tomson
Brine Chemistry Solutions, LLC
8285 El Rio Street, Suite 100
Houston, TX, 77054
ABSTRACT
With the continued development of offshore production in ultra-deepwater (UDW), more and more wells
are exposed to extremely high pressure and temperature (xHPHT) under anoxic condition. In order to
better predict scale formation, scale solubility under these extreme conditions need to be accurate.
Knowledge of the thermodynamic and kinetic properties of this mineral under xHPHT conditions is
important for the solubility studies. Research to expand the amount of data and models for such
minerals at these conditions will reduce offshore production risk and improve human safety in ultradeepwater production.
A novel flow-through apparatus has been developed to perform scale solubility, dissolution and
precipitation studies of various minerals under high pressure (up to 24,000 psig), high temperature (up
to 250 °C), and high total dissolved solids (TDS, up to 360,000 mg/L). This research focused on the
solubility of siderite under strictly anoxic (<<1 ppb O2) xHPHT conditions. This study increased our
understanding of the formation of passive layers (Fe3O4 and FeCO3) and their phase transitions as
temperature increases, as has been observed in corrosion research. In this work, effects of reaction
conditions, including temperature and pressure have been investigated.
Key words: solubility product, siderite, saturation index, scale prediction, corrosion, deepwater
production, ultra high pressure and high temperature (xHPHT), oil and gas industry, strictly anoxic
INTRODUCTION
As the fourth most abundant metal on earth, iron is commonly found in a variety of rock and soil
minerals as Fe2+ and Fe3+. Ferrous carbonate is the main source of iron (II) in nature under anoxic
conditions. The dissolution of naturally formed ferrous carbonate may contribute to the high iron
concentration in the connate water. Iron concentration measured in produced water might be from
various sources including corrosion and dissolution of naturally occurred siderite as well as corrosion
©2015 by NACE International. Requests for permission to publish this manuscript in any form, in part or in whole, must be in writing to
NACE International, Publications Division, 15835 Park Ten Place, Houston, Texas 77084. The material presented and the views expressed in
this paper are solely those of the author(s) and are not necessarily endorsed by the Association.
1
products (Fe3O4 and FeCO3). With the continued development of offshore production in ultra-deepwater
(UDW) Gulf of Mexico (GoM), more and more wells are exposed to extremely high temperature and
pressure (xHPHT) under anoxic conditions. A greater understanding of siderite dissolution and
formation under these conditions is needed to better understand the source of iron in produced waters.
In addition, FeCO3 is also a major source of scale in production systems, which can cause serious
problems. 1 If the connate water with high iron concentration is mixed with produced water, scaling
issues may occur. For example, a potential mechanism for part of the production decline in the Prudhoe
Bay field is siderite scale deposition.2 Therefore, to better predict scale formation, scale solubility under
these conditions must be as accurate as possible.
Siderite (FeCO3) is the most common corrosion product at intermediate temperatures (60-150 °C),
forming a passive layer to protect the metal surface and preventing further corrosion.3-6 However, under
high temperature conditions (> 150 °C), magnetite appears to be the dominant deposit on oil and gas
production pipes and facilities, especially on carbon steel.7-9 It has been suggested that the formation of
ferrous carbonate may be a necessary intermediate step to obtain a protective magnetite layer.10 A
solubility study of siderite will benefit not only understanding of FeCO3 scale formation, but also the
dissolution processes of passive layers for corrosion studies under extreme conditions. Even though
various models have been developed to predict FeCO3 solubility, few of them can make prediction
under xHPHT. More importantly, very few experimental data has been reported to validate the
predictions.
Solubility of siderite has been studied at different temperatures, ionic strength, electrolytes and CO2
partial pressure by various researchers, as listed in Table 1.11-23 Most of the experimental work has
been done below 100 °C. However, even under ambient conditions, solubility product of siderite has ±
0.3 saturation index (SI) unit difference between the reported values from various literature sources.
More interestingly, the way of preparing siderite crystals (wet vs. dry) also gives the pKsp values ± 0.3
SI unit difference. The author can only locate one publication that studied the siderite solubility from 100
°C to 250 °C.22 However, this study was under ionic strength of 0.1 M NaCl and saturated pressures at
these temperatures. Moreover, the effect of ionic strength up to 5 M NaCl on siderite solubility has been
studied only at room temperature by Silva et al..18 In addition, the effect of the partial pressure of CO2
on the dissolution of siderite has also been investigated.23 However, limited research on the effect of
high temperature, high pressure and high ionic strength on solubility of siderite has been performed.
The emphasis of this work is on the solubility of siderite at high temperature (up to 250 °C) and high
pressure (up to 24,000 psig) in 1 M NaCl solution under a constant CO2 partial pressure and strictly
anoxic conditions (<< 1 ppb O2).
©2015 by NACE International. Requests for permission to publish this manuscript in any form, in part or in whole, must be in writing to
NACE International, Publications Division, 15835 Park Ten Place, Houston, Texas 77084. The material presented and the views expressed in
this paper are solely those of the author(s) and are not necessarily endorsed by the Association.
2
Table 1
Summary of siderite solubility product pKsp reports
T (°C)
P (psig)
I (M)
Solution
pKsp (siderite)
References
30
14.7
0.01
NaCl
10.46
17
14.7
0.1
NaClO4
10.12
Smith11
Singer et al.12
22.5
14.7
0.1
NaClO4
10.22
25
14.7
0.1
NaClO4
10.24
30
20
14.7
14.7
0.1
0.002
NaClO4
water
10.25
10.40
50
30
40
50
60
70
80
25
25
43
62
83
94
25
25
25
25
25
25
50
75
100
150
200
250
16.5
15.3
15.8
16.5
17.6
19.2
21.6
14.7
14.7
15.8
17.6
21.6
26.5
14.7
14.7
14.7
14.7
14.7
14.7
16.5
20.3
29.4
83.7
240.0
590.7
1
0.002
0.002
0.002
0.002
0.002
0.002
1
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
NaClO4
water
water
water
water
water
water
NaClO4
water
water
water
water
water
water
water
water
water
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
NaCl
11.20
11.11
11.27
11.88
12.13
12.31
12.57
10.80
10.77
10.94
11.03
11.25
11.42
10.93
11.03
11.03
10.43
9.04
10.93
11.14
11.58
11.91
12.81
13.56
14.62
Bardy et al.13
Reiterer et al.14
Braun16
Bruno et al.15
Greenberg et al.17
Ptacek et al.19
Ptacek et al.20
Jensen et al., (dry crystal)21
Jensen et al., (wet crystal)21
Silva et al.18
P. Bénézeth et al.22
EXPERIMENTAL
Flow-through Apparatus
In this research, by using customized flow-through apparatus (Figure 1), the solubility of FeCO3 has
been investigated. All wetted parts are made of Polytetrafluoroethylene (PTFE) lined UNS N10276* to
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3
prevent corrosion at these conditions in order to minimize Fe concentration from the background. A
high pressure continuous feed pump with maximum pressure 25,000 psig is used to continuously
deliver feeding solutions up to 24,000 psig at constant flow rate. An air actuated back pressure
regulator was connected at the end of the system to maintain constant pressure throughout the system.
A polytetrafluoroethylene (PTFE) lined UNS N10276 column was used to pack siderite particles. A
titanium (Ti) frit was placed at each end of the column to prevent the small particles from flowing out.
Another pump is used to introduce a chelating agent before temperature and pressure drops to prevent
Fe2+ re-precipitation as temperature and pressure decrease to ambient conditions. Flow rate for all the
experiments are adjusted from 0.03 to 0.1 ml/min, the retention time for feed solution in the packed
column is from 35 to 181 minutes, which allows feed solution to equilibrate at desired temperatures and
pressures. All tubing and fittings are rated to a pressure of at least 30,000 psig. The total volume of the
system including the tubing, fittings and the reactor column was approximately 12 ml. Temperature was
controlled by a GC oven.
Cooling
Stage
Column
Sampling
Pump
Back Pressure
Regulator
Oven
Pump (chelating
agent)
Figure 1. Flow-through apparatus for mineral solubility study.
Preparation of Siderite Particles and Feed Solutions
FeCO3 particles were prepared in 1 M NaCl solution. The dissolved oxygen (DO) was removed from the
1 M NaCl solution. The concentration of DO was measured << 1 ppb, indicating a strictly anoxic
condition for FeCO3 formation. Approximately 35 g of ferrous ammonium sulfate hexahydrate (99+%
from Acros organics) was added into the 200 ml bottle and 16 g of sodium bicarbonate (99% from
LabChem†) was added into the 500 ml bottle with continuous CO2 sparging. Both solutions were heated
in a 70 °C water bath. Then the ferrous solution was manually poured into the bicarbonate solution to
produce a white to light grey buff solid, ferrous carbonate. The precipitates were settled and washed
several times with deoxygenated water to remove sodium and ammonium sulfate. Particles were then
dried (as shown in Figure 2) and packed into the column in a N2 filled glove bag. Solids were
characterized by scanning electronic microscope (SEM) and X-Ray diffraction (XRD) to check the
morphology and confirm the structure of FeCO3. In Figure 3, an XRD spectrum of synthesized FeCO3
particles is shown to confirm that the powder is single phase siderite. There are no other peaks in the
spectrum indicating that only siderite was produced. In Figure 4, SEM image shows spherical shaped
particles with single particle size from 0.6 µm to 1.3 µm. Some agglomeration occurred and the
aggregates are up to 2.1 µm. Particle size distribution is narrow with an average size of approximately
0.9 µm (Figure 4, insert).
*
Unified Numbering System for Metals and Alloys (UNS)
†
Trade name
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NACE International, Publications Division, 15835 Park Ten Place, Houston, Texas 77084. The material presented and the views expressed in
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Figure 2. Picture of white to light gray siderite solids synthetized.
PDF-00-012-0531-FeCO3
Exp-FeCO3
450
Intensity (count)
400
350
300
250
200
150
100
50
0
20
30
40
50
60
70
80
2ɵ
Figure 3. XRD spectrum of dried siderite after washing. Black line shows the experimental data.
Red circles show the standard rhombohedral structure pattern of siderite (PDF# 00-012-0531).
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NACE International, Publications Division, 15835 Park Ten Place, Houston, Texas 77084. The material presented and the views expressed in
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5
40
Particle number
35
30
25
20
15
10
5
0
0.59
0.74
0.88
1.03
1.18
1.32
Particle size (µm)
Figure 4. SEM image of synthesized FeCO3 with particle size from 0.6 µm to 1.3 µm.
Feed solution containing 1 M NaCl, 10.6 mg/L Fe2+ (Fe(NH4)2(SO4)2·6H2O, 99+%, Acros) and 103 mg/L
HCO3- (NaHCO3, ACS grade, LabChem Inc.) was used for flow-through solubility study. Solution was
vigorously sparged with 100% CO2 under 1 atm in a pressure vessel to remove dissolved oxygen. The
vessel was then pressurized to ~ 4 atm (60 psig) to promote dissolution of FeCO3 solids. Feed solution
was continuously pumped into the siderite packed column until continuous liquid flow was observed in
the effluent to make sure there were no air bubbles trapped in the system. Then the pressure was
adjusted to the target pressure, followed by adjustment of temperature. Effluent samples were then
collected in Ar purged sample tubes at targeted flow rates. The volume of collected effluent was
measured to calculate the actual flow rate. Effluent was analyzed immediately after sample collection
using HACH method for ferrous iron concentration and total alkalinity. Inductively coupled plasma
atomic emission spectroscopy (ICP-OES) was also used to measure total iron concentration for
validation.
RESULTS AND DISCUSSION
The assumed reaction can be expressed as:
𝐹𝑒𝐶𝑂3,(𝑠) → 𝐹𝑒 2+ + 𝐶𝑂32−
The saturation index (SI) defined as the logarithm of the ion activity product divided by the solubility
product of siderite as shown in equation 1,
𝑎𝐹𝑒2+ 𝑎𝐶𝑂2−
𝑆𝐼𝐹𝑒𝐶𝑂3 = 𝑙𝑜𝑔10 (
3
𝐾𝑠𝑝,𝐹𝑒𝐶𝑂3
𝑚𝐹𝑒2+ 𝛾𝐹𝑒2+ 𝑚𝐶𝑂2− 𝛾𝐶𝑂2−
) = 𝑙𝑜𝑔10 (
3
𝐾𝑠𝑝,𝐹𝑒𝐶𝑂3
3
)
(1)
where 𝑚𝐹𝑒 2+ is the measured Fe2+ molar concentration, 𝑚𝐶𝑂32− is molar concentrations of CO32- which
can be calculated from measured total alkalinity, 𝛾𝐹𝑒 2+ and 𝛾𝐶𝑂32− are activity coefficients of the species
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6
calculated by using Pitzer24-26 theory based ScaleSoftPitzer† under different temperatures and
pressures (Table 2). When equilibrium is reached, SI of FeCO3 should be zero, i.e.
𝐾𝑠𝑝,𝐹𝑒𝐶𝑂3 = 𝑚𝐹𝑒 2+ 𝛾𝐹𝑒 2+ 𝑚𝐶𝑂32− 𝛾𝐶𝑂32−
(2)
Table 2
Calculated activity coefficients in 1 M NaCl
T (°C)
P (psig)
150
150
150
150
250
250
250
250
5534
11240
18680
24000
4856
9345
18780
23390
γ(Fe2+)
0.068
0.079
0.092
0.103
0.014
0.019
0.028
0.033
γ(CO32-)
0.019
0.022
0.024
0.025
0.0022
0.0031
0.0052
0.0053
Solubility of FeCO3 was measured up to 250°C, 24,000 psig and 1 M NaCl. Experimental results
including the temperature (150 °C and 250 °C), pressure (from ~5,000 psig to 24,000 psig), pH (at
ambient condition) as well as the measured Fe2+ and HCO3- concentrations are shown in Table 3. Also
in that table, Ksp values calculated using experimental data (pKsp) and predicted (pKsp*) are listed as
well and the SI values of FeCO3 were calculated. The SI values at 150 °C and lower pressures have
good agreement with the predicted values with variation up to 0.1 SI unit. On the other hand, these
values varied from 0.22 to 0.41 SI units under 150 °C with high pressures (> 20,000 psig) and 250 °C.
Table 3
Experimental and theoretical results for siderite solubility experiments under xHPHT in 1 M NaCl
Exp #
1
2
3
4
5
6
7
8
a
†
log[Alkalinity]a
pH measured
2+ a
T (°C ) P (psig)
log[Fe ] meas measured at
at 25 °C
25 °C
150
5534
5.16
-2.562
-2.267
150
11240
5.31
-2.441
-2.113
150
18680
5.5
-2.321
-1.940
150
24000
5.68
-2.131
-1.756
250
4856
4.82
-3.016
-2.671
250
9345
5.18
-2.498
-2.229
250
18780
5.37
-2.363
-2.045
250
23390
5.56
-2.226
-1.934
[CO32-] calca
x10
7
6.72
12.57
24.57
56.66
5.58
12.62
29.59
48.21
pKsp pKsp* (from
pKsp - pKsp*
(from exp) prediction)
11.64
11.07
10.54
9.93
13.65
13.02
11.74
11.28
11.59
10.97
10.17
9.64
13.24
12.68
11.52
10.95
Molar concentration of species in effluent
Trade name
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7
0.05
0.1
0.37
0.29
0.41
0.34
0.22
0.33
The pressure dependence of pKsp values at 150 °C and 250 °C are shown in Figure 5 and 6
respectively. At both temperatures, pKsp values from both experimental data (blue circles) and
prediction (red diamonds) decrease with increased pressure. The regression of both experimental data
(blue solid line) and prediction (red dotted line) suggest a linear relationship between pKsp and pressure
(R-squared value is 0.9924 at 150 °C and 0.9973 at 250 °C respectively).
13
150 °C
12
y = -8.9582E-05x + 1.2127E+01
R² = 9.9235E-01
pKsp (FeCO3)
11
150 °C,
83.7 psig,
1M NaCl
10
experimental
Predicted
calculated from this study
calculated from prediction
Benezeth et al.
Linear (experimental)
Linear (Predicted)
9
8
R² = 0.9997
7
0
5000
10000
15000
20000
25000
Pressure (psig)
Figure 5. pKsp values of FeCO3 at 150 °C and different pressures in 1 M NaCl. Blue dotsexperimental data, blue solid line-curve fitting of experimental data, green dot-calculated pKsp
value at 150 °C and 83.7 psig from curve fitting of experimental data, red diamonds-predicted
values, red dotted line-curve fitting of predicted values, pink diamond-calculated pKsp value at
150 °C and 83.7 psig from curve fitting of predicted values.
15
250
250
°C,°C
590.3 psig
14
y = -1.2860E-04x + 1.4230E+01
R² = 9.9731E-01
pKsp (FeCO3)
13
250 °C,
590.3 psig,
1M NaCl
12
experimental
Predicted
calculated from this study
calculated from prediction
Benezeth et al.
Linear (experimental)
Linear (Predicted)
11
10
R² = 1
9
0
5000
10000
15000
20000
25000
Pressure (psig)
©2015 by NACE International. Requests for permission to publish this manuscript in any form, in part or in whole, must be in writing to
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8
Figure 6. pKsp values of FeCO3 at 250 °C and different pressures in 1 M NaCl. Blue dotsexperimental data, blue solid line-curve fitting of experimental data, green dot-calculated pKsp
value at 250 °C and 590.3 psig from curve fitting of experimental data, red diamonds-predicted
values, red dotted line-curve fitting of predicted values, pink diamond-calculated pKsp value at
250 °C and 590.3 psig from curve fitting of predicted values.
In order to validate pKsp values under high pressure and their change with pressure, some extrapolation
and calculations have been made because no other experimental data under high pressure and 1 M
NaCl is available. In Figure 5, pKsp value (12.12, green dot) at 150 °C and its saturated pressure 83.7
psig was calculated by using curve fitting equation 3,
𝑝𝐾𝑠𝑝 = −8.9582 × 10−5 𝑃 + 12.127
(3)
where P is the pressure at 150 °C in psig.
At 250 °C and 590.3 psig, pKsp value (14.17, green dot) was calculated by using curve fitting equation
4,
𝑝𝐾𝑠𝑝 = −1.2860 × 10−4 𝑃 + 14.230
(4)
where P is the pressure at 250 °C in psig.
Thus, in Figure 7, the above pKsp values at 150 °C and 250 °C were plotted as green dots and curve
fitted with linear function (solid green line), based on the assumption that pKsp values will decrease
linearly as temperature increases. It is consistent with the published experimental data from Bénézeth
et al.22 (blue crosses, curve fitted with blue dotted line), Greenberg et al.17 (orange squares, curve fitted
with orange dotted line), Braun et al. 16 (purple pluses, curve fitted with purple dotted line) as well as the
predicted pKsp values (red diamonds, curve fitted with red dotted line).
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9
this study-Ksp in 1 M NaCl
calculated from this study
predicted Ksp in 1 M NaCl
Silva-Ksp in 1 M NaCl
Benezeth-Ksp in 0.1 M NaCl
Tomson-Ksp in 0.002 M IS
Braun-Ksp in 0.002 M IS
Linear (this study-Ksp in 1 M NaCl)
Linear (predicted Ksp in 1 M NaCl)
Linear (Benezeth-Ksp in 0.1 M NaCl)
Linear (Tomson-Ksp in 0.002 M IS)
Linear (Braun-Ksp in 0.002 M IS)
16
R² = 0.9932
15
pKsp (FeCO3)
14
R² = 0.9997
R² = 0.9632
13
12
y = 2.0500E-02x + 9.0450E+00
R² = 1.0000E+00
11
R² = 0.9742
10
9
8
0
50
100
150
200
250
300
T (°C)
Figure 7. pKsp values of FeCO3 at different temperatures under water vapor pressure in
solutions with various ionic strength. Green dots-calculated pKsp values from experimental data,
green solid line-curve fitting of experimental data, pink dot-calculated pKsp value at 25 °C and
14.7 psia from curve fitting of experimental data, red diamonds-predicted values, red dotted
line-curve fitting of predicted values, black triangle-calculated pKsp value at 25 °C and 14.7 psia
from Silva’s model18, blue crosses-experimental data from Bénézeth et al.22, blue dotted linecurve fitting of experimental data from Bénézeth et al.22, orange square-experimental data from
Greenberg et al.17, orange dotted line-curve fitting of experimental data from Greenberg et al.17,
purple plus-experimental data from Braun et al.16, purple dotted line-curve fitting of
experimental data from Braun et al..16
Therefore pKsp value (9.56, pink dot) at 25 °C, 14.7 psia in 1 M NaCl can be calculated from curve
fitting equation 5,
𝑝𝐾𝑠𝑝 = −2.05 × 10−2 𝑇 + 9.045
(5)
where T is the temperature in °C.
The black triangle in Figure 7 is the pKsp value (9.039) calculated from equation 6,
−𝑝𝐾𝑠𝑝 = −10.9 + 2.518 𝐼 0.5 − 0.657 𝐼
(6)
where 𝐼 is the ionic strength at ambient condition, the model created by Silva et al. to calculated pKsp
value at ambient condition in solutions with different ionic strength.18 The calculated pKsp value from this
study has 0.52 SI unit difference from the calculated value from Silva et al.. 18 It is a reasonable result
and proves that the pKsp values under xHPHT and their changes with pressure are very accurate under
these extreme conditions.
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10
The solid samples were analyzed by SEM and XRD. After the experiments, the solid changed color
from gray to brick red, and the phase of hematite (Fe2O3, blue dots) associated with siderite (red
squares) were detected by XRD (Figure 8). The transition of these two phases is not defined. It could
be during the experiment at high temperature. Compared with previous characterization of initial
siderite particles, particle size of siderite after experiments increased with better crystallinity. Well
crystallized hematite particles with bipyramide shape and particle size of 0.5-1 µm (Figure 9, in red
circles) were observed as well as small particles of siderite. Magnetite phase is not clearly observed
(green triangles in Figure 8).
1200
exp
1000
FeCO3-00-0012-0531
Fe2O3-01-077-9925
Intensity
800
Fe3O4-00-019-0629
600
400
200
0
20
30
40
50
60
70
80
2 theta
Figure 8. XRD of solid sample after 250 °C experiment. Black line-experimental data, red
squares-siderite phase, blue dots-hematite phase, green triangles-magnetite phase.
Figure 9. SEM of FeCO3 and hematite particles after 250 °C experiment. Red circles show the bipyramid shape of hematite.
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CONCLUSIONS
This study evaluates the solubility of siderite at extreme high temperature and pressure in 1 M NaCl
solution. From comparison between the predicted pKsp values and from the experimental data, there is
confidence that the experimental method used is able to reliably simulate the extreme temperature (up
to 250 °C), pressure (up to 24,000 psig) and strictly anoxic (<< 1 ppb dissolved oxygen) conditions
encountered in ultra-deep water production. This study expands the current experimental data set for
siderite solubility in 1 M NaCl solution under high pressure. Experimental values have a maximum
difference of 0.41 SI unit from the predicted values; which is very accurate at these xHTHP conditions.
Due to the limited data available, the results from this study were used to calculate pKsp value under
ambient condition in 1 M NaCl so that the derived results can be compared with published experimental
data. The derived pKsp value has 0.52 SI unit difference from previous literature, which also validate the
experimental data and the change with pressure. Solids after entire experiments were characterized by
XRD and SEM. The appearance of hematite phase associated with siderite in the solid sample was
observed.
ACKNOWLEDGEMENTS
Funding for the projects is provided through the “Ultra-Deepwater and Unconventional Natural Gas and
Other Petroleum Resources Research and Development Program” authorized by the Energy Policy Act
of 2005. This program—funded from lease bonuses and royalties paid by industry to produce oil and
gas on federal lands—is designed to assess and mitigate risk enhancing the environmental
sustainability of oil and gas exploration and production activities. RPSEA is under contract with the U.S.
Department of Energy’s National Energy Technology Laboratory to administer three areas of research.
RPSEA is a 501(c)(3) nonprofit consortium with more than 180 members, including 24 of the nation's
premier research universities, five national laboratories, other major research institutions, large and
small energy producers and energy consumers. The mission of RPSEA, headquartered in Sugar Land,
Texas, is to provide a stewardship role in ensuring the focused research, development and deployment
of safe and environmentally responsible technology that can effectively deliver hydrocarbons from
domestic resources to the citizens of the United States. Additional information can be found at
www.rpsea.org. The advice from Prof. Mason B. Tomson, Civil and Environmental Engineering
department at Rice University, on the conduct of this research is gratefully acknowledged.
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this paper are solely those of the author(s) and are not necessarily endorsed by the Association.
14