Laboratory Studies of MMP and Hydrocarbon
Mobilization in Conventional and Bakken
Plays using CO2, Methane, and Ethane
© 2014 University of North Dakota Energy & Environmental Research Center.
*Steve Hawthorne, Ph.D., Jim Sorensen, David Miller, Charles
Gorecki, John Hamling, Beth Kurz, Ed Steadman, and John Harju
Energy & Environmental Research Center
Steve Melzer (Melzer Consulting)
Presented at the 21st Annual CO2 Flooding Conference
December 10-11, 2015Midland, Texas
Bakken CO2 Storage and Enhanced
Recovery Program Partners
Bakken Production Optimization Program Membership
How Do We Get More Oil
Out of the Bakken?
• The more we
understand about the
Bakken petroleum
system, the more oil we
recognize in it.
• Currently, only a 3%–
5% recovery factor.
• Small improvements in
recovery yield billions of
barrels of oil.
• Can CO2, or other
gases, be a game
changer in the
Bakken?
As a Commodity to Enhance Oil Recovery
Long Term Goal
New Initiative – “Project Ethane”
• Drivers:– To use regionally low value ethane to produce high
value oil.
• 2–3.2 Bt of CO2 needed yielding 4–7 Bbbl of oil.
• North Dakota currently produces ~33 Mtpy of CO2.
- Ethane is currently more available than CO2 in the Williston Basin. Total ethane entering ND gas plants ≈ 240 MMcfd (170,000 bbl/d).
– Additional benefits
♦ Relieve gathering bottleneck/reduce flaring
♦ Improve pipeline quality methane
♦ Improve quality of NGLs (volatility)
♦ Eventually may be other markets for chemical and industrial applications - Production of power, fertilizer, methanol, other chemicals, etc.
Updates on 3 basic lab experiments:
MMP = multiple contact minimum miscibility
pressure.
Hydrocarbon compositions in the mobilized
“miscible” phase.
Bakken rock extractions at reservoir conditions.
This talk addresses the potential to use CO2 and/or
associated gas hydrocarbons for EOR in tight
unconventional reservoirs based on laboratory
studies.
Basic Properties of Three Fluids
O H Not linear
H Permanent dipole moment
Wets minerals well
Solvates polars, but not nonpolars (sort of)
O=C=O Linear
No permanent dipole moment
Polarizable
“Wets” minerals a little
Solvates nonpolars and moderately polar compounds,
(but not very well)
H3C-CH3 (ethane)
No dipole moment
Not polarizable
Poor at wetting minerals
Solvates nonpolars
3 basic lab experiments:
MMP = multiple contact minimum
miscibility pressure. (ca. 80 lab MMP
determinations)
Hydrocarbon compositions in the
“miscible” phase.
Bakken rock extractions at reservoir
conditions.
Definitions of Multiple Contact “Miscibility”
(MMP)
To a PVT lab: 90% of the oil in a 50 foot “slim tube” of
sand comes out in 1.2 pore volumes (slow and very
expensive but has served conventional EOR well).
To a chemist: miscible fluids mix in any ratio without
forming two phases.
To a petroleum engineer: “I don’t care as long as I get
more oil.”
EERC approach (via Rao, et al.): vanishing interfacial
tension. “Miscibility” is defined as no surface tension
between the CO2- and oil-dominated phases.
MMP by vanishing
interfacial
tension/capillary
rise.
Patent pending
1.12, 0.84, 0.68 mm i.d.
EERC patent pending
MMP (psi) Values for Bakken Live Oils
Cap Rise EOS slim tube
Live oil A 129 C CO2 3180 ±114 3220 3161
Live oil B 126 C CO2 3196 ±139 3150
Does the capillary rise-vanishing
interfacial tension method work?
We now have a less expensive and faster “tool” to study the
effects of reservoir conditions and fluid composition on MMP.
So what about associated gas
compared to CO2?
CO2 is in limited supply (and not always pure).
Natural gas is readily available.
Increased capture and sales of natural gas will
result in excess ethane.
Ethane is very effective at achieving lower
MMPs, methane is not !
API 41.5 Crude (Bakken), 110 C
Ethane is very effective at achieving lower
MMPs, methane is not !
API 38.7 Crude, 42 C
Ethane is very effective at achieving lower
MMPs, methane is not !
API 30.7 Crude, 42 C
0
1000
2000
3000
4000
5000
6000P
ress
ure
, psi
CO2
1468±42
methane
5077±192
ethane
736±8
What about gas mixtures?
y = 28.749x + 1373.2R² = 0.9858
y = 699.12e0.0173x
R² = 0.9923
500
1000
1500
2000
2500
3000
3500
4000
4500
0 20 40 60 80 100
Min
imu
m M
isci
bili
ty P
ress
ure
, psi
Mole % Methane
API 38.7 Crude, CH4/CO2, CH4/ethane, 42C
CH4/CO2
CH4/ethane
How Pure Does My CO2 or Ethane Have To Be?
y = 19.889x + 2515.4R² = 0.9964
y = 1257.5e0.0124x
R² = 0.9923
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 20 40 60 80 100
Min
imu
m M
isci
bili
ty P
ress
ure
, psi
Mole % Methane
Bakken, CH4/CO2, CH4/ethane, 110C
Bakken, CH4/CO2, 110C
Bakken, CH4/ethane, 110C
What about mixed ethane and CO2?
(conventional reservoir oil, 42 oC)
CO2 density, 42 C
1500 psi = 0.62 g/mL
1000 psi = 0.20 g/mL
Pure CO2 MMP 1390 ± 41
CO2 after 540 psi ethane
Trial 1 1009 ± 53
Trail 2 980 ± 62
By adding ethane to CO2 we might be able to do EOR
and store CO2 in shallow reservoirs!
y = 19.889x + 2515.4R² = 0.9964
y = 26.627x + 1317.1R² = 0.9926
1000
1500
2000
2500
3000
3500
4000
4500
5000
0.00 20.00 40.00 60.00 80.00 100.00
Min
imu
m M
isci
bili
ty P
ress
ure
, psi
Mole % Methane in CO2
API 41.5 Bakken Crude, CH4/CO2, 42 and 110C
110 C
42 C
Temperature Greatly Influences MMP
3 basic lab experiments:
MMP = multiple contact minimum
miscibility pressure.
Hydrocarbon compositions in the
“miscible” phase.
Rock extractions at reservoir conditions.
Conventional crude/CO2 behavior, 42 oC
CO2 pressure increased from ambient to 2300
psi, then reduced back to ambient.
Does anything interesting happen
above and below MMP?
© Energy and
Environmental
Research
Center, 20133.5 min
Dissolved Hydrocarbons Affect the Critical Pressure (a lot)
NIST Standard Reference Database, 23. Version 9.0, “Reference Fluid
Thermodynamic and Transport Properties”
Where do all these “extra” phases come from ?
Dissolved Hydrocarbons Affect the Critical Temperature (a lot)
NIST Standard Reference Database, 23. Version 9.0, “Reference Fluid
Thermodynamic and Transport Properties”
Which hydrocarbons partition into this
“miscible” upper phase ?
Which hydrocarbons are lost as pressure drops?
So if the oil and CO2 are
not truly miscible, what oil
components are in the
CO2 “miscible” phase?
We have never observed
true chemical miscibility
(single phase) between
CO2 and crude oil under
any T and P conditions.
8 mL oil
10 mL CO2
0
2
4
6
8
10
12
14
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
mg
Hyd
roca
rbo
n p
er
gram
CO
2
Carbon Number
1500psi Up
2300psi Up
Pressures above MMP increase the amount of mobilized oil, especially higher MW hydrocarbons (42C).
MMP = 1400 psi (10 MPa)
0
2
4
6
8
10
12
14
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
mg
Hyd
roca
rbo
n p
er
Gra
m C
O2
Hydrocarbon Chain Length
2300psi Up
1500psi Down
1250psi Down
Substantial oil precipitates as pressure drops—even if pressure remains
above MMP (especially for higher MW hydrocarbons).
Conventional Reservoir, 42 C
MMP = 1400 psi
0%
2%
4%
6%
8%
10%
12%
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
% o
f to
tal H
C m
ass
Carbon Number
CO2 selectively mobilizes lighter hydrocarbons.
(42 C, API 38.7 crude)
2300 psi CO2
crude oil after 2300 psi CO2
0%
5%
10%
15%
20%
25%
30%
35%
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37+
Pe
rce
nt
of
tota
l HC
Carbon Number
after exposure
mobilized
Methane only mobilizes low MW hydrocarbons.(API 38.7 crude, 2300 psi, 42C)
0%
2%
4%
6%
8%
10%
12%
14%
16%
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37+
Pe
rce
nt
of
tota
l HC
Carbon Number
after exposure
mobilized
Ethane mobilizes all hydrocarbons alike.(API 38.7 crude, 2300 psi, 42 C)
0
100
200
300
400
500
600
700
800
1 2 3 4 5
Tota
l Hyd
roca
rbo
n M
ob
ilize
d, m
g/m
L
Number of Fractions Collected
Total Crude Oil In Mobile Phase, mg/mLAPI 38.7 Crude Oil, 2300 psi, 42 C
mean of 3 runs
CO2
CH4
Ethane
Total Crude Oil Hydrocarbons Mobilized from API 38.7
Crude Oil in CO2, Methane, and Ethane
2300 psi, 42C
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1 2 3 4 5
Tota
l Hyd
roca
rbo
n M
ob
ilize
d, m
g/gr
am
Number of Fractions Collected
Total Crude Oil In Mobile Phase, mg/gramAPI 38.7 Crude Oil, 2300 psi, 42 C
mean of 3 runs
CO2
CH4
Ethane
0
50
100
150
200
250
300
350
400
1 2 3 4 5
Tota
l Hyd
roca
rbo
n M
ob
ilize
d, m
g/m
L
Number of Fractions Collected
Total Crude Oil In Mobile Phase, mg/mLBakken Crude Oil
3000 psi, 110 C, mean of 3 runs
CO2
ethane
0
100
200
300
400
500
600
700
800
900
1000
1 2 3 4 5
Tota
l Hyd
roca
rbo
n M
ob
ilize
d, m
g/gr
am
Number of Fractions Collected
Total Crude Oil In Mobile Phase, mg/gram,Bakken Crude Oil
3000 psi, 110 C, mean of 3 runs
CO2
Ethane
Total Crude Oil Hydrocarbons Mobilized from Bakken
Crude Oil (API 41.5) in CO2, and Ethane
3000 psi, 110C
0
1
2
3
4
5
6
7
1 2 3 4 5
Tota
l Hyd
roca
rbo
n M
ob
ilize
d, b
bl/
ton
Number of Fractions Collected
Total Crude Oil In Mobile Phase, bbl/tonAPI 41.5 Bakken Crude Oil
3000 psi, 110 C, mean of 3 runs
CO2
Ethane
Total Crude Oil Hydrocarbons Mobilized from Two Crude
Oils in CO2 and Ethane at 42 and 110 C
bbl oil/ton injectant
0
2
4
6
8
10
12
14
1 2 3 4 5
Tota
l Hyd
roca
rbo
n M
ob
ilize
d, b
b/t
on
Number of Fractions Collected
Total Crude Oil In Mobile Phase, bbl/tonAPI 38.7 Crude Oil,
2300 psi, 42 C, mean of 3 runs
CO2
Ethane
CO2 vs. Ethane for a 150 tons/d Pilot Scale EOR (Preliminary Estimates based only on oil mobilization results.)
Fluid Results SummaryMMP:
1. Compared to CO2, methane doubles (or triples) the pressure, and
ethane cuts it in half.
2. Up to ca. 10 mole % methane in CO2 or in ethane has a small effect
on MMP, but then MMPs rise rapidly.
3. Higher temperatures raise MMP significantly (well known, but not
always recognized).
4. Initial results indicate that mixing ethane with CO2 could be very
effective.
Hydrocarbons mobilized into “miscible” phase:
1. CO2 has some preference for lower MW hydrocarbons.
2. Methane only mobilizes low MW hydrocarbons.
3. Ethane mobilizes all MW hydrocarbons (up to C34 anyway!).
4. Ethane mobilizes more total oil than CO2, and much more than
methane.
What about other characteristics of the fluids?
1. Will ethane enter oil-wet nanopores better than CO2 and will CO2 be
better at water-wet nanopores?
2. Ethane may cause more oil swelling than CO2—will that be the next
mechanism for Bakken recoveries?
3. Could mixtures of ethane and CO2 enhance EOR and CO2 storage?
3 basic lab experiments:
MMP = multiple contact minimum
miscibility pressure.
Hydrocarbon compositions in the
“miscible” phase.
Bakken rock extractions at reservoir
conditions.
All EOR projects to-date have been in
conventional (permeable) reservoirs that are
“flushed” with CO2.
Unconventional (tight) reservoirs may provide a
large opportunity for EOR and associated carbon
storage—but CO2 is expected to flow through
fractures and “bathe” rather than “flushing” the
rocks.
Is there any evidence that CO2 EOR and storage
can be applied to unconventional reservoirs?
Four general mechanisms for CO2 EOR
1. CO2 “flushes” the oil through the rock (conventional reservoirs
only—mimicked by the slim tube).
2. CO2 changes the bulk oil to make the oil more mobile.
> swelling, lower viscosity
3. Oil is mobilized by the CO2.
> suspension, solvation of oil hydrocarbons
4. A “new” mobile phase of mixed CO2/oil is produced at a
threshold pressure.
> a functional definition of multiple contact miscibility
Miscible or
immiscible
mechanisms
Can we get oil from the rocks?
Four Three general mechanisms for CO2 EOR in
the Bakken play.
1. CO2 “flushes” the oil through the rock (conventional reservoir only).
Mimicked by slim tube (?)
2. CO2 changes the bulk oil to make the oil more mobile.
> swelling, lower oil viscosity
3. Oil is mobilized by the CO2.
> suspension, solvation of oil hydrocarbons
4. A “new” mobile phase of mixed CO2/oil is produced.
> a functional definition of multiple contact miscibility
Can we get oil from the rocks?
The International Center for Applied Energy Technology®The International Center for Applied Energy Technology®
Hypothetical Steps in CO2 EOR
for hydralically-fractured reservoirs
The hypothetical steps address transporting the oil in
the rock matrix to the bulk CO2 in the fractures.
These mechanisms do NOT address subsequent
production/recovery steps.
EOR mechanisms for Oil Recovery from Bakken Rocks
Conventional Reservoir
5 nm ≈ C30 alkane
25,000 nm
25 nm
Where does CO2 have to go for
EOR and storage? Enormous holes for conventional
reservoirs.
Small holes for unconventional
reservoirs.
Itsy-bitsy molecule-sized holes for
shales.
ca. 80,000 nm diameter
ca. 3000 nm long
ca. 11-mm-dia. rod
CO2 Extraction of Source and Reservoir Rock to Mimic Fracture-
Dominated Flow Expected in Tight Systems
Laboratory Exposures Include:
>VERY small core samples (11-mm rod).
• Rock is “bathed” in CO2 to mimic fracture
flow, not swept with CO2 as would be the
case in confined flow-through tests.
• Recovered oil hydrocarbons are collected
periodically and analyzed by gas
chromatography/flame ionization detection
(GC/FID) (kerogen not determined); 100%
recovery based on rock crushed and
solvent extracted after CO2 exposure.
• All exposures at 5000 psi, 110oC to
represent typical Bakken conditions.
There is NO pressure drop across the
sample cell!
There IS no pressure drop across the sample
cell!
There is no PRESSURE DROP across the
sample cell!
There is no pressure drop ACROSS THE
SAMPLE CELL!
(The pressure drop occurs at the outlet of the flow restrictor
into the collection solvent.)
Rock core samples (Middle, Upper, Lower,
and Three Forks) have been extracted from:
Two Dunn County wells.
One McKenzie County well.
One Mountrail County well.
All rocks are used exactly as received. We
do not flood them with oil or water prior to
CO2 (or ethane) exposure. Recovered oil
is the oil originally in the rock. (Except one
case where rock was saturated in oil.)
Laboratory CO2 oil recovery from upper, middle, and lower
Bakken from the one Dunn County well (24 h).
Conv. 1-cm rod
Low Bak, <3.5 mm
Up Bak, <3.5 mm
Mid Bak, 1-cm rod
Up Bak, 1-cm rod
Low Bak, 1-cm rod
Laboratory CO2 oil recovery from upper, middle, and lower
Bakken from a Dunn County well (1st 8 hours).
Conv. 1-cm rod
Low Bak, <3.5 mm
Up Bak, <3.5 mm
Mid Bak, 1-cm rod
Up Bak, 1-cm rod
Low Bak, 1-cm rod
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
Cu
mu
lati
ve %
Hyd
roca
rbo
n R
eco
very
CO2 Exposure time, hours
Middle Bakken and Three Forks
Upper and Lower Bakken Shales
Laboratory CO2 Recovery of oil Hydrocarbons from a single McKenzie County well. (5000 psi, 110 C, well 24123)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
Cu
mu
lati
ve %
Hyd
roca
rbo
n R
eco
very
CO2 Exposure time, hours
Laboratory CO2 Recovery of oil Hydrocarbons from a
single Dunn County well. (5000 psi, 110 C, well 20172)
Middle Bakken
and Three Forks
Lower Bakken Shale
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
% o
f to
tal H
C
CO2 exposure time, hours
Laboratory HC Recovery from Laminated (middle) and Lower Facies with CO2, Mountrail County Well
2500 psi ≈ MMP
5000 psi Laminated
Lower shale7500 psi
7500 psi
5000 psi
MMP ca. 2500
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 10 20 30 40
% o
f to
tal H
C
CO2 exposure time, square root of minutes
HC Recovery from a Mountrail Ct. well. Laminated, Burrowed, Lower, and Upper with CO2
Laminated, Run 1
Laminated, Run 2
Upper, Run 1
Upper, Run 2
Burrowed, Run 1
Burrowed, Run 2
Lower, Run 1
Lower, Run 2
Linear HC recovery vs. the square root of time is
indicates that diffusion is the major controlling
mechanism. (Eide et al., SPE 2015)
So, you can get oil out of Bakken
rock with CO2, but what about
ethane?
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 1 2 3 4 5 6 7 8
% o
f to
tal H
C
Exposure time, hours
Oil-saturated Middle Bakken
Ethane
CO2
CH4/Ethane, 85/15
CH4
11-mm dia. rods were pressurized at 6000 psi with Bakken crude oil
for 36 hours (ambient T) to achieve > 90% pore volume saturation.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
% o
f to
tal H
C
CO2 exposure time, hours
Resaturated Middle Bakken, CO2
sum C #
8
10
12
15
17
20
24
28
32
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
% o
f to
tal H
C
Ethane exposure time, hours
Resaturated Middle Bakken, Ethane
sum C #
8
10
12
15
17
20
24
28
32
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
% o
f to
tal H
C
85/15 CH4/ethane exposure time, hours
Resaturated Middle Bakken, 85/15 CH4/Ethane
sum C #
8
10
12
15
17
20
24
28
32
26
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
% o
f to
tal H
C
CH4 exposure time, hours
Resaturated Middle Bakken, CH4
sum C #
8
10
12
15
17
20
24
28
32
26
Recovery of higher MW HCs are lower with CH4 and CH4/ethane (85/15)
than with CO2 or ethane. Ethane is best with higher MW HCs.
24
26
28
32
24
26
28
32
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25
% o
f to
tal H
C R
eco
vere
d
Exposure time, hours
EthaneCO2
Laboratory Hydrocarbon Recover from Middle Bakken
(Dunn County well) with CO2 and Ethane
(5000 psi, 110 C)
0%
20%
40%
60%
80%
100%
120%
0 5 10 15 20 25
% o
f to
tal H
C
Exposure time, hours
EthaneCO2
Laboratory Hydrocarbon Recover from Lower Bakken
(Dunn County well) with CO2 and Ethane
(5000 psi, 110 C)
How fast does CO2 permeate into
Bakken rock? (preliminary data!)
0.95 sq. cm exposed
surface area on epoxy-
coated rod. CO2 has to
permeate 4 cm.
15.7 sq. cm surface area for uncoated
rod (all previous experiments). CO2
has to permeate 5.5 mm.
4 cm
1.1 cm
0%
20%
40%
60%
80%
100%
120%
0 5 10 15 20 25
% o
f to
tal H
C
CO2 exposure time, hours
Uncoated rod
Hydrocarbon recovery from the Laminated facie
(Mountrail County well, 5000 psi, 110C)
Coated rod
How fast does CO2 permeate into
Bakken rock? (preliminary data!)
0%
20%
40%
60%
80%
100%
0 5 10 15 20 25
% o
f to
tal H
C
CO2 exposure time, hours
sum C #
9
11
13
15
17
CO2 permeates 4-cm length
HC recovery based on diffusion
How fast does CO2 permeate into Bakken rock?HC recovery is related to MW—i.e., diffusion coefficients.
Observations on CO2 and Associated HC
Gases EOR in Bakken Rocks
1. Experimental results support the proposed processes where CO2 flows rapidly
through fractures rather than through the rock, then permeates into the rock.
2. Exponential decay in recovery rates with time, and the large effect of particle
size show a mass-transfer (diffusion) limited recovery process. Higher
exposed surface area greatly increases recovery rates.
3. MMP is NOT a “line in the sand.” More oil is mobilized in the “miscible” phase
as pressure is raised regardless if the pressure is below, at, or above MMP.
4. Oil recovery from Bakken rocks is also faster at higher pressures regardless
of MMP.
5. All fluids tested can recover oil from middle Bakken, Bakken shales, and
Three Forks. Ethane gives the fastest recoveries including higher MW
hydrocarbons CO2 is a close second, and methane is quite poor.
6. Since most of the oil can be extracted from 1-cm rods, even upper and lower
Bakken shales have sufficient connectivity to be accessed by CO2, ethane,
etc.
Fluid Results to Date: CO2 vs Ethane
(recap)
Ethane cuts MMP in half compared to CO2.
Ethane mobilizes more oil in the “miscible”
phase, and is better with higher MW
hydrocarbons.
Ethane extracts oil from Bakken rocks
faster.
(But CO2 is still pretty darned good!)
We need much better understandings of:
Rock and reservoir characterizations
Permeation rates of injected fluids into unfractured rock
Fluid injectivity in the reservoir facies
The nature of natural and induced fractures (in all facies)
Clay swelling from injected fluids (and other changes).
Fluid behavior in nanopores.
Oil vs water wet rocks vs CO2 and ethane
Oil recovery and CO2 storage vs. time (and $$)
Reservoir modeling of conventional vs unconventional plays.
And a whole bunch of other things!!.
We can put CO2 and ethane into Bakken rocks and
efficiently recover oil in the lab, but need to develop a
better understanding of the controlling processes to
move the technology to the field.
Questions?
Thank you!
[email protected]
Acknowledgements
U.S. Department of Energy
National Energy Technology Laboratory
DE-FC26-05NT42592
DE-FC26-08NT43291
AcknowledgmentThis material is based upon work supported by the U.S. Department of Energy
National Energy Technology Laboratory under Award No. DE-FC26-05NT42592 and
Award No. DE-FE0024454.
Disclaimer
This presentation was prepared as an account of work sponsored by an agency of the
United States Government. Neither the United States Government, nor any agency
thereof, nor any of their employees, makes any warranty, express or implied, or assumes
any legal liability or responsibility for the accuracy, completeness, or usefulness of any
information, apparatus, product, or process disclosed or represents that its use would not
infringe privately owned rights. Reference herein to any specific commercial product,
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United States Government or any agency thereof. The views and opinions of authors
expressed herein do not necessarily state or reflect those of the United States
Government or any agency thereof.
