Solution of Benchmark
Problems for CO2 Storage
Min Jin, Gillian Pickup and Eric Mackay
Heriot-Watt University
Institute of Petroleum Engineering
Outline
• Introduction
• Problem 1
– Leakage through an abandoned well
• Problem 2
– Enhanced methane recovery
• Problem 3
– Storage capacity in a geological formation
• Conclusions
Numerical Simulation
• Simulation is a very important tool for CO2
storage
• Can give estimates of
–
–
–
–
migration of CO2 gas
dissolution in brine
build-up of pressure around injection well
etc
Reliability
• Depends on
– Input data
• geological structure
• rock permeability/porosity measurements
• laboratory measurements
• Also depends
– Adequate computer models
• flow equations
• representation of physical processes
Reservoir Simulation
• Codes are complex
• Various different versions available for
– gridding model
– calculating fluid properties
– solving equations
• May get slightly different answers
Benchmark Problems
• Compare solutions using different codes
• If results are the same
– gives confidence in simulation results
• If they are different
– indicates where more work is needed
Stuttgart Workshop, April 2008
• Aim
– Discuss current capabilities of mathematical
and numerical models for CO2 storage
• Compare results of 3 benchmark problems
• Focus model development on open
questions and challenges
• 12 groups participating
web site: http://www.iws.uni-stuttgart.de/co2-workshop/
Heriot-Watt Entry
• Solutions to all 3 problems
• Eclipse 300
– Reservoir simulation software package
– Compositional simulation
– Schlumberger
Outline
• Introduction
• Problem 1
– Leakage through an abandoned well
• Problem 2
– Enhanced methane recovery
• Problem 3
– Storage capacity in a geological formation
• Conclusions
Problem 1
• CO2 plume evolution and leakage through
an abandoned well
leaky well
k = 200 mD,
f = 0.15
aquifer
k = 0 mD,
f = 0.0
aquitard
k = 200 mD,
f = 0.15
aquifer
1000 m
Problem 1
• CO2 plume evolution and leakage through
an abandoned well
leaky well
CO2 injector
aquifer
aquitard
aquifer
Problem 1
• CO2 plume evolution and leakage through
an abandoned well
leaky well
CO2 injector
?
aquifer
aquitard
aquifer
Model Details
• Lateral extent of model: 1000 m x 1000 m
• Separation of wells: 100 m
• Aquifer thickness: 30 m
– perm: 200 mD, poro = 0.15
• Aquitard thickness: 100 m
– impermeable
• Abandoned well
– model as thin column of 1000 mD, poro = 0.15
Details of Fluid Properties
• Problem 1.1
– Reservoir is very deep, ~3000 m
– Simplified fluid properties
• constant with P and T
• Problem 1.2
– Shallower reservoir, <800 m
– CO2 can change state when rising
– More complex fluid properties
Other Inputs to Simulation
• Constant injection rate
– 8.87 kg/s
• Pressure should stay constant at the edges
of the model
• No-flow boundaries top and bottom
Challenges
x
• Gridding
– Coarse over most of model
– Fine near wells
y
Close-up of Grid Centre
injector
leaky well
Challenges
•
Modelling of abandoned well
a) Model as high perm column
b) Model as closed well
• output potential production
high perm cells
closed well
Challenges
•
•
Maintaining pressure constant at
boundaries
Eclipse designed for oil reservoirs
– assumes sealed boundaries
• leads to build up of pressure
•
We added aquifers to sides of the model
– fluids could move into the aquifer
– prevented build up of pressure
Challenges
•
Fluid properties in Problem 1.2
a) User-defined
b) Specified as functions of pressure and
temperature
•
We used constant T = 34 oC
– Tuned equations
• density and pressure similar to specified
values
CO2 Distribution after 100 Days, Problem 1.2
Injector
Leaky well
Gas Sat
0.0
0.2
0.4
0.6
0.8
CO2 Distribution after 2000 Days, Problem 1.2
Inj
leaky well
Gas Sat
0.0
0.2
0.4
0.6
0.8
Results
• Leakage rate for Problem 1.2
0.14
leakage volume/injection volume (%)
0.12
0.10
0.08
0.06
0.04
leaky well modelled
as high perm cells
0.02
0.00
0
500
1000
1500
time (day)
2000
2500
Summary of Problem 1
• Successfully predicted well rate
– Using high perm cells for leaky well
• well model overestimated leakage
– Our results similar to others
• Leakage rate ~ 0.1% injected volume
Outline
• Introduction
• Problem 1
– Leakage through an abandoned well
• Problem 2
– Enhanced methane recovery
• Problem 3
– Storage capacity in a geological formation
• Conclusions
Problem 2
• Enhanced recovery of CH4 combined with
CO2 storage
CO2 injector
producer
45 m
kh = 50 mD
kv = 5mD
f = 0.23
200 m
200 m
Model Details
•
Two versions
1. homogeneous
2. layered
•
•
•
Temperature = 66.7 oC
Depleted reservoir pressure = 35.5 bar
Molecular diffusion = 6 x 10-7 m2/s
Model for Problem 2.2
x
P
I
z
Perm (mD)
0
10
20
30
40
50
60
70
80
90
100
Other Inputs to Simulation
• Constant injection rate for CO2
– 0.1 kg/s
– inject into lower layer
– produce from upper layer
• Constant pressure at production well
– P = 35.5 bar
• No-flow across model boundaries
Challenges
• Mixing of gases
• Changes in physical properties of gas
mixture with composition
– can be modelled in Eclipse 300
• Numerical diffusion
– will artificially increase the molecular diffusion
Result for Problem 2-1
Results – Homogeneous Model
• Mass Flux of CH4 and CO2
3000.00
mass flux (kg/d)
2500.00
2000.00
1500.00
1000.00
500.00
0.00
0
200
400
600
800
1000
1200
time (day)
CH4
CO2
1400
1600
1800
2000
Results – Layered Model
• Mass Flux of CH4 and CO2
3000
mass flux (kg/d)
2500
2000
1500
1000
500
0
0
200
400
600
800
1000
1200
time (day)
CH4
CO2
1400
1600
1800
2000
Results and Summary
• Assume well is shut down when CO2
production reaches 20% by mass
Problem
Model
Shut-in time
(days)
Recovery
Efficiency (%)
2.1
homogeneous
1727
59
2.2
layered
1843
64
• Relatively easy problem
Outline
• Introduction
• Problem 1
– Leakage through an abandoned well
• Problem 2
– Enhanced methane recovery
• Problem 3
– Storage capacity in a geological formation
• Conclusions
Problem 3
• Storage capacity in a geological model
y
Inj
x
porosity
0.17
0.19
0.21
0.23
0.25
z
Model Details
• Lateral dimensions
– 9600 m x 8900 m
• Formation thickness
– between 90 and 140 m
• Variable porosity and permeability
• Depth ~ 3000 m
• Temperature = 100 oC
Challenges
• Simulation of system after injection has
ceased
– CO2 continues to rise due to buoyancy
– Brine moves into regions previously occupied
by CO2
– Brine can occupy small pores, trapping CO2 in
larger pores
• additional trapping mechanism
• hysteresis
Challenges
• Trapping of CO2 by hysteresis
CO2 displacing brine
Plume of
rising CO2
brine displacing CO2
after Doughty, 2007
CO2 Distribution after 25 Years
X
with
hysteresis
Y
Gas Sat
0.0
0.2
0.5
0.8
CO2 Distribution after 50 Years
X
with
hysteresis
Y
Gas Sat
0.0
0.2
0.5
0.8
Results
• Mass of CO2 in formation over time
1.4E+10
Mass of CO2 (kg)
1.2E+10
1.0E+10
8.0E+09
total
free
dissolved
6.0E+09
4.0E+09
2.0E+09
0.0E+00
0
5000
10000
Time (days)
15000
20000
Results
• Leakage of CO2 across the boundaries
CO2 inter-region mass flow rate for Problem 3
1.6
no hysteresis
P3-1
P3-2
1.4
Mass Flow rate (kg/s)
1.2
1
0.8
with hysteresis
0.6
0.4
0.2
0
0
2000
4000
6000
8000
10000
Time (day)
12000
14000
16000
18000
20000
Summary of Problem 3
• CO2 did not move towards the fault
– moved up-dip
– leaked across model boundary
• Hysteresis did make difference, but not
much difference in this example
• About 0.2 of the injected CO2 dissolved
after 50 years
Outline
• Introduction
• Problem 1
– Leakage through an abandoned well
• Problem 2
– Enhanced methane recovery
• Problem 3
– Storage capacity in a geological formation
• Conclusions
Conclusions
• Benchmark solutions highlight difficulties
– Adaptation of simulator for oil/gas reservoirs
to CO2 storage
– Difficulties are surmountable
– Schlumberger created new module for CO2
storage
• Participation in the workshop
– Giving us confidence in simulations
Acknowledgements
• We thank Schlumberger for letting us use
the Eclipse simulation software
Solution of Benchmark
Problems for CO2 Storage
Min Jin, Gillian Pickup and Eric Mackay
Heriot-Watt University
Institute of Petroleum Engineering