Characterising multiphase flow in heterogeneous rocks
Characterising multiphase flow in heterogeneous rocks Samuel Jackson, Simeon Agada, Catriona Reynolds & Samuel Krevor Department of Earth Science & Engineering, Imperial College London, UK
SPE London Evening Meeting, 30th January 2018
Introduction & Motivations •
•
•
Relative permeability controls plume migration at large scale. Capillary pressure heterogeneity controls relative permeability, which with hysteresis govern residual trapping.
100m
We must accurately characterise these multiphase flow functions to efectively model plume migration and storage.
2/34
Capillary dominated flow 100m
h r
Injection rate, Q [Mt/yr.]
3/34
How does this impact relative permeability? •
Relative permeability at scales of cm-m in heterogeneous rocks highly dependent on: –
Capillary number
–
Capillary pressure heterogeneity
20cm C. Reynolds (2016) Ph.D thesis Imperial College London
4/34
Low potential flow at large scales Fine scale solution • VL rel perm - mm scale. • Heterogeneous Pc curves - mm scale.
CO2 injection
‘Correct’ upscaled solution • Equiv rel perm - cm-m scale. • Single Pc curve - cm-m scale.
‘Incorrect’ upscaled solution • VL rel perm - cm-m scale. • Single Pc curve - cm-m scale.
Li and Benson (2015) Ad. Wat. Res., doi: 10.1016/j.advwatres.2015.07.010
5/34
Low potential flow at large scales •
Equivalent relative permeability required to accurately model subsurface fow on cm-m scale grid blocks.
Impractical to measure for many flow regimes in the laboratory.
Solution: Use experiments & calibrated numerical models to find equivalent functions.
6/34
UK Carbon Capture & Storage setting Quartz rich permeable sandstones: Bentheimer ‘Homogenou s’ outcrop Bunter S. North sea
Today’s talk
Captain N. North sea
7/34
Characterisation approach overview •
Conduct two steady-state relative permeability core flood experiments with medical X-ray scanning: High flow rate, viscous limit experiment • Porosity • Absolute permeability • Viscous limit relative permeability Low flow rate, capillary limit experiment • Capillary pressure heterogeneity
•
Calibrate a digital rock core model and use to simulate core floods •. Derive equivalent relative permeabilities numerically, without experimental constraints
8/34
Characterisation approach – 1/7 •
•
•
Conduct a viscous limit & capillary limit steady-state relative permeability core flood experiment.
Bunter sandstone L = 15.1cm, r = 1.8cm
Bentheimer sandstone L = 19.8cm, r = 1.8cm 9/34
Characterisation approach – 2/7 Post-process experimental data. Medical X-Ray CT data used to create 3D gas/liquid saturations.
–
Coarsen saturations maps to improve precision.
–
Filter pressure transducer data. 3.81 cm
1x
5x
N2 Saturation
N2 Saturation
–
N2 Saturation
•
10x
10/34
Characterisation approach – 3/7 •
Find viscous limit properties from high flow rate experiments: –
Porosity
–
Absolute permeability
–
Relative permeability through regression in SENDRA.
11/34
Characterisation approach – 3/7 •
Find average capillary pressure properties. –
Capillary pressure - mercury intrusion data conversion.
12/34
Characterisation approach – 4/7 •
•
Characterise the capillary heterogeneity using low flow rate experiment Assume slice average Pc curves as the first guess.
Pc = c1
Pc = c2
Pini, R. & Benson, S.M. (2017) Adv. Wat. Res. DOI:10.1016/j.advwatres.2017.08.011 Krause, M. & Benson, S.M. (2015) Adv. Wat. Res. DOI: 10.1016/j.advwatres.2015.07.009
13/34
Characterisation approach – 5/7
te n u B
Flow direction
r
eim h t Ben r
e
20cm 14/34
Characterisation approach – 6/7 •
Build the 3D model in CMG IMEX.
•
Simulate the low flow rate core flood experiments.
nt e rim e p Ex
ion t a l u Sim
15/34
Characterisation approach – 7/7 •
Calibrate the capillary pressure heterogeneity iteratively.
16/34
Iteratively calibrated simulation results
eri p x E 5 0.97
2) = O C t , f( n e m
ula m i S 5 0.97
2) = O , f(C n o ti
Bunter
)= 2 N ( f nt, e erim p x E 29 9 9 . 0 )= 2 N , f( n o i lat u m Si 29 9 0.9
Bentheimer 17/34
Relative Permeability, krN , krw [-]
10
-1
Simulation equivalent k r
2
Experimental uncertainty
-2
Experiment equivalent k r Viscous limit k r
10
-3
10-4 0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
Water Saturation, S w [-]
(a)
(b) 10-1 Simulation equivalent k r
2
Relative Permeability, krCO , krw [-]
Iteratively calibrated simulation results
10
-2
10
Viscous limit k r
-3
10
10-4 0.10
(c)
Experiment equivalent k r
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
Water Saturation, Sw [-]
(d)
18/34
Characterising using a single dataset •
Can we calibrate using less data?
•
What happens when we calibrate Pc(Sw) with other experimental data?
•
Calibrate using:
High flow rate (viscous limit) exp data vs Low flow rate (capillary limit) exp data 19/34
Characterising using a single dataset •
Low flow rate (capillary limit) scaling vs high flow rate (viscous limit) scaling
20/34
Experimental uncertainty
Iteratively calibrated results using high flow rate data (a)
(c)
(b)
(d)
21/34
Using the calibrated model Simulating experiments outside laboratory conditions. 1) With end efects
22/34
Using the calibrated model Simulating experiments outside laboratory conditions. 2) Without end efects
23/34
Using the calibrated model Simulating experiments outside laboratory conditions. 3) Rotated capillary pressure heterogeneity.
24/34
Using the calibrated model Simulating experiments outside laboratory conditions. 3) Rotated capillary pressure heterogeneity.
25/34
What does this mean for plume migration?
?
26/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 50 days Viscous Limit
Capillary Limit
27/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 150 days
Δr = 35m
Viscous Limit
Capillary Limit
28/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 250 days
Δr = 32m
Viscous Limit
Capillary Limit
29/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 350 days
Δr = 31m
Viscous Limit
Capillary Limit 8% decrease in r 5% increase Avg. ΔP
30/34
What does this mean for residual trapping?
31/34
Residual trapping – Capillary heterogeneity efects 1.0 0.9
2
Residual CO 2 saturation, S CO [-]
0.8
0.6
0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Residual CO2 saturation SCO2 [-]
0.5
Residual CO2 saturation SCO2 [-]
Bunter
0.7
Exp 37 Voxel average Exp 37 Slice average Exp 37 Core average Exp 38 Voxel average Exp 38 Slice average Exp 38 Core average Land model, C = 1.3 Land model, C = 0.0
Initial CO 2 saturation, S CO [-] 2
1.0
0.8
Exp 41 Voxel average Exp 41 Slice average Exp 41 Core average Land model, C = 2.0 Land model, C = 0.0
Initial CO2 saturation SCO2 [-]
Initial CO2 saturation SCO2 [-]
2
Captain
Residual CO 2 saturation, S CO [-]
0.9
Bunter simulation With Pc heterogeneity
0.7 0.6 0.5
Bunter simulation Without Pc heterogeneity
0.4
Olugbade (2017) Digital Rock Core Simulaton of CO2 Storage, MSc Thesis, Imperial College London
0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Initial CO 2 saturation, SCO [-] 2
0.8
0.9
1.0
32/34
Conclusions
33/34
Thank you Pre-print paper available now: Characterising multiphase fow in heterogeneous sandstones https://eartharxiv.org/wcxny www.krevorlab.co.uk
NERC highlights grant NE/N016173/1
DOI: 10.17605/OSF.IO/WCXNY
34/34
SPE London Evening Meeting, 30th January 2018
Introduction & Motivations •
•
•
Relative permeability controls plume migration at large scale. Capillary pressure heterogeneity controls relative permeability, which with hysteresis govern residual trapping.
100m
We must accurately characterise these multiphase flow functions to efectively model plume migration and storage.
2/34
Capillary dominated flow 100m
h r
Injection rate, Q [Mt/yr.]
3/34
How does this impact relative permeability? •
Relative permeability at scales of cm-m in heterogeneous rocks highly dependent on: –
Capillary number
–
Capillary pressure heterogeneity
20cm C. Reynolds (2016) Ph.D thesis Imperial College London
4/34
Low potential flow at large scales Fine scale solution • VL rel perm - mm scale. • Heterogeneous Pc curves - mm scale.
CO2 injection
‘Correct’ upscaled solution • Equiv rel perm - cm-m scale. • Single Pc curve - cm-m scale.
‘Incorrect’ upscaled solution • VL rel perm - cm-m scale. • Single Pc curve - cm-m scale.
Li and Benson (2015) Ad. Wat. Res., doi: 10.1016/j.advwatres.2015.07.010
5/34
Low potential flow at large scales •
Equivalent relative permeability required to accurately model subsurface fow on cm-m scale grid blocks.
Impractical to measure for many flow regimes in the laboratory.
Solution: Use experiments & calibrated numerical models to find equivalent functions.
6/34
UK Carbon Capture & Storage setting Quartz rich permeable sandstones: Bentheimer ‘Homogenou s’ outcrop Bunter S. North sea
Today’s talk
Captain N. North sea
7/34
Characterisation approach overview •
Conduct two steady-state relative permeability core flood experiments with medical X-ray scanning: High flow rate, viscous limit experiment • Porosity • Absolute permeability • Viscous limit relative permeability Low flow rate, capillary limit experiment • Capillary pressure heterogeneity
•
Calibrate a digital rock core model and use to simulate core floods •. Derive equivalent relative permeabilities numerically, without experimental constraints
8/34
Characterisation approach – 1/7 •
•
•
Conduct a viscous limit & capillary limit steady-state relative permeability core flood experiment.
Bunter sandstone L = 15.1cm, r = 1.8cm
Bentheimer sandstone L = 19.8cm, r = 1.8cm 9/34
Characterisation approach – 2/7 Post-process experimental data. Medical X-Ray CT data used to create 3D gas/liquid saturations.
–
Coarsen saturations maps to improve precision.
–
Filter pressure transducer data. 3.81 cm
1x
5x
N2 Saturation
N2 Saturation
–
N2 Saturation
•
10x
10/34
Characterisation approach – 3/7 •
Find viscous limit properties from high flow rate experiments: –
Porosity
–
Absolute permeability
–
Relative permeability through regression in SENDRA.
11/34
Characterisation approach – 3/7 •
Find average capillary pressure properties. –
Capillary pressure - mercury intrusion data conversion.
12/34
Characterisation approach – 4/7 •
•
Characterise the capillary heterogeneity using low flow rate experiment Assume slice average Pc curves as the first guess.
Pc = c1
Pc = c2
Pini, R. & Benson, S.M. (2017) Adv. Wat. Res. DOI:10.1016/j.advwatres.2017.08.011 Krause, M. & Benson, S.M. (2015) Adv. Wat. Res. DOI: 10.1016/j.advwatres.2015.07.009
13/34
Characterisation approach – 5/7
te n u B
Flow direction
r
eim h t Ben r
e
20cm 14/34
Characterisation approach – 6/7 •
Build the 3D model in CMG IMEX.
•
Simulate the low flow rate core flood experiments.
nt e rim e p Ex
ion t a l u Sim
15/34
Characterisation approach – 7/7 •
Calibrate the capillary pressure heterogeneity iteratively.
16/34
Iteratively calibrated simulation results
eri p x E 5 0.97
2) = O C t , f( n e m
ula m i S 5 0.97
2) = O , f(C n o ti
Bunter
)= 2 N ( f nt, e erim p x E 29 9 9 . 0 )= 2 N , f( n o i lat u m Si 29 9 0.9
Bentheimer 17/34
Relative Permeability, krN , krw [-]
10
-1
Simulation equivalent k r
2
Experimental uncertainty
-2
Experiment equivalent k r Viscous limit k r
10
-3
10-4 0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
Water Saturation, S w [-]
(a)
(b) 10-1 Simulation equivalent k r
2
Relative Permeability, krCO , krw [-]
Iteratively calibrated simulation results
10
-2
10
Viscous limit k r
-3
10
10-4 0.10
(c)
Experiment equivalent k r
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
Water Saturation, Sw [-]
(d)
18/34
Characterising using a single dataset •
Can we calibrate using less data?
•
What happens when we calibrate Pc(Sw) with other experimental data?
•
Calibrate using:
High flow rate (viscous limit) exp data vs Low flow rate (capillary limit) exp data 19/34
Characterising using a single dataset •
Low flow rate (capillary limit) scaling vs high flow rate (viscous limit) scaling
20/34
Experimental uncertainty
Iteratively calibrated results using high flow rate data (a)
(c)
(b)
(d)
21/34
Using the calibrated model Simulating experiments outside laboratory conditions. 1) With end efects
22/34
Using the calibrated model Simulating experiments outside laboratory conditions. 2) Without end efects
23/34
Using the calibrated model Simulating experiments outside laboratory conditions. 3) Rotated capillary pressure heterogeneity.
24/34
Using the calibrated model Simulating experiments outside laboratory conditions. 3) Rotated capillary pressure heterogeneity.
25/34
What does this mean for plume migration?
?
26/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 50 days Viscous Limit
Capillary Limit
27/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 150 days
Δr = 35m
Viscous Limit
Capillary Limit
28/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 250 days
Δr = 32m
Viscous Limit
Capillary Limit
29/34
Equivalent relative permeability impacts: 2D sharp interface model 1Mt/yr. t = 350 days
Δr = 31m
Viscous Limit
Capillary Limit 8% decrease in r 5% increase Avg. ΔP
30/34
What does this mean for residual trapping?
31/34
Residual trapping – Capillary heterogeneity efects 1.0 0.9
2
Residual CO 2 saturation, S CO [-]
0.8
0.6
0.4 0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Residual CO2 saturation SCO2 [-]
0.5
Residual CO2 saturation SCO2 [-]
Bunter
0.7
Exp 37 Voxel average Exp 37 Slice average Exp 37 Core average Exp 38 Voxel average Exp 38 Slice average Exp 38 Core average Land model, C = 1.3 Land model, C = 0.0
Initial CO 2 saturation, S CO [-] 2
1.0
0.8
Exp 41 Voxel average Exp 41 Slice average Exp 41 Core average Land model, C = 2.0 Land model, C = 0.0
Initial CO2 saturation SCO2 [-]
Initial CO2 saturation SCO2 [-]
2
Captain
Residual CO 2 saturation, S CO [-]
0.9
Bunter simulation With Pc heterogeneity
0.7 0.6 0.5
Bunter simulation Without Pc heterogeneity
0.4
Olugbade (2017) Digital Rock Core Simulaton of CO2 Storage, MSc Thesis, Imperial College London
0.3 0.2 0.1 0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Initial CO 2 saturation, SCO [-] 2
0.8
0.9
1.0
32/34
Conclusions
33/34
Thank you Pre-print paper available now: Characterising multiphase fow in heterogeneous sandstones https://eartharxiv.org/wcxny www.krevorlab.co.uk
NERC highlights grant NE/N016173/1
DOI: 10.17605/OSF.IO/WCXNY
34/34
