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Multi-scale multi-phase flow upscaling Philip Ringrose Statoil ASA & NTNU, Norway
IEAGHG Modelling and Monitoring Network Meeting, 6-8th July 2016 Edinburgh, Scotland
Nano-scale metre-scale
Geological models
Full-field simulation grids
7 juli 2016 Classification: Open
© Statoil ASA
Reservoir model (km)
Lithofacies model (m)
Handling a highly complex problem Goal: Build consistent multi-scale and multi-phase reservoir flow simulation models
To do this we need:
Consistent comparison of measurements at different scales
Rock-specific functions for the flow processes
A geo-statistical framework (representative models)
Pore network model (mm)
7 juli 2016 2 Classification: Open © Statoil ASA
Rock type 1
Rock type 2
1. Identify lamina and pore types from core
2. Calculate multiphase flow functions
3. Apply functions in lithofacies models
Upscaled curves
1,0E-06
1,0E-04
1,0E-02
1,0E+00
0 0,25 0,5 0,75 1Sg
Krgx VEKrgy VLKrogx VEKrogy VL
4. Upscale lithofacies models
Pore to Field Workflow: Statfjord Rustad et al., 2008 (SPE 113005)
5. Significantly improved history
match
7 juli 2016 3 Classification: Open © Statoil ASA
The Representative Elementary Volume (REV) (after Bear 1972)
Pore
Grain Mainly smaller pores
Mainly Larger pores
7 juli 2016 4 Classification: Open © Statoil ASA
Pore Network Modelling
Pore-space characterisation • Example core analysis, thin section, backscatter SEM mineralogical studies and
pore-scale modelling used to estimate multiphase flow properties
• In Salah CCS project (Lopez et al. 2011, Ringrose et al., 2011)
Grain characterisation (cathodoluminescence)
Mineral identification (BSEM)
7 juli 2016 5 Classification: Open © Statoil ASA
The REV concept as a framework for upscaling The Representative Elementary Volume concept gives the framework for understanding geological and measurement scales
Pore-scale model
Lithofacies model
Geomodel
Lengthscale [m]
Per
mea
bilit
y (m
d)
Lamina REV
0.01 0.1 1 10 0.001 0.0001
Pore type 2
Pore type 1 Lithofacies REV Stratigraphic REV
Lithofacies 2
Lithofacies 1
1
10
100
1000
Probe Perm.
Core plugs
Logging tools
Seismic data & well tests
Thin section & SEM Scales of measurement
From Nordahl & Ringrose (2008) and Ringrose & Bentley (2015)
7 juli 2016 6 Classification: Open © Statoil ASA
Multi-scale REV and fluid forces The Balance of Forces concept merged with the REV concept is useful to indicate which scales most affect flow
Capillary-dominated Viscous-dominated
Gravity-dominated
Measurement Volume [m3] (log scale)
Per
mea
bilit
y
Lamina REV Lithofacies
REV
Sequence REV
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 10-9 10-10 10-11 10-12 104
e.g. capillary trapping is likely to be important for rocks with strong permeability contrasts at the <20cm scale
Capillary trapping
Viscous fingering and
channeling
Fluid segregation
7 juli 2016 7 Classification: Open © Statoil ASA
Fluid forces and scaling group theory • The controls on two-phase immiscible flow can be captured in a set of dimensionless
ratios or scaling groups (Ringrose et al., 1993; Li and Lake, 1995)
)/(2
dSdPkxu
CapillaryViscous
cx
COx µ∆=
)/( dSdPzg
CapillaryGravity
c
∆∆=
ρ
Length scale (grid size)
Capillary Pressure gradient
Darcy’s Law
zgxq
GravityViscous CO
∆∆
∆=
ρµ
2
Where ∆x, ∆z are total system dimensions, Dr is the fluid density difference, µCO2 is the viscosity of CO2 and dPc/dS is the capillary pressure gradient wrt saturation
Which forces control CO2 storage? Fluid process and domains for a
hypothetical GCS reservoir (Oldenburg et al. 2016)
7 juli 2016 8 Classification: Open © Statoil ASA
Two-phase Steady-State Solutions Numerous recipes for solving multi-phase flow problems (incl. dynamic, non-steady state)
Steady-state solutions for immiscible two-phase flow are the end-member cases:
• Viscous limit (VL): The assumption that the flow is steady state at a constant fractional flow. Capillary pressure assumed to be negligible.
• Capillary equilibrium (CE): The assumption that saturations are controlled by the capillary pressure curves. Applied pressure gradients assumed to be negligible.
• Gravity-Capillary equilibrium (GCE): Similar to CE, except that the saturations are controlled by the effects of gravity:
• Vertical equilibrium (VE): a simplified gravity equilibrium assumption but with capillary forces neglected
Viscous dominated
Gravity dominated
Capillary dominated
Force ratio in the CO2
reservoir ?
7 juli 2016 9 Classification: Open © Statoil ASA
• Okwen et al. (2010) derived the storage efficiency factors, ε, as a function of Γ for various mobility ratios (residual brine saturation, Sr = 0.15)
• For higher gravity numbers Γ>10 there is a significant loss in storage efficiency
Analytical solutions for a buoyant plume
Storage efficiency ε vs. gravity factor Γ (from Okwen et al. 2010)
well
b
QBk 22 λρπ ∆
=Γ
• Nordbotten et al. (2005) and Nordbotten & Celia (2006) proposed a dimensionless group, Γ , to characterise an ideal solution for CO2 injection into a confined aquifer (a version of the viscous-gravity ratio):
7 juli 2016 10 Classification: Open © Statoil ASA
Insights from Sleipner • Important insights into
CO2 flow dynamics from the seismic time-lapse data Gravity segregation and top-
structure control of plume shape
Multi-layer system with thin-bed effects on seismic
Insights on dissolution rate
Producers Injector
Injection point
Permedia BOS
• High-resolution simulation from Cavanagh (2013): Sleipner Layer-9 reference
model (time = 2008)
Sleipner 4D seismic imaging (Furre et al. 2015; Kiær 2015)
7 juli 2016 11 Classification: Open © Statoil ASA
VE applied to Sleipner • Nilsen et al. (2011) tested various VE models to look at vertical segregation of CO2 and
brine for the Sleipner (Layer 9) reference model
• They showed that vertical segregation occurs in a relatively short time and that the system reaches vertical equilibrium before the end of the injection period
Example VE simulation result from Nilsen et al. (2011): • Layer 9 cross-section after
32 years injection
CO2 trapped as residual saturation
Mobile CO2 (structural tapping)
7 juli 2016 12 Classification: Open © Statoil ASA
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0Rel
ativ
e Pe
rmea
bilit
y / P
c(ba
rs)
Sw
Input rock functions
krw Rock 1
krg Rock 1
Pc Rock 1
krw Rock 2
krg Rock 2
Pc Rock 2
CE applied to Snøhvit
Rock 1 = 100md Rock 2 = 2000md
Upscale
0,0
0,2
0,4
0,6
0,8
1,0
0,0 0,2 0,4 0,6 0,8 1,0
Rel
ativ
e Pe
rmea
bilit
y
Sw
Upscale Layered Model Analytical Capillary Limit Solution
krgx (CE)krgz (CE)krwx (CE)krwz (CE)
Horizontal CO2 flow
Vertical CO2 flow
• Analytical CE upscaling for a layered medium with CO2-brine functions
• Based on Snøhvit Tubåen data: lithofacies-scale, fluvio-deltaic system, assumes 20:1 permeability contrast
• Note how anisotropy in CO2 flux varies with saturation
7 juli 2016 13 Classification: Open © Statoil ASA
Summary: CO2 storage flow upscaling • Well-established routines for building multi-scale and multi-phase reservoir flow
simulation models
• This highly complex problem should be handled using the multi-scale REV concept – geology has inherent characteristic lengthscales
• The CO2-brine flow modeling problem requires careful assessment of the gravity, viscous and capillary force ratios
• CO2 storage is dominated by gravity and capillary forces
• Multi-scale approaches should be used to improve forecasts and models of CO2 storage processes
Migrating CO2 plume
Residual CO2
Convective mixing and CO2 dissolution in brine
CO2 in structural traps
Conceptual sketch – CO2 storage flow processes
7 juli 2016 14 Classification: Open © Statoil ASA
This presentation, including the contents and arrangement of the contents of each individual page or the collection of the pages, are owned by Statoil. Copyright to all material including, but not limited to, written material, photographs, drawings, images, tables and data remains the property of Statoil. All rights reserved. Any other kind of use, reproduction, translation, adaption, arrangement, any other alteration, distribution or storage of this presentation, in whole or in part, without the prior written permission of Statoil is prohibited. The information contained in this presentation may not be accurate, up to date or applicable to the circumstances of any particular case, despite our efforts. Statoil cannot accept any liability for any inaccuracies or omissions.
Multi-scale, multi-phase flow upscaling
Philip Ringrose www.statoil.com
© Statoil ASA
7 juli 2016 15 Classification: Open © Statoil ASA
References • Cavanagh, A. J. 2013. Benchmark Calibration and Prediction of the Sleipner CO2 Plume from 2006 to 2012. Energy Procedia, 37, 3529-3545. • Furre, Anne-Kari, Anders Kiær, and Ola Eiken, 2015. CO2-induced seismic time shifts at Sleipner. Interpretation 3.3 (2015): SS23-SS35. • Kiær, A. F. 2015. Fitting top seal topography and CO2 layer thickness to time-lapse seismic amplitude maps at Sleipner. Interpretation, 3(2),
SM47-SM55. • Li, D. & Lake, L. W., 1995. Scaling Fluid Flow Through Heterogeneous Permeable Media. SPE Advanced Technology Series, Vol. 3(1), p. 188-
197 • Lopez, O., Idowa, N., Störer, S., Rueslatten, H., Boassen, T., Leary, S. & Ringrose, P., 2011. Pore-scale modelling of CO2-brine Flow Properties
at In Salah, Algeria. Energy Procedia, Volume 4, 3762-3769. • Nilsen, H. M., Herrera, P. A., Ashraf, M., Ligaarden, I., Iding, M., Hermanrud, C., ... & Keilegavlen, E. 2011. Field-case simulation of CO2-plume
migration using vertical-equilibrium models. Energy Procedia, 4, 3801-3808. • Nordahl, K., & Ringrose, P. S. 2008. Identifying the representative elementary volume for permeability in heterolithic deposits using
numerical rock models. Mathematical geosciences, 40(7), 753-771. • Nordbotten, J. M., & Celia, M. A., 2006. Similarity solutions for fluid injection into confined aquifers. Journal of Fluid Mechanics, 561, 307-
327. • Nordbotten, J. M., Celia, M. A., & Bachu, S., 2005. Injection and storage of CO2 in deep saline aquifers: Analytical solution for CO2 plume
evolution during injection. Transport in Porous media, 58(3), 339-360. • Okwen, R. T., Stewart, M. T., & Cunningham, J. A. 2010. Analytical solution for estimating storage efficiency of geologic sequestration of CO
2. International Journal of Greenhouse Gas Control, 4(1), 102-107. • Oldenburg, C. M., Mukhopadhyay, S., & Cihan, A. 2016. On the use of Darcy's law and invasion-percolation approaches for modeling
large-scale geologic carbon sequestration. Greenhouse Gases: Science and Technology, 6(1), 19-33. • Ringrose, P. S., Sorbie, K.S., Corbett, P.W.M., & Jensen, J.L. 1993. Immiscible flow behaviour in laminated and cross-bedded sandstones. J.
Petroleum Science and Engineering, 9, 103-124. • Ringrose, P. S., Roberts, D. M., Gibson-Poole, C. M., Bond, C., Wightman, R., Taylor, M. & Østmo, S. 2011. Characterisation of the Krechba
CO2 storage site: Critical elements controlling injection performance. Energy Procedia, 4, 4672-4679. • Ringrose, P., & Bentley, M. 2015. Reservoir model design. Springer. • Rustad, A. B., Theting, T. G., & Held, R. J. 2008. Pore space estimation, upscaling and uncertainty modelling for multiphase properties. In SPE
Symposium on Improved Oil Recovery. Society of Petroleum Engineers.