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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


The Representative Elementary Volume (REV) (after Bear 1972)

Pore

Grain Mainly smaller pores

Mainly Larger pores


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)


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)


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


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)


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 ?


• 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):


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)


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)


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


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


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Multi-scale, multi-phase flow upscaling

Philip Ringrose www.statoil.com

© 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.

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