Upscaling mechanical rock properties and pore fluid pressure: An application to geomechanical modelling
Peter Schutjens and Jeroen Snippe Shell U.K. Exploration & Production Aberdeen
DEVEX 2009, Aberdeen May 12 and 13 2009
Format
1) Introduction and problem definition
2) Our approach to upscaling
3) Example: Formation 6n_7 in Ennio reservoir
4) Including the shales
5) Conclusions
Photograph by K. Beuhl, SINTEF Petroleum, Norway
Earth shows compositional and structural variation at all scales
Both inhomogeneity and anisotropy in rocks influence the location of the hydrocarbons, as well as the potential to produce these.
Static and dynamic models must capture sufficient detail of rock composition and structure to represent reality, while maintaining practically useful: No huge data volumes, and run in hours to days
reservoir unit
overburden
High compressibility rock
underburden
Reuss “iso-stress” problem Voigt “iso-strain” problem
Realistic geology
How to capture control of meso-scale structures on stress, strain, displacement ?
Upscaling is honoring geology detail in an effective way
Upscaling helps to focus on what is really important in the model
Low compressibility rock
Deformation, compaction or expansion, stress change and displacement inside and around the depleting reservoir
Basin geomechanical model has three sets of input parameters:
1) Sedimentary and structural geology,
2) depletion from reservoir fluid-flow models 4) distribution of rock mechanical properties
3 2 1
h is geobody thickness, Svert is total vertical stress, Pp is pore fluid pressure, Cm,p is volumetric compressibility by depletion under uniaxial-strain conditions (axial compaction, no radial deformation)
Biot-Willis coefficient
Ennio geomechanical model: Detail Ennio geology in PETREL
Tom McKay and Fiona Fairhurst
Upscaling is honoring geology detail in an effective way. Approach must be as simple as possible (transparent), of practical use, and mathematically and physically robust.
11 stacked reservoir units
EW cross section through geomechanical model Ennio reservoir
1 km
11 stacked reservoir units
W N
Ennio sandstones: Depletion in Jan. 2016 (wrt. before production)
MPa
Form. 6n_7
Format
1) Introduction and problem definition
2) Our approach to upscaling
3) Example: Formation 6n_7 in Ennio reservoir
4) Including the shales
5) Conclusions
Upscaling principle and guiding boundary condition
Δh1 = ((ΔS1/α)-ΔPp1)* Cm,p1
Similar constraint applies to upscale pore fluid pressures: Displacement at top cell-stack is same before and after upscaling.
Upscaling of pore pressures from fluid-flow simulator must be done in conjunction with upscaling of bulk-volume compressibility.
Δhus=((ΔSus/α)-ΔPus)*Cm,p,us
Assumption 1: Δhus=Δh1+Δh2+Δh3+Δh4+Δh5
Assumption 2: εradial,x1-x5= εradial,us= 0
Before upscaling After upscaling
Δh2 = ((ΔS2/α)-ΔPp2)* Cm,p2
Δh3 = ((ΔS3/α)-ΔPp3)* Cm,p3
Δh4 = ((ΔS4/α)-ΔPp4)* Cm,p4
Δh5 = ((ΔS5/α)-ΔPp5)* Cm,p5
Upscaling: Parameter definition
Uniaxial-strain compressibility* defined as
Effective stress change:
Net to Gross
Compressibility description
where Pp1 is the initial pore fluid pressure and where Pp2 is the final pressure, with Pp2 < Pp1. • m and n describe the linear dependence of Cm,p on porosity • q and r describe how Cm,p changes linearly with depletion. *) Uniaxial compressibility Cmp: Unit 1 microsip = 10-6/psi = 1.45 x 10-4/MPa
Upscaling: Importance of averaging over net or over gross volume
Upscaled Net-to-Gross (i.e. weighted with gross height)
Upscaled porosity (i.e. weighted with nett height)
Upscaled saturation (i.e. weighted with pore height’)
Upscaled compressibility
where:
(and where the subscripts ‘N’ denote weighting with nett height)
Format
1) Introduction and problem definition
2) Our approach to upscaling
3) Example: Formation 6n_7 in Ennio reservoir
4) Including the shales
5) Conclusions
Upscaled formation porosity and NtG of Ennio formation 6n_7
Porosity (fraction of BV), Net-to-Gross before production 1 km
W E
Determination of Ennio sandstone compressibility in laboratory deformation experiments (room T., Ktest=ΔSrad/ΔSax, Pp=1 atm.)
Net-sand depletion based on upscaled pore fluid pressures
MPa Till 2005 Till 2013 Till 2016
1 km 1 MPa = 145 psi
Upscaled porosity and upscaled sand compressibility Cm,p,us
(*10-5/MPa), valid over time period before prod. to 2005
Porosity (fraction of bulk vol.) 1 km
Upscaled porosity and upscaled net-sand compressibility Cm,p,us
(*10-5/MPa) Bef. prod. to 2005 2005 to 2013 2013 to 2016
Good agreement between Cm,p,us-maps indicates no significant correlation between porosity and amount of depletion in the sands
1 km
Format
1) Introduction and problem definition
2) Our approach to upscaling
3) Example: Formation 6n_7 in Ennio reservoir
4) Including the shales
5) Conclusions
So… what about the shales ?
So far we assumed shales to be incompressible. In that case they do not play role in depletion-induced downward displacement
But is this a correct assumption ?
Probably not, because we know from field data, slow-loading (!) laboratory tests and modelling work that mudstones and shales compact by increasing total stress or by decreasing Pp
reservoir unit
overburden
low φ–k mudstone
high φ–k mudstone
So far < Cm,p> has been a net-sand-volume weighted average
Shales are connected to the compacting reservoirs, and they will show displacements, deformations and stress changes as well This example: Sands up to 5% vertical compaction; mudstones up to 0.5% vertical extension, reduction in total vertical stress of up to 4 MPa
The Leading Edge (May 2008)
Towards an upscaled formation for geomechanical simulator
Harmonic averaging between upscaled net-sand compressibility and assumed shale compressibility.
Effective stress law should reflect combined effect of ΔPp and ΔSv The reservoir sands will mainly compact as a result of depletion, and to a lesser extent expand due to total stress reduction
The reservoir shales will mainly expand as a result of total stress reduction, but they may also compact due to depletion (pore pressure diffusion to the bounding depleting sandstones)
Upscaled Ennio 6n_7
But what is the shale compressibility during production ?
Three chosen values for compressibility of reservoir shale during production
Comparison upscaled net-sand and gross-rock compressibility
with Cm_shale=0/MPa
(*10-5/MPa) Upscaled net-sand Cm Upscaled gross-rock Cm
1 km
Upscaled gross-rock compressibility Cm,gross
(*10-5/MPa) Cm_shale=0/MPa Cm-shale=2x10-5/MPa Cm_shale=4x10-5/MPa
1 km
So what are the mechanical properties of mudstone during depletion-induced reservoir compaction ?
Stiff Sloppy
Elastodynamic (ED) Drained (from ED) Drained (Horsrud 2001) Drained (Shell correlation)
Norwegian Form. Eval., Nov. 5 2008
2/3 1/3
The mechanical properties of mudstone depend on the problem
Based on one experiment on undrained slowly-loaded mudstone
Elastodynamic (ED) Drained (from ED) Drained (Horsrud 2001) Drained (Shell correlation)
Upscaling of mechanical properties and pore fluid pressure should be done simultaneously
Our approach involves including (experimentally-obtained) description of clean-sand compressibility as a function of initial (reference) porosity and depletion in the upscaling algorithm
Maps of upscaled net-sand compressibility now reflect the position of high-porosity channel bodies (detail 100 m)
Upscaling involves inclusion of shales as a geomechanical unity, i.e. with a finite (albeit) small compressibility.
Role of reservoir shales in upscaling is complex, depending e.g. on pore pressure response over production timescales. Coupled-problem analysis combining the effects of Sv and Pp
Upscaled compressibility is controlled by the porosity, net-to-gross, level of depletion, and geomechanical response shales
Conclusions
Thank you. Any questions ?
Upscaling mechanical rock properties and pore fluid pressure: An application to geomechanical modelling
Peter Schutjens and Jeroen Snippe Shell U.K. Exploration & Production Aberdeen
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