Upscaling mechanical rock properties and pore fluid ...

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

Earth shows compositional and structural variation at all scales

Photograph by K. Beuhl, SINTEF Petroleum, Norway

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

Upscaling is honoring geology detail in an effective way

overburden

High compressibility rock reservoir
Low compressibility rock unit

underburden Voigt “iso-strain” problem

Reuss “iso-stress” problem

How to capture Upscaling

control of meso- helps to focus
scale structures on what is

on stress, strain, really important
displacement ? in the model

Realistic geology

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 Biot-Willis
4)  distribution of rock mechanical properties coefficient

1 23

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)

Ennio geomechanical model: Detail Ennio geology in PETREL

11 stacked
reservoir units

Upscaling is honoring geology detail in an Tom McKay and Fiona Fairhurst
effective way. Approach must be as simple as
possible (transparent), of practical use, and
mathematically and physically robust.

EW cross section through geomechanical model Ennio reservoir

1 km

WN

11 stacked
reservoir units

Ennio sandstones: Depletion in Jan. 2016 (wrt. before production)

Form.
6n_7

MPa

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

Before upscaling After upscaling

Δh1 = ((ΔS1/α)-ΔPp1)* Cm,p1 Assumption 1:
Δh2 = ((ΔS2/α)-ΔPp2)* Cm,p2 Δhus=Δh1+Δh2+Δh3+Δh4+Δh5
Δh3 = ((ΔS3/α)-ΔPp3)* Cm,p3
Δh4 = ((ΔS4/α)-ΔPp4)* Cm,p4 Assumption 2:
Δh5 = ((ΔS5/α)-ΔPp5)* Cm,p5 εradial,x1-x5= εradial,us= 0

Δhus=((ΔSus/α)-ΔPus)*Cm,p,us

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.

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
WE

Porosity (fraction of BV), Net-to-Gross
before production
1 km

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 MPa = 145 psi 1 km

Upscaled porosity and upscaled sand compressibility Cm,p,us

Porosity (fraction of bulk vol.) (*10-5/MPa), valid over time 1 km
period before prod. to 2005

Upscaled porosity and upscaled net-sand compressibility Cm,p,us

1 km

(*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

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 ?

overburden So far < Cm,p> has been a net-
high φ–k mudstone sand-volume weighted average

low φ–k mudstone reservoir
unit

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

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

Upscaled
Ennio 6n_7

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)

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

(*10-5/MPa) Upscaled net-sand Cm Upscaled gross-rock Cm
with Cm_shale=0/MPa

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 ? Norwegian Form. Eval., Nov. 5 2008

Elastodynamic (ED)
Drained (from ED)
Drained (Horsrud 2001)
Drained (Shell correlation)

Sloppy Stiff

Based on one experiment on undrained slowly-loaded mudstone

Elastodynamic (ED)
Drained (from ED)
Drained (Horsrud 2001)
Drained (Shell correlation)

2/3 1/3

The mechanical properties of mudstone depend on the problem

Conclusions


  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