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