Upscaling mechanical rock properties and pore fluid pressure: An application to geomechanical modelling

Transcription

1 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

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3 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

4 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

5 Upscaling is honoring geology detail in an effective way overburden High compressibility rock Low compressibility rock reservoir unit underburden Reuss iso-stress problem How to capture control of mesoscale structures on stress, strain, displacement? Realistic geology Voigt iso-strain problem Upscaling helps to focus on what is really important in the model

6 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 Biot-Willis coefficient h is geobody thickness, S vert is total vertical stress, P p is pore fluid pressure, C m,p is volumetric compressibility by depletion under uniaxial-strain conditions (axial compaction, no radial deformation)

7 Ennio geomechanical model: Detail Ennio geology in PETREL 11 stacked reservoir units 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. Tom McKay and Fiona Fairhurst

8 EW cross section through geomechanical model Ennio reservoir 1 km W N 11 stacked reservoir units

9 Ennio sandstones: Depletion in Jan (wrt. before production) Form. 6n_7 MPa

10 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

11 Upscaling principle and guiding boundary condition Before upscaling Δh 1 = ((ΔS 1 /α)-δp p1 )* C m,p1 Δh 2 = ((ΔS 2 /α)-δp p2 )* C m,p2 Δh 3 = ((ΔS 3 /α)-δp p3 )* C m,p3 After upscaling Assumption 1: Δh us =Δh 1 +Δh 2 +Δh 3 +Δh 4 +Δh 5 Assumption 2: ε radial,x1-x5 = ε radial,us = 0 Δh 4 = ((ΔS 4 /α)-δp p4 )* C m,p4 Δh 5 = ((ΔS 5 /α)-δp p5 )* C m,p5 Δh us =((ΔS us /α)-δp us )*C m,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.

12 Upscaling: Parameter definition Uniaxial-strain compressibility* defined as Effective stress change: Net to Gross Compressibility description where P p1 is the initial pore fluid pressure and where P p2 is the final pressure, with P p2 < P p1. m and n describe the linear dependence of C m,p on porosity q and r describe how C m,p changes linearly with depletion. *) Uniaxial compressibility C mp : Unit 1 microsip = 10-6 /psi = 1.45 x 10-4 /MPa

13 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)

14 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

15 Upscaled formation porosity and NtG of Ennio formation 6n_7 W E Porosity (fraction of BV), Net-to-Gross before production 1 km

16 Determination of Ennio sandstone compressibility in laboratory deformation experiments (room T., K test =ΔS rad /ΔS ax, P p =1 atm.)

17 Net-sand depletion based on upscaled pore fluid pressures MPa Till 2005 Till 2013 Till MPa = 145 psi 1 km

18 Upscaled porosity and upscaled sand compressibility C m,p,us Porosity (fraction of bulk vol.) (*10-5 /MPa), valid over time period before prod. to km

19 Upscaled porosity and upscaled net-sand compressibility C m,p,us 1 km (*10-5 /MPa) Bef. prod. to to to 2016 Good agreement between C m,p,us -maps indicates no significant correlation between porosity and amount of depletion in the sands

20 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

21 So what about the shales? overburden high φ k mudstone low φ k mudstone reservoir unit So far < C m,p > has been a netsand-volume weighted average 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 P p

22 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)

23 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 ΔP p and ΔS v 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)

24 But what is the shale compressibility during production? Three chosen values for compressibility of reservoir shale during production

25 Comparison upscaled net-sand and gross-rock compressibility (*10-5 /MPa) Upscaled net-sand C m Upscaled gross-rock C m 1 km with C m_shale =0/MPa

26 Upscaled gross-rock compressibility C m,gross (*10-5 /MPa) C m_shale =0/MPa C m-shale =2x10-5 /MPa C m_shale =4x10-5 /MPa 1 km

27 So what are the mechanical properties of mudstone during depletion-induced reservoir compaction? Norwegian Form. Eval., Nov Elastodynamic (ED) Drained (from ED) Drained (Horsrud 2001) Drained (Shell correlation) Sloppy Stiff

28 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

29 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 S v and P p Upscaled compressibility is controlled by the porosity, net-togross, level of depletion, and geomechanical response shales

30 Upscaling mechanical rock properties and pore fluid pressure: An application to geomechanical modelling Peter Schutjens and Jeroen Snippe Shell U.K. Exploration & Production Aberdeen Thank you. Any questions?