1. James A. Craig

2. Compaction and Subsidence Compaction Subsidence SubsidenceCompaction Ratio Reservoir Stress Path Compaction Drive Mechanism Definitions of Pore Compressibility Produced Fluid Volume Initial Volume of Oil-In-Place

3. During petroleum production fluid pressure declines This reduction of pore pressure in the reservoir increases the effective stress and making the rock itself to shrink (compact). This leads to associated displacement field on the surface called Subsidence. Reservoir geomechanics is becoming an increasingly important part of reservoir management. Compaction can be a drive mechanism

4. Examples of locations with significant subsidence: Valhalla, NCS Goose Creek, Texas, USA Wilmington, Long Beach, LA, USA (about 9 meters) Ekofisk, NCS Bolivar, Venezuela Groningen, The Netherlands.

5. Conditions for compaction and subsidence Reservoir rock must be soft (highly compressible), weak, and poorly consolidated. Reservoir must be thick considerably. Large depletion (pore pressure reduction). Large areal extent compared with reservoir thickness to prevent shielding by the overburden.

6. Problems associated with compaction and subsidence Offshore platform safety Environmental challenges (e.g. risk of flooding in land operations) Casing collapse in reservoir Associated seismicity

7. Possible solutions Account for possible compaction and subsidence in platform and casing design. Pressure maintenance (e.g. water injection). Platform jackup.

8. Usual assumptions Elastic rock behaviour Uniaxial compaction Vertical stress fully carried by reservoir (no arching) Often Biots constant = 1 (not always)

9. 1 1 2 1 f h h P E

10. Uniaxial compaction (plane wave) modulus is: E Compaction coefficient/uniaxial compressibility is: Therefore: h P f h OR H 1 1 1 2 H 1 m C H h hCmPf

11. h = compaction (unit of length) h = reservoir thickness (unit of length) Pf = pore pressure reduction (unit of stress) = Poissons ratio (dimensionless) E = Youngs modulus (unit of stress) = Biots constant (dimensionless)

12. Nucleus of strain model Developed by Geertsma (1973) OR 2 2 2 1 1 f z h P D u H D R 2 2 2 1 1 z f m D u h P C D R

13. uz = subsidence (unit of length) h = reservoir thickness (unit of length) D = reservoir depth (unit of length) R = reservoir radius (unit of length)

14. And 2 2 2 1 1 z f m D u h P C D R m f h hC P - Ratio z u S C h 2 2 - Ratio 2 1 1 D S C D R 2 1 - Ratio 2 1 1 1 S C R D

15. Reservoir stress path means Stress Evolution during depletion. Stress evolution is a result of change in horizontal stresses (while vertical stress remains constant) during depletion in a uniaxial reservoir compaction. Reservoir stress path can be defined by the Stress Path Coefficients.

16. v H h h v H h P P P f f f v v = arching coefficient H & h = describe the change in the horizontal stress field = ratio of effective horizontal stress to effective vertical stress

17. In terms of effective stress concept: Assume a full rotational symmetry in the horizontal plane: Assume vertical stress remains constant as pore pressure changes: From h H 0 v H h 1 v 1 2 1 h H

18. Compaction in terms of stress path is given as: 1 2 1 v h Using the effective stress concept: f h h P E 2 v h f h h P E

19. Compaction drive aids production of hydrocarbon by compression/expansion of reservoir fluids and rocks.

20. There are 2 ways to define pore compressibility: Based on constant pore pressure Based on constant external stress

21. Constant Pore Pressure (Drained Isotropic Loading) p , c V 1 1 p K V p , c p Pf const C Cp,c = pore compressibility with variation to confining stress (Pa-1, bar-1, atm-1, or psi-1) Vp = pore volume (unit of volume) , 1 1 1 p c fr s C K K

22. Constant External Stress p , p V 1 1 p K V P p , p p f const C Cp,p = pore compressibility with variation to pore pressure (Pa-1, bar-1, atm-1, or psi-1) Vp = pore volume (unit of volume) , 1 1 1 1 p p fr s s C K K K

23. In terms of reservoir stress path: For an ellipsoidal reservoir: Then: , 1 1 1 1 p p fr s s C K K K 2 1 2 3 1 , 1 2 1 2 1 1 3 1 3 1 p p fr s C K K

24. Vprod Vp Ctotal Pf Vprod = produced fluid volume (unit of volume) Ctotal = total reservoir compressibility total f p, p C C C

25. Cf CgSg CoSo CwSw Cf = reservoir fluid compressibility Cg = gas compressibility Co = oil compressibility Cw = water compressibility Sg = gas saturation So = oil saturation Sw = water saturation

26. In soft rocks (low stiffness high compressibility), the pore compressibility will enhance production. This is called Compaction Drive. In hard rocks (high stiffness low compressibility), the pore fluid compressibility will be the drive.

27. B S o o V V p OIP prod , B C P oi total f Vp,OIP = initial volume of oil-in-place (unit of volume) Boi = initial oil formation volume factor Bo = present oil formation volume factor