Geomechanics of Reservoir and Production Engineering
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RESERVOIR GEOMECHANICS James A. Craig
Transcript
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