Effects of loading rate and saturating fluid on chalk mechanical behavior Ø. Johnsen, F. Cuisiat, and L. Grande

Transcription

1 Effects of loading rate and saturating fluid on chalk mechanical behavior Ø. Johnsen, F. Cuisiat, and L. Grande 9th Euroconference on Rock Physics and Geomechanics Trondheim Norway October 2011

2 Motivation Many oil and gas fields in the North Sea are found in very porous overpressured chalk formations which compact significantly during the lifetime of the field contributes significantly to the recovery mechanism, in some areas of the Valhall field up to % sea bed settlement (ref Valhall and Ekofisk) Implications for foundation, and well casing failure Reservoir compaction: 1) result of changes in effective stresses, 2) water weakening of the chalk during massive seawater injection. Chalk mechanical behavior is susceptible to changes in several parameters: Pore fluid composition, porosity, strain/load rate Chalk exhibit pronounced creep deformations under constant load at high stresses or near the strain rate dependent elastic-plastic limit

3 Background for current tests In situ conditions Stress / Pore pressure (MPa) Total vertical stress σ V 22.5 Initial total horizontal stress σ H 18.0 Initial octahedral stress σ oct 19.5 Initial Reservoir Pressure P o 13.5 Initial Effective vertical stress σ V 9.0 Initial Effective horizontal stress σ H 4.5 Initial Effective octahedral stress σ oct 6.0 Pore fluid Salt Concentration (g/l) NaCl 58 KCl - CaCl 2, 6 H 2 O 55.6 MgCl 2, 6 H 2 O 8.5 Gas and brine (~30%) saturated Conducted tests Uniaxial strain, depletion (CAUST) -vertically drilled plugs Depth (m) Porosity (%) Fluid type brine brine dry brine brine Isotropic, drained -horizontally drilled plugs Depth (m) Porosity (%) Fluid type % brine brine % brine brine brine brine

4 Experimental approach 0% brine saturation directly built into triax for test 100% brine saturated built directly into triax and saturated in the cell 30% brine saturation saturated in vacuum chamber w/diluted solution, evaporation to target weight/saturation level, Homogeneous fluid distribution along the core axis verified with X-ray CT

5 Results fluid and porosity effects Pore fluid composition has a pronounced effect on the behavior of chalk: - Alters stiffness, elastic-plastic transition (pore collapse), creep rate. Water weakening effect upon flooding: - Instantaneous permanent deformation and increase of creep rate - Radical increase up to 15% water saturation in initially oil saturated chalk - Not as well documented for water flooding in initially gas saturated samples Hickmann 2004

6 Results fluid and porosity effects Joint Chalk Research (JCR) database

7 Results fluid and porosity effects Before Pc After Pc Trend line C pe =1/(K n) K = 83596e 11.3 n C bp = Trend line dε v dp λ = ( 1+ e )p λ = 0.032e 4. 1n 0 (after JCR database and Hickman 2004)

8 Results fluid and porosity effects Failure envelope largely depend on saturating fluid and porosity ULG (Collin 2002, Schroeder 2009) and NGI 2010 data

9 Results rate sensitivity but also on load rate! PASACHALK 2004 Hickmann 2004

10 Results rate sensitivity (load phase) 36.2% 30.6% 33.8% 36.9% 37.8% Et = Δσ oct / Δε oct σ mean = σ oct

11 Results rate sensitivity (0.01MPa/h) 36.2% 30.6% 33.8% E t =0.50 E t =0.97 E t =0.81 E t = % 37.8% Porosity = E t

12 Results rate sensitivity (0.10MPa/h) E t = % 30.6% 33.8% E t =0.60 E t =0.28 E t =0.74 T brine saturated Strain hardening Volumetric Strain (ms) y = x R 2 = y = x R 2 = y = x R 2 = Effective Vertical Stress σ' v (MPa)

13 Results rate sensitivity (1.0MPa/h) 36.2% 30.6% E t = % E t =0.75 E t =0.26 E t =0.55 Strain hardening 36.9% 37.8% E t =0.50 E t =0.50 E t =0.21 E t =0.24

14 Results rate sensitivity (10.0MPa/h) 36.2% 30.6% 33.8% 36.9% 37.8% Load rate = E t E t =0.17 E t =0.19

15 . Results rate sensitivity (load phase) Test type Fluid type Porosity (%) Mean stress (MPa) Mean stress rate (MPa/h) Isotropic brine Isotropic brine Isotropic brine Isotropic Isotropic 30% brine 30% brine p1 2.. p p1 p b Visco-plastic rate dependent compaction model (de Waal) ε c v p = + b, o ε v bp ε v p p 2 1 ε = ε p ln p b =. p ln. p v2 v1 b

16 Results rate sensitivity (creep phase) σ mean = 32.0 MPa ε C t v ε = + vot bcb, o p ln 1 bcb, o p = bcb o p τ = bc p / ε c,, b, o vo t ε v C = c t + τ σ mean = 50.3 MPa Mean Stress p (MPa) Slope inverse strain rate vs time Offset τ / C c (ms) c b,0 (/MPa) 1/ C c ε vo b

17 Results rate sensitivity (creep phase) Volumetric strain (ms) harlingen eoct-t T1840 creep-1 b = b = Volumetric strain (ms) harlingen eoct-t T1840 creep Time, t (hours) Time, t (hours) (dry) to (fully water-saturated) Priol (2006), Lixhe outcrop chalk b 3.1n = Kristiansen & Plischke (2010), e Valhall field

18 Relating laboratory data to field b 40 Harlingen Chalk - Trend lines for field depletion rates Leroueil 2006 b Isotropic yield stress at pore collapse, field loading rate (MPa) HAR-high HAR-med HAR-low increasing value of b Porosities not compatible with in situ stress state Porosity

19 Modelling field deformation Initialize stresses, pressure, porosity dependent parameters Porosity (%) % porosity 30 % porosity σ = σ + du v σ = σ + K du h v h Update stresses and pore pressure Plastic compressibility C b Y = ( 1+ e0 ) p eqv Pore collapse? p eqv p c, field Elastic compressibility Calculate increments of volumetric strain and void ratio d ε = C dp vol vol Main loop repeated n times, du= u/n λ b vol q = eqv ε = ε + dε ( σ v + σ h ) ( σ σ ) p = 2 de = Update variables vol 1 C b = K ( 0 1+ e ) dε Calculate equivalent compressibility C eqv = v h 2 q p eqv = p + 2 M + p N vol e e = e de n = 1+ e ε vol ( u u) 0 Volumetric Strain (ms) Equivalent Bulk Compressibility (/bar) % porosity % porosity Reservoir Pressure (bars) % porosity 25 % porosity x 10-4 Reservoir Pressure (bars) % porosity 32 % porosity 30 % porosity 25 % porosity Reservoir Pressure (bars)

20 Summary Demonstrated porosity, rate and saturating fluid effects on mechanical behavior: Chalk exhibit rate dependent stiffness: 0.01MPa/h > 0.10 MPa/h > 1.00 MPa/h >10.00 MPa/h Only subtle difference between mech. response at 30% brine saturation as vs100% saturation (Pc and Et slightly higher, b slightly lower) The elastic and plastic compression properties of the chalk have been compared to available data from open literature: fit within the general scatter observed for chalk and proposed porosity-dependent correlations. Laboratory experiments have been analyzed within the frame work proposed by de Waal (1986) to characterize the time and rate dependent behavior: agreement with other chalk data from the open literature. A simple model is developed, and based on the defined material correlations it estimates the volumetric strain due to depletion.