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Investigation of Stress Field and Fracture Development During Shale Maturation Using Analog Rock Systems

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Abstract

The emergence of hydrocarbons within shale as a major recoverable resource has sparked interest in fluid transport through these tight mudstones. Recent studies suggest the importance to recovery of microfracture networks that connect localized zones with large organic content to the inorganic matrix. This paper presents a joint modeling and experimental study to examine the onset, formation, and evolution of microfracture networks as shale matures. Both the stress field and fractures are simulated and imaged. A novel laboratory-scale, phase-field fracture propagation model was developed to characterize the material failure mechanisms that play a significant role during the shale maturation process. The numerical model developed consists of coupled solid deformation, pore pressure, and fracture propagation mechanisms. Benchmark tests were conducted to validate model accuracy. Laboratory-grade gelatins with varying Young’s modulus were used as scaled-rock analogs in a two-dimensional Hele-Shaw cell apparatus. Yeast within the gelatin generates gas in a fashion analogous to hydrocarbon formation as shale matures. These setups allow study and visualization of host rock elastic-brittle fracture and fracture network propagation mechanisms. The experimental setup was fitted to utilize photoelasticity principles coupled with birefringence properties of gelatin to explore visually the stress field of the gelatin as the fracture network developed. Stress optics image analysis and linear elastic fracture mechanics (LEFM) principles for crack propagation were used to monitor fracture growth for each gelatin type. Observed and simulated responses suggest gas diffusion within and deformation of the gelatin matrix as predominant mechanisms for energy dissipation depending on gelatin strength. LEFM, an experimental estimation of principal stress development with fracture growth, at different stages was determined for each gelatin rheology. The interplay of gas diffusion and material deformation determines the resulting frequency and pattern of fractures. Results correlate with Young’s modulus. Experimental and computed stress fields reveal that fractures resulting from internal gas generation are similar to, but not identical to, type 1 opening mode.

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Abbreviations

Α :

Cross-sectional area (m2)

b :

Biot coefficient (1)

D :

Diffusion coefficient (m2/s)

Ε :

Francfort–Marigo energy functional (J)

Ε m :

Young’s modulus (Pa)

e :

Infinitesimal strain tensor

f σ :

Stress-fringe factor (N/mm/fringe)

G c :

Critical energy release rate (J/m2)

k :

Permeability tensor (m2)

K :

Bulk modulus (Pa)

K dry :

Drained bulk modulus

K c :

Fracture toughness \(( {\text{Pa}}\sqrt {\text{m}} )\)

K d :

Darcy permeability (nD)

K I :

Stress-intensity factor \(( {\text{Pa}}\sqrt {\text{m}} )\)

h :

Sample thickness (m)

H c :

Length of host matrix (m)

H i :

Length of fracture i (m)

l :

Fracture length (m)

L :

Length of sample (m)

M :

Biot modulus (Pa)

N :

Fringe order

OL:

Ordinary light

P e :

Elastic pressure (Pa)

P p :

Propagation pressure (Pa)

PL:

Polarized Light

q :

Fluid source term (kg/s)

r :

Radius from crack tip to stress element (m)

Re:

Reynold’s number

S av :

Average fracture spacing (m)

W c :

Width of host matrix (m)

u :

Displacement field (m)

u f :

Fracture velocity (m/s)

V i :

Dead volume (m3)

w :

Fracture opening (m)

w f :

Fracture thickness (m)

y :

Fracture width (m)

α d :

Pulse decay semilog slope (s−1)

β :

Gas compressibility (Pa−1)

ϵ :

Length-scale parameter (m)

φ :

Phase-field variable (1)

Φ :

Strain energy density (J)

γ s :

Surface energy (J s−1)

Γ :

Crack surface area (m2)

ρ :

Density (kg/m3)

η :

Viscosity (Pa s)

σ :

Biot effective stress (Pa)

σ i :

Principal stress in i direction (Pa)

σ total :

Total stress (Pa)

ϑ :

Angle of stress element (°)

ϑ ss :

Steady-state time (s)

ν :

Poisson ratio

References

  • Allix, P., Burnham, A., Fowler, T., Herron, M., Kleinberg, R., Symington, B.: Coaxing oil from shale. Oilfield Rev. 22(4), 4–15 (2011)

    Google Scholar 

  • Ambrosio, L., Tortorelli, V.M.: Approximation of functional depending on jumps by elliptic functional via t-convergence. Commun. Pure Appl. Math. 43(8), 999–1036 (1990)

    Google Scholar 

  • American Association of Petroleum Geologists (AAPG). Kerogen; AAPG: Tulsa, OK, March 3, 2016. http://wiki.aapg.org/Kerogen

  • Amor, H., Marigo, J.J., Maurini, C.: Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J. Mech. Phys. Solids 57(8), 1209–1229 (2009)

    Google Scholar 

  • Anderson, E.R.: Propagation and Interaction of Pressurized Cracks in Photoelastic Gelatin. MS Thesis, Stanford University, Stanford, CA (1978)

  • Arvanitoyannis, I., Psomidau, E., Nakayama, A., Aiba, S., Yamamoto, N.: Edible films made from gelatin, soluble starch, and polyols, Part 3. Food Chem. 60(4), 593–604 (1997)

    Google Scholar 

  • Baek, T.H., Kim, M.S., Hong, D.P.: Fringe analysis for photoelasticity using image processing techniques. Int. J. Softw. Eng. Appl. 8(4), 91–102 (2014). https://doi.org/10.14257/ijseia.2014.8.4.11

    Article  Google Scholar 

  • Bangerth, W., Hartmann, R., Kanschat, G.: A general-purpose object-oriented finite element library. ACM Trans. Math. Softw. 33(4), 24 (2007)

    Google Scholar 

  • Brace, W., Walsh, J., Frangos, W.: Permeability of granite under high pressure. J. Geophys. Res. 73(6), 2225–2236 (1968)

    Google Scholar 

  • Berg, R.R., Gangi, A.F.: Primary migration by oil-generation microfracturing in low-permeability source rocks: application to the Austin Chalk, Texas. AAPG Bull. 83, 727–756 (1999)

    Google Scholar 

  • Bloom, O.T.: U.S. Patent No. 1,540,979. Washington, DC: US Patent and Trademark Office (1925)

  • Bochev, P.B., Dohrmann, C.R., Gunzburger, M.D.: Stabilization of low-order mixed finite elements for the Stokes equations. SIAM J. Numer. Anal. 44(1), 82–101 (2006)

    Google Scholar 

  • Borja, R.I.: Plasticity: Modeling & Computation. Springer (2013)

  • Bostrom, N., Leu, G., Pomerantz, D., Machlus, M., Herron, M., Kleinberg, R.: Realistic oil shale pyrolysis programs: kinetics and quantitative analysis. Oil Shale Symposium (2009)

  • Bourdin, B., Francfort, G.A., Marigo, J.J.: Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48(4), 797–826 (2000)

    Google Scholar 

  • Bourdin, B., Francfort, G.A., Marigo, J.J.: The variational approach to fracture. J. Elast. 91(1), 5–148 (2008)

    Google Scholar 

  • Bourdin, B., Chukwudozie, C.P., Yoshioka, K.: A variational approach to the numerical simulation of hydraulic fracturing. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (2012)

  • Burnham, A.K., Singleton, M.F.: High pressure pyrolysis of green river oil shale. In: Geochemistry and Chemistry of Oil Shales, ACS Symposium Series 230. American Chemical Society (1983)

  • Burnham, A.K.: Chemistry and kinetics of oil shale retorting, in oil shale: a solution to the liquid fuel dilemma. In: ACS Symposium Series 1032, American Chemical Society (2010)

  • Capuano, R.M.: Evidence of fluid flow in microcracks in geopressured shales. AAPG Bull. 77, 1303–1314 (1993)

    Google Scholar 

  • Charmette, C., Sanchez, J., Gramain, Ph, Rudatsikira, A.: Gas transport properties of poly(ethylene oxide-co-epichlorohydrin) membranes. J. Membr. Sci. 230, 161–169 (2004). https://doi.org/10.1016/j.memsci.2003.10.043

    Article  Google Scholar 

  • Chen, Z., Bunger, A.P., Zhang, X., Jeffrey, R.G.: Cohesive zone finite element-based modelling of hydraulic fractures. Acta Mech. Solida Sin. 22(5), 443–452 (2009)

    Google Scholar 

  • Chukwudozie, C., Bourdin, B., Yoshioka, K.: A variational phase-field model for hydraulic fracturing in porous media. Comput. Methods Appl. Mech. Eng. 347, 957–982 (2019)

    Google Scholar 

  • Dally, J., Riley, W.: Experimental Stress Analysis, 3rd edn. McGraw-Hill, New York (1991)

    Google Scholar 

  • Di Giuseppe, E., Funiciello, F., Corbi, F., Ranalli, G., Mojoli, G.: Gelatins as rock analogs: a systematic study of their rheological and physical properties. Tectonophysics 473(3–4), 391–403 (2009)

    Google Scholar 

  • du Rouchet, J.: Stress fields, a key to oil migration. AAPG Bull. 65, 445–459 (1981)

    Google Scholar 

  • Erdogan, F., Sih, G.C.: On the crack extension in plates under plane loading and transverse shear. J. Basic Eng. 85(4), 519–525 (1963)

    Google Scholar 

  • Glatz, G., Castanier, L.M., Kovscek, A.R.: Visualization and quantification of thermally induced porosity alteration of immature source rock using X-ray computed tomography. Energy Fuels 30(10), 8141–8149 (2016). https://doi.org/10.1021/acs.energyfuels.6b01430

    Article  Google Scholar 

  • Glatz, G., Lapene, A., Castanier, L.M., Kovscek, A.R.: An experimental platform for triaxial high-pressure/high-temperature testing of rocks using computed tomography. Rev. Sci. Instrum. 89, 045101 (2018). https://doi.org/10.1063/1.5030204

    Article  Google Scholar 

  • Griffith, A.: The phenomena of rupture and flow in solids. Royal Society of London. Series A. 221, 163–198 (1921)

    Google Scholar 

  • Francfort, G.A., Marigo, J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319–1342 (1998)

    Google Scholar 

  • Heister, T., Wheeler, M.F., Wick, T.: A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach. Comput. Methods Appl. Mech. Eng. 290, 466–495 (2015)

    Google Scholar 

  • Hintermüller, M., Ito, K., Kunisch, K.: The primal-dual active set strategy as a semismooth newton method. SIAM J. Optim. 13(3), 865–888 (2002)

    Google Scholar 

  • Hubbert, M.: Theory of scale models as applied to the study of geologic structures. Bull. Geol. Soc. Am. 48(10), 1459–1517 (1937)

    Google Scholar 

  • Irwin, G.: Fracture dynamics. Fracturing of Metals, 152 (1948)

  • Ji, S.H., Park, Y.J., Lee, K.K.: Influence of fracture connectivity and characterization level on the uncertainty of the equivalent permeability in statistically conceptualized fracture networks. Transp. Porous Media 87(2), 385–395 (2011)

    Google Scholar 

  • Jiang, J., Yang, J.: Coupled fluid flow and geomechanics modeling of stress-sensitive production behavior in fractured shale gas reservoirs. Int. J. Rock Mech. Min. Sci. 101, 1–12 (2018)

    Google Scholar 

  • Ju, Y., Zheng, Z., Xie, H., Wang, L., He, K.: Experimental visualization methods for three-dimensional stress fields of porous solids. Exp Tech. 41, 331–344 (2017)

    Google Scholar 

  • Kavanagh, J.L., Menand, T., Sparks, R.S.J.: An experimental investigation of sill formation and propagation in layered elastic media. Earth Planet. Sci. Lett. 245, 799–813 (2006)

    Google Scholar 

  • Kavanagh, J.L., Menand, T., Daniels, K.A.: Gelatine as a crustal analogue: determining elastic properties for modelling magmatic intrusions. Tectonophysics 582, 101–111 (2013)

    Google Scholar 

  • Kavanagh, J.L., Boutelier, D., Cruden, A.R.: The mechanics of sill inception, propagation and growth: experimental evidence for rapid reduction in magmatic overpressure. Earth Planet. Sci. Lett. 421, 117–128 (2015)

    Google Scholar 

  • Kobchenko, M., Hafver, A., Jettestuen, E., Renard, F., Galland, O., Jamtveit, B., Meakin, P., Dysthe, D.K.: Drainage fracture networks in elastic solids with internal fluid generation. Europhys. Lett. 102, 66002 (2013)

    Google Scholar 

  • Kobchenko, M., Hafver, A., Jettestuen, E., Renard, F., Galland, O., Jamtveit, B., Meakin, P., Dysthe, D.K.: Evolution of a fracture network in an elastic medium with internal fluid generation and expulsion. Phys. Rev. E 90(052801), 1–9 (2014)

    Google Scholar 

  • Lash, G.G., Engelder, T.: An analysis of horizontal microcracking during catagenesis: example from Catskill delta complex. AAPG Bulletin 89, 1433–1449 (2005)

    Google Scholar 

  • Le-Doan, T.-V., Bostrom, N.W., Burnham, A.K., Kleinberg, R.L., Pomerantz, A.E., Allix, P.: Experimental study of green river oil shale pyrolisis. SPE paper 168715 presented at the Unconventional Resources Technology Conference (URTeC) held in Denver, CO. Aug. 12-14 (2013)

  • Lee, S., Mikelic, A., Wheeler, M.F., Wick, T.: Phase-field modeling of proppant-filled fractures in a poroelastic medium. Comput. Methods Appl. Mech. Eng. 312, 509–541 (2016)

    Google Scholar 

  • Lee, S., Mikelic, A., Wheeler, M.F., Wick, T.: Phase-field modeling of two phase fluid filled fractures in a poroelastic medium. Multisc. Model. Simul. 16(4), 1542–1580 (2018)

    Google Scholar 

  • Li, F.: Study of Stress Measurement Using Polariscope. PhD Thesis, Georgia Institute of Technology, Atlanta, GA (2010)

  • Mauthe, S., Miehe, C.: Hydraulic fracture in poro-hydro-elastic media. Mech. Res. Commun. 80, 69–83 (2017)

    Google Scholar 

  • Márquez, X.M., Mountjoy, E.W.: Microcracks due to overpressures caused by thermal cracking in well-sealed Upper Devonian reservoirs, deep Alberta basin. AAPG Bull. 80, 570–588 (1996)

    Google Scholar 

  • McCarthy, K., Rojas, K., Niemann, M., Palmowski, D., Peters, K., Stankiewicz, A.: Basic petroleum geochemistry for source rock evaluation. Oilfield Rev. 23, 2 (2011)

    Google Scholar 

  • Miehe, C., Welschinger, F., Hofacker, M.: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. Int. J. Numer. Methods Eng. 83(10), 1273–1311 (2010a)

    Google Scholar 

  • Miehe, C., Hofacker, M., Welschinger, F.: A phase-field model for rate independent crack propagation: robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng. 199(45), 2765–2778 (2010b)

    Google Scholar 

  • Mohammadnejad, T., Andrade, J.E.: Numerical modeling of hydraulic fracture propagation, closure and reopening using xfem with application to in situ stress estimation. Int. J. Numer. Anal. Methods Geomech. 40(15), 2033–2060 (2016)

    Google Scholar 

  • Özkaya, I.: A simple analysis of oil-induced fracturing in sedimentary rocks. Mar. Pet. Geol. 5, 293–297 (1988)

    Google Scholar 

  • Phillips, J.W.: Experimental Stress Analysis. Ch. 6. http://www.ifsc.usp.br/~lavfis/images/BDApostilas/ApEfFotoelastico/photoelasticity.pdf. Accessed 4 Dec 2017 (2008)

  • Ramesh, K.: Digital Photoelasticity. Advanced Techniques and Applications. Springer Berlin Heidelberg, Berlin (2000)

    Google Scholar 

  • Ross-Murphy, S.: Structure and rheology of gelatin gels: recent progress. Polymer 33(12), 2622–2627 (1992)

    Google Scholar 

  • Sigma-Aldrich. Gelatin Product Information Sheet, CAS RN 9000-70-8. https://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Sigma/Product_Information_Sheet/2/g9382pis.pdf. Accessed 21 Feb 2018

  • Takada, A.: Experimental study of propagation of liquid-filled crack in gelatin: shape and velocity in hydrostatic stress condition. J. Geophys. Res. 95(B6), 8471–8481 (1990)

    Google Scholar 

  • Takada, A.: Accumulation of magma in space and time by crack interaction. In: Ryan, M.P. (ed.) Magmatic Systems, pp. 241–257. Academic Press, San Diego (1994)

    Google Scholar 

  • Talukdar, S., Gallango, O., Vallejos, C., Ruggiero, A.: Observations on the primary migration of oil in the La Luna source rocks of the Maracaibo Basin, Venezuela. Oil Gas Sci. Technol. Rev. IFP. 43(3), 357–370 (1988)

    Google Scholar 

  • Tanné, E., Li, T., Bourdin, B., Marigo, J.J., Maurini, C.: Crack nucleation in variational phase-field models of brittle fracture. J. Mech. Phys. Solids 110, 80–99 (2018)

    Google Scholar 

  • ten Grotenhuis, S.M., Piazolo, S., Pakula, T., Passchier, C., Bons, P.D.: Are polymers suitable rock analogs? Tectonophysics 350, 35–47 (2002)

    Google Scholar 

  • Timoshenko, S., Goodier, J.: Theory of Elasticity. McGraw-Hill Higher Education, New York (1970)

    Google Scholar 

  • van Otterloo, J., Cruden, A.R.: Rheology of pig skin gelatine: defining the elastic domain and its thermal and mechanical properties for geological analogue. Tectonophysics 683, 86–97 (2016)

    Google Scholar 

  • Vishay Precision Group. Introduction to Analysis by the PhotoStress Method. Tech Note TN-702-2 (2011)

  • Watanabe, T., Masuyama, T., Nagaoka, K., Tahara, T.: Analog experiments on magma-filled cracks: competition between external stresses and internal pressure. Earth Planets Space 54, 1247–1261 (2002)

    Google Scholar 

  • White, J.A., Borja, R.I.: Stabilized low-order finite elements for coupled solid deformation/fluid-diffusion and their application to fault zone transients. Comput. Methods Appl. Mech. Eng. 197(49–50), 4353–4366 (2008)

    Google Scholar 

  • White, J.A., Castelletto, N., Tchelepi, H.A.: Block-partitioned solvers for coupled poromechanics: a unified framework. Comput. Methods Appl. Mech. Eng. 303, 55–74 (2016)

    Google Scholar 

  • Wu, Y.S., Ye, M., Sudicky, E.A.: Fracture-flow-enhanced matrix diffusion in solute transport through fractured porous media. Transp. Porous Media 81(1), 21 (2010)

    Google Scholar 

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Acknowledgements

This work was supported by TOTAL S.A. through the STEMS project, a research collaboration between TOTAL S.A. and Stanford University. BV, JY, and ARK acknowledge support as part of the Center for Mechanistic Control of Unconventional Formations (CMC-UF), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science under DOE (BES) Award DE-SC0019165. Additionally, we thank the Industrial Affiliates of SUPRI-A and SUPRI-B for their ancillary support.

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  1. B. Vega and J. Yang have contributed equally to this work.

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  1. Energy Resources Engineering, Stanford University, Stanford, CA, USA

    B. Vega, J. Yang, H. Tchelepi & A. R. Kovscek

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  1. B. Vega
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Vega, B., Yang, J., Tchelepi, H. et al. Investigation of Stress Field and Fracture Development During Shale Maturation Using Analog Rock Systems. Transp Porous Med 131, 503–535 (2020). https://doi.org/10.1007/s11242-019-01355-2

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