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

  • B. VegaEmail author
  • J. Yang
  • H. Tchelepi
  • A. R. Kovscek


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.


Shale rock maturation Analog rock systems Phase-field fracture propagation model Stress field Gelatin 

List of Symbols


Cross-sectional area (m2)


Biot coefficient (1)


Diffusion coefficient (m2/s)


Francfort–Marigo energy functional (J)


Young’s modulus (Pa)


Infinitesimal strain tensor


Stress-fringe factor (N/mm/fringe)


Critical energy release rate (J/m2)


Permeability tensor (m2)


Bulk modulus (Pa)


Drained bulk modulus


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


Darcy permeability (nD)


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


Sample thickness (m)


Length of host matrix (m)


Length of fracture i (m)


Fracture length (m)


Length of sample (m)


Biot modulus (Pa)


Fringe order


Ordinary light


Elastic pressure (Pa)


Propagation pressure (Pa)


Polarized Light


Fluid source term (kg/s)


Radius from crack tip to stress element (m)


Reynold’s number


Average fracture spacing (m)


Width of host matrix (m)


Displacement field (m)


Fracture velocity (m/s)


Dead volume (m3)


Fracture opening (m)


Fracture thickness (m)


Fracture width (m)


Pulse decay semilog slope (s−1)


Gas compressibility (Pa−1)


Length-scale parameter (m)


Phase-field variable (1)


Strain energy density (J)


Surface energy (J s−1)


Crack surface area (m2)


Density (kg/m3)


Viscosity (Pa s)


Biot effective stress (Pa)


Principal stress in i direction (Pa)


Total stress (Pa)


Angle of stress element (°)


Steady-state time (s)


Poisson ratio



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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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Energy Resources EngineeringStanford UniversityStanfordUSA

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