Analytical model of gas transport in heterogeneous hydraulically-fractured organic-rich shale media

Dian Fan, Amin Ettehadtavakkol

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Multiple gas transport mechanisms and geological parameters influence total gas production in hydraulically-fractured organic-rich shale reservoirs. The absolute and relative contributions of these processes and parameters vary significantly with the scale of the medium, from pore scale to field scale. The objective of this study is to investigate the impact of these geological parameters and transport processes in organic-rich shale production at field scale. We develop a multi-porosity analytical model which honors pressure- and space-dependent geological properties and gas transport processes in a multi-stage, hydraulically-fractured horizontal well of shale reservoir. The model premises distinct pores in kerogen, inorganic clay, induced fracture, and hydraulic fracture. Multiple flow zones are modeled: unstimulated reservoir volume (USRV), stimulated reservoir volume (SRV), and hydraulic fractures (HF). Compared to the earlier analytical models, the new model accounts for more comprehensive transport mechanisms and medium properties: gas diffusion and desorption in kerogen matrix and organopores, slip flow in inorganic matrix pores, transient Darcy flow from matrix to induced fractures, Darcy flow in both induced and hydraulic fractures, tortuosity of induced fractures, and pressure-dependent permeabilities. These enhanced features introduce important complexities to the analytical solution challenges that are discussed and resolved in detail. Extensive lab and field data for Eagle Ford shale are presented in the new model. Sensitivity analyses are conducted to study the flow contribution from organic and inorganic media. The results show that first, the impacts of gas diffusion, TOC, and organoporosity at pore and core scale are largely eclipsed at field scale by slip flow in inorganic matrix and anomalous diffusion within complex induced-fracture network. Second, fracture tortuosity and the Klinkenberg effect are dominant factors during early- and intermediate-time production. Third, gas diffusion in kerogen matrix is negligible compared to gas desorption and diffusion in organopores. Fourth, permeability variations with pore pressure have a significant impact on late-time production from fractured low-permeability reservoirs. The derived analytical solutions in Laplace space serve as simple but robust tools for studying gas transport in fractured organic shale formation. The field application is validated by matching results for an Eagle Ford shale well. Finally, there is a discussion of the present model's limitations and potential future extensions.

Original languageEnglish
Pages (from-to)625-640
Number of pages16
StatePublished - 2017


  • Analytical solution
  • Anomalous diffusion
  • Diffusion and slip flow
  • Hydraulically-fractured well
  • Pressure-sensitive formation
  • Transient gas transport


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