Upscaling fluid flow in reservoir rocks: Applications from critical path analysis

Abstract:

Relating a property’s value at a large scale (e.g., field) to its value at a smaller scale (e.g., core) is called upscaling. It has been a long-standing problem in hydrology and reservoir engineering and an active subject of research in the past several decades. In this study, we address applications from critical path analysis (CPA) and statistical physics [1] to scale up fluid flow in porous media. CPA was first developed to study transport in systems with broad conductance distributions and has been successfully applied to heterogeneous and conventional rocks [2,3]. Its recent applications to uniform sphere and glass bead packs representing homogeneous porous media with narrow conductance distributions demonstrated that CPA is indeed applicable to a wide range of porous materials from uniform packs [4,5] to tight porous rocks [6] and shales [7]. In this study, we review such applications and discuss that if the pore space is accurately characterized, CPA provides a promising approach for upscaling flow and transport in rocks.

References

[1] Ambegaokar V, Halperin BI, Langer JS. Hopping conductivity in disordered systems. Phys Rev B 1971;4:2612–20.

[2] Katz AJ, Thompson AH. Quantitative prediction of permeability in porous rock. Phys Rev B 1986;34:8179–81.

[3] Hunt AG. Applications of percolation theory to porous media with distributed local conductances. Adv Water Resour 2001;24:279–307.

[4] Ghanbarian B. Applications of critical path analysis to uniform grain packings with narrow conductance distributions: II. Water relative permeability. Adv Water Resour 2020;137:103524.

[5] Ghanbarian B. Applications of critical path analysis to uniform grain packings with narrow conductance distributions: I. Single-phase permeability. Adv Water Resour 2020;137:103529.

[6] Ghanbarian B, Torres-Verdín C, Skaggs TH. Quantifying tight-gas sandstone permeability via critical path analysis. Adv Water Resour 2016;92:316–22.

[7] Zhang J, Scherer GW. Permeability of shale by the beam-bending method. Int J Rock Mech Min Sci 2012;53:179–91.