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Experimental Investigation of Stress-Dependency of Relative Permeability in Rock Fractures

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Abstract

This study investigates the stress-dependency of relative permeability in rock fractures. Previous studies provide contradictory evidence of the influence of increasing stress on the relative permeability of fractures. Some studies suggest that irreducible water saturation increases, while others show the reverse. In an attempt to resolve these differences, laboratory core flooding experiments are applied to measure the relative permeability of nitrogen–water mixtures in a fracture under various states of effective stress. Simultaneous X-ray CT measurements are made of aperture and water saturation distributions in the fracture. Two effective stress levels, 2.07 and 5.52 MPa, are applied to investigate the stress-dependency. For both states of stress, the measurements show that the relative permeability to gas is very low until a critical saturation is reached. As gas saturation increases beyond the critical value, relative permeability to gas increases quickly while water becomes essentially immobile. Results also demonstrate that increasing stress lowers the irreducible water saturation and the end-point non-wetting phase relative permeability when the experiments are conducted at the same flow rate. Using invasion percolation theory with the fracture aperture maps made at the two different effective stresses, capillary pressure curves are calculated and used to explain changes in phase interference at different stress levels. Finally, the preferential flow paths are analyzed at both stress levels. We use this analysis to reconcile flow regimes observed in earlier studies, and conclude that the differences between them can be explained by the relative importance of viscous and capillary forces. Specifically, if the experiments are designed to keep the capillary number constant, the irreducible water saturation increases with increasing confining stress. If the experiments are conducted at the same flow rate, higher confining stress decreases the irreducible water saturation, as was observed in these experiments. The analysis and data presented here also suggest that small increases in the water saturation of a fracture may dramatically reduce gas flow rates. This may present an additional and unexplored explanation for rapid production decline of gas wells in fractured reservoirs.

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Abbreviations

A :

Cross-sectional area of the rock fracture (\(\hbox {mm}^{2}\))

Ca :

Capillary number

\(CT_\mathrm{MA}\) :

Missing CT attenuation (HU)

\(CT_\mathrm{air}\) :

Air CT number (HU)

\(CT_\mathrm{wat}\) :

Water CT number (HU)

\({CT}_\mathrm{mat}\) :

Average CT value of the rock matrix (HU)

d :

Fracture aperture (mm)

g :

Gravitational constant (\(\hbox {m}/\hbox {s}^{2}\))

R :

Resolution, or voxel size (mm)

\(S_\mathrm{w}\) :

Water saturation of a voxel

\(S_\mathrm{wf}\) :

Water saturation of the fracture

k :

Intrinsic permeability (mD)

\(k_{r,i}\) :

Relative permeability

P :

Fluid pressure (Pa)

Q :

Water flow rate (\(\hbox {m}^{3}/\hbox {s}\))

\(q_{i}\) :

Volumetric flow rate (\(\hbox {m}^{3}/\hbox {s}\))

R :

Core radius (mm)

\({\phi }\) :

Porosity

\(\mu \) :

Viscosity (\(\hbox {Pa-s}/\hbox {m}^{2}\))

\(\rho \) :

Density (\(\hbox {kg}/\hbox {m}^{3}\))

\(\gamma \) :

Interfacial tension between two fluid phase (N/m)

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Acknowledgments

This work has been supported by ENI. The authors are grateful to Rani Calvo from the Geological Survey of Israel for providing the Zenifim sandstone sample used in this study.

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  1. Department of Energy Resources Engineering, Stanford University, Stanford, CA, 94305, USA

    Da Huo & Sally M. Benson

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Correspondence to Da Huo.

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Huo, D., Benson, S.M. Experimental Investigation of Stress-Dependency of Relative Permeability in Rock Fractures. Transp Porous Med 113, 567–590 (2016). https://doi.org/10.1007/s11242-016-0713-z

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