Abstract
Nanoscale spontaneous imbibition is a common process in nanoporous soil and unconventional reservoirs. Due to the complexity of these natural nanoporous media, the relevant spontaneous imbibition dynamics are still unclear. Thus, this paper studies spontaneous imbibition dynamics of liquids into a nanoporous carbon scaffold (NCS, with controllable wettability and pore geometry). The effects of evaporation and surfactant on spontaneous imbibition are also examined. For low-volatility liquids, a linear relationship between spontaneous imbibition height (\(H\)) and square root of time (\(\sqrt{t}\)) is observed. A modified Lucas–Washburn (L–W) equation is developed to describe the corresponding dynamics and to predict the NCS effective radius and the advancing water contact angle. A dimensionless time function is presented, which includes the properties of solid and liquid and their interactions, and can be used for upscaling spontaneous imbibition data in nanoporous media from laboratory to reservoir scales. Both a larger NCS pore diameter and pore throat diameter cause faster imbibition. The addition of surfactant into an aqueous solution increases the imbibition rate, although this influence is suppressed with pore size decrease. In contrast, for high-volatility liquids, a significant deviation from the linear relationship between \(H\) and \(\sqrt{t}\) is found at late times. The modified L–W equation is further developed to include evaporation effect. This study thus provides fundamental understanding of spontaneous imbibition dynamics at nanoscales. The developed theoretical models are expected to be applicable to important problems such as water infiltration into soil, fracturing fluid loss in unconventional reservoirs, and electrolyte migration in electrochemical devices.
Article Highlights
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A new nanoporous material (with controllable wettability and pore geometry) is used to study nanoscale spontaneous imbibition dynamics;
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The effects of pore geometry, surfactant, and evaporation on liquid imbibition in nanoporous media are explored;
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The presented new models can characterize spontaneous imbibition dynamics in nanoporous porous media accurately.
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Abbreviations
- NCS:
-
Nanoporous carbon scaffold
- NCS 22–7:
-
NCS with pore diameter of 22 nm and pore throat diameter of 7 nm
- NCS 50–12:
-
NCS with pore diameter of 50 nm and pore throat diameter of 12 nm
- NCS 85–16:
-
NCS with pore diameter of 85 nm and pore throat diameter of 16 nm
- NCS 85–35:
-
NCS with pore diameter of 85 nm and pore throat diameter of 35 nm
- PD:
-
Pore diameter (nm)
- PTD:
-
Pore throat diameter (nm)
- \({\theta }_{e}\) :
-
Equilibrium contact angle (°)
- \({\theta }_{a}\) :
-
Advancing contact angle (°)
- \(\gamma\) :
-
Interfacial tension between liquid and vapor (mN/m)
- \({R}_{e}\) :
-
Effective radius (nm)
- \(R\) :
-
Capillary/tube radius (nm)
- \(H\) :
-
Spontaneous imbibition height/distance (mm)
- \({h}_{e}\) :
-
Equilibrium height (m)
- \({P}_{c}\) :
-
Capillary pressure (Pa)
- \({k}_{w}\) :
-
Water permeability (\({{\mu m}}^{2}\))
- \(t\) :
-
Time (s)
- \({t}_{D}\) :
-
Dimensionless time
- \({S}_{w}\) :
-
Water saturation
- \(\varnothing\) :
-
Porosity
- \(v\) :
-
Spontaneous imbibition rate (m/s)
- \(\tau\) :
-
Tortuosity
- \(e\) :
-
Evaporation rate (\({\mu m/s}\))
- b :
-
NCS thickness (\({\mu m}\))
- \(g\) :
-
Gravitational constant (N/kg)
- \(\mu\) :
-
Liquid viscosity (\(\mathrm{mPa}\bullet \mathrm{s}]\))
- \(\rho\) :
-
Liquid density (kg/m3)
- \({R}^{2}\) :
-
Correlation coefficient
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Acknowledgements
V.I.B. acknowledges the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support, as well as support from the Canada Research Chairs program. C.R.C. thanks the sponsors of the Tight Oil Consortium (TOC) and Ovintiv and Shell for support of his Chair position in Unconventional Gas and Light Oil Research in the Department of Geoscience at the University of Calgary. C.R.C. and B.P. also thank the funding support from a NSERC Collaborative Research and Development Grant (CRDPJ 505339 – 2016) grant for this research. B.P. also acknowledges funding support from the Chinese Scholarship Council and TOC, while M.A. extends her acknowledgements to the Egyptian Cultural Affairs and Missions Sector for scholarship support as well as NSERC support through a CREATE grant.
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Pan, B., Clarkson, C.R., Atwa, M. et al. Spontaneous Imbibition Dynamics of Liquids in Partially-Wet Nanoporous Media: Experiment and Theory. Transp Porous Med 137, 555–574 (2021). https://doi.org/10.1007/s11242-021-01574-6
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DOI: https://doi.org/10.1007/s11242-021-01574-6