Abstract
Spontaneous imbibition controls the movement of water from the environment into natural and engineered porous construction materials (e.g. stone, concrete, cement, etc.), which can affect the durability of the material and the overall building design. We demonstrate that in contrast to current simplistic approaches, a full description of the process, enabling predictions of sorptivity for different flow conditions and material properties, as well as the water saturation profile, requires the determination of capillary pressure, absolute and relative permeability, and the impact of the initial water saturation. We measured the sorptivity of a homogeneous Bentheimer sandstone for both initially dry and wet conditions for three replicate experiments to demonstrate how to match the measurements to an analytical model to determine the wetting phase (water) relative permeability. The impact of initial water saturation was also studied. We suggest that using imbibition rate is a robust, quick and accurate way to estimate water relative permeability which avoids uncertainties inherent in traditional steady-state measurements. Furthermore, this then allows a complete mathematical treatment of imbibition, to predict the saturation profile as a function of time and the sorptivity for different porous material and fluid properties. Overall this work provides a theoretical and experimental framework that significantly improves our characterization of water transport in a wide range of construction and building materials.
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Abbreviations
- A :
-
Area (m2)
- A cap :
-
Capillary water absorption coefficient (kg·(m−2s−0.5))
- C :
-
Sorptivity (m s−0.5)
- c :
-
Fitting parameter
- D :
-
Capillary dispersion (m3/s)
- F :
-
Capillary fractional flow
- K :
-
Permeability (m2 or D)
- P :
-
Pressure (Pa)
- q :
-
Flow rate per unit area (m/s)
- s :
-
Saturation
- m :
-
Mass (kg)
- t :
-
Time (s)
- x :
-
Length (m)
- V :
-
Imbibed volume per unit area (m)
- β :
-
Dummy integration variable
- μ :
-
Viscosity (Pa s)
- ρ :
-
Density (kg/m3)
- ϕ :
-
Porosity
- ω :
-
Boltzmann variable
- a:
-
Air
- ana:
-
Analytical results
- c:
-
Capillary
- exp:
-
Experimental
- i:
-
Initial value of water phase
- ra:
-
Relative permeability of air
- rw:
-
Relative permeability of water
- w:
-
Water (wetting phase)
- * :
-
Inlet state
- ave:
-
Integral average value
- guess:
-
Estimated value
- max:
-
Maximum value
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Acknowledgements
This work was supported by grants from the National Natural Science Foundation of China (52076189) and “the Fundamental Research Funds for the Central Universities” (2021QNA4010).
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Qu, ML., Lu, SY., Lin, Q. et al. Characterization of Water Transport in Porous Building Materials Based on an Analytical Spontaneous Imbibition Model. Transp Porous Med 143, 417–432 (2022). https://doi.org/10.1007/s11242-022-01776-6
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DOI: https://doi.org/10.1007/s11242-022-01776-6