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Phase Transition in Geomaterials Under Unsaturated Conditions

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Abstract

The freezing and thawing processes in sandstones under unsaturated conditions are methodically explored via the low-field nuclear magnetic resonance (NMR) technique. To precisely monitor the water content and distribution during the freezing and thawing processes, a special Carr–Purcell–Meiboom–Gill (CPMG) pulse sequence is proposed, leading pulse-induced temperature perturbations to be minimized. The results exhibit totally dissimilar water distributions in the two processes even under the same saturation: the freezing process retains more water in large pores, while the thawing process contains less water in large pores. This observation is primarily attributed to the ink-bottle effect occurring during the freezing: large pores with narrow entrances do not freeze until the entrance freezes. In addition, phase transition duration depends on the initial water saturation, for instance, the duration of the thawing process increases from 7 to 12 min as the initial water saturation varies from 40% to 80%. Through NMR observation, this phenomenon is associated with the variation of surface-to-volume ratio: high saturation is associated with the presence of water in large pores; the latter owns a small surface-to-volume ratio and accordingly involves a longer phase transition duration. After the assessment of surface-to-volume ratio, the intrinsic kinetic rate coefficient is further estimated to be 4.6 × 10–12 mol cm−2 s−1 ℃−1 for the ice thawing process in the studied rock. This value is five orders of magnitude lower than that found in the literature for the thawing process in bulk condition, i.e., 7.5 × 10–7 mol cm−2 s−1 ℃−1. We suggest that the small intrinsic kinetic rate coefficient addressed in the present work could be related to the constrained effect in rocks.

Highlights

  • A special pulse sequence with minimized temperature perturbation is developed to perform the freezing/thawing experiment.

  • The difference in water distribution is attributed to the effect of ink-bottle pores in the freezing and thawing processes.

  • Phase transition time increases with initial water saturation, which is lucidly explained by the nuclear magnetic resonance measurement that directly gives rise to information about the surface-to-volume ratio.

  • The intrinsic kinetic rate coefficient for ice melting within sandstones is estimated.

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Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

Abbreviations

B 0 :

Magnetic field intensity

B i :

Biot number

C :

Specific heat

F p :

Shape factor of the pore space

L :

Latent heat

M, M 0 :

Magnetization intensity; the total magnetization intensity

N :

Number of nuclei

S :

Surface

S w :

Water saturation

T 2 i :

Relaxation time for the water in the ith pore space

T, T env, T m :

Temperature; environment temperature; melting point temperature

V :

Volume

f i :

Mass fraction of water in ith pore space

h :

Convection coefficient

k 0, k i :

Intrinsic kinetic rate coefficient; kinetic rate coefficient

l :

Characteristic length

n 0, n i :

Initial moles of the ice; moles of the ice

r :

Pore size

s :

Spin quantum number of the nucleus

t :

Time

ɸ :

Volumetric water content

γ :

Gyromagnetic ratio

ƞ :

Moles of the ice per unit volume

κ :

Boltzmann’s constant

λ :

Thermal conductivity

ϴ i :

Volumetric fraction of the ice

ρ 2 :

Surface relaxivity

ρ c, ρ i :

Density of the rock (c) and ice (i)

\(\xi\) :

Planck’s constant

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Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant No. U20B6005, 22127812 and 51809275).

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Authors and Affiliations

  1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China

    Jiuhui Cheng, Xuanzhe Xia, Zhiqiang Liu & Linlin Wang

  2. Department of Offshore Oil and Gas Engineering, College of Safety and Ocean Engineering, China University of Petroleum, Beijing, China

    Jiuhui Cheng, Xuanzhe Xia & Linlin Wang

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  1. Jiuhui Cheng
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Cheng, J., Xia, X., Liu, Z. et al. Phase Transition in Geomaterials Under Unsaturated Conditions. Rock Mech Rock Eng 56, 8677–8691 (2023). https://doi.org/10.1007/s00603-023-03514-w

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