The Phase Change Heat of Water in the Pore Space of Rocks Based on DSC Studies
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Methods
2.2.1. Methods for Determining Physical Characteristics
2.2.2. Differential Scanning Calorimetry (DSC)
2.2.3. Thermoporometry
2.2.4. Mercury Intrusion Porosimetry (MIP)
2.2.5. Scanning Electron Microscopy (SEM)
2.2.6. X-Ray Diffraction
2.2.7. Transmitted Light Optical Microscopy
3. Results and Discussion
3.1. Characteristics of the Rock Samples
3.2. Physical Properties
3.3. Thermal Effects
- The influence of narrow pores on increasing the capillary pressure in the liquid. Higher capillary pressure can change the phase change temperature of the fluid (e.g., freezing point), which in turn affects the heat of fusion.
- In narrow pores, fluid molecules are strongly adsorbed on the pore walls, which changes their thermodynamic properties. These surface interactions can lead to a change in the phase change heat compared to free water [42].
- In very narrow pores, fluids can adopt molecular structures different from those in the free state. This change in structure can affect the energy required for a phase transition, often increasing the heat of the phase transition.
- (1)
- Adsorbed water forms a partially ordered structure due to interactions between water molecules and the pore surface. These interactions reduce the energy needed to change the phase of water, resulting in a lower heat of phase change.
- (2)
- The thickness of the non-freezable adsorbed water layer is more significant when the pores are filled with water than when there are only a few layers of water on the pore surface. Non-freezing water is closely bound to the pore surface, and the amount of it depends on the degree of pore filling. When the pores are completely filled with water, more water interacts with the pore surface, which increases the thickness of the non-freezing water layer. As a result, the heat released during the phase change is converted into a less significant mass of freezable water.
3.4. Thermoporometry—Pore Size Distribution
4. Conclusions
- (1)
- For all rocks examined using the DSC method, a significant share of endothermic effects was observed in the range of −30 to −2 °C. The higher the phase change energy in this temperature range, the greater the observed share of ice calculated on the basis of endothermic effects to the amount of water. For the dolomite DO1, regardless of the adopted equation for the heat of phase change, the calculated amount of ice is greater than the amount of water. This fact suggests that the values of the heat of phase change in some systems may be higher than 334.2 J/g.
- (2)
- The thickness of the non-freezing water layer has the greatest impact on the cumulative pore volume calculated using the TMP method. The smallest difference between the theoretical porosity and the accumulated pore volume obtained by the TMP method is obtained by assuming a constant value of the heat of phase change and zero thickness of the non-freezing layer. The calculated pore volume corresponding to the melting of ice is particularly sensitive to assumptions about the thickness of the non-freezing layer of adsorbed water.
- (3)
- The obtained conclusions suggest the need for further research on the phase change of water in a porous medium and the thickness of non-freezable water.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
DSC | differential scanning calorimetry method |
ESUM | total energy of phase change |
Ei | amount of energy of phase change at temperature Ti |
L(T) | heat of phase change |
MIP | mercury intrusion porosimetry method |
mice-total | cumulative calculated cumulative |
ms | dry mass of the rock |
mw | water mass |
nv | volumetric absorption |
P | porosity |
rcl | radius of liquid–solid interphase curvature |
rgl | radius of gas–liquid interphase curvature |
rp | pore radius |
r1, r2 | radii of interface curvature. |
T | temperature |
T0 | freezing temperature of bulk liquid 273.2 K |
TMP | thermoporometry method |
Vfreezable | volume occupied by freezing water, |
Vl | volume of liquid |
Vnonfreezable | volume occupied by non-freezing water strongly adsorbed to the pore surface |
Vs | volume of skeleton |
Vsample | sample volume |
γlc | solid–liquid surface tension |
γcl | surface tension at the solid–liquid interface, |
γcg | surface tension at the solid–gas interface, |
ΔT | difference between the temperature T and the temperature 273.2 K |
θ | contact angle |
νm | liquid density |
ρs | density |
ρw | water density |
ρl | density of liquid |
Appendix A
Appendix B
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Rock Code | Material Description |
---|---|
DO1 | Fine-crystalline ankerite-calcite dolomite rock with a crystalline structure and massive texture (Figure A1). The dolomite rock is composed of ankerite (CaFe(CO3)2) with an admixture of dolomite. The rock’s volume consists of 80% crystals 30 to 90 μm in size. |
CA1 | Microsparitic limestone with calcite veins, characterized by a very fine crystalline structure and a random, massive texture (Figure A1). The sample is 100% composed of calcite (Figure A2); 55% of it is microspar (crystals with a diameter of 5–10 μm). |
CA2 | The calcite content in the rock is over 95% (Figure A2). Quartz is also detected, in small amounts, and calcite veins are observed in optical microscopy. Minerals sized between 15–60 μm constitute 97% of the sample. |
Rock Code | Density— MIP (kg/m3) | Density— Hydrostatic Method (kg/m3) | Density— Le Chatelier * (kg/m3) | Apparent Density—MIP (kg/m3) | Apparent Density—Hydrostatic Method (kg/m3) | Porosity—MIP (%) | Porosity—Hydrostatic Method (%) |
---|---|---|---|---|---|---|---|
DO1 | 2839 | 2840 | 2827 | 2765 | 2772 | 2.59 | 2.41 |
CA1 | 2708 | 2718 | 2717 | 2675 | 2679 | 1.24 | 1.43 |
CA2 | 2724 | 2724 | 2710 | 2688 | 2681 | 1.49 | 1.57 |
Rock Code | Sample Code | ms—Dry Mass (g) | mw—Water Mass (g) |
---|---|---|---|
DO1 | DO1.1 | 22.4863 | 0.1669 |
DO1.2 | 24.0267 | 0.1673 | |
CA1 | CA1.1 | 27.4902 | 0.0540 |
CA1.2 | 26.8650 | 0.0686 | |
CA2 | CA2.1 | 27.6880 | 0.0668 |
CA2.2 | 27.4585 | 0.1008 | |
ms—dry mass of the rock, mw—mass of water in the sample, calculated on the basis of the difference between the mass of the sample saturated with water and the mass of ms. |
Sample Code | Total energy (J/g) | Energy for T < −20 °C (J/g) | Energy for −20 °C ≤ T < −2 °C (J/g) | Energy for T > −2 °C (J/g) |
---|---|---|---|---|
DO1.1 | 2.578 | 0.313 | 0.376 | 1.889 |
DO1.2 | 2.526 | 0.133 | 0.461 | 1.922 |
CA1.1 | 0.656 | 0.026 | 0.249 | 0.380 |
CA1.2 | 0.828 | 0.053 | 0.331 | 0.443 |
CA2.1 | 0.466 | 0.039 | 0.179 | 0.247 |
CA2.2 | 0.668 | 0.033 | 0.250 | 0.384 |
Sample Code | The Mass of Water in the Sample (g) | Calculated Total Ice Mass (g) | The Ratio of the Calculated Total Ice Mass to the Water Mass mice-total/mw (g/g) | ||
---|---|---|---|---|---|
A Variant | B Variant | A Variant | B Variant | ||
DO1.1 | 0.1669 | 0.1744 | 0.1770 | 1.06 | 1.06 |
DO1.2 | 0.1673 | 0.1820 | 0.1844 | 1.09 | 1.10 |
CA1.1 | 0.0540 | 0.0542 | 0.0552 | 1.00 | 1.02 |
CA1.2 | 0.0686 | 0.0669 | 0.0686 | 0.98 | 1.00 |
CA2.1 | 0.0668 | 0.0388 | 0.0400 | 0.58 | 0.60 |
CA2.2 | 0.1008 | 0.0551 | 0.0563 | 0.55 | 0.59 |
Rock Code | Sample Volume (cm3) | Volume Occupied by Water (cm3) | Volumetric Water Absorption (%) |
---|---|---|---|
DO1.1 | 8.13 | 0.167 | 2.05 |
DO1.2 | 8.75 | 0.167 | 1.91 |
CA1.1 | 10.28 | 0.054 | 0.53 |
CA1.2 | 10.04 | 0.069 | 0.68 |
CA2.1 | 10.30 | 0.067 | 0.65 |
CA2.2 | 10.22 | 0.101 | 0.99 |
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Stępień, P.; Spychał, E.; Nartowska, E. The Phase Change Heat of Water in the Pore Space of Rocks Based on DSC Studies. Materials 2024, 17, 4049. https://doi.org/10.3390/ma17164049
Stępień P, Spychał E, Nartowska E. The Phase Change Heat of Water in the Pore Space of Rocks Based on DSC Studies. Materials. 2024; 17(16):4049. https://doi.org/10.3390/ma17164049
Chicago/Turabian StyleStępień, Piotr, Edyta Spychał, and Edyta Nartowska. 2024. "The Phase Change Heat of Water in the Pore Space of Rocks Based on DSC Studies" Materials 17, no. 16: 4049. https://doi.org/10.3390/ma17164049