- Email: [email protected]
Study on phase changes of ice and salt in saline soils
Cold Regions Science and Technology 172 (2020) 102988
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Study on phase changes of ice and salt in saline soils Xusheng Wan a b
a,b
a,⁎
b
b
T b
, Enlong Liu , Enxi Qiu , Mengfei Qu , Xiang Zhao , F.J. Nkiegaing
b
State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and Hydropower, Sichuan University, Chengdu 610065, China School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu 610500, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Sulfate saline soils Phase change Thermodynamic principle Cooling temperature curve Unfrozen water content
The occurrence of different ice and salt phases in saline soils may result in severe failure in engineering practice. Therefore, studying the phase changes of these two components may improve the understanding of saline soils. Through a series of cooling experiments on sulfate saline soils, the internal temperature variation of soils is obtained to study the rule of salt crystallization and the effect of salt on liquid water content. Based on the thermodynamic principle, the heat transfer equation is expressed considering the phase changes of ice and salt, and the control volume approach is applied to discretize the differential equation of heat transfer. Combined with the internal temperature curve of the soils, the discrete equations allow the calculation of ice porosity variation, salt crystal porosity, and unfrozen water content in saline soils. Additionally, the equations provide a useful general criterion for salt crystallization at different temperatures. Experimental and theoretical results confirm that unfrozen water content in saline soils decreases as the salt content increases, and that liquid water content is lower in salt-free soils. In addition, the concentration of salt solution in soils with low salt content increases owing to the phase change between water and ice; salt crystallization can only occur if the concentration reaches 20% at a negative temperature.
1. Introduction Saline soils, a generic term for solonchak and alkali soils, are widely distributed across China and constitute 2% of the total land area. Sulfate saline soils are most prevalent in Sinkiang, Qinghai, Gansu, Ningxia, Shaanxi, and Inner Mongolia (Wan et al., 2019). Currently, this phenomenon is crossing the borders of China and spreading worldwide to the Mediterranean basin, California, and Southeast Asia (Serrano and Gaxiola, 1994; Shaterian et al., 2005), where the scale of the soil salinity problem is increasing. Moreover, frozen saline soil is a typical feature of the Arctic coast and Central Siberia (Hivon and Sego, 1993; Bohren and Albrecht, 1998). Air temperature alterations between cold and warm periods will result in a significant transformation in the physical and mechanical properties of saline soils, owing to recurrent salt crystallization and deliquescence in soils. The resulting salt expansion and frost heave in saline soils; together with physical and chemical reactions, they represent a significant obstacle for the construction of local infrastructures, such as transportation, industry, and civil construction. Salt crystallization is the primary reason for salt expansion in sulfate soils. It begins as sodium sulfate decahydrate forms, which causes salt expansion (Steiger and Asmussen, 2008; Hamilton and Hall, 2008;
⁎
Shafiezadeh et al., 2018). However, this phenomenon can occur only if the supersaturation ratio of the solution is greater than its initial value and the condition of relative humidity for soils is satisfied. Scholars have used the Pitzer model to calculate the supersaturation ratio of salt solution in porous media (Steiger, 2005; Espinosa et al., 2008; Partanen et al., 2014). The initial supersaturation ratio and temperature are considered important conditions for estimating the crystallization and dissolution of salt. Mokni et al. (2010) developed a salt transfer coupled model by considering the soil constitutive relationship. Combining their model with the balanced equation of salt crystallization and dissolution, the rule of salt expansion deformation at room temperature can be solved. Dynamic models were established successively based on the thermodynamic principle in a porous medium to discuss the processes of salt crystallization and growth (Koniorczyk, 2012; Derluyn, 2012; Wu et al., 2017). However, most of the aforementioned research studies primarily concentrated on salt crystallization and the initial supersaturation ratio in brick, concrete, rock, and other construction materials, instead of soil. When soil related to salt phase change is examined, salt expansion is generally studied at the normal temperature or under steady-salt crystallization. Wan et al. (2017a) provided the initial supersaturation ratio of solutions and the initial crystallization temperature in saline soils at a negative temperature; however, predictability
Corresponding author. E-mail address: [email protected] (E. Liu).
https://doi.org/10.1016/j.coldregions.2020.102988 Received 4 July 2019; Received in revised form 31 December 2019; Accepted 5 January 2020 Available online 07 January 2020 0165-232X/ © 2020 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
as that of the in situ soil. The mass water content of all soils was close to 18% after the vacuum saturation process; soil deformation was controlled by the lid of the aluminum box and a minute displacement was allowed.
regarding the dynamic variation of salt and ice crystals is lacking. Currently, a few methods are available for testing salt concentration change in saline soils at a negative temperature. Many experimental studies focused on the relationship between unfrozen water content and temperature. Additionally, scholars have regressed this relationship as an exponential or power function using a large number of experimental data, based on which the theoretical model of frost heave has been established for frozen soil (Ishizaki et al., 1996; McKenzie et al., 2007; Ge et al., 2011; Lai et al., 2014; Song and Dang, 2018; Xu et al., 2019a; Xu et al., 2019b). Based on the chemical potential energy balance of ice and water, the Clapeyron equation establishes the ice–water pressure balance relationship under different temperatures, and it is widely used in water-heat models for numerical calculations (Zhou and Li, 2012; Kurylyk and Watanabe, 2013; Painter and Karra, 2014; Wan et al., 2015; Wu et al., 2018; Dall'Amico et al., 2011). The relationship between the water freezing curve and soil water potential energy has been established by combining the Clapeyron equation and the soil–water characteristic curve (Kurylyk and Watanabe, 2013; Zhou et al., 2019). Moreover, the pore size distribution in soils has been applied to estimate unfrozen water content at different temperatures (Kozlowski, 2016; Wang et al., 2017). However, most studies focused on the phase transition between ice and water of soils without salt content. When saline soils are involved, only the effect of salt on freezing temperature is considered. Coupling issues regarding water freezing and salt crystallization as well as ice content are not included during temperature change. Typical sodium sulfate soils are the research subject of this study. A thermal conduction equation considering ice and salt phase changes is proposed based on the thermodynamic principle. A series of laboratory cooling tests on sulfate soils was designed at temperatures ranging from room temperature to −20 °C. The rule of salt crystallization and liquid water content, varying with temperature, were studied through experimental and theoretical analyses. This research is valuable for understanding the properties of saline soils and studying the land surface processes of sulfate saline soils in cold regions.
2.2. Experimental apparatus and testing method Thermistors (accuracy of ± 0.01 °C) were inserted into the centers of the samples encased by waterproof plastic sheets, and a preformed hole was sealed using plasticine. Subsequently, the samples were placed in a cold bath (accuracy of ± 0.05 °C) at a constant temperature of 25 °C for 30 min or longer. Next, the temperature decreased to −20 °C and the samples were stored at this temperature for 2 h. The cooling rate of the cold bath ranged from 0.75 to 0.85 °C/min. The data acquisition system was a DT80 date taker with the interval set to 10 s. Salt crystallization and phase change between water and ice increased the soil temperature by releasing the latent heat of phase change. Therefore, the initial temperature of salt crystallization and water freezing can be ascertained from the jump point on the cooling curve.
2.3. Experimental results The cooling curves of sulfate soils are shown in Fig. 1. The initial freezing temperature of each soil sample is shown as a green line, and the onset temperature of salt crystallization is denoted by a red line. The initial freezing temperature of sodium sulfate soils decreases as the salt content increases (the concentration of salt solution increases); however, their initial freezing temperature (freezing point) increases rapidly and then decreases as the salt content increases when the salt crystallizes above the initial freezing temperature. The cooling curve of the temperature rises slightly at −11.4 °C as a result of salt crystallization, when the concentration of salt solution is 4.44%; the onset temperature of salt crystallization increases with the concentration. When the concentration is greater than or equal to 10%, the salt crystallizes above the freezing point of the soils. For salt solutions with low salt concentration, the temperature difference on the cooling curve is not evident owing to low crystallization. Therefore, the internal temperature difference with time can be adopted to ascertain the onset temperature of salt crystallization for soils with low salt content, such as 0.7–0.9%. The results are shown in Fig. 2. A phase change between ice and water occurs when the soil temperature decreases to the freezing point, and the temperature difference appears as a sudden increase or decrease on the curve. When the concentration of the salt solution is equal to or > 4.44%, the internal temperature difference exhibits an increasing trend in a small time period after a large number of phase changes between ice and water, which is caused by the increase in soil temperature owing to the heat released by salt crystallization (Fig. 2). However, for a 3.89% concentration salt solution, such an increase is not observed in the temperature difference curve; therefore, it can be deduced that salt crystals are not generated when the concentration is < 3.89% above −20 °C.
2. Experiment design 2.1. Soil samples and related parameters The soil sampled in our study was collected from Beiluhe, on the Chinese Qinghai–Tibet Plateau, located in the continuous permafrost zone. The soil was locally salinized and sodium sulfate is the most prevalent in the study area. The mass water content in situ was 18%, with a plastic limit of 14.5% and a liquid limit of 23.8%. The original soil samples were desalinated repeatedly with distilled water to remove the effects of other ionic components. The soil samples were subsequently dried, crushed, and sifted. The soil particle distribution is shown in Table 1. The soil samples were prepared at room temperature, and salt contents of the samples were 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0%, 1.1%, 1.2%, 1.4%, 1.6%, 1.8%, 2.1%, 2.3%, 2.6%, 2.9% and 3.2%, for the concentrations of salt solution of 0%, 0.56%, 1.11%, 1.67%, 2.22%, 2.78%, 3.33%, 3.89%, 4.44%, 5.00%, 5.56%, 6.11%, 6.67%, 7.78%, 8.89%, 10.00%, 11.67%, 12.78%, 14.44%, 16.11%, and 17.78%, respectively. The prepared samples were sealed at 25 °C for 24 h to ensure a uniform distribution of ions and water. Next, the test samples were inserted into iron boxes of diameter 3.3 cm and height 3.8 cm, and the dry density of the test samples was controlled to 1.82–1.84 g/cm3; hence, their density remained the same
3. Analysis of ice and salt phase changes 3.1. Heat balance equation and key thermal parameters In the cooling process of sulfate saline soils, when the concentration of the salt solution exceeds a specific supersaturation state, salt crystallization is initiated, and the phase change between water and ice appears at a negative temperature. Without considering fluid motion in soils, the heat balance equation can be expressed as Eqs. (1-a), (1-b) when the phase change occurs in saturated saline soils (Wu et al., 2017).
Table 1 Soil particle distribution. < 1 μm 14.5%
1–5 μm 38.5%
5–10 μm 23.2%
10–20 μm 15.4%
> 20 μm 8.4%
2
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 1. Cooling curves of sodium sulfate soils (T0 is the temperature of the cold bath and Tin refers to the core temperature of the soil samples).
refers to the heat conductivity coefficient of substance j; T is the temperature. Soil is a three-phase loose system, and the following relationship exists in saturated soils:
⎡⎛ ∂ (Lcryst nc ρc ) ∂ (L wi ni ρi ) ⎞ ⎤ ⎞ ⎤ ∂ ⎡⎛ = ∇ ⎢ ∑ λ j n j ∇T ⎥ − ⎢ ∑ cj nj ρj ⎟ T⎥ − ⎜ ⎟ t t ∂ ∂t ⎢ ⎜ j ∂ ⎢ ⎠ ⎥ ⎠ ⎥ ⎣⎝ j ⎦ ⎣⎝ ⎦ (1-a)
∑ nj = 1
⎡⎛ ∂ (Lcryst nc ρc ) ∂ (L wi ni ρi ) ⎞ ⎤ ⎞ ⎤ ∂ ⎡⎛ = ∇ ⎢ ∑ λ j n j ∇T ⎥ − ⎢ ∑ cj nj ρj ⎟ T⎥ − ⎜ ⎟ t t ∂t ⎢ ⎜ j ∂ ∂ ⎢ ⎠ ⎥ ⎠ ⎥ ⎦ ⎣⎝ ⎣⎝ j ⎦ (1-b)
(2)
j
For the salt solution, the heat conductivity coefficient λl can be calculated using Eq. (3) (Wang and Sun, 2002): −3/2
λ −2/3 βwc ⎞ + λe−2/3 wc + λl = ⎜⎛ w ⎟ wc + 1 ⎠ w ⎝ c+1
where cj refers to the specific heat capacity of substance j; j = c, i, l, s represents salt crystal, ice, salt solution, and soil particle, respectively; ρj refers to the density of substance j; nj refers to the ratio of volume occupied by substance j to the total volume of soil; Lcryst is the crystallization enthalpy; Lwi is the latent heat of water during freezing; λj
(3)
where λw is the heat conductivity coefficient of pure water, λe the heat conductivity coefficient of electrolyte, wc the concentration of the salt
Fig. 2. Internal temperature difference of sodium sulfate soils (Tc refers to the metastable supercooling temperature, Tf the freezing point, and Ts the temperature of salt crystallization). 3
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
solution (the mass of dissolved solute per unit mass), and β the related constant. The heat conductivity coefficient of pure water changes with temperature; this rule can be regressed by the obtained experimental data (Li and Fu, 2007), and the specific relationship is written as follows:
λ w = 0.56 − 9.08 × 10−6T 2 + 2.0966 × 10−3T
follows:
Lcryst = f (wc , T ) ≈ (14.169T − 252.84) wc2 + ( −10.474T + 212.88) wc + (−0.019T 2 − 0.6737T − 201.48) (8)
(4)
The phase diagram of sodium sulfate solution exhibits a close relationship with temperature (Koniorczyk, 2012). When the temperature is lower than 32.4 °C and the concentration of sodium sulfate solution is higher than its saturated concentration, sodium sulfate appears in the sodium sulfate decahydrate form (mirabilite). The change in salt concentration is primarily determined by salt crystallization and the phase change between water and ice. Water molecules will be transformed when sodium sulfate undergoes crystallization, which results in a decrease in salt concentration. On the contrary, a continuous phase transition between water and ice deteriorates the quality of the solvent (water); therefore, the salt concentration increases. Mirabilite cannot be generated in a relatively low humidity. Considering the approximate saturated soil samples designed in a closed system, the effect of relative humidity on salt crystal morphology is not considered in our calculation; therefore, mirabilite is assumed to be generated in the cooling process only if the supersaturation ratio exceeds its initial value. Because the liquid transfer is not considered in the theoretical model, the frost and salt heave are small. If we confine the displacement of the soil, the following relationship exists:
According to Eqs. (3) and (4), the heat conductivity coefficient of the salt solution is affected by both temperature and concentration; therefore, λl can be expressed as a function of concentration and temperature.
λl = f (wc , T )
(5)
Regarding the change in specific heat capacity of pure water in a specific temperature range, the effect of temperature on cl cannot be ignored; therefore, cl can be regressed as a function of salt concentration and temperature by experimental data, as follows (Pruppacher and Klett, 1997; Li and Fu, 2007): (6-a)
cl = −0.044wc + c w where
c w = 4180, T ≥ 0°C 4
c w (T ) =
∑ aj T j, T < 0°C (6-b)
j=0
with T in °C; a0 = 4.18 × 10 , a1 = −11.3, a2 = −9.71 × 10−2, a3 = 1.83 × 10−2, and a4 = 1.13 × 10−3. For a low concentration of salt solution, for calculation convenience, we assumed that the volume of the solution is equal to the volume of water. Hence, 3
ρl ≈ ρw (1 + wc )
n 0 ≈ nc + ni + nl
(9)
where n0 is the initial porosity of soils. The concentration of the salt solution can be formulated as Eq. (10) without considering the relocation diffusion of the concentration:
(7)
wc =
Lcryst increases as the temperature decreases or the salt concentration increases, using the relation shown in Fig. 3 (Espinosa and Scherer, 2008). Both temperature and salt concentration significantly affect the crystallization enthalpy of mirabilite (Fig. 3). Through data fitting, Lcryst can be expressed as a quadratic polynomial of the salt solution, and the coefficients are a function of temperature. The expression of Lcryst is as
ρw wc,0 n 0 − ρc nc MS / M ρw (n 0 − nc − ni )
(10)
where M is the relative molecular mass of mirabilite, Ms the relative molecular mass of sodium sulfate, and wc,0 the initial concentration of the salt solution. The partial differential of each variable parameter mentioned previously can be expressed as
Fig. 3. Crystallization enthalpy of mirabilite. 4
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
∂Lcryst
coordinates are expressed as follows:
∂f (wc , T ) ∂wc ∂f (wc , T ) ∂T + = ∂wc ∂t ∂T ∂t ∂t ∂cl ∂cl ∂wc ∂cl ∂wc = + ∂t ∂wc ∂t ∂wc ∂T ∂wc ∂wc ∂nc ∂wc ∂ni = + ∂t ∂nc ∂t ∂ni ∂t
x = r cos φ y = r sin φ z=z
(15)
where r refers to the radius of the cylinder, φ the angle, and z the height of the cylinder. Because x and y is a function of r and φ, therefore
(11)
where
∂φ ∂x ∂φ ∂y
ρ Ms wc,0 n 0 ∂wc nc 1 ⎤ = − c ⎡ + ⎢ (n 0 − ni − nc )2 ⎥ ∂nc (n 0 − ni − nc )2 ρw M ⎣ (n 0 − ni − nc ) ⎦ ρc Ms wc,0 n 0 ∂wc nc = − ∂ni (n 0 − ni − nc )2 ρw M (n 0 − ni − nc )
∂T ∂T ∂r ∂T = + ∂x ∂r ∂x ∂φ ∂T ∂T ∂r ∂T = + ∂y ∂r ∂y ∂φ
Therefore, based on the functional relationship above, Eqs. (1-a), (1b) can be simplified to
When we substitute Eqs. (15) and (16) into Eq. (12), the differential equation of heat conduction can be obtained using coordinate transformation, as follows:
∂T ∂n ∂n + LC c + Li i = ∇ (λ∇T ) ∂t ∂t ∂t
LT
(12)
LT
where
(16)
∂T ∂n ∂n 1 ∂ ⎛ ∂T ⎞ 1 ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ + LC c + Li i = + 2 λ ⎜λ ⎟ + λ ∂t ∂t ∂t r ∂r ⎝ ∂r ⎠ r ∂φ ⎝ ∂φ ⎠ ∂z ⎝ ∂z ⎠ (17)
LT = cc ρc nc + ci ρi ni + cs ρs (1 − n 0) + ρc nc
∂Lcryst
Multiplying both sides of this equation by r, followed by integrating the partial differential equation when the cooling time increases by △t, we obtain
∂T
LC = ρc cc T + ρc Lcryst +
∂Lcryst ∂ws ⎡ ∂c ρc nc − (ρw nl + ρw wc nl ) l − ρw cl nl ⎤ ⎥ ∂nc ⎢ ∂wc ∂wc ⎦ ⎣
t + Δt
∫ ∭ r ⎛⎝LT ∂∂Tt
∂Lcryst ∂ws ⎡ ∂c ρn − (ρw nl + ρw wc nl ) l − ρw cl nl ⎤ ⎥ ⎢ c c ∂wc ∂ni ⎣ ∂wc ⎦ λ = λi ni + λ c nc + λs (1 − n 0) + λl (n 0 − ni − nc )
Li = ρi ci T + ρi L wi +
1+
T f∗ T ∗f R Lwi
t
V
⎣
⎜
⎟
⎝
⎠
⎝
⎠⎦
(18)
where V refers to the volume of the representative elementary volume. The control volume approach was adopted to discretize the differential equation of heat transfer, and the process is detailed in the Appendix. In the calculation, the boundary conditions are stated as follows:
− T f∗ ln a w
V
∂nc ∂n + Li i ⎞ drdφdzdt = ∂t ∂t ⎠
∫ ∭ ⎡⎢ ∂∂r ⎛⎝λr ∂∂Tr ⎞⎠ + 1r ∂∂φ ⎛λ ∂∂Tφ ⎞ + r ∂∂z ⎛λ ∂∂Tz ⎞ ⎤⎥ drdφdzdt
When T > Tf,initial, ni = 0. Tf,initial is the initial freezing temperature of soil; for sulfate saline soils, the freezing temperature Tf can be calculated using the following equation (Wan et al., 2015):
Tf =
t t + Δt
+ LC
⎧ r = 1.65cm ⎪ z = 1.9cm ⎨ T = T0 ⎪ 0 ≤ φ ≤ 2π ⎩
(14)
where T⁎f refers to the freezing temperature of pure water, i.e., 273.15K; R is the gas constant; aw is the water activity, which is a function of the salt solution concentration, and the value decreases as the concentration increases. The cooling of soil samples in the experiment is a heat transfer problem in cylindrical coordinates, and the temperature at any point can be shown, as in Fig. 4. The mathematical relationships between cylindrical and rectangular
(19)
The central temperatures of Tin can be obtained in the test and hence can be considered a known quantity. In the calculation at a random time △tk (k = 1, 2, 3, …), when △nc,k or △ni,k < 0, we used △nc,k or △ni,k = 0. The basic soil parameters and related thermodynamic parameters are shown in Table 2. The change of internal temperature in soils shown in Fig. 1 at any time △tj can be written as follows:
Tj = Tj − 1 + ΔTj
(20)
The above experiment shows that salt will not crystallize when salt content is < 0.7% and nc = 0. Moreover, the internal temperature change Tin can be obtained from our test data shown in Fig. 1. The porosity occupied by ice and unfrozen water at any time △tj can be expressed using Eq. (21) as follow:
ni, j = ni, j − 1 + Δni, j nl, j = n 0 − ni, j
(21)
Two variables (ice and salt crystal content) appear when the salt crystallizes above or below the freezing point (Fig. 1). However, the equation presented above cannot be solved for two unknown variables. Therefore, we assumed that salt crystallization caused the cooling curve to shift toward the right in the coordinate system. If no salt crystal is formed, the cooling curve will change as per the dashed line shown in Fig. 5 (similar to the cooling curve of soils without salt). For example, the ice volume content can be calculated based on the curve of the dashed line, assuming that a phase change occurs between ice and water (using Eq. (A.4)). Therefore, the porosity occupied by ice can be
Fig. 4. Temperature at any point in cylindrical coordinates. The dashed cylinder represents the soil sample, arrows show the direction of heat transfer, and T0 is the boundary condition decided by the temperature of the cold bath. 5
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Table 2 Table of symbols used. Symbols
Name
Value or Range
T T0 Tf,initial aw T⁎f R Lwi Lcryst cw ci cl cs cc λl λw λe λi λs λc ρw ρdry ρs ρc ρi ρl n n0 ni nc ns Ms M β
temperature temperature of cold bath initial freezing temperature of soil water activity absolute temperature gas constant latent heat of water freezing latent heat of salt crystallization specific heat capacity of water specific heat capacity of ice specific heat capacity of salt solution specific heat capacity of soil particle specific heat capacity of salt crystal thermal conductivity of salt solution thermal conductivity of water thermal conductivity of electrolyte thermal conductivity of ice thermal conductivity of soil particle thermal conductivity of salt crystal density of water density of dry soil density of soil particle density of salt crystal density of ice density of salt solution soil porosity initial soil porosity soil porosity of ice soil porosity of salt crystal soil porosity of soil particle relative molecular mass of Na2SO4 relative molecular mass of Na2SO4•10H2O constant term
273.15 8.314 333.7
1874 (Lai et al., 2014) 2360 (Lai et al., 2014) 1920
0.285 2.22 (Lai et al., 2014) 1.2 (Wu et al., 2017) 0.5 1000 1820 2700 1465 917
0.33
0.67 142 322 −7.8773 × 10−3 (Wang and Sun, 2002)
Unit K or °C K or °C K or °C dimensionless K J/(K·mol) kJ/kg kJ/kg J/(kg·K) J/(kg·K) J/(kg·K) J/(kg·K) J/(kg·K) W/(m·K) W/(m·K) W/(m·K) W/(m·K) W/(m·K) W/(m·K) kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 dimensionless dimensionless dimensionless dimensionless dimensionless g/mol g/mol dimensionless
crystallization becomes stable when the temperature decreases, and the concentration of the salt solution approaches the saturated concentration (Wan et al., 2017a). Hence, salt crystallization below the freezing point can be calculated approximately according to the saturation concentration. The saturated concentration of sodium sulfate solution can be expressed as Eq. (22) (Wan et al., 2017a):
considered a known quantity to determine the change in salt crystal content combined with the real cooling curve. Salt crystallizes above the freezing point when the initial salt content of soils increases to 1.8%. A salt solution is always in the supersaturation state before salt crystallization occurs; therefore, when crystals separate from the salt solution, the concentration will decrease significantly owing to a large amount of mirabilite generation. Salt
Fig. 5. Assumed curve of saline soils without salt crystallization. 6
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 6. Variation in ice and salt crystal contents with temperature for different salted soils. a) Variation in ice and unfrozen water volume contents of saline soils with low salt; b) Variation in ice and salt crystal volume contents of saline soils in low temperature; c) Salt crystallization law of soils with high salt content; d) Variation in ice and salt crystal contents in highly salted soils with temperature.
wc, sat = 0.449 × 1.077T
The salt solution concentration increases as the soil temperature decreases, and salt crystals are generated only when the concentration reaches 20%. The salt crystal content increases as the soil temperature decreases, and the amount of salt crystals increases with the salt content; accordingly, the change in the corresponding concentration increases. The concentration of the salt solution with high salt content decreases quickly and tends to be stable. The increase in salt content decreases the ice content, with ice content becoming stable rapidly. Apart from the ice–water phase change, another part of the water transported by salt crystallization is transformed into the solid phase. Therefore, these soils with different salt contents change only slightly. The unfrozen water content of soils with 0.8%, 1.1%, and 1.4% salt content ranges from 5.0% to 5.9% at −20 °C (Fig. 6b). As shown in Fig. 6c, salt crystal content can be calculated based on the cooling curve before the transition phase between water and ice. A salt solution is always in the supersaturation state before salt crystallization occurs; therefore, when a crystal separates from the salt solution, the concentration will decrease considerably owing to the generation of a large amount of mirabilite. Salt crystallization becomes stable with decreasing temperature, and the salt solution concentration approaches the saturated concentration (Fig. 6c). Therefore, salt crystallization below the freezing point can be calculated approximately according to the saturation concentration. Ice and salt crystals are generated simultaneously, and their changes are shown in Fig. 6d.
(22)
where wc,sat is the saturated concentration, and T is < 32.4 °C. 3.2. Calculation results and analysis The variation in porosity occupied by ice and unfrozen water in different salted soils are shown in Fig. 6. The water in soils begins to freeze and the ice volume content increases when the soil temperature decreases to the freezing point; this increasing trend decreases continuously as temperature decreases and tends to be stable. The calculated result shows that the unfrozen water content is 5.4% at −20 °C in soils without salt. However, the ice content decreases slightly in soils with low salt content, while the unfrozen water content increases. For soils with 0.2% and 0.7% salt contents, the unfrozen water contents are 5.8% and 7% at −20 °C, respectively. The concentration of the salt solution can be calculated using Eq. (10), which increases as the temperature decreases. When temperature ranges from room temperature to −20 °C, the concentration of the solution in saline soils with a 0.2% salt content increases from 1.1% to 6%. For saline soils with a 0.7% salt content, the concentration increases from 3.9% to 18.2% at the same temperature change (Fig. 6a). Salt crystallizes when salt content increases. The variation of ice and salt crystals, unfrozen water content, and concentration of salt solution with temperature are shown in Fig. 6b. 7
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 7. Simulation and test values of soil temperature changing with time. The line is the calculated value and the small circle refers to the experimental data.
where S refers to the supersaturation ratio. The change rule of S with temperature is shown in Fig. 9. Initially, the supersaturation ratio increases as the temperature decreases when the salt solution enters the supersaturation state (S > 1) from the undersaturated state (S < 1). Once the supersaturation ratio becomes higher than the initial ratio, the salts will crystallize. In addition, the concentration of the solution decreases and reduces the supersaturation ratio (Fig. 9). The initial supersaturation ratio decreases as the initial salt content increases, which indicates that the salt crystallization formation is much easier for highly salty soils. If salt crystallization is only achieved below the freezing point, the initial supersaturation is much larger than that above the freezing point. Therefore, salt crystallization becomes increasingly difficult or crystallization is avoided as the initial salt content decreases. The external cooling rate affects the unsteady-state interval of sodium sulfate soils. Generally, the unsteady-state range decreases as the cooling rate decreases; hence, sodium sulfate decahydrate crystallizes more easily (Wan et al., 2017b). The initial supersaturation ratio is calculated at different temperatures, as shown in Fig. 10. The initial supersaturation ratio increases as temperature decreases, and it increases significantly when the temperature is lower than −2 °C. The Boltzmann function (black line in Fig. 10) and the exponential function (red line in Fig. 10) are used to describe the change rule of the initial supersaturation ratio with temperature; all their values are within the shaded portion between the two curves. The initial supersaturation ratio approaches the Boltzmann function at the temperature ranging from −8 to 8 °C, and the value is close to the exponential function in another temperature range. Furthermore, salt crystallization is more difficult in the temperature range from −3 to −12 °C, as the initial supersaturation ratio in this temperature range is typically 3–5 times higher than the ratio occurring above the freezing point. Furthermore, the heat balance equation above is suitable for other saline soils. For sodium chloride soils, salt phase change need not be considered owing to the stable characteristics of the sodium chloride solution; sodium chloride dihydrate forms only at extremely high concentrations and low temperatures (Swenne, 1983; Derluyn, 2012). Therefore, the calculation method is the same as that of sodium sulfate soils with low salt content; nc can be assumed as zero. The sole
At the freezing point, a large number of phase changes between water and ice cause the salt solution concentration to increase rapidly; hence, the salt crystal content increases at the freezing point. Subsequently, it changes weakly and tends to be stable as the water–ice phase transition occurs. Moreover, salt crystallization inhibits the formation of ice crystals; the more salt crystals are generated, the more the ice content decreases. For soils with 3.2% salt content, the salt crystal content is 2.9% greater than that of soils with 2.6% salt content; however, by contrast, the ice content decreases by 3% (Fig. 6d).
4. Discussion Next, we validate the current solution. Some numerical simulations have been performed to verify the accuracy of the heat transfer equation established in our study. The central temperature of sulfate saline soils without phase change was considered in our simulations, i.e., nc = ni = 0. It is clear from Fig. 7 that the heat transfer model can well simulate the change in soil temperature under the changing temperature of the cold bath. The accuracy of the calculation from Eq. (21) is verified by comparing the calculated results and the test value, as shown in Fig. 8. The calculations of water content without phase change are relatively close to those from the tests (Wen et al., 2012; Wan et al., 2015); therefore, the model can simulate the phase change as a function of temperature change. For salt crystallization above the freezing point, the unfrozen water content changes quickly at the freezing point and stabilizes at −8 °C. It is noteworthy that the amount of unfrozen water is less than that of soils without salt. When the salt contents are 2.6% and 3.2%, the unfrozen water contents are 4.3% and 4.5% at −20 °C, respectively, while the unfrozen water content of soil without salt is 5.6% at the same temperature. Therefore, the higher the salt content, the larger is its effect on the liquid water content (no phase change); this phenomenon results in a smaller unfrozen water content below the freezing point. The supersaturation ratio is defined as the ratio of the actual concentration of salt solution to its saturated concentration, as follows:
S=
wc wc, sat
(23) 8
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 8. Comparisons of calculation and test results.
Fig. 9. Supersaturation ratio of sodium sulfate soils varying with temperature.
5. Conclusions
difference between these two salts is their effect on the freezing temperature of soils. In general, a decrease in freezing point is more clearly shown by sodium chloride than sodium sulfate soils (Bing and Ma, 2011; Wan et al., 2015). For other unstable salts, the property is different. Their ice and salt transformations can be studied under the assumption in Section 3.1, based on the heat balance equation and the internal cooling curve of soils, provided that their crystalline morphologies and latent heats of phase change are known. Salt transfers, under the action of soil water potential, affects heat transfer when the temperature changes. Moreover, soil deformation caused by salt and frost heaving changes the volume ratio occupied by each substance, thereby varying the physical parameters. Hence, salt movement and more precise soil parameters pertaining to the salt and water phase change should be considered in future studies to explore the joint effect of salt and frost expansion in detail.
This paper presents a study on the change rule of salt crystallization and unfrozen water content according to the thermodynamic principle and cooling down tests of sulfate saline soils. Furthermore, the interaction between ice and salt phase changes is elaborated. The conclusions are summarized as follows: 1) When the concentration of salt solution in soils was < 4.44%, salt crystals did not generate at the temperature ranging from room temperature to −20 °C, and the concentration increased to 18.2% as the temperature decreased. Moreover, the unfrozen water content of these soils was higher than those of soils without salt. 2) Salt crystallization in soils could occur below the freezing point when the initial concentration of the salt solution was higher than 4.44% and tended to be stable as the temperature decreased. Only 9
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 10. Initial supersaturation ratio at different temperatures.
analyzed the results. Dr. Enlong Liu discussed the results, wrote and revised the manscript. Dr.Enxi Qiu, Dr. Mengfei Qu, Dr. Xiang Zhao, and Dr. F.J.Nkiegaing made contributions in designing the tests and analyzing the results.
salt crystallization below the freezing point could reduce the amount of ice content; the ice content decreased as the initial salt content increased, but the unfrozen water content indicated little change. 3) Salt crystallization formed above the freezing point in soils caused the unfrozen water content to be lower than that of soils without salt. Moreover, unfrozen water became stable in soils with a higher salt content at −10 °C; it did not change below this temperature. 4) Salt crystallization only occurred when the supersaturation ratio of salt solution was higher than the initial supersaturation ratio; this initial supersaturation ratio of sulfate soils was within the Boltzmann function range and exponential function intersection. The salt concentration approached saturation as the temperature decreased in highly salty soils. Additionally, the initial supersaturation ratio changed slightly at positive temperatures compared with the value below the freezing point. As the temperature decreased below the freezing point, it became increasingly difficult to initiate salt crystallization.
Declaration of Competing Interest The authors declare that there are no conflicts of interest regarding the publication of this paper. Paper title: Studying the Phase Changes of Ice and Salt in Saline Soils. The authors: Xusheng Wan, Enlong Liu, Enxi Qiu, Mengfei Qu, Xiang Zhao, F.J.Nkiegaing.
Acknowledgments This research was supported by the National Natural Science Foundation of China (41601068), Young Scholars Development Fund of Southwest Petroleum University (201599010104), and Scientific Research Starting Project of Southwest Petroleum University (2015QHZ025).
Author contribution statement Dr. Xusheng Wan performed the tests, wrote the manuscript and
Appendix A
10
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. A.1. Schematic diagram of control volume of cylinder. a, b, c, d, e, and f refer to the front, back, left, right, top, and bottom surface of microelement △v, respectively.
For any microelement, as shown in Fig. A.1, the left side of Eq. (18) can be simplified as follows: t + Δt
∫ ∭ rLT ∂∂Tt drdφdzdt = ra +2 rb
LT , a + LT , b Δr ΔφΔz Δt (Tp − T p0 ) 2
∫ ∭ rLc ∂∂ntc drdφdzdt = ra +2 rb
Lc, a + Lc, b Δr ΔφΔz Δt (nc, p − nc0, p ) 2
∫ ∭ rLi ∂∂nti drdφdzdt = ra +2 rb
L i, a + L i, b Δr ΔφΔz Δt (ni, p − ni0, p) 2
t t + Δt
V
t t + Δt
V
t
V
(A.1)
where Tp, nc,p, ni,p refers to the temperature, porosity occupied by salt crystal, and porosity occupied by ice crystal at point P, respectively. T0p, n0c,p, n0i,p are the Tp, nc,p, ni,p at the initial state. For n0c,p and n0i,p, their values are zero initially. The right side of Eq. (18) can be simplified as follows: t + Δt
∫ ∭ ∂∂r ⎛⎝λr ∂∂Tr ⎞⎠ drdφdzdt = ΔφΔz Δt ⎡⎢λb rb
t t + Δt
∫∭ t t + Δt
⎣
V
V
Tb − Tp (δr )b
Tp − Ta ⎤ (δr )a ⎥ ⎦
Tp − Tc ⎤ Td − Tp 1 ∂ ⎛ ∂T ⎞ rb Δz Δt ⎡λd ⎜λ ⎟ drdφdzdt = ln − λc ⎢ ( ) (δφ)c ⎥ δφ r ∂φ ⎝ ∂φ ⎠ ra d ⎣ ⎦
∫ ∭ r ∂∂z ⎛λ ∂∂Tz ⎞ drdφdzdt = ra +2 rb Δr ΔφΔt ⎡⎢λe t
− λa ra
V
⎝
⎠
⎣
Te − Tp (δz )e
− λf
Tp − Tf ⎤ (δz )f ⎥ ⎦
(A.2)
Assuming that the temperature variation is linear from the outside to the inside, for a cylinder sample, Eq. (18) can be simplified at any time △tj as follows:
LT , a + LT , b Lc, a + Lc, b L i, a + L i, b Δr ΔφΔz ΔTp, j + Δr ΔφΔz Δncp, j + Δr ΔφΔz Δni,pj= 2 2 2 T0, j − Tin, j T0, j − Tin, j 2 ⎡ ⎤ ΔφΔz (λb rb − λ a ra ) + (ra + rb )Δr Δφ (λ e − λ f ) ⎥ z r ra + rb ⎢ ⎦ ⎣
(A.3)
If no salt crystal is generated, then Eq. (A.3) can be transformed to
LT , a + LT , b L i, a + L i, b Δr ΔφΔz ΔTp, j + Δr ΔφΔz Δni,pj= 2 2 T0, j − Tin, j T0, j − Tin, j 2 ⎡ ⎤ ΔφΔz (λb rb − λ a ra ) + (ra + rb )Δr Δφ (λ e − λ f ) ⎥ z r ra + rb ⎢ ⎣ ⎦
(A.4)
The discrete formula can be used to calculate the variation in ice or salt crystal content with temperature change when the internal and external temperatures of soils are known; this process can be programmed using Matlab for calculations.
maximum temperature. Cold Reg. Sci. Technol. 122, 18–25. Kurylyk, B.L., Watanabe, K., 2013. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils. Adv. Water Resour. 60, 160–177. Lai, Y., Pei, W., Zhang, M., Zhou, J., 2014. Study on theory model of hydro-thermal–mechanical interaction process in saturated freezing silty soil. Int. J. Heat Mass Transf. 78, 805–819. Li, H.C., Fu, B., 2007. Practical Chemistry Handbook. Chemical Industry Press, Beijing (in Chinese). McKenzie, J.M., Voss, C., Siegel, D., 2007. Groundwater flow with energy transport and water–ice phase change:Numerical simulations, benchmarks, and application to freezing in peat bogs. Advanced Water Resources 30, 966–983. Mokni, N., Olivella, S., Alonao, E.E., 2010. Swelling in clayey soils induced by the presence of salt crystals. Appl. Clay Sci. 47, 105–112. Painter, S.L., Karra, S., 2014. Constitutive model for unfrozen water content in subfreezing unsaturated soils. Vadose Zone J. 13 (4), 334–338. Partanen, J.I., Hasan, M., Vahteristo, K.P., 2014. Determination of the Pitzer Interaction Parameters at 273.15 K from the Freezing-Point Data Available for Solutions of UniUnivalent Electrolytes. Indystrial & Engineering Chemistry Research 53 (49), 19351–19358. Pruppacher, H.R., Klett, J.D., 1997. Microphysics of Cloulds and Precipitation. Kluwer Acadamic Pubishers, New York, Bston, Dordrecht, London, Moscow. Serrano, R., Gaxiola, R., 1994. Microbial models and salt stress tolerance in plants. Crit. Rev. Plant Sci. 13 (2), 121–138. Shafiezadeh, M., Moradi, H., Fakheran, S., 2018. Evaluating and modeling the spatiotemporal pattern of regional-scale salinized land expansion in highly sensitive shoreline landscape of southeastern Iran. Journal of Arid Land 10 (6), 946–958. Shaterian, J., Waterer, D., De Jong, H., Tanino, K.K., 2005. Differential stress responses to NaCl salt application in early-and late-maturing diploid potato clones. Environ. Exp. Bot. 54 (3), 202–212. Song, M.S., Dang, C.B., 2018. Review on the measurement and calculation of frost characteristics. Int. J. Heat Mass Transf. 124, 586–614.
References Bing, H., Ma, W., 2011. Laboratory investigation of freezing point of saline soil. Cold Reg. Sci. Technol. 67, 79–88. Bohren, C.F., Albrecht, B.A., 1998. Atmospheric Thermodynamics. Oxford Univeristy Press, New York. Dall’Amico, M., Endrizzi, S., Gruber, S., Rigon, R., 2011. A robust and energy –conserving model of freezing variably-saturated soil. Cryosphere 5, 469–484. Derluyn, H., 2012. Salt Transport and Crystallization in Porous Limestone: Neutron-X-Ray Imaging and Poromechanical Modeling. PhD Dissertation. University of Zurich, Zürich, pp. 9–27. Espinosa, R.M., Scherer, G.W., 2008. Study of sodium sulfate salts crystallization in limestone. Environ. Geol. 56, 605–621. Espinosa, R.M., Franke, L., Deckelmann, G., 2008. Phase changes of salts in porous materials: crystallization, hydration and deliquescence. Constr. Build. Mater. 22, 1758–1773. Ge, S., McKenzie, J., Voss, C., Wu, Q., 2011. Exchange of groundwater and surface-water mediated by permafrost response to seasonal and long term air temperature variation. Geophys. Res. Lett. 38, L14402. https://doi.org/10.1029/2011GL047911. Hamilton, A., Hall, C., 2008. Sodium sulfate heptahydrate: a synchrotron energy-dispersive diffraction study of an elusive metastable hydrated salt. J. Anal. At. Spectrom. 23 (6), 840–844. Hivon, E.G., Sego, D.C., 1993. Distribution of saline permafrost in the Northwest Territories, Canada. Can. Geotech. J. 30, 506–514. Ishizaki, T., Maruyama, M., Furukawa, Y., Dash, J., 1996. Premelting of ice in porous silica glass. J. Cryst. Growth 163 (4), 455–460. Koniorczyk, M., 2012. Salt transport and crystallization in non-isothermal, partially saturated porous materials considering ions interaction model. Int. J. Heat Mass Transf. 55 (4), 665–679. Kozlowski, T., 2016. A simple method of obtaining the soil freezing point depression, the unfrozen water content and the pore size distribution curves from the DSC peak
11
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Wen, Z., Ma, W., Feng, W., Deng, Y., Wang, D., Fan, Z., Zhou, C., 2012. Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibet silty clay. Environmental Earth Science 66 (5), 1467–1476. Wu, D., Lai, Y., Zhang, M., 2017. Thermo-hydro-salt-mechanical coupled model for saturated porous media based on crystallization kinetics. Cold Reg. Sci. Technol. 133, 94–107. Wu, D., Zhou, X., Jiang, X., 2018. Water and Salt Migration with phase Change in Saline Soil during Freezing and Thawing Processes. Groundwater 56 (5), 742–752. Xu, X., Li, Q., Lai, Y., Pang, W., Zhang, R., 2019a. Effect of moisture content on mechanical and damage behavior of frozen loess under triaxial condition along with different confining pressures. Cold Reg. Sci. Technol. 157, 110–118. Xu, X., Zhang, W., Fan, C., Li, G., 2019b. Effects of temperature, dry density and water content on the thermal conductivity of Genhe silty clay. Results in Physics. https:// doi.org/10.1016/j.rinp.2019.102830. Zhou, J., Li, D., 2012. Numerical analysis of coupled water, heat and stress in saturated freezing soil. Cold Region Science and Technology 72, 43–49. Zhou, Y., Zhou, J., Shi, X., 2019. Practical models describing hysteresis behavior of unfrozen water in frozen soil based on similarity analysis. Cold Reg. Sci. Technol. 157, 215–223.
Steiger, M., 2005. Crystal growth in porous materials—I: the crystallization pressure of large crystals. J. Cryst. Growth 282, 455–469. Steiger, M., Asmussen, S., 2008. Crystallization of sodium sulfate phases in porous materials: the phase diagram Na2SO4 -H2O and generation of stress. Geochim. Cosmochim. Acta 72, 4296–4306. Swenne, D.A., 1983. The eutectic crystallization of NaCl·H2O and ice. Eindhoven University of Technology. https://doi.org/10.6100/IR50645. Wan, X., Lai, Y., Wang, C., 2015. Experimental Study on the Freezing Temperatures of Saline Silty Soils. Permafr. Periglac. Process. 26 (2), 175–187. Wan, X., Hu, Q., Liao, M., 2017a. Salt crystallization in cold sulfate saline soil. Cold Reg. Sci. Technol. 137, 36–47. Wan, X., You, Z., Wen, H., William, Crossley, 2017b. An experimental study of salt expansion in sodium saline soils under transient conditions. Journal of Arid Land 9 (6), 865–878. Wan, X., Gong, F., Qu, M., Qiu, E., Zhong, C., 2019. Experimental study of the salt transfer in a cold sodium sulfate soil. KSCE J. Civ. Eng. 23 (4), 1573–1585. Wang, K., Sun, X., 2002. A new method for calculating the thermal conductivity of electrolyte aqueous solution. Chem. Eng. 30 (1), 60–63 (in Chinese). Wang, C., Lai, Y., Zhang, M., 2017. Estimating soil freezing characteristic curve based on pore-size distribution. Appl. Therm. Eng. 124, 1049–1060.
12
Contents lists available at ScienceDirect
Cold Regions Science and Technology journal homepage: www.elsevier.com/locate/coldregions
Study on phase changes of ice and salt in saline soils Xusheng Wan a b
a,b
a,⁎
b
b
T b
, Enlong Liu , Enxi Qiu , Mengfei Qu , Xiang Zhao , F.J. Nkiegaing
b
State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and Hydropower, Sichuan University, Chengdu 610065, China School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu 610500, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Sulfate saline soils Phase change Thermodynamic principle Cooling temperature curve Unfrozen water content
The occurrence of different ice and salt phases in saline soils may result in severe failure in engineering practice. Therefore, studying the phase changes of these two components may improve the understanding of saline soils. Through a series of cooling experiments on sulfate saline soils, the internal temperature variation of soils is obtained to study the rule of salt crystallization and the effect of salt on liquid water content. Based on the thermodynamic principle, the heat transfer equation is expressed considering the phase changes of ice and salt, and the control volume approach is applied to discretize the differential equation of heat transfer. Combined with the internal temperature curve of the soils, the discrete equations allow the calculation of ice porosity variation, salt crystal porosity, and unfrozen water content in saline soils. Additionally, the equations provide a useful general criterion for salt crystallization at different temperatures. Experimental and theoretical results confirm that unfrozen water content in saline soils decreases as the salt content increases, and that liquid water content is lower in salt-free soils. In addition, the concentration of salt solution in soils with low salt content increases owing to the phase change between water and ice; salt crystallization can only occur if the concentration reaches 20% at a negative temperature.
1. Introduction Saline soils, a generic term for solonchak and alkali soils, are widely distributed across China and constitute 2% of the total land area. Sulfate saline soils are most prevalent in Sinkiang, Qinghai, Gansu, Ningxia, Shaanxi, and Inner Mongolia (Wan et al., 2019). Currently, this phenomenon is crossing the borders of China and spreading worldwide to the Mediterranean basin, California, and Southeast Asia (Serrano and Gaxiola, 1994; Shaterian et al., 2005), where the scale of the soil salinity problem is increasing. Moreover, frozen saline soil is a typical feature of the Arctic coast and Central Siberia (Hivon and Sego, 1993; Bohren and Albrecht, 1998). Air temperature alterations between cold and warm periods will result in a significant transformation in the physical and mechanical properties of saline soils, owing to recurrent salt crystallization and deliquescence in soils. The resulting salt expansion and frost heave in saline soils; together with physical and chemical reactions, they represent a significant obstacle for the construction of local infrastructures, such as transportation, industry, and civil construction. Salt crystallization is the primary reason for salt expansion in sulfate soils. It begins as sodium sulfate decahydrate forms, which causes salt expansion (Steiger and Asmussen, 2008; Hamilton and Hall, 2008;
⁎
Shafiezadeh et al., 2018). However, this phenomenon can occur only if the supersaturation ratio of the solution is greater than its initial value and the condition of relative humidity for soils is satisfied. Scholars have used the Pitzer model to calculate the supersaturation ratio of salt solution in porous media (Steiger, 2005; Espinosa et al., 2008; Partanen et al., 2014). The initial supersaturation ratio and temperature are considered important conditions for estimating the crystallization and dissolution of salt. Mokni et al. (2010) developed a salt transfer coupled model by considering the soil constitutive relationship. Combining their model with the balanced equation of salt crystallization and dissolution, the rule of salt expansion deformation at room temperature can be solved. Dynamic models were established successively based on the thermodynamic principle in a porous medium to discuss the processes of salt crystallization and growth (Koniorczyk, 2012; Derluyn, 2012; Wu et al., 2017). However, most of the aforementioned research studies primarily concentrated on salt crystallization and the initial supersaturation ratio in brick, concrete, rock, and other construction materials, instead of soil. When soil related to salt phase change is examined, salt expansion is generally studied at the normal temperature or under steady-salt crystallization. Wan et al. (2017a) provided the initial supersaturation ratio of solutions and the initial crystallization temperature in saline soils at a negative temperature; however, predictability
Corresponding author. E-mail address: [email protected] (E. Liu).
https://doi.org/10.1016/j.coldregions.2020.102988 Received 4 July 2019; Received in revised form 31 December 2019; Accepted 5 January 2020 Available online 07 January 2020 0165-232X/ © 2020 Elsevier B.V. All rights reserved.
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
as that of the in situ soil. The mass water content of all soils was close to 18% after the vacuum saturation process; soil deformation was controlled by the lid of the aluminum box and a minute displacement was allowed.
regarding the dynamic variation of salt and ice crystals is lacking. Currently, a few methods are available for testing salt concentration change in saline soils at a negative temperature. Many experimental studies focused on the relationship between unfrozen water content and temperature. Additionally, scholars have regressed this relationship as an exponential or power function using a large number of experimental data, based on which the theoretical model of frost heave has been established for frozen soil (Ishizaki et al., 1996; McKenzie et al., 2007; Ge et al., 2011; Lai et al., 2014; Song and Dang, 2018; Xu et al., 2019a; Xu et al., 2019b). Based on the chemical potential energy balance of ice and water, the Clapeyron equation establishes the ice–water pressure balance relationship under different temperatures, and it is widely used in water-heat models for numerical calculations (Zhou and Li, 2012; Kurylyk and Watanabe, 2013; Painter and Karra, 2014; Wan et al., 2015; Wu et al., 2018; Dall'Amico et al., 2011). The relationship between the water freezing curve and soil water potential energy has been established by combining the Clapeyron equation and the soil–water characteristic curve (Kurylyk and Watanabe, 2013; Zhou et al., 2019). Moreover, the pore size distribution in soils has been applied to estimate unfrozen water content at different temperatures (Kozlowski, 2016; Wang et al., 2017). However, most studies focused on the phase transition between ice and water of soils without salt content. When saline soils are involved, only the effect of salt on freezing temperature is considered. Coupling issues regarding water freezing and salt crystallization as well as ice content are not included during temperature change. Typical sodium sulfate soils are the research subject of this study. A thermal conduction equation considering ice and salt phase changes is proposed based on the thermodynamic principle. A series of laboratory cooling tests on sulfate soils was designed at temperatures ranging from room temperature to −20 °C. The rule of salt crystallization and liquid water content, varying with temperature, were studied through experimental and theoretical analyses. This research is valuable for understanding the properties of saline soils and studying the land surface processes of sulfate saline soils in cold regions.
2.2. Experimental apparatus and testing method Thermistors (accuracy of ± 0.01 °C) were inserted into the centers of the samples encased by waterproof plastic sheets, and a preformed hole was sealed using plasticine. Subsequently, the samples were placed in a cold bath (accuracy of ± 0.05 °C) at a constant temperature of 25 °C for 30 min or longer. Next, the temperature decreased to −20 °C and the samples were stored at this temperature for 2 h. The cooling rate of the cold bath ranged from 0.75 to 0.85 °C/min. The data acquisition system was a DT80 date taker with the interval set to 10 s. Salt crystallization and phase change between water and ice increased the soil temperature by releasing the latent heat of phase change. Therefore, the initial temperature of salt crystallization and water freezing can be ascertained from the jump point on the cooling curve.
2.3. Experimental results The cooling curves of sulfate soils are shown in Fig. 1. The initial freezing temperature of each soil sample is shown as a green line, and the onset temperature of salt crystallization is denoted by a red line. The initial freezing temperature of sodium sulfate soils decreases as the salt content increases (the concentration of salt solution increases); however, their initial freezing temperature (freezing point) increases rapidly and then decreases as the salt content increases when the salt crystallizes above the initial freezing temperature. The cooling curve of the temperature rises slightly at −11.4 °C as a result of salt crystallization, when the concentration of salt solution is 4.44%; the onset temperature of salt crystallization increases with the concentration. When the concentration is greater than or equal to 10%, the salt crystallizes above the freezing point of the soils. For salt solutions with low salt concentration, the temperature difference on the cooling curve is not evident owing to low crystallization. Therefore, the internal temperature difference with time can be adopted to ascertain the onset temperature of salt crystallization for soils with low salt content, such as 0.7–0.9%. The results are shown in Fig. 2. A phase change between ice and water occurs when the soil temperature decreases to the freezing point, and the temperature difference appears as a sudden increase or decrease on the curve. When the concentration of the salt solution is equal to or > 4.44%, the internal temperature difference exhibits an increasing trend in a small time period after a large number of phase changes between ice and water, which is caused by the increase in soil temperature owing to the heat released by salt crystallization (Fig. 2). However, for a 3.89% concentration salt solution, such an increase is not observed in the temperature difference curve; therefore, it can be deduced that salt crystals are not generated when the concentration is < 3.89% above −20 °C.
2. Experiment design 2.1. Soil samples and related parameters The soil sampled in our study was collected from Beiluhe, on the Chinese Qinghai–Tibet Plateau, located in the continuous permafrost zone. The soil was locally salinized and sodium sulfate is the most prevalent in the study area. The mass water content in situ was 18%, with a plastic limit of 14.5% and a liquid limit of 23.8%. The original soil samples were desalinated repeatedly with distilled water to remove the effects of other ionic components. The soil samples were subsequently dried, crushed, and sifted. The soil particle distribution is shown in Table 1. The soil samples were prepared at room temperature, and salt contents of the samples were 0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0%, 1.1%, 1.2%, 1.4%, 1.6%, 1.8%, 2.1%, 2.3%, 2.6%, 2.9% and 3.2%, for the concentrations of salt solution of 0%, 0.56%, 1.11%, 1.67%, 2.22%, 2.78%, 3.33%, 3.89%, 4.44%, 5.00%, 5.56%, 6.11%, 6.67%, 7.78%, 8.89%, 10.00%, 11.67%, 12.78%, 14.44%, 16.11%, and 17.78%, respectively. The prepared samples were sealed at 25 °C for 24 h to ensure a uniform distribution of ions and water. Next, the test samples were inserted into iron boxes of diameter 3.3 cm and height 3.8 cm, and the dry density of the test samples was controlled to 1.82–1.84 g/cm3; hence, their density remained the same
3. Analysis of ice and salt phase changes 3.1. Heat balance equation and key thermal parameters In the cooling process of sulfate saline soils, when the concentration of the salt solution exceeds a specific supersaturation state, salt crystallization is initiated, and the phase change between water and ice appears at a negative temperature. Without considering fluid motion in soils, the heat balance equation can be expressed as Eqs. (1-a), (1-b) when the phase change occurs in saturated saline soils (Wu et al., 2017).
Table 1 Soil particle distribution. < 1 μm 14.5%
1–5 μm 38.5%
5–10 μm 23.2%
10–20 μm 15.4%
> 20 μm 8.4%
2
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 1. Cooling curves of sodium sulfate soils (T0 is the temperature of the cold bath and Tin refers to the core temperature of the soil samples).
refers to the heat conductivity coefficient of substance j; T is the temperature. Soil is a three-phase loose system, and the following relationship exists in saturated soils:
⎡⎛ ∂ (Lcryst nc ρc ) ∂ (L wi ni ρi ) ⎞ ⎤ ⎞ ⎤ ∂ ⎡⎛ = ∇ ⎢ ∑ λ j n j ∇T ⎥ − ⎢ ∑ cj nj ρj ⎟ T⎥ − ⎜ ⎟ t t ∂ ∂t ⎢ ⎜ j ∂ ⎢ ⎠ ⎥ ⎠ ⎥ ⎣⎝ j ⎦ ⎣⎝ ⎦ (1-a)
∑ nj = 1
⎡⎛ ∂ (Lcryst nc ρc ) ∂ (L wi ni ρi ) ⎞ ⎤ ⎞ ⎤ ∂ ⎡⎛ = ∇ ⎢ ∑ λ j n j ∇T ⎥ − ⎢ ∑ cj nj ρj ⎟ T⎥ − ⎜ ⎟ t t ∂t ⎢ ⎜ j ∂ ∂ ⎢ ⎠ ⎥ ⎠ ⎥ ⎦ ⎣⎝ ⎣⎝ j ⎦ (1-b)
(2)
j
For the salt solution, the heat conductivity coefficient λl can be calculated using Eq. (3) (Wang and Sun, 2002): −3/2
λ −2/3 βwc ⎞ + λe−2/3 wc + λl = ⎜⎛ w ⎟ wc + 1 ⎠ w ⎝ c+1
where cj refers to the specific heat capacity of substance j; j = c, i, l, s represents salt crystal, ice, salt solution, and soil particle, respectively; ρj refers to the density of substance j; nj refers to the ratio of volume occupied by substance j to the total volume of soil; Lcryst is the crystallization enthalpy; Lwi is the latent heat of water during freezing; λj
(3)
where λw is the heat conductivity coefficient of pure water, λe the heat conductivity coefficient of electrolyte, wc the concentration of the salt
Fig. 2. Internal temperature difference of sodium sulfate soils (Tc refers to the metastable supercooling temperature, Tf the freezing point, and Ts the temperature of salt crystallization). 3
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
solution (the mass of dissolved solute per unit mass), and β the related constant. The heat conductivity coefficient of pure water changes with temperature; this rule can be regressed by the obtained experimental data (Li and Fu, 2007), and the specific relationship is written as follows:
λ w = 0.56 − 9.08 × 10−6T 2 + 2.0966 × 10−3T
follows:
Lcryst = f (wc , T ) ≈ (14.169T − 252.84) wc2 + ( −10.474T + 212.88) wc + (−0.019T 2 − 0.6737T − 201.48) (8)
(4)
The phase diagram of sodium sulfate solution exhibits a close relationship with temperature (Koniorczyk, 2012). When the temperature is lower than 32.4 °C and the concentration of sodium sulfate solution is higher than its saturated concentration, sodium sulfate appears in the sodium sulfate decahydrate form (mirabilite). The change in salt concentration is primarily determined by salt crystallization and the phase change between water and ice. Water molecules will be transformed when sodium sulfate undergoes crystallization, which results in a decrease in salt concentration. On the contrary, a continuous phase transition between water and ice deteriorates the quality of the solvent (water); therefore, the salt concentration increases. Mirabilite cannot be generated in a relatively low humidity. Considering the approximate saturated soil samples designed in a closed system, the effect of relative humidity on salt crystal morphology is not considered in our calculation; therefore, mirabilite is assumed to be generated in the cooling process only if the supersaturation ratio exceeds its initial value. Because the liquid transfer is not considered in the theoretical model, the frost and salt heave are small. If we confine the displacement of the soil, the following relationship exists:
According to Eqs. (3) and (4), the heat conductivity coefficient of the salt solution is affected by both temperature and concentration; therefore, λl can be expressed as a function of concentration and temperature.
λl = f (wc , T )
(5)
Regarding the change in specific heat capacity of pure water in a specific temperature range, the effect of temperature on cl cannot be ignored; therefore, cl can be regressed as a function of salt concentration and temperature by experimental data, as follows (Pruppacher and Klett, 1997; Li and Fu, 2007): (6-a)
cl = −0.044wc + c w where
c w = 4180, T ≥ 0°C 4
c w (T ) =
∑ aj T j, T < 0°C (6-b)
j=0
with T in °C; a0 = 4.18 × 10 , a1 = −11.3, a2 = −9.71 × 10−2, a3 = 1.83 × 10−2, and a4 = 1.13 × 10−3. For a low concentration of salt solution, for calculation convenience, we assumed that the volume of the solution is equal to the volume of water. Hence, 3
ρl ≈ ρw (1 + wc )
n 0 ≈ nc + ni + nl
(9)
where n0 is the initial porosity of soils. The concentration of the salt solution can be formulated as Eq. (10) without considering the relocation diffusion of the concentration:
(7)
wc =
Lcryst increases as the temperature decreases or the salt concentration increases, using the relation shown in Fig. 3 (Espinosa and Scherer, 2008). Both temperature and salt concentration significantly affect the crystallization enthalpy of mirabilite (Fig. 3). Through data fitting, Lcryst can be expressed as a quadratic polynomial of the salt solution, and the coefficients are a function of temperature. The expression of Lcryst is as
ρw wc,0 n 0 − ρc nc MS / M ρw (n 0 − nc − ni )
(10)
where M is the relative molecular mass of mirabilite, Ms the relative molecular mass of sodium sulfate, and wc,0 the initial concentration of the salt solution. The partial differential of each variable parameter mentioned previously can be expressed as
Fig. 3. Crystallization enthalpy of mirabilite. 4
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
∂Lcryst
coordinates are expressed as follows:
∂f (wc , T ) ∂wc ∂f (wc , T ) ∂T + = ∂wc ∂t ∂T ∂t ∂t ∂cl ∂cl ∂wc ∂cl ∂wc = + ∂t ∂wc ∂t ∂wc ∂T ∂wc ∂wc ∂nc ∂wc ∂ni = + ∂t ∂nc ∂t ∂ni ∂t
x = r cos φ y = r sin φ z=z
(15)
where r refers to the radius of the cylinder, φ the angle, and z the height of the cylinder. Because x and y is a function of r and φ, therefore
(11)
where
∂φ ∂x ∂φ ∂y
ρ Ms wc,0 n 0 ∂wc nc 1 ⎤ = − c ⎡ + ⎢ (n 0 − ni − nc )2 ⎥ ∂nc (n 0 − ni − nc )2 ρw M ⎣ (n 0 − ni − nc ) ⎦ ρc Ms wc,0 n 0 ∂wc nc = − ∂ni (n 0 − ni − nc )2 ρw M (n 0 − ni − nc )
∂T ∂T ∂r ∂T = + ∂x ∂r ∂x ∂φ ∂T ∂T ∂r ∂T = + ∂y ∂r ∂y ∂φ
Therefore, based on the functional relationship above, Eqs. (1-a), (1b) can be simplified to
When we substitute Eqs. (15) and (16) into Eq. (12), the differential equation of heat conduction can be obtained using coordinate transformation, as follows:
∂T ∂n ∂n + LC c + Li i = ∇ (λ∇T ) ∂t ∂t ∂t
LT
(12)
LT
where
(16)
∂T ∂n ∂n 1 ∂ ⎛ ∂T ⎞ 1 ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ + LC c + Li i = + 2 λ ⎜λ ⎟ + λ ∂t ∂t ∂t r ∂r ⎝ ∂r ⎠ r ∂φ ⎝ ∂φ ⎠ ∂z ⎝ ∂z ⎠ (17)
LT = cc ρc nc + ci ρi ni + cs ρs (1 − n 0) + ρc nc
∂Lcryst
Multiplying both sides of this equation by r, followed by integrating the partial differential equation when the cooling time increases by △t, we obtain
∂T
LC = ρc cc T + ρc Lcryst +
∂Lcryst ∂ws ⎡ ∂c ρc nc − (ρw nl + ρw wc nl ) l − ρw cl nl ⎤ ⎥ ∂nc ⎢ ∂wc ∂wc ⎦ ⎣
t + Δt
∫ ∭ r ⎛⎝LT ∂∂Tt
∂Lcryst ∂ws ⎡ ∂c ρn − (ρw nl + ρw wc nl ) l − ρw cl nl ⎤ ⎥ ⎢ c c ∂wc ∂ni ⎣ ∂wc ⎦ λ = λi ni + λ c nc + λs (1 − n 0) + λl (n 0 − ni − nc )
Li = ρi ci T + ρi L wi +
1+
T f∗ T ∗f R Lwi
t
V
⎣
⎜
⎟
⎝
⎠
⎝
⎠⎦
(18)
where V refers to the volume of the representative elementary volume. The control volume approach was adopted to discretize the differential equation of heat transfer, and the process is detailed in the Appendix. In the calculation, the boundary conditions are stated as follows:
− T f∗ ln a w
V
∂nc ∂n + Li i ⎞ drdφdzdt = ∂t ∂t ⎠
∫ ∭ ⎡⎢ ∂∂r ⎛⎝λr ∂∂Tr ⎞⎠ + 1r ∂∂φ ⎛λ ∂∂Tφ ⎞ + r ∂∂z ⎛λ ∂∂Tz ⎞ ⎤⎥ drdφdzdt
When T > Tf,initial, ni = 0. Tf,initial is the initial freezing temperature of soil; for sulfate saline soils, the freezing temperature Tf can be calculated using the following equation (Wan et al., 2015):
Tf =
t t + Δt
+ LC
⎧ r = 1.65cm ⎪ z = 1.9cm ⎨ T = T0 ⎪ 0 ≤ φ ≤ 2π ⎩
(14)
where T⁎f refers to the freezing temperature of pure water, i.e., 273.15K; R is the gas constant; aw is the water activity, which is a function of the salt solution concentration, and the value decreases as the concentration increases. The cooling of soil samples in the experiment is a heat transfer problem in cylindrical coordinates, and the temperature at any point can be shown, as in Fig. 4. The mathematical relationships between cylindrical and rectangular
(19)
The central temperatures of Tin can be obtained in the test and hence can be considered a known quantity. In the calculation at a random time △tk (k = 1, 2, 3, …), when △nc,k or △ni,k < 0, we used △nc,k or △ni,k = 0. The basic soil parameters and related thermodynamic parameters are shown in Table 2. The change of internal temperature in soils shown in Fig. 1 at any time △tj can be written as follows:
Tj = Tj − 1 + ΔTj
(20)
The above experiment shows that salt will not crystallize when salt content is < 0.7% and nc = 0. Moreover, the internal temperature change Tin can be obtained from our test data shown in Fig. 1. The porosity occupied by ice and unfrozen water at any time △tj can be expressed using Eq. (21) as follow:
ni, j = ni, j − 1 + Δni, j nl, j = n 0 − ni, j
(21)
Two variables (ice and salt crystal content) appear when the salt crystallizes above or below the freezing point (Fig. 1). However, the equation presented above cannot be solved for two unknown variables. Therefore, we assumed that salt crystallization caused the cooling curve to shift toward the right in the coordinate system. If no salt crystal is formed, the cooling curve will change as per the dashed line shown in Fig. 5 (similar to the cooling curve of soils without salt). For example, the ice volume content can be calculated based on the curve of the dashed line, assuming that a phase change occurs between ice and water (using Eq. (A.4)). Therefore, the porosity occupied by ice can be
Fig. 4. Temperature at any point in cylindrical coordinates. The dashed cylinder represents the soil sample, arrows show the direction of heat transfer, and T0 is the boundary condition decided by the temperature of the cold bath. 5
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Table 2 Table of symbols used. Symbols
Name
Value or Range
T T0 Tf,initial aw T⁎f R Lwi Lcryst cw ci cl cs cc λl λw λe λi λs λc ρw ρdry ρs ρc ρi ρl n n0 ni nc ns Ms M β
temperature temperature of cold bath initial freezing temperature of soil water activity absolute temperature gas constant latent heat of water freezing latent heat of salt crystallization specific heat capacity of water specific heat capacity of ice specific heat capacity of salt solution specific heat capacity of soil particle specific heat capacity of salt crystal thermal conductivity of salt solution thermal conductivity of water thermal conductivity of electrolyte thermal conductivity of ice thermal conductivity of soil particle thermal conductivity of salt crystal density of water density of dry soil density of soil particle density of salt crystal density of ice density of salt solution soil porosity initial soil porosity soil porosity of ice soil porosity of salt crystal soil porosity of soil particle relative molecular mass of Na2SO4 relative molecular mass of Na2SO4•10H2O constant term
273.15 8.314 333.7
1874 (Lai et al., 2014) 2360 (Lai et al., 2014) 1920
0.285 2.22 (Lai et al., 2014) 1.2 (Wu et al., 2017) 0.5 1000 1820 2700 1465 917
0.33
0.67 142 322 −7.8773 × 10−3 (Wang and Sun, 2002)
Unit K or °C K or °C K or °C dimensionless K J/(K·mol) kJ/kg kJ/kg J/(kg·K) J/(kg·K) J/(kg·K) J/(kg·K) J/(kg·K) W/(m·K) W/(m·K) W/(m·K) W/(m·K) W/(m·K) W/(m·K) kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 dimensionless dimensionless dimensionless dimensionless dimensionless g/mol g/mol dimensionless
crystallization becomes stable when the temperature decreases, and the concentration of the salt solution approaches the saturated concentration (Wan et al., 2017a). Hence, salt crystallization below the freezing point can be calculated approximately according to the saturation concentration. The saturated concentration of sodium sulfate solution can be expressed as Eq. (22) (Wan et al., 2017a):
considered a known quantity to determine the change in salt crystal content combined with the real cooling curve. Salt crystallizes above the freezing point when the initial salt content of soils increases to 1.8%. A salt solution is always in the supersaturation state before salt crystallization occurs; therefore, when crystals separate from the salt solution, the concentration will decrease significantly owing to a large amount of mirabilite generation. Salt
Fig. 5. Assumed curve of saline soils without salt crystallization. 6
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 6. Variation in ice and salt crystal contents with temperature for different salted soils. a) Variation in ice and unfrozen water volume contents of saline soils with low salt; b) Variation in ice and salt crystal volume contents of saline soils in low temperature; c) Salt crystallization law of soils with high salt content; d) Variation in ice and salt crystal contents in highly salted soils with temperature.
wc, sat = 0.449 × 1.077T
The salt solution concentration increases as the soil temperature decreases, and salt crystals are generated only when the concentration reaches 20%. The salt crystal content increases as the soil temperature decreases, and the amount of salt crystals increases with the salt content; accordingly, the change in the corresponding concentration increases. The concentration of the salt solution with high salt content decreases quickly and tends to be stable. The increase in salt content decreases the ice content, with ice content becoming stable rapidly. Apart from the ice–water phase change, another part of the water transported by salt crystallization is transformed into the solid phase. Therefore, these soils with different salt contents change only slightly. The unfrozen water content of soils with 0.8%, 1.1%, and 1.4% salt content ranges from 5.0% to 5.9% at −20 °C (Fig. 6b). As shown in Fig. 6c, salt crystal content can be calculated based on the cooling curve before the transition phase between water and ice. A salt solution is always in the supersaturation state before salt crystallization occurs; therefore, when a crystal separates from the salt solution, the concentration will decrease considerably owing to the generation of a large amount of mirabilite. Salt crystallization becomes stable with decreasing temperature, and the salt solution concentration approaches the saturated concentration (Fig. 6c). Therefore, salt crystallization below the freezing point can be calculated approximately according to the saturation concentration. Ice and salt crystals are generated simultaneously, and their changes are shown in Fig. 6d.
(22)
where wc,sat is the saturated concentration, and T is < 32.4 °C. 3.2. Calculation results and analysis The variation in porosity occupied by ice and unfrozen water in different salted soils are shown in Fig. 6. The water in soils begins to freeze and the ice volume content increases when the soil temperature decreases to the freezing point; this increasing trend decreases continuously as temperature decreases and tends to be stable. The calculated result shows that the unfrozen water content is 5.4% at −20 °C in soils without salt. However, the ice content decreases slightly in soils with low salt content, while the unfrozen water content increases. For soils with 0.2% and 0.7% salt contents, the unfrozen water contents are 5.8% and 7% at −20 °C, respectively. The concentration of the salt solution can be calculated using Eq. (10), which increases as the temperature decreases. When temperature ranges from room temperature to −20 °C, the concentration of the solution in saline soils with a 0.2% salt content increases from 1.1% to 6%. For saline soils with a 0.7% salt content, the concentration increases from 3.9% to 18.2% at the same temperature change (Fig. 6a). Salt crystallizes when salt content increases. The variation of ice and salt crystals, unfrozen water content, and concentration of salt solution with temperature are shown in Fig. 6b. 7
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 7. Simulation and test values of soil temperature changing with time. The line is the calculated value and the small circle refers to the experimental data.
where S refers to the supersaturation ratio. The change rule of S with temperature is shown in Fig. 9. Initially, the supersaturation ratio increases as the temperature decreases when the salt solution enters the supersaturation state (S > 1) from the undersaturated state (S < 1). Once the supersaturation ratio becomes higher than the initial ratio, the salts will crystallize. In addition, the concentration of the solution decreases and reduces the supersaturation ratio (Fig. 9). The initial supersaturation ratio decreases as the initial salt content increases, which indicates that the salt crystallization formation is much easier for highly salty soils. If salt crystallization is only achieved below the freezing point, the initial supersaturation is much larger than that above the freezing point. Therefore, salt crystallization becomes increasingly difficult or crystallization is avoided as the initial salt content decreases. The external cooling rate affects the unsteady-state interval of sodium sulfate soils. Generally, the unsteady-state range decreases as the cooling rate decreases; hence, sodium sulfate decahydrate crystallizes more easily (Wan et al., 2017b). The initial supersaturation ratio is calculated at different temperatures, as shown in Fig. 10. The initial supersaturation ratio increases as temperature decreases, and it increases significantly when the temperature is lower than −2 °C. The Boltzmann function (black line in Fig. 10) and the exponential function (red line in Fig. 10) are used to describe the change rule of the initial supersaturation ratio with temperature; all their values are within the shaded portion between the two curves. The initial supersaturation ratio approaches the Boltzmann function at the temperature ranging from −8 to 8 °C, and the value is close to the exponential function in another temperature range. Furthermore, salt crystallization is more difficult in the temperature range from −3 to −12 °C, as the initial supersaturation ratio in this temperature range is typically 3–5 times higher than the ratio occurring above the freezing point. Furthermore, the heat balance equation above is suitable for other saline soils. For sodium chloride soils, salt phase change need not be considered owing to the stable characteristics of the sodium chloride solution; sodium chloride dihydrate forms only at extremely high concentrations and low temperatures (Swenne, 1983; Derluyn, 2012). Therefore, the calculation method is the same as that of sodium sulfate soils with low salt content; nc can be assumed as zero. The sole
At the freezing point, a large number of phase changes between water and ice cause the salt solution concentration to increase rapidly; hence, the salt crystal content increases at the freezing point. Subsequently, it changes weakly and tends to be stable as the water–ice phase transition occurs. Moreover, salt crystallization inhibits the formation of ice crystals; the more salt crystals are generated, the more the ice content decreases. For soils with 3.2% salt content, the salt crystal content is 2.9% greater than that of soils with 2.6% salt content; however, by contrast, the ice content decreases by 3% (Fig. 6d).
4. Discussion Next, we validate the current solution. Some numerical simulations have been performed to verify the accuracy of the heat transfer equation established in our study. The central temperature of sulfate saline soils without phase change was considered in our simulations, i.e., nc = ni = 0. It is clear from Fig. 7 that the heat transfer model can well simulate the change in soil temperature under the changing temperature of the cold bath. The accuracy of the calculation from Eq. (21) is verified by comparing the calculated results and the test value, as shown in Fig. 8. The calculations of water content without phase change are relatively close to those from the tests (Wen et al., 2012; Wan et al., 2015); therefore, the model can simulate the phase change as a function of temperature change. For salt crystallization above the freezing point, the unfrozen water content changes quickly at the freezing point and stabilizes at −8 °C. It is noteworthy that the amount of unfrozen water is less than that of soils without salt. When the salt contents are 2.6% and 3.2%, the unfrozen water contents are 4.3% and 4.5% at −20 °C, respectively, while the unfrozen water content of soil without salt is 5.6% at the same temperature. Therefore, the higher the salt content, the larger is its effect on the liquid water content (no phase change); this phenomenon results in a smaller unfrozen water content below the freezing point. The supersaturation ratio is defined as the ratio of the actual concentration of salt solution to its saturated concentration, as follows:
S=
wc wc, sat
(23) 8
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 8. Comparisons of calculation and test results.
Fig. 9. Supersaturation ratio of sodium sulfate soils varying with temperature.
5. Conclusions
difference between these two salts is their effect on the freezing temperature of soils. In general, a decrease in freezing point is more clearly shown by sodium chloride than sodium sulfate soils (Bing and Ma, 2011; Wan et al., 2015). For other unstable salts, the property is different. Their ice and salt transformations can be studied under the assumption in Section 3.1, based on the heat balance equation and the internal cooling curve of soils, provided that their crystalline morphologies and latent heats of phase change are known. Salt transfers, under the action of soil water potential, affects heat transfer when the temperature changes. Moreover, soil deformation caused by salt and frost heaving changes the volume ratio occupied by each substance, thereby varying the physical parameters. Hence, salt movement and more precise soil parameters pertaining to the salt and water phase change should be considered in future studies to explore the joint effect of salt and frost expansion in detail.
This paper presents a study on the change rule of salt crystallization and unfrozen water content according to the thermodynamic principle and cooling down tests of sulfate saline soils. Furthermore, the interaction between ice and salt phase changes is elaborated. The conclusions are summarized as follows: 1) When the concentration of salt solution in soils was < 4.44%, salt crystals did not generate at the temperature ranging from room temperature to −20 °C, and the concentration increased to 18.2% as the temperature decreased. Moreover, the unfrozen water content of these soils was higher than those of soils without salt. 2) Salt crystallization in soils could occur below the freezing point when the initial concentration of the salt solution was higher than 4.44% and tended to be stable as the temperature decreased. Only 9
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. 10. Initial supersaturation ratio at different temperatures.
analyzed the results. Dr. Enlong Liu discussed the results, wrote and revised the manscript. Dr.Enxi Qiu, Dr. Mengfei Qu, Dr. Xiang Zhao, and Dr. F.J.Nkiegaing made contributions in designing the tests and analyzing the results.
salt crystallization below the freezing point could reduce the amount of ice content; the ice content decreased as the initial salt content increased, but the unfrozen water content indicated little change. 3) Salt crystallization formed above the freezing point in soils caused the unfrozen water content to be lower than that of soils without salt. Moreover, unfrozen water became stable in soils with a higher salt content at −10 °C; it did not change below this temperature. 4) Salt crystallization only occurred when the supersaturation ratio of salt solution was higher than the initial supersaturation ratio; this initial supersaturation ratio of sulfate soils was within the Boltzmann function range and exponential function intersection. The salt concentration approached saturation as the temperature decreased in highly salty soils. Additionally, the initial supersaturation ratio changed slightly at positive temperatures compared with the value below the freezing point. As the temperature decreased below the freezing point, it became increasingly difficult to initiate salt crystallization.
Declaration of Competing Interest The authors declare that there are no conflicts of interest regarding the publication of this paper. Paper title: Studying the Phase Changes of Ice and Salt in Saline Soils. The authors: Xusheng Wan, Enlong Liu, Enxi Qiu, Mengfei Qu, Xiang Zhao, F.J.Nkiegaing.
Acknowledgments This research was supported by the National Natural Science Foundation of China (41601068), Young Scholars Development Fund of Southwest Petroleum University (201599010104), and Scientific Research Starting Project of Southwest Petroleum University (2015QHZ025).
Author contribution statement Dr. Xusheng Wan performed the tests, wrote the manuscript and
Appendix A
10
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Fig. A.1. Schematic diagram of control volume of cylinder. a, b, c, d, e, and f refer to the front, back, left, right, top, and bottom surface of microelement △v, respectively.
For any microelement, as shown in Fig. A.1, the left side of Eq. (18) can be simplified as follows: t + Δt
∫ ∭ rLT ∂∂Tt drdφdzdt = ra +2 rb
LT , a + LT , b Δr ΔφΔz Δt (Tp − T p0 ) 2
∫ ∭ rLc ∂∂ntc drdφdzdt = ra +2 rb
Lc, a + Lc, b Δr ΔφΔz Δt (nc, p − nc0, p ) 2
∫ ∭ rLi ∂∂nti drdφdzdt = ra +2 rb
L i, a + L i, b Δr ΔφΔz Δt (ni, p − ni0, p) 2
t t + Δt
V
t t + Δt
V
t
V
(A.1)
where Tp, nc,p, ni,p refers to the temperature, porosity occupied by salt crystal, and porosity occupied by ice crystal at point P, respectively. T0p, n0c,p, n0i,p are the Tp, nc,p, ni,p at the initial state. For n0c,p and n0i,p, their values are zero initially. The right side of Eq. (18) can be simplified as follows: t + Δt
∫ ∭ ∂∂r ⎛⎝λr ∂∂Tr ⎞⎠ drdφdzdt = ΔφΔz Δt ⎡⎢λb rb
t t + Δt
∫∭ t t + Δt
⎣
V
V
Tb − Tp (δr )b
Tp − Ta ⎤ (δr )a ⎥ ⎦
Tp − Tc ⎤ Td − Tp 1 ∂ ⎛ ∂T ⎞ rb Δz Δt ⎡λd ⎜λ ⎟ drdφdzdt = ln − λc ⎢ ( ) (δφ)c ⎥ δφ r ∂φ ⎝ ∂φ ⎠ ra d ⎣ ⎦
∫ ∭ r ∂∂z ⎛λ ∂∂Tz ⎞ drdφdzdt = ra +2 rb Δr ΔφΔt ⎡⎢λe t
− λa ra
V
⎝
⎠
⎣
Te − Tp (δz )e
− λf
Tp − Tf ⎤ (δz )f ⎥ ⎦
(A.2)
Assuming that the temperature variation is linear from the outside to the inside, for a cylinder sample, Eq. (18) can be simplified at any time △tj as follows:
LT , a + LT , b Lc, a + Lc, b L i, a + L i, b Δr ΔφΔz ΔTp, j + Δr ΔφΔz Δncp, j + Δr ΔφΔz Δni,pj= 2 2 2 T0, j − Tin, j T0, j − Tin, j 2 ⎡ ⎤ ΔφΔz (λb rb − λ a ra ) + (ra + rb )Δr Δφ (λ e − λ f ) ⎥ z r ra + rb ⎢ ⎦ ⎣
(A.3)
If no salt crystal is generated, then Eq. (A.3) can be transformed to
LT , a + LT , b L i, a + L i, b Δr ΔφΔz ΔTp, j + Δr ΔφΔz Δni,pj= 2 2 T0, j − Tin, j T0, j − Tin, j 2 ⎡ ⎤ ΔφΔz (λb rb − λ a ra ) + (ra + rb )Δr Δφ (λ e − λ f ) ⎥ z r ra + rb ⎢ ⎣ ⎦
(A.4)
The discrete formula can be used to calculate the variation in ice or salt crystal content with temperature change when the internal and external temperatures of soils are known; this process can be programmed using Matlab for calculations.
maximum temperature. Cold Reg. Sci. Technol. 122, 18–25. Kurylyk, B.L., Watanabe, K., 2013. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils. Adv. Water Resour. 60, 160–177. Lai, Y., Pei, W., Zhang, M., Zhou, J., 2014. Study on theory model of hydro-thermal–mechanical interaction process in saturated freezing silty soil. Int. J. Heat Mass Transf. 78, 805–819. Li, H.C., Fu, B., 2007. Practical Chemistry Handbook. Chemical Industry Press, Beijing (in Chinese). McKenzie, J.M., Voss, C., Siegel, D., 2007. Groundwater flow with energy transport and water–ice phase change:Numerical simulations, benchmarks, and application to freezing in peat bogs. Advanced Water Resources 30, 966–983. Mokni, N., Olivella, S., Alonao, E.E., 2010. Swelling in clayey soils induced by the presence of salt crystals. Appl. Clay Sci. 47, 105–112. Painter, S.L., Karra, S., 2014. Constitutive model for unfrozen water content in subfreezing unsaturated soils. Vadose Zone J. 13 (4), 334–338. Partanen, J.I., Hasan, M., Vahteristo, K.P., 2014. Determination of the Pitzer Interaction Parameters at 273.15 K from the Freezing-Point Data Available for Solutions of UniUnivalent Electrolytes. Indystrial & Engineering Chemistry Research 53 (49), 19351–19358. Pruppacher, H.R., Klett, J.D., 1997. Microphysics of Cloulds and Precipitation. Kluwer Acadamic Pubishers, New York, Bston, Dordrecht, London, Moscow. Serrano, R., Gaxiola, R., 1994. Microbial models and salt stress tolerance in plants. Crit. Rev. Plant Sci. 13 (2), 121–138. Shafiezadeh, M., Moradi, H., Fakheran, S., 2018. Evaluating and modeling the spatiotemporal pattern of regional-scale salinized land expansion in highly sensitive shoreline landscape of southeastern Iran. Journal of Arid Land 10 (6), 946–958. Shaterian, J., Waterer, D., De Jong, H., Tanino, K.K., 2005. Differential stress responses to NaCl salt application in early-and late-maturing diploid potato clones. Environ. Exp. Bot. 54 (3), 202–212. Song, M.S., Dang, C.B., 2018. Review on the measurement and calculation of frost characteristics. Int. J. Heat Mass Transf. 124, 586–614.
References Bing, H., Ma, W., 2011. Laboratory investigation of freezing point of saline soil. Cold Reg. Sci. Technol. 67, 79–88. Bohren, C.F., Albrecht, B.A., 1998. Atmospheric Thermodynamics. Oxford Univeristy Press, New York. Dall’Amico, M., Endrizzi, S., Gruber, S., Rigon, R., 2011. A robust and energy –conserving model of freezing variably-saturated soil. Cryosphere 5, 469–484. Derluyn, H., 2012. Salt Transport and Crystallization in Porous Limestone: Neutron-X-Ray Imaging and Poromechanical Modeling. PhD Dissertation. University of Zurich, Zürich, pp. 9–27. Espinosa, R.M., Scherer, G.W., 2008. Study of sodium sulfate salts crystallization in limestone. Environ. Geol. 56, 605–621. Espinosa, R.M., Franke, L., Deckelmann, G., 2008. Phase changes of salts in porous materials: crystallization, hydration and deliquescence. Constr. Build. Mater. 22, 1758–1773. Ge, S., McKenzie, J., Voss, C., Wu, Q., 2011. Exchange of groundwater and surface-water mediated by permafrost response to seasonal and long term air temperature variation. Geophys. Res. Lett. 38, L14402. https://doi.org/10.1029/2011GL047911. Hamilton, A., Hall, C., 2008. Sodium sulfate heptahydrate: a synchrotron energy-dispersive diffraction study of an elusive metastable hydrated salt. J. Anal. At. Spectrom. 23 (6), 840–844. Hivon, E.G., Sego, D.C., 1993. Distribution of saline permafrost in the Northwest Territories, Canada. Can. Geotech. J. 30, 506–514. Ishizaki, T., Maruyama, M., Furukawa, Y., Dash, J., 1996. Premelting of ice in porous silica glass. J. Cryst. Growth 163 (4), 455–460. Koniorczyk, M., 2012. Salt transport and crystallization in non-isothermal, partially saturated porous materials considering ions interaction model. Int. J. Heat Mass Transf. 55 (4), 665–679. Kozlowski, T., 2016. A simple method of obtaining the soil freezing point depression, the unfrozen water content and the pore size distribution curves from the DSC peak
11
Cold Regions Science and Technology 172 (2020) 102988
X. Wan, et al.
Wen, Z., Ma, W., Feng, W., Deng, Y., Wang, D., Fan, Z., Zhou, C., 2012. Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibet silty clay. Environmental Earth Science 66 (5), 1467–1476. Wu, D., Lai, Y., Zhang, M., 2017. Thermo-hydro-salt-mechanical coupled model for saturated porous media based on crystallization kinetics. Cold Reg. Sci. Technol. 133, 94–107. Wu, D., Zhou, X., Jiang, X., 2018. Water and Salt Migration with phase Change in Saline Soil during Freezing and Thawing Processes. Groundwater 56 (5), 742–752. Xu, X., Li, Q., Lai, Y., Pang, W., Zhang, R., 2019a. Effect of moisture content on mechanical and damage behavior of frozen loess under triaxial condition along with different confining pressures. Cold Reg. Sci. Technol. 157, 110–118. Xu, X., Zhang, W., Fan, C., Li, G., 2019b. Effects of temperature, dry density and water content on the thermal conductivity of Genhe silty clay. Results in Physics. https:// doi.org/10.1016/j.rinp.2019.102830. Zhou, J., Li, D., 2012. Numerical analysis of coupled water, heat and stress in saturated freezing soil. Cold Region Science and Technology 72, 43–49. Zhou, Y., Zhou, J., Shi, X., 2019. Practical models describing hysteresis behavior of unfrozen water in frozen soil based on similarity analysis. Cold Reg. Sci. Technol. 157, 215–223.
Steiger, M., 2005. Crystal growth in porous materials—I: the crystallization pressure of large crystals. J. Cryst. Growth 282, 455–469. Steiger, M., Asmussen, S., 2008. Crystallization of sodium sulfate phases in porous materials: the phase diagram Na2SO4 -H2O and generation of stress. Geochim. Cosmochim. Acta 72, 4296–4306. Swenne, D.A., 1983. The eutectic crystallization of NaCl·H2O and ice. Eindhoven University of Technology. https://doi.org/10.6100/IR50645. Wan, X., Lai, Y., Wang, C., 2015. Experimental Study on the Freezing Temperatures of Saline Silty Soils. Permafr. Periglac. Process. 26 (2), 175–187. Wan, X., Hu, Q., Liao, M., 2017a. Salt crystallization in cold sulfate saline soil. Cold Reg. Sci. Technol. 137, 36–47. Wan, X., You, Z., Wen, H., William, Crossley, 2017b. An experimental study of salt expansion in sodium saline soils under transient conditions. Journal of Arid Land 9 (6), 865–878. Wan, X., Gong, F., Qu, M., Qiu, E., Zhong, C., 2019. Experimental study of the salt transfer in a cold sodium sulfate soil. KSCE J. Civ. Eng. 23 (4), 1573–1585. Wang, K., Sun, X., 2002. A new method for calculating the thermal conductivity of electrolyte aqueous solution. Chem. Eng. 30 (1), 60–63 (in Chinese). Wang, C., Lai, Y., Zhang, M., 2017. Estimating soil freezing characteristic curve based on pore-size distribution. Appl. Therm. Eng. 124, 1049–1060.
12