Experimental Procedures

A comprehensive experimental system (Figure 6-2) is designed to investigate the effectiveness of cyclic cryogenic fracturing in terms of the deterioration of pore structure and the change in gas sorption kinetics. The experimental platform consists of three main parts as freeze-thawing (F-T) system, gas ad/desorption isotherm and kinetic measurements, pore structural characterization. The F-T system is composed of a vacuum insulated thermal bottle with double-wall stainless steel interior and exterior for freezing and a glassware beaker for thawing. The double-layer insulator provides enough temperature retention time for freezing and strength for the endurance of the F-T forces.

The gas ad/desorption isotherm and kinetic measurements were obtained using a high-pressure sorption experimental apparatus presented in Chpater 3. This apparatus allows measuring gas sorption up to 3000 psi, which can simulate gas sorption ad/desorption

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behavior of coal at both saturated and undersaturated conditions. Besides, the data acquisition system employed in this experimental sorption system continuously delivers the pressure readings to user-interface with a rate of up to 1000 data points per second.

This allows for accurate measurements of gas sorption kinetics and diffusion coefficient.

In the determination of pore characteristics, physical sorption of N2 at 77 K and CO2 at 273 K were conducted with an ASAP 2020 physisorption analyzer (Micromeritics, USA) following the testing procedure documented in the ISO (2016).

The prepared coal sample was evenly divided into two groups. One is the reference group as the raw coal sample, and the other is the experimental group that would undergo a series of freeze-thawing cycles. In order to include the water-ice expansion force in the freezing process, the experimental group was first saturated with water by fully immersing the sample in the distilled water. Once an apparent boundary forms between the clear water and coal particles, the water-saturated sample was made by filtering out from the suspension and air-drying, and then subject to F-T cycles. Figure 6-3 displays the experimental images captured at different times during the freezing and thawing operations. The coal sample was frozen in the thermal bottle filled with LN2 for 60 mins (see Figure 6-3(a)), where the fluid level of LN2 kept almost the same for the entire one-hour freezing. This was desired since heat transfer mostly occurred between LN2 and the coal sample rather than the atmosphere; otherwise, LN2 would vanish soon to cool the surrounding air. The frost started to form around 10 mins indicating the production of the frost-shattering forces. Followed by the freezing operation, the coal sample was thawed at room temperature of 25℃. The thawing operation lasted about 240 mins until a thermal

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equilibrium was reached, as shown in Figure 6-3(b). For multiple F-T cycles, the same freeze-thawing procedures would be repeated, and a portion of the coal sample was retrieved after one and three cycles (1F-T and 3F-T coal).

The freeze-thawed and raw coal sample were dried in the vacuum drying oven at

−0.1 MPa and 60 °C for subsequent measurements on pore structure and gas sorption behavior. The coal samples subject to the different number of F-T cycles were used to study the effectiveness of cyclic cryogenic treatments on the pore structural deterioration and modification of gas sorption kinetics.

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Figure 6-2: The experimental system. (a) is a freeze-thawing system, where the coal sample is first water saturated in the glassware beaker and then subject to cyclic liquid nitrogen injection. In between the successive injections, the sample is thawed at room temperature.

The freeze-thawed coal samples and the raw sample are sent to the subsequent measurements ((b) and (c)). (b) is the experimental setup for measuring the gas sorption kinetics. This part of the experiment is to evaluate the change in gas sorption and diffusion behavior of coal after cryogenic treatment. (c) is the low-pressure adsorption system for the determination of surface area and porosimetry of pore structure of the coal sample. This step is to evaluate the pore-scale damage caused by the cryogenic treatment to the coal sample.

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Figure 6-3: The process diagram of freeze-thawing treatment: (a) freezing operation; (b) thawing operation.

142 6.4.3 Micromechanical Analysis

The effects of freeze-thaw on the pore structure of coal have been extensively studied in laboratories as presented in this work and various studies (Cai et al., 2014a; Xu et al., 2017; Zhai et al., 2016). However, a mechanistic model of the involved multi-physics is sparely discussed in the literature. A rational evaluation of pore structural deterioration is essential in predicting the induced change in gas sorption and transport properties in CBM reservoirs by cyclic liquid nitrogen injections. Hori and Morihiro (1998) proposed a micromechanical model to study the mechanical degradation of concrete at very low temperatures, and their analysis was employed by this work to estimate the damage degree of the nanopore system of coal in response to the repetition of freezing and thawing. In their model, a nanopore with a radius of ao is modeled as a microcrack with half crack length of ao. ao becomes an after n^th cycle of freezing and thawing, i.e., an = an(ao). Figure 6-4 is a graphical illustration of a deteriorating nanopore of coal, where the fractured pore is represented by a growing microcrack. The growth of cracks can be solved with fracture mechanics. For simplicity, we neglect the interaction among different pores, and the solution is obtained by treating each pore as an isolated crack in an infinite medium. The extremely low-temperature environment created by liquid nitrogen gives rise to a rapid cooling rate and yields a sudden thermal shock to the coal matrix. Water contained in the nanopores expands as the temperature of the coal matrix is lowered to sufficiently cold temperature. This volume expansion induces local tensile stress and causes damage to the

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pores, which are depicted in Figure 6-4 as a pair of concentrated forces acting on the crack center.

Figure 6-4: Hori and Morihiro’s model of fractured micropore (Hori and Morihiro, 1998).

The nanopore system of coal is modeled as a micro cracked solid. The pair of concentrated forces normally acting on the crack center represents the crack opening forces produced by the freezing action of pore water.

We first develop a mechanistic model for determining the deterioration degree due to the freezing of water and then couple it with heat conduction analysis. Under the application of a pair of concentrated forces, the crack opening displacement ([𝑢(𝑥)]) is given by (Sneddon, 1946),

[𝑢(𝑥)] =4(1 − 𝜈²)

𝜋𝐸 𝑃_𝑤(ln |𝑎

𝑥| + √𝜋(1 − (𝑥/𝑎)²)) ( 6-1 )

where 𝜈 and 𝐸 are the elastic moduli of the coal matrix. 𝑃_𝑤 is the magnitude of crack opening forces, i.e., the frost pressure induced by the freezing of water. 𝑎(𝑎₀) is the half crack length of a crack with an initial crack length of 𝑎₀ before 𝑛^th freeze-thawing cycles, i.e., 𝑎(𝑎₀) = 𝑎_𝑛−1(𝑎₀).

The crack opening displacement (⁡[𝑢(𝑎)]̅̅̅̅̅̅̅̅⁡) of a single microcrack with half crack length of 𝑎 can be found as,

144 determined by (Hori and Morihiro, 1998; Nemat-Nasser and Hori, 2013)

𝜀^𝑐 = ∫ [𝑢(𝑎)]̅̅̅̅̅̅̅̅

where 𝜌(𝑎₀) is the crack density function. In this work, it is set as porosity and can be extrapolated from pore size distribution measured from low pressure gas sorption.

The deterioration degree is characterized by the magnitude of 𝜀^𝑐, which is dependent upon the evaluation of 𝑃_𝑤. 𝑃_𝑤⁡increases as pore water are being frozen, and some portion of it remains after thawing. The residual strain due to the generation of residual stress characterizes the constant expansion of pore volume after freezing and thawing and its magnitude corresponds to the deterioration degree of pore structure. This residual stress is crack opening forces acting at the crack center as shown in Figure 16, and its magnitude is 𝑃_𝑤. Hori and Morihiro (1998) showed that 𝑃_𝑤 is proportional to the maximum pressure for the freezing of water (𝑃_𝑐).

Thus,

𝑃_𝑤 = 𝐴(𝑇, 𝑎)⁡𝛽_𝑚𝑃_𝑐 ( 6-4 )

where 𝐴 is the frozen water content in a micropore with a radius of 𝑎 at temperature 𝑇. 𝛽_𝑚 is the fraction of stress retained after completely thawing of the coal matrix and the removal of 𝑃_𝑐. The magnitude of 𝛽_𝑚 depends on the material heterogeneity that different parts undergo different deformations (Beer et al., 2014).

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Although the deterioration only proceeds when the water content exceeds 90%

(Rostasy et al., 1979), we assume 100% saturation for simplicity. For this reason, the maximum pressure due to the freezing of pore water (𝑃_𝑐) can be approximated by the strength of a nanopore with a radius of 𝑎. Nielsen (1998) showed that for a porous material, the pore strength exhibited an inverse relationship with the pore size, which took a form of

𝑃_𝑐 = 𝐾_𝑐√1/𝑎 ( 6-5 )

where 𝐾_𝑐 is the fracture toughness of the material or the coal matrix.

With Eq. (6-3) – Eq. (6-5), the internal pressure of nanopore as well as the crack strain induced by the freezing of water (𝑃_𝑤) can be determined.

𝜀^𝑐 = 2√𝜋𝐴(𝑇, 𝑎)𝛽𝑚

⁡(1 − 𝜈²)𝐾_𝑐

𝐸 ∫ √1/𝑎⁡𝑑𝜌(𝑎₀)

𝜌(𝑎_𝑚𝑎𝑥) 𝜌(𝑎_𝑚𝑖𝑛)

( 6-6 )

The deterioration analysis will be coupled with the heat conduction analysis. As with the crack strain, only a portion of the thermal strain remains after thawing. The residual thermal strain is proportional to the temperature gradient and 𝛽_𝑚 as,

𝜀^𝑡= 𝛽_𝑚⁡𝛼_𝐿 𝑇 ( 6-7 )

where 𝛼_𝐿 is the linear coefficient of thermal expansion. Due to a drop in temperature, 𝜀^𝑡 is a negative value.

The overall nanopore dilation (𝜀) due to the repetition of freezing and thawing is a sum of thermal strain and crack strain in response to the freezing of pore water, and it reflects the deterioration degree and the effectiveness of cyclic liquid nitrogen injections.

𝜀 = 𝜀^𝑡+ 𝜀^𝑐 ( 6-8 )

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Practically, volumetric strain (𝜀^𝑣) may be more useful. For spherical pores, 𝜀^𝑣can be approximated as 4/3𝜋𝜀³. The magnitude of 𝜀 characterizes the deterioration degree of pore structure induced by cyclic liquid nitrogen injections.