#
Strength Reduction of Coal Pillar after CO_{2} Sequestration in Abandoned Coal Mines

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## Abstract

**:**

_{2}geosequestration is currently considered to be the most effective and economical method to dispose of artificial greenhouse gases. There are a large number of coal mines that will be scrapped, and some of them are located in deep formations in China. CO

_{2}storage in abandoned coal mines will be a potential option for greenhouse gas disposal. However, CO

_{2}trapping in deep coal pillars would induce swelling effects of coal matrix. Adsorption-induced swelling not only modifies the volume and permeability of coal mass, but also causes the basic physical and mechanical properties changing, such as elastic modulus and Poisson ratio. It eventually results in some reduction in pillar strength. Based on the fractional swelling as a function of time and different loading pressure steps, the relationship between volumetric stress and adsorption pressure increment is acquired. Eventually, this paper presents a theory model to analyze the pillar strength reduction after CO

_{2}adsorption. The model provides a method to quantitatively describe the interrelation of volumetric strain, swelling stress, and mechanical strength reduction after gas adsorption under the condition of step-by-step pressure loading and the non-Langmuir isothermal model. The model might have a significantly important implication for predicting the swelling stress and mechanical behaviors of coal pillars during CO

_{2}sequestration in abandoned coal mines.

## 1. Introduction

_{2}to greenhouse efficiency was 63% [1]. According to statistics, fossil fuel combustion and industrial emissions of CO

_{2}accounted for about 78% of total CO

_{2}emission in the ten years from 2000 to 2010 [2]. Currently, CO

_{2}storage in oil and gas fields, brine water, deep unmined coal seams and deep sea are considered to be effective and practical ways to reduce atmospheric CO

_{2}level, helping to slow global climate change and temperature rise trends, in the event that fossil fuels remain in use as a primary energy source. In the 2013 technology roadmap, the international energy agency (IEA) proposed an integrated approach to drop greenhouse gas emission by reducing the use of fossil fuels, improving energy efficiency, implementing new energy sources and carbon capture and sequestration (CCS) technology [3]. In addition, with the successful exploitation of coalbed methane and shale gas, its considerable economic benefit prompted many countries to begin in order to regard shale gas, coalbed methane, as alternative unconventional energy. Many scholars have proposed using CO

_{2}to enhanced coalbed methane (ECBM) production, and the presence of CO

_{2}will mechanically weaken the coal and thus create fractures, helping to increase the permeability, improve the coalbed methane production yield and simultaneously sequestrate CO

_{2}[4,5,6,7,8]. In addition, for the residual space volume constituted by goaf areas and principle infrastructures in abandoned coal mines, some researchers proposed CO

_{2}sequestration in abandoned coal mines following the example of natural gas storage in it [9,10,11,12], which will be a potential option for CO

_{2}disposal because China has a large number of scrapped coal mines, and 541 key coal mines will be gradually closed by 2020. CO

_{2}can be stored in abandoned coal mines in three states: adsorbed on the remaining coal, free in empty space or dissolved in mine water.

_{2}in coal can result in coal matrix swelling due to the fact that it has the highest adsorption potential compared with other fluids such as CH

_{4}and N

_{2}. Currently, two mechanisms are applied to explain the adsorption-induced swelling in coal. On the one hand, several authors have widely researched the polymer structure, degree of cross-linking, three-dimensional polymeric network structures, as well as flexibility characteristics of coal macromolecules from the perspective of chemistry and molecules, and consider that the lower molecular-weight solvent, such as CO

_{2}and CH

_{4}, can enter the macromolecule cross-linked polymer mesh, causing the coal matrix macromolecular structure rearrangement, resulting in swelling [13,14,15,16,17]. One the other hand, some scholars attribute the swelling being due to the formation of microfractures as the result of different pore systems, maceral components and mineral stiffness [18,19,20,21]. Hol et al. [22] considered CO

_{2}induced both reversible (i.e., adsorption-induced swelling and elastic compression) and irreversible (i.e., adsorption-induced microfracturing) strains under unconfined conditions.

_{2}sequestration in coal seams are concerned with the coal reservoir permeability behavior, the adsorption-induced swelling of coal matrix can compress the pore space and cleat system to result in the distinct decrease of the permeability of coal mass, and several models have been proposed from the consideration of effective stress, cleat volume compressibility, gas sorption-induced strain effect as well as pressure pulse decay [23,24,25,26,27,28,29]. Ranjith et al. [30] developed a triaxial equipment to study the gas fluid flow and found that coal mass permeability for CO

_{2}decreased largely with the increase of effective stress than that of N

_{2}, due to the matrix swelling by CO

_{2}adsorption in coal. In addition, Verma and Sirvaiya [31] utilized the artificial neural network (ANN) to predict the Langmuir volume and pressure constants during CO

_{2}adsorption in coal, and that the ANN method was more accurate than other models in their study.

_{2}adsorption on the strength of coal have been studied widely [32,33,34]. According to Gibbs’ theory, when a more reactive, higher-chemical-energy adsorbate is used to displace the original adsorbate in solid adorbent, the surface energy of rock mass would reduce, which can lead to some reduction in initiation tension stress for fracturing and eventually the coal becomes more prone to damage. In addition, considering the thermodynamics of adsorption of gases in porous solids, the changes in surface energy at the interface between the gas adsorbate and solid adsorbent result in swelling through the conversion between surface free energy and elastic strain energy [35,36]. Based on the theory and experiment proposed by Meyers, a theoretical model was derived by Pan and Connell [37] through the energy balance approach. Hol et al. [38] developed a thermodynamic model based on statistical mechanics, and the model combined adsorption in a stress-supporting solid with the poroelastic to derive the relationship of stress–strain-sorption of coal under unconfined swelling condition. Liu et al. [39] revised the model derived by Hol et al. [38], and a corrected expression was obtained based on both statistical mechanics and kinetic approaches. Furthermore, Hol et al. [40] found the apparent bulk modulus determined for CO

_{2}-equilibrated state was approximately 25% lower compared to the evacuated state through experiment data analysis. Ranjith et al. [32] studied the crack closure, crack initiation and crack damage of coal subjected to saturation with CO

_{2}. Ranjith and Perera [41] considered the effects of the cheat system on strength reduction of coal after CO

_{2}adsorption. Perera et al. [42] experimented with adsorption of gaseous and super-critical CO

_{2}on bituminous coal from the Southern Sydney Basin, Australia, and studied the mechanical properties of coal sample before and after adsorption. The results showed that, compared with the natural state uniaxial compressive strength (UCS), the gaseous CO

_{2}saturation reduced UCS by 53% and elastic modulus by 36% using gas saturation pressure of 6 MPa. However, the supercritical CO

_{2}saturation reduced UCS by 79% and elastic modulus by 74% using super-critical saturation pressure of 8 MPa. It is shown that the phase of CO

_{2}has a significant effect on physical properties of coal, the adsorption capacity, swelling effect and strength parameters.

_{2}adsorption causes the coal mass to break down along the cleat system easily due to the fact that the adsorption mainly affects the cohesion of coal, and the reduction of cohesive force leads to the apparent plastic deformation areas. However, for the internal friction angle, it decreases to a certain extent and no longer keeps changes. Pillars with a large number of cleats and fractures act as sealing walls when CO

_{2}is stored in goafs and drifts. It means that the stability of the pillar decides the safety and sealing of CO

_{2}sequestration. Based on the above discussions and conclusions, it is significantly important to discuss the strength reduction of the coal pillar after CO

_{2}injection in the abandoned coal mines. In this paper, we focus our attention on strength reduction of the pillar when CO

_{2}sequestration in abandoned coal mines, through the relationship of sorption-strain based on unconfined conditions, and swelling-stress under uniaxial conditions. Finally, a strength reduction model is proposed to qualitatively understand the effects of CO

_{2}adsorption on the strength and failure mechanics of coal pillar in abandoned coal mines.

## 2. Theoretical Model

#### 2.1. Adsorption-Induced Swelling Strain

_{2}adsorption-induced volume strain has been studied by many researchers under unconfined conditions or uniaxial strain conditions [28,38,42]. In this section, we consider the adsorption-induced strain from the perspective of unconfined conditions. It is easy to measure the volumetric strain value of test coal samples when carrying out a gas adsorption experiment in the laboratory under unconfined conditions. As shown in Figure 3, the sample is a cube with the side length l. Two lengths are measured as the base values for volume calculation. One located at parallel (l

_{pa}) to its bedding plane, and the other is perpendicular (l

_{pe}). The parallel and perpendicular displacements were Δl

_{pa}and Δl

_{pe}, respectively.

_{0}), and the volume increment was calculated based on the reference value with the pressure increasing step-by-step.

_{i}

_{−1}(the swelling at the end of time exposure to P

_{i}

_{−1}). At the ith adsorption pressure step, Q(t)

_{i}is the swelling at the end of time exposure to P

_{i}. The fractional swelling increment is q

_{i}(t) during the coal sample is exposed to P

_{i}[45]:

_{i}(t) is the volume strain change of the ith pressure step, which ranges from 0 to 1. q

_{i}(t) = 0 means that adsorption just recently occurs at the P

_{i}pressure step, and the swelling increment instantaneously changes with the adsorption amount. q

_{i}(t) = 1 indicates that the swelling has reached equilibrium at the given gas pressure P

_{i}. In order to facilitate the use of the elastic mechanic theory, Equation (4) is converted to the form as follows:

_{vi}(t) means the fractional volumetric swelling increment from P

_{i}

_{−1}to P

_{i}.

_{i}pressure step, the fractional strain variation of the sample is Δε

_{Pi}from P

_{i}

_{−1}to P

_{i}

_{i}is the pressure increment from P

_{i}

_{−1}to P

_{i}. E

_{s}is the elastic modulus of coal matrix solid, which is not equivalent to the Young’s modulus (E

_{P}) that takes the elasticity of micropores into account. The relationship between the elastic modulus E

_{s}and the Young’s modulus E

_{P}can be expressed as [47]:

_{s}and ρ are the density of the solid phase (skeletal density) and apparent density, respectively.

_{s}is the Poisson ratio of the solid frame, ranging from −1 to 0.5, ν is the effective Poisson ratio, and $\mathsf{\varphi}$ is the porosity. In the process of deduction, it was assumed that the pore shape was cylindrical and the pores were randomly distributed. The relationships of E

_{P}/E

_{s}− ρ/ρ

_{s}as well as ν − ν

_{s}based on the research data of Bentz et al. [48] are shown in Figure 4.

_{i}and ε

_{i}, respectively. Two parts are included, gas adsorption induced matrix swelling strain Δε

_{vi}, taken as positive, and adsorption pressure loading induced strain Δε

_{Pi}, taken as negative:

_{0}and the volume at the time of t. In addition, the changes of Young’s modulus and Poisson ratio are also contained.

#### 2.2. Adsorption-Induced Stress under Uniaxial Conditions

_{2}gas (fluid) is injected in goaf, this adsorption behavior will occur in the pillar. Under the uniaxial condition, adsorption-induced swelling strain occurs on the two sides adjacent to goafs and drifts, but the swelling strain of the direction perpendicular to bedding is inhibited, resulting in the swelling stress occurring in the vertical direction (z axial, Figure 3). The swelling stress can decrease crack initiation stress, resulting in the damage of the coal pillar. In this section, we consider the derivation of swelling stress in the direction perpendicular to bedding.

_{i}

_{−1}to P

_{i}can be calculated by Formula (15). The swelling stress includes two parts. The first part is the adsorption-induced swelling stress, and the second is volume-compressed stress:

_{n}, the pillar perfectly reaches adsorption equilibrium, and the fractional swelling variation does not change and the linear strain also remains constant. In this case, the swelling stress is the cumulative value of stress increments at overall adsorption pressure steps:

_{iz}(t) is the total swelling stress considering the adsorption occurring in the pillar in the vertical direction where swelling strain is inhibited under the uniaxial condition. The swelling stress is a cumulative value by step-by-step pressures loading from 1st to nth steps.

#### 2.3. Mechanical Strength Change after Gas Adsorption

_{2}injection in abandoned coal mines, while it shrinks when gas is expelled from coal mass. Adsorption expansion will inevitably lead to some changes in the mechanical properties of the pillar, such as the above mentioned parameters, elastic modulus, Poisson’s ratio, bulk modulus as well as shear modulus, due to these parameters being highly effected by adsorption-induced fracturing. All of these variations result in the decrease of pillar strength during CO

_{2}sequestration in abandoned coal mines. Hu et al. [49] demonstrated that the adsorption of gas exhibits dual effects on the physical properties of coal, mechanical (swelling stress) and non-mechanical (erosion effect) effects. The swelling effect leads to the decrease of the interaction between coal particles, while the erosion effect reduces the surface energy and lowers the surface tension of the coal mass. Gas adsorption mainly affects the cohesion, and the decrease of cohesion leads to obvious plastic deformation of coal, but, for the internal friction angle, it decreases to a certain extent and the hold over no longer changes. Hol et al. [40] verified that gas sorption can lead to a decrease in bulk modulus, while an increase in swelling caused the strain hysteresis to be oversized during the process of loading–unloading. Hagin and Zoback [50] compared the adsorption characteristics of CO

_{2}with that of helium, and found that the Young’s modulus decreased after the CO

_{2}saturation adsorption. Simultaneously, the static bulk modulus reduced by an order of magnitude. Yang and Zoback [51] observed that CO

_{2}injection into coal samples resulted in the volume increase, and the coal sample became more viscous and less elastic. Ranjith and Perera [41] considered the effects of cleat density and direction on CO

_{2}adsorption-induced strength reduction.

^{2}). Furthermore, the relationship between the solid linear expansion strain and the change in surface tension is as follows:

_{0}and γ

_{s}are the vacuum state and surface tension after gas adsorption, respectively, and λ can be described as Equation (19) [52]:

_{s}is the apparent modulus.

_{n}for the nth adsorption step is expressed as function of time and swelling stress:

## 3. Discussion

#### 3.1. Swelling Strain and Swelling Stress

_{i}(t) and isotropic linear strain (ε

_{iz}(t)) in the z axial direction (Figure 3) as function of time after equilibrium by adsorption pressure increasing step-by-step under unconfined conditions. In connection with swelling strain, Hol et al. [38] and Liu et al. [39] considered thermodynamic models of gas adsorption and studied the effect of stress on the adsorption concentration of gas as well as sorption behavior. Their starting point is different from this paper based on directly volumetric changes. In the paper of Liu et al. [39], they established the relationship of internal energy, chemical potential, entropy change as well as stress–strain work on a single molecule of gas absorbed by the coal matrix cube. The strain was divided into mean extensional strain and deviatoric strain. In the deviation process of volumetric strain in this paper, it is easy to measure the strain increment without considering the thermodynamic process of adsorption. However, the coupling based on thermodynamic between stress–strain-sorption is significant important to understand the effect of pressure and temperature on adsorption in coal matrix. The swelling strain was divided into a reversible part and irreversible part under unconfined conditions [53]. Similarly, Wang et al. [54] divided strain into two parts at an isothermal condition. One is the mechanical deformation meeting the Hooke law stress–strain relationship and is calculated by the effective stress. The other is the deformation induced by gas adsorption or desorption. In Section 2, we do not mention it because not only an elastic strain but also an irreversible strain are converted to swelling stress considered from a macro perspective in the vertical direction under uniaxial loading.

_{2}adsorption on the coal mass can be described in a multi adsorbed layer model, i.e., the Brunauer-Emmett-Teller (BET) adsorption type model.

_{p}is the pore pressure.

_{2}and H

_{2}S storage in coal seam, Chikatamarla et al. [59] also calculated the frictional expansion strain by the Langmuir model:

_{L}, P

_{L}are gas adsorption volume, adsorption pressure, Langmuir volume and Langmuir pressure, respectively. In addition, ε

_{V}and ε

_{L}are, respectively, the strain at given pressure and strain at infinite pressure, and p

_{e}is the Langmuir pressure constant, which is equal to the pressure value when the strain at the pressure is half of the Langmuir maximum strain.

_{a}and ε

_{r}are, respectively, the axial strain and the radial strain.

_{ob}denotes the overburden pressure, a and b are empirical constants, V

_{r}denotes the vitrinite reflectance of coal, and γ denotes the bulk density of the gas. p, ε

_{L}and P

_{L}are consistent with Equations (28) and (29).

_{0}is the saturation pressure of gas, P is the adsorption pressure, V

_{m}is the maximum adsorption volume at the time the entire adsorbent surface is covered with a complete single molecular layer, and C is a constant related to the net heat of adsorption.

_{2}is sequestrated in deep unmined coal seams, where it is confined in states of high temperature and high pressure. Under the situation that CO

_{2}may exhibit a supercritical state that includes dual characteristics of gas and liquid, and the density of supercritical CO

_{2}fluid is close to that of the liquid, but the viscosity of which is similar to that of the gas. The diffusion coefficient of supercritical CO

_{2}is nearly one hundred times of that of the liquid.

#### 3.2. Stress and Strength Reduction

_{I}(Figure 9). The strain is considered including two parts: the first part is the coal matrix strain induced by the internal swelling stress, and the second part is the volume strain of the fracture. Their work modified the form of effective stress, so that the corrected expression of effective stress can directly reflect its impact on the permeability. Nevertheless, the elastic modulus, Poisson’s ratio as well as other parameters are variable rather than fixed values during the occurrence of coal matrix adsorption swelling. These variates are not taken into account in the derivation of theory and formula, which leads to some errors in the accuracy of the model.

_{2}adsorption and mechanical behavior of coal, and held that peak strength could decrease when coal is saturated with CO

_{2}. However, they did not comprehensively interpret the strength reduction mechanism. In this research, pillars are assumed to reach equilibrium on both sides of goaf after the mining working finished, and pillars are under the uniaxial condition. The coal pillar strength reduction is theoretically analyzed, and adsorption can increase the swelling stress on the faces of microfractures and cleats, resulting in effective stress decreasing. Under the condition of uniaxial conditions, if the loading pressure remains constant, and no swelling occurs, cracks could maintain the equilibrium state. However, when adsorption behaviors take place, the crack surface tension changes, and swelling stress emerges by swelling strain being inhibited. The stress needed to cause crack initiation is decreased, leading to coal pillars potentially being more prone to failure. The model proposed in this paper can describe the effect of swelling stress on strength clearly.

_{2}sequestration in abandoned coal mines, the strength change of coal pillars must be emphasized to prevent CO

_{2}leakage from goafs. To accurately predict the swelling stress in the vertical direction and strength reduction of pillars, much more research and many more approaches are still required.

## 4. Conclusions

_{2}is stored in abandoned coal mines. The volumetric swelling strain is theoretically derived as a function of time by adsorption pressure increasing step-by-step under unconfined conditions. In connection with the conditions of coal pillars in abandoned coal mines, and a uniaxial loading model is proposed by simplifying the actual condition. Swelling strain in a direction perpendicular to bedding is inhibited when CO

_{2}adsorption is in the pillar. The effect of adsorption on pillar strength reduction is theoretically analyzed and deduced. Our findings can be summarized as follows:

- There are a large number of coal mines that will be closed and some of them are located in deep formations in China. CO
_{2}storage in abandoned coal mines could be a potential option for greenhouse gas disposal. - The volume strain and swelling stress, as a function of time, and different loading pressure steps are deduced. Equation (15) is used to describe swelling stress considering coal has already had prior swelling deformation under the condition of step-by-step non-linear loading and a non-Langmuir isothermal model. The model presented in this paper is different from other models, in which only the initial state and the final equilibrium state are considered, and the incremental swelling process is neglected.
- A theoretical model based on linear swelling stress–strain work is proposed to calculate the reduction ratio of coal pillar strength under uniaxial conditions. This theoretical model can be used to describe strength reduction during adsorption under adsorption pressure loading step-by-step.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 4.**(

**a**) The relationship of E

_{P}/E

_{s}and ρ/ρ

_{s}; (

**b**) the linear figure of ν against ν

_{s}($\mathsf{\varphi}$ = 0.07) [48].

**Figure 7.**The reduction ratio curve of adsorption strength (${\mathsf{\sigma}}_{\mathrm{c}i}^{2}(t)$) to original strength (${\mathsf{\sigma}}_{\mathrm{c}0}^{2}$) over time. The swelling strain data are collected from [45].

**Figure 9.**Graphical description of the internal swelling stress ([64]).

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**MDPI and ACS Style**

Du, Q.; Liu, X.; Wang, E.; Wang, S.
Strength Reduction of Coal Pillar after CO_{2} Sequestration in Abandoned Coal Mines. *Minerals* **2017**, *7*, 26.
https://doi.org/10.3390/min7020026

**AMA Style**

Du Q, Liu X, Wang E, Wang S.
Strength Reduction of Coal Pillar after CO_{2} Sequestration in Abandoned Coal Mines. *Minerals*. 2017; 7(2):26.
https://doi.org/10.3390/min7020026

**Chicago/Turabian Style**

Du, Qiuhao, Xiaoli Liu, Enzhi Wang, and Sijing Wang.
2017. "Strength Reduction of Coal Pillar after CO_{2} Sequestration in Abandoned Coal Mines" *Minerals* 7, no. 2: 26.
https://doi.org/10.3390/min7020026