Adsorption behaviour and thermodynamics of water on deep reservoir and its influence on CO₂ sequestration

Abstract

In this study, the adsorption experiments of water vapour on deep reservoir were conducted. The thermodynamics for water vapour adsorption were analysed. Results illustrate that primary binding centres have stronger affinity than secondary binding centres. Water molecule will be preferentially trapped at primary binding centres in low-pressure region. In high-pressure region, secondary adsorption predominates. Primary adsorption spontaneity increases with pressure. At secondary binding centres and total binding centres, the spontaneity degree quickly improves and then slowly decreases as pressure increases. The transfer of water molecules from the more energetic binding centres to the less binding centres leads to the initial reduction in entropy loss (ΔS) and isosteric heat of adsorption (Q_st). The late enhancement in ΔS and Q_st is caused by the growing water clusters. Water vapour adsorption can promote CH₄ desorption. By occupying adsorption sites and reducing pore connectivity, water vapour adsorption causes an unfavourable effect on CO₂ sequestration.

KEYWORDS:

• Water
• deep reservoir
• adsorption thermodynamics
• pore structure
• cluster networks

1. Introduction

At present, hydraulic fracturing technology is widely applied to enhance the reservoir permeability [1–4]. However, as the polar molecule, water molecule possesses the stronger adsorption affinity on matrix surface relative to the nonpolar molecules (CO₂, CH₄ and N₂) and can replace the pre-adsorbed CO₂ and CH₄ molecules, which has an adverse effect on the behaviours for CO₂ and CH₄ adsorption [1]. Meanwhile, once the water molecule is adsorbed on the opening of the pore or the clay minerals are swelling during the hydration process, the pore throat will reduce or be entirely blocked, decreasing the diffusion capacity of CO₂ and CH₄ [2]. Therefore, understanding the reservoir–water interaction is of great significance to CO₂ geological sequestration.

To date, to better implement CO₂ storage in deep reservoir, many efforts have been performed regarding the reservoir–water interaction [1–6]. The influences of external factors (pressure and temperature) and internal characteristics of reservoir on water molecule adsorption process have been studied [1–5]. Svabova et al. [2] by measuring the adsorption isotherms and kinetic curves of water molecule on Czech reservoir found that the reservoir containing more surface functional groups has the greater uptake together with lower reaction constant. Charriere and Behra [1] investigated the adsorption/desorption characteristics of water molecule on deep reservoir and pointed out that the uptake of water molecule on reservoir is associated with inorganic matter proportion and oxygen content. McCutcheon et al. [5] discussed the adsorption hysteresis phenomenon of water molecule on eight deep reservoirs. Their results indicated that the hysteresis in low-pressure is affected by the swelling of reservoir and the hysteresis in high pressure is related to the pore shape. Wu et al. [3] constructed macromolecular reservoir structural model and analysed the adsorption behaviours of water molecule under different temperatures and pressure up to 100 kPa. They discovered that as the pressure increases, water–water interaction plays an increasingly important role in water adsorption. Yang et al. [4] illustrated that the different adsorption characteristics of water molecule on deep reservoir are closely relevant to oxygen-containing functional groups number and pore development degree. Obviously, the published literatures have confirmed that adsorption of water molecule on deep reservoir is generally governed through surface functional groups and inner pore structure [7]. Our previous research has exhibited that the oxygenated functional groups of low-rank coal reservoir are more abundant, and high-rank coal reservoir has more complex and rich pore system [8]. Correspondingly, the water-holding ability of coal reservoir displays a U-shaped change trend with increasing metamorphic degree, that is, the natural moisture content of low-rank coal reservoir and high-rank coal reservoir is higher than that of medium-rank coal reservoir [9]. The lower moisture content usually brings about less attention on the adsorption of water on medium-rank coal reservoir and its effect on CO₂ storage. Hence, more attempts should be focused on medium-rank coal reservoir–water interaction.

The adsorption process is often accompanied by the heat release, the rearrangement of adsorbed molecules, the loss of freedom of adsorbed molecules, the decrease in the disorder degree in fluid/solid interface and even the change of pore structure of solid material [10]. For better understanding, the mechanism for fluid adsorption at solid surface, the thermodynamics parameters, such as entropy loss (ΔS), Gibbs free energy change (ΔG), isosteric heat of adsorption (Q_st) and surface potential (Ω), should be systematically discussed. These thermodynamics parameters change with the course of adsorption and all have own physical meaning to interpret the adsorption behaviour. Up till now, there is little information provided about the thermodynamics for water molecule adsorption on deep reservoir [3,5]. McCutcheon et al. [5] adopted the net heat of adsorption to estimate the interaction between adsorbed water molecule and matrix surface. Their results illuminated that the net heat of adsorption for water on matrix surface shows the growing trend with increased oxygen content and a decrease trend with increased loading. Wu et al. [3] analysed the Q_st value for water on deep reservoir by molecular simulation technology. They pointed out that the heat released by water adsorption on the secondary adsorption centres is different from that on the primary adsorption centres. It is clear that not only the thermodynamics of water molecule adsorption on deep reservoir is rarely studied, but also the published data is mainly concentrated on the change of heat over the water adsorption process. The parameters of ΔS, Ω and ΔG for water adsorption on deep reservoir have not been comprehensively researched, and further investigation about the adsorption thermodynamics for water molecule on deep reservoir is necessary and meaningful.

In this study, we focus on the performance and thermodynamics for water vapour adsorption on deep reservoir and its influence on CO₂ sequestration. Firstly, the adsorption isotherms for water vapour were measured and correlated to D’Arcy and Watt model. Secondly, the adsorption behaviours on primary binding centres and secondary binding centres were compared. Then, the systematical research about adsorption thermodynamics for water vapour was conducted. Lastly, the effect of water vapour on the behaviour for CO₂ adsorption was discussed. This research will offer an improved understanding of the interaction of deep reservoir–water and promote the geological sequestration of CO₂.

2. Experimental details

2.1. Collection of sample

After collecting requied sample from deep reservoir, the sample was sent to the laboratory immediately to avoid the change of physicochemical properties causing by air oxidation. The proximate and petrographic analysis results are given in Table 1. The proximate analysis including ash (A_ad), equilibrium moisture (M_ad), fixed carbon (FC_ad) and volatile matter (V_daf) was performed based on GB/T 212–2008 standard. The mean maximum vitrinite reflectance (R_o,max) was conducted following GB/T 6948-2008 standard.

Table 1. Proximate and petrographic analysis results.

	Proximate, wt%
Sample	Mad	Aad	Vdaf	FCad	Ro,max (%)
Deep reservoir	3.01	15.20	13.40	70.83	1.78

2.2. FTIR measurement

The surface chemical characteristics affect the adsorption of water vapour greatly [11,12]. Generally, there is strong binding energy to maintain the adsorbed water molecule being bound tightly to surface functional groups. In this study, the surface functional groups distribution was analysed through FTIR spectrometry (Vertex 70, Bruker Corp).

2.3. Pore structure information analysis

2.3.1. Micropore morphology characterization

In this study, the pore classification is based on IUPAC recommendation. The pores with diameter less than 2 nm and larger than 50 nm are called micropores and macropores, respectively. The pores with diameter between 2 and 50 nm are called mesopores. The physisorption for CO₂ was carried out at 273.15 K to gain the micropore morphology using a Micromeritics ASAP-2020M apparatus. After adsorption measurement, the adsorption isotherms and pore structure parameters were automatically generated by instrument’s computer software.

2.3.2. Macro- and mesopore morphology characterization

The macro- and mesopore morphology were analysed through the adsorption of N₂ using a Micromeritics ASAP-2020M apparatus at 77 K. For N₂ adsorption experiment, the setting of relative pressure ranges from 0.001 to 0.995. Before conducting experiment, the sample was grinded into 60–140 mesh particle sizes. The outgas temperature for N₂ adsorption is 478.15 K [13]. Barret–Joyner–Halenda (BJH) model and Brunauer–Emmett–Teller (BET) were adopted to obtain the macro- and mesopore volume and surface area, respectively.

2.4. Isothermal adsorption measurement for water vapour

The adsorption experiments for water vapour were performed using IGA-100B gravimetric adsorption apparatus (Hiden Analytical Ltd.) with the experiment temperatures of 298, 308 and 318 K. Under each temperature condition, the relative pressure for water vapour (P/P₀) ranges from 0 to 0.90, and the relative pressure interval is 0.05. Before conducting experiment, the sample was outgassed at 383 K to eliminate the effect of impurities and moisture on adsorption behaviours.

3. Theoretical section

3.1. Adsorption model

The adsorption isotherms are frequently used as basis to interpret the adsorption phenomena. It not only quantitatively evaluates material adsorptive potential, but also provides the explanation on the adsorption mechanism. In addition, the correlation between experimental pressure and the accessibility of pore and the information related to adsorption/desorption rate, surface characteristics and pore network can also be analysed [14]. Currently, to better deal with the adsorption isotherm, various adsorption models have been proposed depending on different theoretical hypotheses, such as monolayer adsorption, multilayer adsorption and micropore filling. The suitable adsorption isotherm models for describing water adsorption include mainly Dent model, Modified Dent model, Cooperative Multimolecular Sorption (CMMS) model and D’Arcy and Watt model [15,16]. Among the adsorption isotherm models, D’Arcy and Watt model has successfully been adopted to treat water vapour adsorption curve on deep reservoir [5]. Hence, the obtained isotherms were correlated to D’Arcy and Watt model.

D’Arcy and watt model belongs to the sum of Langmuir model and original Dubinin–Serpinsky model [15]. It assumes that primary binding site and secondary binding site both have only one type. Thereby, primary binding site number and secondary binding site number can be estimated through D’Arcy and Watt model. Equation (1) gives the form of D’Arcy and Watt model [15]. (1) $m=\frac{\mathrm{AKP}}{1+\mathrm{KP}}+\frac{\mathrm{akP}}{1-\mathrm{kP}}$(1) where P represents pressure; m represents the mass adsorbed; A and a are the surface concentration for primary binding sites and secondary binding sites, respectively; K is the constant which can measure the attraction for adsorbate and a primary binding site; and k is the constant which can measure the attraction for adsorbate and a secondary binding site.

In Equation (1), the first term represents the contribution of Langmuir type and can quantity the adsorption amount at primary binding sites, and the secondary term represents the contribution of BET type and can quantity the uptake on secondary binding sites [5]. Accordingly, adsorption amounts on primary binding sites and secondary binding sites can be calculated through the first term and the second term in Equation (1), respectively.

The accuracy of the fitting results for D’Arcy and Watt model was evaluated by the sum of squares of the error (SSE), the root-mean-square error (RMSE) and the coefficient of determination (R²). SSE, R² and RMSE were gained by Equations (2), (3) and (4), respectively. The larger value of R² and smaller values of SSE and RMSE suggest the better goodness-of-fit. (2) $\begin{array}{rl}& \text{SSE}={\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2\end{array}$(2) (3) $\begin{array}{rl}& R^2=1-{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2/{\sum }_{i=1}^n{(y_i-\overline{y_i})}^2\end{array}$(3) (4) $\begin{array}{rl}& \text{RMSE}={\left[\frac{1}{n}{\sum }_{i=1}^n(y_i-\widehat{y_i})\right]}^{1/2}\end{array}$(4) where n is data point number; y_i, $\widehat{y_i}$ and $\overline{y_i}$ represent the experiment data, fitting data and the mean of experiment data, respectively.

3.2. Thermodynamics of adsorption

In this study, the adsorption thermodynamics parameters of entropy loss (ΔS), Gibbs free energy change (ΔG), isosteric heat of adsorption (Q_st) and surface potential (Ω) were discussed. Q_st refers to the heat effect produced in the process of adsorption and can be employed to measure the intermolecular bonding for adsorbent and adsorbate [7]. When assuming that Q_st is independent on temperature, Q_st can be calculated by Clausius–Clapeyron equation at different temperatures as shown in Equations (5) and (6) [8]. (5) $\begin{array}{rl}& Q_{\mathrm{st}}=R{T}^2(\mathrm{\partial ln}P/\mathrm{\partial T}{)}_m\end{array}$(5) (6) $\begin{array}{rl}& \ln P=-\frac{Q_{\mathrm{st}}}{\mathrm{RT}}+C\end{array}$(6) where T represents the temperature; R and C are universal gas constant and constant term, respectively. Q_st can be gained from the linear relationship of lnP and 1/T.

The required minimum isotherm work to retain a certain quantity of adsorbate molecule on adsorbent matrix surface is regarded as Ω [17]. ΔG is a critical parameter to estimate the spontaneity variation during the adsorption process [18]. Equations (7) and (8) present the getting methods for Ω and ΔG, respectively [8]. (7) $\begin{array}{rl}& \mathrm{\Omega }=-\mathrm{RT}{\int }_0^P\mathrm{md}(\ln P)\end{array}$(7) (8) $\begin{array}{rl}& \mathrm{\Delta }G=\mathrm{\Omega }/m=\left(-\mathrm{RT}{\int }_0^P\mathrm{mdln}P\right)/m\end{array}$(8) When gaseous adsorbate molecule is trapped in the adsorption sites, the degree of freedom of movement for adsorbate molecule and the disorder degree of gas–solid system will decrease. ΔS is the parameter that can be taken to evaluate the restricted mobility for adsorbate molecule and the change of gas–solid interface disorderliness [18]. Equation (9) gives the calculation method of ΔS. (9) $\mathrm{\Delta }S=(\mathrm{\Delta H}-\mathrm{\Delta G})/T$(9) where ΔH is enthalpy change and is equal to −Q_st.

3.3. Adsorption affinity

At low-pressure condition, with increasing experimental pressure, adsorption amount enhances linearly. This correlation can be expressed through Henry’s law. In Henry’s region, the adsorption amount is very small, and the adsorbed density on adsorbent surface is extremely low. Therefore, in Henry’s region, the interaction among adsorbed molecules on matrix surface can be ignored, and each adsorbate molecule can independently contact with the matrix surface [19]. Meanwhile, adsorbate molecule-adsorbent surface force predominates within Henry’s region. The interaction of adsorbate molecule-adsorbent surface is directly correlated with Henry’s constant [20]. Accordingly, taking Henry’s constant to evaluate the adsorption affinity is reasonable. A greater Henry’s constant suggests the stronger adsorption affinity for adsorbate molecule on adsorbent surface.

As presented in Equation (10), the correlation between adsorption quantity and equilibrium pressure should be expressed by a virial expansion to determine Henry’s constant (K_H) [19]. (10) $\text{ln}(m/P)=A0+A_{1}m+A_2{m}^2+$(10) where A₀, A₁ and A₂ represent the virial coefficients. K_H is related to A₀, and K_H= exp(A₀).

When m is low, the high-order term in Equation (10) can be ignored, and Equation (10) can be expressed as Equation (11). (11) $\text{ln}(P/m)=-A_0-A_{1}m$(11) Through matching the linear range of ln(P/m) vs. m, A₀ can be obtained, and then K_H value can be gained.

4. Results and discussion

4.1. Surface functional groups distribution

The gained FTIR spectra are depicted in Figure 1. The 3600–3750 cm⁻¹ region is owing to the O–H stretch vibration. The absorption peaks between 3000 and 3600 cm⁻¹ are relevant to hydroxyl structures. The peak range at 2800–3000 cm⁻¹ is caused by aromatic and aliphatic structures [21]. The obvious peak appearing at 2350 cm⁻¹ can be assigned to C≡C stretch vibration between 1900 and 2500 cm⁻¹. The region of 1000–1800 cm⁻¹ can offer relevant information on oxygen-containing structures. In the zone of 1350–1450 cm⁻¹, the aliphatic banding modes are observed. The 700–900 cm⁻¹ region is found due to aromatic C–H vibration modes. The infrared adsorption spectra of 500–600 cm⁻¹ are related to mineral matter [22].

Figure 1. FTIR spectra for adopted sample.

4.2. Pore morphology information

4.2.1. Macro- and mesopore structure information

The collected desorption and adsorption isotherms of N₂ are presented in Figure 2(a). The corresponding macro- and mesopore size distribution is given in Figure 2(b). At P/P₀ > 0.45, the adsorption and desorption isotherms do not coincide, and the hysteresis loop is very obvious. The adsorption isotherm for N₂ belongs to type II isotherm and has no plateau up to high P/P₀, suggesting the incomplete packing of pore structure. The hysteresis loop for N₂ exhibits the characteristics of H3 loop, indicating that the pore is slit- or plate shaped [21]. Remarkably, at P/P₀ of about 0.45, the desorption isotherm has a “forced closure” phenomenon, which is caused by the hemispherical meniscus instability during the desorption of adsorbate molecule at the pores with about 4 nm critical diameter [23]. As displayed in Figure 2(b), the macro- and mesopore size distribution is segmented. Over the region of 1.5–4.0 nm and 7.0–36.9 nm, sample has continuous pore size distribution.

Figure 2. N₂ adsorption/desorption isotherms at 77 K (a) and macropore and mesopore size distribution (b).

Table 2 gives the macro- and mesopore structure parameters. The BET-specific surface area (S_BET) is 0.60 m²/g. The total pore volume (V_t) measured by N₂ adsorption is 0.000865 cm³/g. The ratios of mesopore volume (V_mes) to V_t and micropore volume (V_mic) to V_t are 79.26% and 20.74%, respectively. It is apparent that S_BET and V_t are mainly contributed by mesopore.

Table 2. Macro- and mesopore structure parameters.

Sample	SBET (m^2/g)	Vt (cm^3/g)	Vmac (cm^3/g)	Vmes (cm^3/g)	Vmic (cm^3/g)	Vmac/Vt (%)	Vmes/Vt (%)	Vmic/Vt (%)
Deep reservoir	0.60	8.65E−4	0	6.86E−4	1.79E−4	0	79.26	20.74

Note: V_mac is the macropore volume.

4.2.2. Micropore structure information

The obtained adsorption isotherm of CO₂ is plotted in Figure 3(a). As demonstrated by previous studies, the micropore structure determined by NLDFT model has less error [24–26]. Thereby, the micropore structure determined by NLDFT model is adopted. The micropore size distributions are depicted in Figure 3(b). The micropore specific surface area (S_CO2) and micropore volume (V_CO2) are summarized in Table 3. The V_CO2 and S_CO2 values are 0.04 cm³/g and 125.80 m²/g, respectively. The main micropore sizes are around 0.35, 0.45, 0.50, 0.53, 0.60, 0.65 and 0.80 nm.

Figure 3. Measured adsorption isotherm for CO₂ at 273.15 K (a) and micropore size distribution (b).

Table 3. The V_CO2 and S_CO2.

Sample	calculated model	VCO2 (cm^3/g)	SCO2 (m^2/g)
Deep reservoir	NLDFT	0.04	125.80

4.3. Behaviours of adsorption for water vapour

4.3.1. Isotherms of adsorption for water vapour

The isotherms as a function of P/P₀ for the adsorption of water vapour are illustrated in Figure 4(a). When P/P₀ > 0.20, the uptake for water vapour is positively correlated with temperature. This phenomenon is also discovered for the adsorption of water vapour on montmorillonite and illite [16]. The abnormal relationship between uptake and temperature is caused by the increase in temperature and the enhancement in pressure. If P/P₀ is 0.5, the P values at 298, 308 and 318 K are 1.1673, 2.1237 and 3.6883 kPa, respectively. Under the same P/P₀, the larger experimental temperature, the greater pressure. Even though higher temperature is deleterious to adsorption process, the greater pressure is conducive to water molecule adsorption. As a result, the abnormal phenomenon between temperature and uptake occurs.

Figure 4. Uptakes of water vapour as a function of relative vapour pressure (a) and vapour pressure (b).

Figure 4(b) exhibits the adsorption isotherms as a function of P. Under the same P condition, decreasing temperature increases adsorption amount. High temperature can improve the excitation of adsorbed molecule and weak the interaction energy of adsorbed molecule with matrix [7]. Thereby, at high-temperature condition, the adsorbed molecule tends to be desorbed from surface binding sites, leading to the decrease in adsorption amount. The shape of all isotherms as a function of P is type II isotherm. The rapid increase in adsorption amount under low-pressure region is caused by the trapping on strongly binding centres, and then the slow and linear improvement of uptake caused by the trapping on weakly binding centres and the beginning of the formation of cluster. Under high-pressure condition, the steep uptake is resulted from the continuous growth of cluster and subsequent capillary condensation phenomenon.

The fitting result of isotherms through D’Arcy and Watt model is elucidated in Figure 4(b). Table 4 lists the obtained fitting variations for D’Arcy and Watt model. As exhibited in Figure 4(b), D’Arcy and Watt model coincides well with the isothermal adsorption curves. Meanwhile, R² values are all greater than 0.99, and SSE and RMSE values are lower than 0.0003 and 0.004, respectively. In addition, the residual plots at three temperatures are presented in Figure 5, which also reflects a good matching effect. Therefore, employing D’Arcy and watt model is reasonable. K values are all clearly larger than those of k. The evidently bigger value of K than k suggests that secondary binding centres have weaker attraction than primary binding centres. Improving temperature leads to the decrease in K and k, illustrating that higher temperature can weak the attraction.

Figure 5. Residual plots for D’Arcy and watt model at three temperatures.

Table 4. D’Arcy and watt modelling parameters of adsorption isotherms for water vapour.

		Model coefficients				Goodness of fit indexes
Sample	T (K)	A (mmol/g)	K (kPa^−1)	a (mmol/g)	k (kPa^−1)	R^2	SSE	RMSE
Deep reservoir	298	0.2942	1.6218	0.5122	0.1938	0.9994	2.7294E−4	3.8940E−3
	308	0.2947	0.6664	0.6520	0.1104	0.9999	2.8989E−5	1.2691E−3
	318	0.2591	0.5190	0.7226	0.0687	0.9999	1.4466E−4	2.8349E−3

4.3.2. Evaluation of primary adsorption and secondary adsorption for water vapour

The gained isotherms on primary binding centres, secondary binding centres and total adsorption centres at three temperatures are shown in Figure 6. Clearly, the performances for primary adsorption and secondary adsorption differ much from each other. At the early phase, the uptake on primary binding centres improves rapidly, while the increase of uptake on secondary binding centres is very slow. This behaviour indicates that water molecules can be adsorbed preferentially on the primary binding centres. In low-pressure region, primary adsorption governs the adsorption process. Previous investigations have reported that surface functional groups possess the high binding energy which can act as the primary binding centres [11,12]. Meanwhile, as pointed out by Chen et al. [27], the injected water molecules are inclined to be trapped on the specific binding centres rather than to be retained indiscriminately on material surface, which indirectly supports the primary binding sites concept. As presented in Figure 1, the FTIR measurement result shows that there are some functional groups including oxygenated functional groups on surface. The –COOH and –OH groups can act either as H bond donors or as H bond acceptors, while the groups only containing oxygen can adsorb water molecule via H bond acceptor interactions. Accordingly, the different behaviours of adsorption for water vapour on two type binding centres under low-pressure condition can be explained.

Figure 6. Isotherms of water vapour adsorption on primary centres, secondary centres and total adsorption centres

With the enhancement in pressure, the increasing rate for adsorption amount on primary binding centres gradually decreases, and the uptake of primary adsorption slowly approaches to the saturation value. Contrarily, the increasing rate for adsorption amount on secondary binding centres continuously enlarges, and the uptake for secondary adsorption enhances quickly. Hence, with increasing pressure, secondary adsorption is becoming more important. The constantly unobvious primary adsorption is caused by the less and less available primary binding centres. Coal is a complex porous material, containing both inorganic and organic matters. The inorganic matters, such as montmorillonite and illite clays, always have very strong adsorption affinity for water and are hydrophilic [16]. The organic matters, for example kerogen, show the characteristics of hydrophobicity [7]. Through investigating the contact angles of water on coal matrix surface, Gutierrez-Rodriguez et al. [28] found that there are three kinds of adsorption sites, i.e. hydrophilic adsorption sites, weakly hydrophobic adsorption sites and strongly hydrophobic adsorption sites, on coal surface. Meanwhile, many scholars have illustrated that water molecules on primary binding centres and the weakly binding sites (hydrophobic adsorption sites) can play the role of secondary binding centres [2,12,29]. As given in Figure 7, on the one hand, owing to the strong molecular forces between injected water molecules, under medium-pressure region, the water molecules will be retained on the hydrophobic adsorption sites by the formation of cluster networks. On the other hand, as the adsorption process continues, the subsequent water molecules can also be trapped by the form of multilayer adsorption on the pre-adsorbed water molecules. These pre-adsorbed water molecules are firstly retained on primary binding centres (hydrophilic sites). Therefore, with increasing pressure, the three-dimensional cluster networks constantly grow and bridge with adjacent clusters networks, and the multilayer adsorption continuously advances. The cluster networks formation and multilayer adsorption can account for the increasingly significant secondary adsorption under medium-pressure region.

Figure 7. Schematic of adsorption process of water molecules (corrected from Ref. [7])

Under the high-pressure condition, the uptake on primary binding centres approaches to saturation. Contrarily, over the high-pressure region, the increase rate of uptake on secondary binding centres improves fast, and the adsorption quantity on secondary binding centres increases quickly without saturation. It can be seen from Figure 7 that, with the increase in pressure, many smaller water clusters can continuously gather to form highly ordered structures. These highly ordered structures can stably be trapped on inner pore space. Meanwhile, with increasing pressure, the adsorbed water molecules by multilayer adsorption and formation of cluster can further fill the complex pore system through capillary condensation [7]. Accordingly, the capillary condensation can explain the rapid improvement on secondary binding centres at high-pressure condition. By comparing primary adsorption behaviour and secondary adsorption behaviour, we can discover that secondary adsorption dominates the adsorption of water vapour on bituminous coal under high pressure. It should be noted that due to the continuous improvement in clusters size, if the three-dimensional clusters are formed around the opening of inner pore, the diffusion ability for other molecules into inner pore obviously reduces [2]. In addition, as the proximal clusters further bridge together, the connected pore system can be separated into many smaller and isolated regions, which is detrimental to the adsorption and diffusion of other adsorbates [30]. When studying the effect of the adsorption of water vapour on coalbed methane recovery and CO₂ sequestration, secondary adsorption, especially the formation of clusters, should be focused on.

For primary adsorption, the isotherms are type I isotherm associated with monolayer adsorption. For secondary adsorption, the isotherms correspond to type III isotherm. To better understand the mechanism on primary binding centres, the isotherms for primary adsorption were dealt with using Langmuir model. The results show that Langmuir model coincides very well with the primary adsorption isotherms. Considering that one of hypotheses of Langmuir model is that the interaction among adsorbed adsorbates can be ignored [31,32] and primary adsorption is controlled by surface functional groups, it can be inferred that the attraction between adsorbed water molecules on primary binding centres is very weak and the functional groups distribution on bituminous coal is relatively scattered. The type III isotherm for secondary adsorption suggests that water molecules on secondary binding centres have the weaker interaction with bituminous coal surface and secondary adsorption originates mainly from the intermolecular binding of water.

The shape of isotherms on total binding centres is dominated by primary and secondary adsorption. Published data reveals that the isotherm shape for water is affected through inner pore structure, surface physicochemistry properties of adsorbent and experiment pressure [11]. Under low-pressure condition, the uptake is mainly provided by primary adsorption, which can interpret the fast rise for isotherms on total binding centres. Under medium-pressure condition, the flat isotherm on total binding centres is attributed to the continuously decreasing primary adsorption and the constantly increasing secondary adsorption. Under high-pressure condition, the quick enhancement in uptake on total binding centres is mainly caused by the cluster formation and capillary condensation. Moreover, Svabova et al. [2] pointed out that the type II isotherm can indirectly reflect that the density of surface oxygenated functional groups is moderate. The findings of Svabova et al. [2] support the functional groups distribution on bituminous coal is relatively scattered.

As described in Figure 6, primary adsorption isotherm is above the secondary adsorption isotherm in low-pressure region. With the increase in pressure, primary adsorption isotherm and secondary adsorption isotherm intersect. Subsequently, the secondary adsorption isotherm exceeds primary adsorption isotherm. Primary adsorption amount depends on surface functional groups number. The amount of secondary adsorption is affected by the available pore volume. The bigger quantity of secondary adsorption than primary adsorption illustrates that pore structure of bituminous coal affects the adsorption of water vapour more greatly than its surface chemical property.

4.3.3. Affinity of adsorption for water vapour

The obtained Henry’s constant (K_H) is summarized in Table 5. Clearly, K_H on total binding centres is the largest, while K_H on secondary binding centres is the smallest, indicating that primary binding centres possess the stronger affinity for water molecules than secondary binding centres. K_H value calculation is mainly according to the adsorption data over low-pressure region. Meanwhile, K_H value at primary binding centres is close to that at total binding centres. Therefore, the calculation result of K_H confirms the preferential adsorption on primary binding centres at the early stage. The calculation result of K_H also suggests that secondary adsorption is not by the direct interaction of water molecule-bituminous coal surface but by the binding of water molecules.

Table 5. Adsorption affinity coefficients for water vapour on total, primary and secondary centres.

			KH (mmol/g/kPa)
Sample	Adsorbate	T (K)	Total centres	Primary centres	Secondary centres	Data
Deep reservoir	Water vapour	298	0.65262	0.54267	0.10492	This study
		308	0.27821	0.21233	0.07611
		318	0.17441	0.15182	0.05303
Bituminous coal	CH4	288	0.00019			Du et al. [8]
		308	0.00015
		328	0.00012
Bituminous coal	CO2	288	0.00122			Du et al. [8]
		308	0.00093
		328	0.00079

With improving temperature, K_H values on primary, secondary and total binding centres all decrease. High temperature reduces the affinity on bituminous coal. As temperature increases, water molecule-bituminous coal surface interaction weakens, leading to the reduction in K_H.

4.4. Thermodynamics characteristics of adsorption for water vapour

4.4.1. Evaluation of surface potential

The calculated surface potentials (Ω) on primary, secondary and total binding centres are given in Figure 8. With the increase in pressure, Ω changes more negative, which shows that the trapping of water molecules demands more isotherm work under high-pressure [17]. For Ω on primary binding centres, the increase of Ω is mainly because of the selective adsorption. Initially, water is preferentially retained on the adsorption centres with bigger binding energy. Once these adsorption sites are employed, water is adsorbed on the adsorption centres with smaller binding energy. To maintain the water molecules on the less energetic centres, more isotherm work is required. For Ω on secondary binding centres, cluster networks size is growing with pressure. When the cluster networks size approaches the pore size, the gathering of molecules becomes more difficult, resulting in the increase in isotherm work.

Figure 8. Surface potential on primary binding centres, secondary binding centres and total binding centres.

Under different temperatures, higher temperature corresponds to the less negative Ω. The study of Mofarahi and Bakhtyari [33] has displayed that higher adsorption quantity can lead to larger (more negative) surface potential. As shown in Figure 6, increasing temperature causes a reduction in adsorption amount. Hence, high temperature brings about less negative surface potential. Meanwhile, the values of Ω all display a reduction upon to zero when the vapour pressure, i.e. adsorption quantity approaches zero, which is attributed to the equal surface potentials of contaminated adsorbent and uncontaminated adsorbent under low adsorption loading [34].

It can be found from Figure 8 that, at 298 K, over the whole vapour pressure range, Ω on primary binding centres is more negative than that on secondary binding centres. However, at 308 and 318 K, with increasing vapour pressure, the curves of Ω on two binding centres intersect. When temperature is 308 and 318 K, for the initial adsorption, Ω absolute value on primary binding centres is greater, while for the late adsorption, Ω absolute value on secondary binding centres is bigger. Moreover, as the temperature improves, the ratio of the vapour pressure value at the intersection to the total vapour pressure value decreases. This phenomenon illustrates that the enhancement in temperature affects primary adsorption more greatly. As given in Figure 9, at higher temperature, the final value of m₂/m₁ is bigger, confirming that enhancing temperature has a more adverse effect on primary adsorption. Furthermore, it is clear that for primary adsorption, the increase rate of Ω consistently decreases with vapour pressure, while the increase rate of Ω slowly improves with vapour pressure for the secondary adsorption. The decreasing increase rate of Ω on primary binding centres indirectly reflects that primary adsorption mainly occurs at the early phase and is affected by the binding energy of surface sites. The improved increase rate of Ω on secondary binding centres indirectly suggests that high-pressure benefits secondary adsorption.

Figure 9. Ratio of uptake on secondary binding centres (m₂) to that on primary binding centres (m₁).

4.4.2. Evaluation of Gibbs free energy change

When the pore surface of bituminous coal is formed, the force of pore surface is unbalanced. The surface carbon atoms are attracted to the interior of coal phase vertically and have a tendency to move towards the interior of the coal [35]. This tendency enables the carbon atoms on the surface to obtain an additional energy, namely surface-free energy. In the process of equilibrium, the coal surface often tries to adsorb other materials around to lower the surface-free energy [36]. Meanwhile, the surface of coal is actually a collection of many broken chemical bonds. These broken chemical bonds are very active and unstable. They can easily interact with other molecules or atoms around to reduce the surface-free energy and reach a new energy balance state [37]. Gibbs free energy change (ΔG) refers to the increment in surface-free energy per unit area, and the greater ΔG suggests that the adsorbent has the higher potential to trap the adsorbate molecules for reducing surface-free energy. Hence, ΔG can be reasonably employed to estimate spontaneity.

The calculated results for ΔG on bituminous coal on primary, secondary and total binding centres are depicted in Figure 10. The values of ΔG on three kinds of binding centres are negative, demonstrating the spontaneous process of adsorption. As plotted in Figure 10, as the vapour pressure enhances, ΔG on primary adsorption centres displays a continuous improvement. High pressure improves the spontaneity for water-primary centres system. For ΔG on secondary binding centres, ΔG rapidly enhances to maximum and then gradually reduces. Accordingly, in the initial stage, enhancing pressure is beneficial for adsorption on secondary binding centres. With improving pressure, the spontaneity of water-secondary centres system decreases. The effect of pressure on ΔG on secondary centres is mainly due to the growing size of cluster networks. Svabova et al. [2] have pointed out that once the clusters networks are formed around the pores throat, the pore volume and the accessibility for molecules into the internal pore both decreases. Meanwhile, as demonstrated by Brennan et al [30], the physically connected and continuous pore space can be deteriorated by formed water clusters by separating the pore volume to several isolated regions. The formation of single larger cluster-behaviour is detrimental to secondary adsorption and gives rise to the reduction in the spontaneity at late phase. Similarly, it can be seen from Figure 10 that with the improvement of pressure, ΔG on total binding centres firstly increases and then constantly decreases. This variation illuminates that high pressure reduces the adsorption spontaneity at the late stage, agreeing with the findings of Wang et al. [16].

Figure 10. Gibbs free energy change on primary binding centres, secondary binding centres and total binding centres.

Noticeably, ΔG variation on bituminous coal is affected through ΔG on primary binding centres and secondary binding centres. In low-pressure range, ΔG is mainly influenced by primary adsorption, and ΔG increases with pressure. In the high-pressure region, water vapour adsorption is mainly offered by secondary adsorption, and ΔG shows a decreasing trend. By comparing ΔG on primary binding centres and secondary binding centres, it is seen that ΔG absolute value on primary binding centres is obviously greater than that on secondary binding centres, which indicates that primary adsorption has the higher spontaneity degree and can be used to explain the preferential adsorption on primary binding centres.

On primary, secondary and total binding centres, the relationships between ΔG and temperature are different and complex. On primary binding centres, improving temperature decreases the absolute value of ΔG, and high temperature weakens the attraction and reduces the adsorption spontaneity. On secondary binding centres, the change of ΔG with temperature is not constant. In the early stage, lower temperature is related to lager absolute value for ΔG. Contrarily, in the late stage, the improvement in temperature leads to the bigger absolute value for ΔG. The investigation of Tang et al. [38] has indicated that cluster networks formation is more difficult under high-temperature condition. Correspondingly, the formed larger cluster networks at low-temperature block the internal pore system more completely. At the late stage when clusters are the main form of adsorption, high temperature can improve the spontaneity of secondary adsorption. On the bituminous coal (total binding centres), the relationship of ΔG with temperature is complex in low-pressure region, and decreasing temperature causes the reduction in adsorption spontaneity in high-pressure region.

4.4.3. Evaluation of isosteric heat of adsorption

Figure 11(a) shows the calculation process of Q_st. Figure 11(b) gives the calculation result of Q_st. As depicted in Figure 11(b), the value of Q_st ranges from 34 kJ/mol to 51 kJ/mol at a water vapour adsorption of 0.05–0.85 mmol/g. It is apparent that the enthalpy change (ΔH) value is negative, demonstrating that the exothermic feature of the adsorption. When the adsorption loading is lower than 0.6 mmol/g, Q_st value decreases with loading. At the adsorption loading larger than 0.6 mmol/g, Q_st value slowly enhances. The published literatures have reported that when the adsorbent surface is not energetically homogeneous, the adsorbate–adsorbate interaction cannot be ignored and Q_st value changes with adsorption loading (surface coverage) [39]. The decrease of Q_st for water vapour on bituminous coal confirms the nature of energy heterogeneity for bituminous coal surface. It is generally accepted that the change of Q_st with increased loading is controlled through adsorbate–adsorbate interaction and adsorbent–adsorbate interaction [35]. Meanwhile, for some porous materials with heterogeneous surface, the vertical interaction of adsorbent–adsorbate weakens with increasing coverage, while the lateral interaction of adsorbate–adsorbate enhances as the coverage increases [39]. At the initial phase, water molecules will selectively occupy the more active binding centres with the release of greater interaction energy. With the adsorption loading enhances, water vapour adsorption is forced to occur on the less active binding centres with the release of lower interaction energy. For example, compared with –OH group, –COOH group has the stronger adsorption ability for water molecules [6]. The transfer of water vapour adsorption from more favourable binding centres to less active binding centres gives rise to the initial decrease of Q_st. The decrease of Q_st illuminates that adsorbate–adsorbent interaction has a more evident influence on adsorption process at low surface coverage condition and indirectly verifies that primary adsorption is predominant over the low-pressure region. At the late phase, water cluster networks begin to form, and secondary adsorption becomes more and more important. With increasing surface coverage, the injected water molecules constantly gather on formed clusters, and the interaction among adsorbed molecules continuously enhances, resulting in the slow improvement of Q_st in high surface coverage condition. The late increase of Q_st also indirectly identifies the dominant roles of secondary adsorption and adsorbate–adsorbate interaction when majority of primary binding centres are occupied.

Figure 11. Calculation process (a) and calculation result (b) of isosteric heat of adsorption for water vapour.

It should be noticed that the liquefaction enthalpy (ΔH_liq) for water is −44 kJ/mol [40]. For the adsorption loading smaller than 0.1 mmol/g, the absolute value of ΔH is larger than that of ΔH_liq. This exhibits that relative to the interactions between water molecules occurring under the liquid state, the interaction of water molecule with the more energetic adsorption site on bituminous coal surface is stronger.

4.4.4. Evaluation of entropy loss

Besides Q_st, entropy loss (ΔS) is also one of the significant thermodynamics parameters. The calculated result of ΔS on bituminous coal is elucidated in Figure 12. ΔS values at three temperatures are all negative. The negative value for ΔS indicates that water vapour adsorption on bituminous coal includes the associative mechanism. Firstly, negative ΔS suggests the decrease in disorder degree at solid/gas interface. Then, negative ΔS points out that no obvious variation in the internal structure for bituminous coal occurs.

Figure 12. Entropy loss for water vapour.

As depicted in Figure 12, the value of ΔS is not constant, indicating the heterogeneous process for the adsorption of water vapour on bituminous coal. When the loading is lower than 0.2 mmol/g, ΔS absolute value rapidly reduces as loading enhances. Then, within the loading range of 0.2–0.6 mmol/g, ΔS absolute value slowly decreases with loading. For the loading bigger than 0.6 mmol/g, ΔS absolute value slowly increases with loading. As reported by Zhou et al. [41], the course of adsorption is usually accompanied by the freedom loss for adsorbed molecules and the production of more orderly packing on adsorbent. At initial stage, water is firstly retained on the adsorption centres with biggest binding energy, and the molecule movement is severely restricted. Because the translational degree of freedom is larger than rotational degree of freedom [42], the loss of freedom is mainly translational degree of freedom. As the preferential binding centres are occupied, adsorption mainly appears on the binding centres with lower energy. Hence, the restriction of adsorbed molecules progressively becomes weak, and molecule freedom increases, which cause the reduction in entropy loss. With adsorption goes on, secondary adsorption becomes the main trapping form for water molecules by the formation of clusters. These clusters will continuously gather and grow to form individually larger and highly ordered network structure, which can take up a larger amount of pore space. On the one hand, for a given size of pore, the absolute value of ΔS increases with adsorbate molecule size due to the more confinement and the more loss of translational entropy for larger molecule [42]. On the other hand, the smaller pore can produce the greater intensive entropy by hindering the structured fluid formation [43]. Therefore, the growing size of water cluster networks and the decreasing pore volume give rise to the improvement for ΔS at late stage.

For the pore structures with different shapes, the adsorption abilities differ from each other due to the overlap of interaction energy profile between fluid and pore wall in various degree. According to the investigation of Liu et al. [44], it is reported that the adsorption quantity for CO₂ and CH₄ is ordered as slit-shaped pore < wedge-shaped pore < bottleneck pore < cylinder-shaped pore. Similarly, pore geometry also has an important effect on adsorbate packing because of the confinement in different directions. The spherical pore confines the adsorbate molecule the most, followed by cylindrical pore and slit pore in sequence [43]. As discussion in Section 4.2, the pore structure of bituminous coal is slit- or plate shaped. Accordingly, the confinement of adsorbed water molecules on bituminous coal surface is weaker. In addition, combined with Figures 11 and 12, we can see that the variation of ΔS is in accordance with that of Q_st. The more orderly adsorbate packing can bring about more heat release [45]. Thus, the change of Q_st follows the change of ΔS. Generally, the release of more heat is deleterious to adsorption process. For the optimization of adsorption process design, the heat release and packing efficiency both should be considered.

4.5. Influence of water vapour on adsorption performances of CO₂ and CH₄

In previous study about CH₄ and CO₂ adsorption on bituminous coal, it is found that at the temperature of 288 K and pressure up to 1.80 MPa, the largest adsorption quantities for CH₄ and CO₂ are 0.20 and 0.80 mmol/g, respectively [8]. As described in Figure 4, the obtained greatest adsorption amounts on bituminous coal for water molecule at 298, 308 and 318 K are 0.90, 1.10 and 1.30 mmol/g, respectively. It should be noted that for the adsorption measurement of water vapour, the biggest vapour pressure is lower than 9 kPa. When the equilibrium pressure is 9 kPa, the uptakes of CO₂ and CH₄ on bituminous coal are extremely low and can even be ignored. Thereby, the adsorption ability for water vapour on bituminous coal is evidently greater than those for CO₂ and CH₄. As confirmed by Zhou et al. [6], owing to the strong dipole moment for water molecule, the negatively surface atoms have the stronger attraction for water molecule over the nonpolarity molecules of CH₄ and CO₂. Table 5 gives the comparison of K_H for water vapour, CH₄ and CO₂ on bituminous coal. K_H values for CO₂ and CH₄ are quite smaller than that for water vapour, demonstrating that bituminous coal possesses a stronger affinity for water molecule. By comparison with the Van der Waals forces between nonpolarity molecules (such as N₂, CH₄ and CO₂) and material surface, the intermolecular bonding between water molecule and material surface (such as ion-dipole attraction and hydrogen bonding) is much higher [7]. Hence, the trapping of water molecules on bituminous coal surface is more firm, and bituminous coal will preferentially adsorb water molecule. Even though the surface binding sites have been occupied by CH₄ or CO₂ molecule, the injected water molecule can still be retained on those binding sites through the displacement of pre-adsorbed CH₄ or CO₂.

When investigating the adsorption of CO₂ and CH₄ on bituminous coal, it is found that the isotherms of both gases are well correlated to Langmuir model [8], suggesting that the mechanism of CO₂ and CH₄ adsorption on bituminous coal is monolayer adsorption. On the contrary, as discussed above, the mechanism of the adsorption of water vapour on bituminous coal is different, and water molecules prefer to form cluster networks with increasing loading. Thereby, CO₂ and CH₄ adsorption on bituminous coal is two-dimensional, while water vapour adsorption on bituminous coal is three-dimensional, agreeing with the finding of Brennan et al. [30]. The three-dimensional networks can obviously reduce the available pore volume and worsen the pore system connectivity and reservoir permeability. When exploiting the coalbed methane, water vapour adsorption can cause an enhancement in CH₄ desorption, which is conducive to CH₄ recovery. However, for the geological sequestration of CO₂ in deep coal seams, the adsorption of water vapour can clearly reduce CO₂ storage ability and worsen CO₂ diffusion process, causing an unfavourable effect on CO₂ sequestration.

5. Conclusions

This study reports the adsorption measurement for water vapour at 298, 308 and 318 K. The analysis of adsorption thermodynamics for water vapour was conducted. The influence of water vapour on CO₂ and CH₄ adsorption was discussed. The following conclusions can be gained.

Primary adsorption is monolayer adsorption and plays a dominant role in the initial phase. With increasing pressure, the effect of primary adsorption becomes weaker, and secondary adsorption becomes evident. In high-pressure region, secondary adsorption predominates.

For primary adsorption, increasing pressure improves the adsorption spontaneity. On secondary and total binding centres, the adsorption spontaneity quickly enhances and then slowly decreases as the pressure increases. At the early stage, Q_st and ΔS decrease fast, while Q_st and ΔS slow increase at the late stage. The K_H value for water vapour is clearly higher than those for CO₂ and CH₄. Water vapour adsorption can promote CH₄ desorption and recovery and hinder CO₂ sequestration.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data applied to support the results in this study are available from the corresponding author upon request.

Additional information

Funding

This work was supported by Opening Foundation of Research and Development Center for the Sustainable Development of Continental Sandstone Mature Oilfield by National Energy Administration [grant number 33550000-22-ZC0613-0213]; National Natural Science Foundation of China [grant number 5226400, 42272202]; Yunnan Fundamental Research Projects [grant number 202101BE070001-039]; Yunnan Provincial Department of Education Science Research Fund Project [grant number 2022J0055] and Scientific and Technological Project of Henan Province [grant number 222102320060].