Supercritical-CO2 Adsorption Quantification and Modeling for a Deep Coalbed Methane Reservoir in the Southern Qinshui Basin, China.

Accurate depiction of the adsorption capacity of supercritical CO2 (ScCO2) by existing adsorption models is an important focus for deep coal seams in CO2-enhanced coalbed methane (CO2-ECBM) recovery. To investigate the applicability of different adsorption models for the adsorption isotherms of ScCO2, the validities of 10 different adsorption models were analyzed, based on analyses of the adsorption characteristics of ScCO2 from deep coal seams of the Southern Qinshui Basin, China. These models include the Langmuir (L) model, two-parameter Langmuir (TL) model, Toth (T) model, Langmuir-Freundlich (LF) model, extended Langmuir (EL) model, double parameter Brunauer-Emmett Teller model, three-parameter BET (TBET) model, Dubinin-Radushkevich (D-R) model, Dubinin-Astakhov (D-A) model, and Ono-Kondo lattice (OK) model. These models were tested for both the excess and absolute adsorption capacities of ScCO2 under various temperatures and pressures. The simulation accuracy of the different adsorption models was analyzed. The optimal models for the adsorption of ScCO2 in deep coal seams were selected based on a comprehensive analysis of the simulation parameters, standard error, and residual sum of squares. There were obvious differences in the validity of the different adsorption models in terms of the excess adsorption capacity and absolute adsorption capacity of ScCO2. The D-A and D-R models are the optimal adsorption models for the adsorption isotherms of the excess adsorption of ScCO2 for the whole tested pressure range. The T, TL, and D-R models are the optimal adsorption models in simulation of the excess adsorption capacity of ScCO2 for the selected adsorption models when the equilibrium pressure is divided into two sections at the point of 8.13 MPa. In simulation of the absolute adsorption capacity of ScCO2, the TBET and LF models are the optimal adsorption models among the selected models when the equilibrium pressure is less than or equal to 8.13 MPa. The linear, exponential, logarithmic, power function, and polynomial adsorption simulation all have good precision in the simulation of the absolute adsorption capacity of ScCO2 when the pressure is beyond 8.13 MPa.

Introduction

Deep coalbed methane (CBM) is a clean energy source and is considered as one of the primary natural gas resources in China.[1,2] Compared with shallow CBM reservoirs, deep-CBM formations have some unique reservoir properties because of the greater burial depth. For example, deep-CBM formations commonly have high gas content with high initial reservoir pressure, ultralow permeability, and high-stress conditions. These combined reservoir characteristics pose challenges for CBM exploration and development.[2−4] Enhanced CBM production through sequestration of CO2 in deep coal seams is one attractive alternative to increase gas recovery and simultaneously reduce greenhouse gas emission to the atmosphere.[3,5−13] CO2-enhanced CBM technology appears to be a “win–win” innovative technology for environmentally friendly energy production. However, there are key technical challenges to be solved before it can be commercially implemented, including injection optimization, methane–CO2 counter-diffusion quantification, multicomponent gas adsorption and competitive adsorption, and phase modification of CO2 under in situ reservoir pressure and temperature conditions, among others.[14−21] Thus, supercritical CO2 (ScCO2) adsorption behavior under the in situ conditions of deep coal seams needs to be investigated in detail for reservoir assessment and evaluation of enhanced gas production potential.

Adsorption isotherms of CO2 in coal are the effective method for estimating the capability and potential of enhanced coalbed methane recovery with CO2 injection (CO2-ECBM).[9,22−25] Many adsorption models have previously been employed to evaluate the excess adsorption capacity of coals. These models include the Freundlich model, Langmuir (L) model, Brunauer–Emmett–Teller (BET) model, Dubinin–Radushkevich (D–R) model, Dubinin–Astakhov (D–A) model, and Ono–Kondo (OK) model.[26−30] In addition, the ideal adsorbed solution model and the two-dimensional equation of state have been applied to determine mixed-gas adsorption.[31−34] To compare the validity of different adsorption models, some previous studies were conducted to evaluate the accuracy of the various models.[33,35] For a wide pressure range of CO2 adsorption, the L model was found to be ineffective in modeling high-pressure CO2 adsorption because of the unique phase change behavior of CO2 at high pressures, which does not occur for either CH4 or N2.[36] Commonly, all adsorption models used to depict gas adsorption behavior in most previous studies have been applied for bituminous coal reservoirs in relatively shallow coal seams.[34,37,38] Thus, the validity of these models has been limited for the simulation of gas adsorption behaviors from deep-CBM reservoirs, under the conditions of high and ultrahigh pressure and temperature.

Because deep-CBM formations are normally associated with high temperature and pressure, CO2 usually exists in a supercritical condition during injection. It is essential to investigate the validity of the different adsorption models used for modeling ScCO2 adsorption in deep coal seams. The Southern Qinshui Basin (SQB) in China is a mature CBM development with a deep-CBM reservoir,[39−41] with semianthracite and anthracite. In this study, 10 different models were tested and compared based on semianthracite and anthracite from the SQB. These models are the L model, two-parameter Langmuir (TL) model, Toth (T) model, Langmuir–Freundlich (LF) model, extended Langmuir (EL) model, double parameter BET (DBET) model, three-parameter BET (TBET) model, D–R model, D–A model, and OK model. These models were used in simulation studies to investigate the accuracy and reliability of adsorption modeling in reservoir simulation results and to optimize the appropriate model for ScCO2 adsorption through comparative analysis. The obtained results lay the foundation for deep-CBM reservoir development and CO2-enhanced CBM production optimization.

Review of Adsorption Isotherm Models

Table summarizes all adsorption models used in this work. Each model is depicted in the following sections.

Table 1

Adsorption Model Equations and Simulation Parameters Used in This Study

model name	model equations	equation nos	simulation parameters
L model		(1)	VL, PL
TL model		(2)	ninf, KL
T model		(3)	VL, Kb
LF model		(4)	VL, Kb
EL model		(5)	VL, Kb, n
DBET model		(6)	Vm, C, p0
TBET model		(7)	Vm, C, p0
D–R model		(9)	V0, D, n
D–A model		(10)	V0, D
OK model		(11)

L Model and Its Derivative Models

The L model assumes that the surfaces of the adsorbent are homogeneous and that adsorption occurs on a flat surface. The adsorption is local, specific, and occurs at a limited number of sites under a monolayer of adsorbate, and each localized site can accommodate only one adsorbate.[42] Based on the above assumptions, the L model can be derived aswhere V is the adsorption volume (cm3/g), VL is the Langmuir volume (cm3/g), p is the pressure of adsorption equilibrium (MPa), and PL is the Langmuir pressure (MPa).

The TL model was established by introducing the density of the free phase and density of the adsorbed phase in conjunction with the L model; the TL model can be defined aswhere nexcess is the excess adsorption capacity (mmol/g), ninf is the absolute adsorption capacity when the pore surface is fully covered by CO2 (mmol/g), p is the pressure of adsorption equilibrium (MPa), ρCO is the density of the free phase (g/m3), KL is the Langmuir coefficient simulated by the adsorption model, and ρsorbed is the density of the adsorption phase.[43]

The T, LF, and EL models were established by adopting three parameters: the binding constant Kb, model parameter n, and the Langmuir pressure PL, based on the L model.

Tóth formulated a three-parameter equation. Although the use of the Langmuir’s isotherm implies a homogeneous surface, the choice of the isotherm suggests a heterogeneous surface if n ≠ 1 (0 < n ≤ 1).[44] The T model (eq ), LF model (eq ), and EL model (eq ) can be derived, respectively, aswhere p is the pressure of adsorption equilibrium, MPa; PL is the Langmuir pressure (MPa); V is the adsorption volume when the pressure reaches equilibrium (cm3/g); VL is the Langmuir volume (cm3/g); Kb is the binding constant (m3·[t·(MPa)]−1); and n is a model parameter associated with the temperature and the distribution of coal pores.

BET Model

Brunauer et al. established poly-molecular layer theory based on the Langmuir adsorption theory by modifying the monolayer assumption into multilayer sorption potential.[45] Following Brunauer et al.’s work, the DBET model (eq ) and TBET model (eq ) were derived, respectively, as

In eq , p0 can be obtained as followswhere pc = 7.38 MPa is the critical pressure of CO2; p0 is the saturated vapor pressure (MPa); Tc = 304.25 K is the critical temperature of CO2; Vm is the adsorption capacity parameter of the monolayer (cm3/g); C is a constant associated with the adsorption heat and the liquefied adsorbate; p is the pressure of adsorption equilibrium (MPa); and n is a model parameter associated with the temperature and the distribution of coal pores.

D–R Model and D–A Model

The D–R and D–A models were developed based on the adsorption potential theory.[46,47] The D–R model can be derived asand the D–A model can be derived aswhere V0 is the micropore volume (cm3/g), D is a constant associated with the net adsorption heat, P0 is the saturated vapor pressure (MPa), and n is a model parameter associated with the temperature and distribution of coal pores.

OK Model

The OK model is based on lattice theory and was originally proposed by Ono and Kondo and extended by Sudibandriyo et al.[48,49]where Γ is the total adsorption capacity of each layer (mmol/g), Γ0 is the theoretical monolayer saturation adsorption density (mmol/g), ρ∞ is the density of CO2 ontology phase (mmol/L), ρmc is the density of the adsorbed phase, taken as 23.3636 mmol/L, εs is the contact potential energy between adsorbate molecules and the micropore surface (J), k is a constant of 1.38065 × 10–23 J/k, and T is the experiment temperature (K).

Materials and Methods

Origin and Characteristics of Coal

The coal in the SQB is mostly semianthracite and anthracite. In this study, fresh coal samples from coal seam no. 3, named the Yuwu, Sihe, and Chengzhuang samples, were collected from the Yuwu, Sihe, and Chengzhuang coal mines in the SQB, respectively; the characteristics of these coal samples are shown in Table . The samples were collected by columnar sampling according to Chinese National Standard GB/T475-2008[50] and were prepared into pulverized coal samples by crushing and screening fresh air-dried grains to the particle size range of 0.18–0.25 mm, according to Chinese National Standard GB/T16773-2008.[51] Coal petrography, proximate analyses, and specific surface analyses were conducted according to Chinese National Standards GB/T8899-2013, GB/T212-2008, and GB/T21650-2008.[52−54] An AXIO Imager M1m microspectrophotometer made by Zeiss, Germany, was used for coal petrography measurements (maceral composition and Ro,max), and a TriStar II3020 made by Micromeritics Instrument Corporation, USA, was used for measurement of specific surface area.

Table 2

Burial Depth, Ro,max, Maceral of Experimental Coal Samplesa

			maceral mass fraction
			vitrinite (%)
sample ID	burial depth (m)	Ro,max (%)	telocollinite	desmocollinite	inertinite (%)	exinite (%)	mineral (%)
Yuwu	539	2.18	12.90	60.76	23.16	0	3.18
Sihe	326	3.37	20.56	59.28	18.36	0	1.80
Chengzhuang	457	2.97	19.80	56.00	21.40	0	2.80

Note: Ro,max is the maximum vitrinite reflectance (%).

Mercury intrusion porosimetry (MIP) was conducted to analyze the pore size distribution for all coal samples, using the Autopore IV 9500 made by Micromeritics Instrument, USA, at pressure up to 60 000 psia (413.7 MPa) following ISO 15901-1-2016.[55] The pore surface areas of all coal samples were analyzed by applying the BET theory, which is a multilayer adsorption theory (Gregg and Sing, 1982).[56] Micropore observations and mineral quantitative analyses of anthracite samples were performed on a ZEISS Sigma field emission-scanning electron microscope (FE-SEM operating at 20 kV, equipped with an energy dispersive spectrometer for analysis of minerals composition) and abided by Chinese Petroleum and Natural Gas Industry Standards SY/T 5162-2014 and SY/T 6189-1996, respectively.[57,58]

Experimental Apparatus

The CO2 adsorption isotherm was measured using the volumetric method and we followed the recommended procedure of Chinese National Standard GB/T 19560-2008.[59] An independent high-pressure isotherm adsorption instrument DXF-II was developed in-house; the system is shown in Figure . The system includes a vacuum-pumping system, isothermal adsorption system, gas supercharging system, computer-control system, and a gas cylinder of CO2. A schematic diagram of the experimental apparatus was previously reported in the corresponding research.[60]

Figure 1

Schematic diagram of high-pressure isothermal adsorption instrument-DXF-II.

Experimental Procedure and Measurement Conditions

In this study, pure CO2 adsorption experiments were conducted at 45, 62.5, and 80 °C, respectively (Table ). The temperatures and pressures were selected according to the corresponding coal burial depths of 1000, 1500, and 2000 m. The adsorption isothermal experiment of ScCO2 was carried out after equilibrium moisture treatment of all coal samples.

Table 3

Experimental Parameters of Adsorption Isothermal Experiments

coal seam depth (m)	experimental temperature (°C)	pressure (MPa)
1000	45.0	10
1500	62.5	15
2000	80.0	20

Helium as a reference gas is widely used to determine the free volume of sample cells in adsorption experiments, regardless of the low-pressure and high-pressure conditions, because helium is non-adsorbing and inert, according to published references internationally.[22,61,62] A complete experiment for ScCO2 adsorption consists of five consecutive steps: (1) checking system airtightness; system airtightness, including the reference cell, sample cell, and tubing, was checked with helium at 10 MPa. If the system pressure remained constant for 6 h, the system was regarded to have good airtightness.[51] Then, the system was degassed under a high vacuum of 10–3 Pa for at least 24 h prior to beginning the measurements. (2) Setting experimental conditions; CO2 and helium were injected into reference cells at high pressure (above 10 MPa). The temperature of the sample cell and gas reference cells was set to 45 °C. The confining pressure and the opening pressure of the liquid-displacement valve were set to 10 MPa using a Gilson pump. The equilibrium time for adsorption was beyond 12 h. After temperature and pressure equilibrium were achieved, tubing and sample cells were degassed once again. (3) Calibrating errors; measurements of free-space volume calibration and pore pressure-induced water displacement were conducted using helium at pressures between 2.0 and 9.5 MPa. (4) Adsorption measurements were run by increasing the CO2 injection pressure in a step-wise manner to a maximum of 10 MPa. CO2 was injected into the sample cell by a booster pump until the sample reached adsorption equilibrium. The variations of pressure and temperature of the sample cell and gas reference cells were continuously monitored by an online data acquisition system.

After measurement of ScCO2 adsorption at the temperature of 45 °C, the same sample cell and pipelines were degassed once again. The experimental temperature was reset to 62.5 °C, CO2 and helium were injected into the cells at high pressure (above 16 MPa), and the confining pressure and opening pressure of the liquid-displacement valve were set to 16 MPa using a Gilson pump. After the temperature and pressure of the apparatus reached equilibrium, the measurement procedures (3) and (4) were repeated. At 62.5 °C, the adsorption measurements were run to the final pressure of 16 MPa. After this, the temperature was increased to 80 °C, and the adsorption measurements were run by increasing the CO2 injection pressure to 20 MPa.

Calculation of Adsorption Capacity

Adsorption capacity can be determined according to the manometric/volumetric method and the gravimetric method.[22,26,32,38,61,62] The gravimetric method requires a very accurate balance to determine the amount of gas sorbed at a constant pressure, the volumetric method requires very accurate determination of cell and free-space volumes, and the manometric method can determine the amount of the gas sorbed by means of pressure readings.

The excess (Gibbs) adsorption capacity obtained in the experiment is distinguished from the actual adsorption capacity, especially in a state of high pressure; therefore, the excess adsorption capacity and the absolute adsorption capacity were calculated, respectively. The density of the adsorbed phase for CO2 was calculated according to the van der Waals equation of ideal gas.[43]

Based on the equilibrium pressure and experimental temperature from the reference cells and sample cells, the excess adsorption capacity under different equilibrium pressures was calculated according to the manometric method.

Simulation Method

During the simulation, the pressure of adsorption equilibrium was selected as the independent variable, the adsorption capacity was selected as the dependent variable, and the simulation parameters were calculated by the Newton iterative method. Based on the obtained simulation formulas, the simulation model values could be calculated from the different adsorption models. The regression coefficients (R2) and correlation coefficients (R) of the simulation formulas were calculated based on the experimental values and simulation values of the adsorption capacity.

Experimental Results, Adsorption Modeling, & Discussion

Thermal Maturity, Coal Maceral, and Coal Quality

The vitrinite reflectance and coal maceral composition are listed in Table . The proximate analysis results are given in Table . To carry out the gas adsorption experiments, each coal sample was pulverized into 60–80 mesh size, and ∼100 g of air-dried powder sample was collected. The prepared coal samples were placed in an environmental chamber for equilibrium moisture treatment.

Table 4

Proximate Analysis Results of Experimental Coal Samplesa

sample ID	Mad (%)	Aad (%)	Vdaf (%)	Fcd (%)	St,d (%)	Qgr,d (MJ/kg)	Hdaf (%)
Sihe	1.48	13.12	6.32	81.39	0.28	30.52	3.40
Chengzhuang	2.71	12.18	6.94	81.72	0.34	30.94	3.56
Yuwu	1.10	11.98	13.44	76.19	0.25	31.17	3.79

Note: Aad is the ash content (%), Mad is the water content, air-drying basis; Vdaf is the volatile content, dry ash-free basis; Fcd is the constant carbon content; St,d is the sulfur content, moisture-free basis; Qgr,d is the calorific value, air-drying basis; Hdaf is the hydrogen content, dry ash-free basis.

Pore Size Distribution and Genetic Types of Pores

The pore size distribution curves determined using MIP show that the incremental pore volumes with pore diameters lower than 100 nm comprise a considerable proportion (Figure ). Tables and 6 show the pore volumes and their percentages for different types of the pores and the surface areas and their percentages for different types of the pores.

Figure 2

Incremental pore volume plots for Yuwu sample (a), Sihe sample (b), and Chengzhuang sample (c) using by MIP.

Table 5

Pore Structure Parameters of Different Coal Samples by MIPa

	pore volume (10–4 mL g–1)					volume fraction of PSD (%)
sample	V1	V2	V3	V4	Vt	V1/Vt	V2/Vt	V3/Vt	V4/Vt
Yuwu	24.70	21.16	110.09	190.76	346.71	7.12	6.10	31.75	55.03
Sihe	29.18	9.28	86.12	200.02	324.60	8.99	2.86	26.53	61.62
Chengzhuang	37.49	16.45	101.50	228.36	383.80	9.77	4.28	26.45	59.50

Notes: V1–V4, pore volume of macropore (>1000 nm in diameter), mesopore (100–1000 nm in diameter), transitional pore (10–100 nm in diameter), and micropore (<10 nm in diameter), respectively; Vt, total pore volume; V1/Vt to V4/Vt, pore volume fraction from macropore, mesopore, transitional pore, and micropore in the total pore volume, respectively; φMIP, total porosity, %.

Table 6

Surface Area of Pores with Different Pore Radii from Coal Samples by MIPa

	surface area (m2g–1)					percentage of PSD on surface area (%)
sample	S1	S2	S3	S4	St	S1/St	S2/St	S3/St	S4/St
Yuwu	0.002	0.05	2.11	15.72	17.87	0.011	0.263	11.79	87.94
Sihe	0.001	0.02	1.80	16.66	18.49	0.005	0.108	9.75	90.13
Chengzhuang	0.002	0.03	2.10	19.03	21.17	0.009	0.142	9.93	89.92

Notes: S1–S4, surface area of macropore (>1000 nm in diameter), mesopore (100–1000 nm in diameter), transitional pore (10–100 nm in diameter), and micropore (<10 nm in diameter), respectively; St, total surface area; S1/St to S4/St, percentage of surface area from macropore, mesopore, transitional pore, and micropore in the total surface area, respectively.

According to Tables and 6, the proportions of transitional pores and micropores in terms of the total pore volume and surface area are dominant, which indicates that transitional pores and micropores play the dominant role in gas adsorption. In addition, the pore volumes and surface areas from all coal samples indicate that the Chengzhuang sample has the highest values of pore volume and pore surface area, the Yuwu sample has the lowest value of surface area from transitional pores and micropores, and the Sihe sample has the lowest pore volume from transitional pores and micropores, which suggest that the growth of transitional pores and micropores in the Sihe sample is better than that in the Yuwu sample and will be beneficial to ScCO2 adsorption.

The genetic types of pores in coal from the SQB, China have been discussed in the relevant work[63,64] and include gas pores, shrinkage-induced pores, and mineral-related pores. Figure shows the pore types and mineral compositions in all coal samples. The pore types in all coal samples include gas pores (Figure a,d,e), shrinkage-induced pores (Figure b), and mineral-related pores such as intercrystalline pores and dissolution pores (Figure b,d,f); the types of minerals include kaolinite, pyrite, and barite (Figure b–d,f).

Figure 3

Pore types and mineral composition in Yuwu coal sample (a,b), Sihe coal sample (c,d), and Chengzhuang sample (e,f) by FE-SEM.

Experimental Results of CO2 Adsorption

The excess adsorption isotherms of pure CO2 from the Yuwu, Sihe, and Chengzhuang coal mines at temperatures of 45, 62.5, and 80 °C are plotted in Figure . As shown in Figure , the excess adsorption capacity generally increases with increase in pressure. However, the excess adsorption capacity starts to decrease after a certain pressure is reached for different temperature conditions, that is, the excess adsorption capacity exhibits a maximum around the critical pressure.[65,66] The higher the operating temperature, the higher the pressure where the excess adsorption starts to decrease, as shown in Figure . This decrease of excess adsorption is expected as the adsorbed phase volume is not yet corrected.[67] Meanwhile, variation of the excess adsorption capacity under low pressure calculated based on the free volume determined with helium is different from the excess adsorption capacity under high pressure calculated based on the free volume determined with helium, and there is a negative adsorption phenomenon, that is, the excess adsorption capacity shows a decrease when the pressure reaches a peak, caused by the density of the adsorbed phase, based on the synthetic measurement of the free volume.[67,68] The cause of the negative adsorption is controversial, but it does not affect the work described in this paper.

Figure 4

Excess adsorption isotherms of ScCO2 adsorption at temperatures of 45 °C (318 K), 62.5 °C (333.5 K), and 80 °C (349 K) from Yuwu coal mine (a), Sihe coal mine (b), and Chengzhuang coal mine (c).

Figure presents the absolute adsorption capacities of pure CO2 for the Yuwu, Sihe, and Chengzhuang coal mines at the temperatures of 45, 62.5, and 80 °C. As shown in Figure , the absolute capacity increases with the increase of pressure. Based on comparison with the excess adsorption capacities (Figure ) and the absolute adsorption capacities (Figure ) of ScCO2, the absolute capacity of ScCO2 is always higher than the excess adsorption capacity of ScCO2 at all equilibrium pressures. The comparison results indicate that there are significant differences between the excess adsorption capacity of ScCO2 and the absolute adsorption capacity of ScCO2 for the tested deep coal samples. Moreover, the variation of the excess adsorption capacity of ScCO2 or the absolute adsorption capacity of ScCO2 has similar features at different temperatures. The different adsorption capacities of ScCO2 from deep coal seams demonstrate that accurate adsorption modeling requires proper model screening.

Figure 5

Absolute adsorption isotherms of ScCO2 adsorption at temperatures of 45 °C (318 K), 62.5 °C (333.5 K), and 80 °C (349 K) from Yuwu coal mine (a), Sihe coal mine (b), and Chengzhuang coal mine (c).

Modeling of Coal Sorption with Different Models and Their Comparison

Taking the Sihe sample as an example, comparison of the experimental and modeled results at the temperatures of 45 °C (318 K), 62.5 °C (333.5 K), and 80 °C (349 K) is shown in Figures –8. Because the unit of adsorption capacity in the TL and OK models is mmol, which is different from the other adsorption models, the figures showing adsorption capacity are plotted separately (Figures –13). The R2 and R of the simulation results from the different adsorption models are listed in Table .

Figure 6

Comparison of experimental and different model simulation results of excess adsorption isotherms of ScCO2 adsorption at the temperature of 45 °C (318 K) from Sihe coal mine; units of excess adsorption capacity are cm3/g (a) and mmol (b), respectively.

Figure 8

Comparison of experimental and different model simulation results of excess adsorption isotherms of ScCO2 adsorption at the temperature of 80 °C (349 K) from Sihe coal mine; units of excess adsorption capacity are cm3/g (a) and mmol (b), respectively.

Figure 13

Comparison of experimental and different model simulation results of absolute adsorption isotherms of ScCO2 adsorption with the equilibrium pressure beyond 8.13 MPa and at the temperature of 80 °C (349 K) from Sihe coal mine; units of absolute adsorption capacity are cm3/g (a) and mmol (b), respectively.

Table 7

Simulation Degree of Different Models for Excess Adsorption Capacity of ScCO2 at Different Temperatures

		simulation results from different model
temperature	simulation degree	L model	T model	LF model	EL model	TL model	DBET model	TBET model	D–R model	D–A model	OK model
45 °C (318 K)	R2	0.98	0.99	0.99	0.98	0.96	0.98	0.99	0.99	0.99	0.94
	R	0.99	1.00	1.00	0.99	0.98	0.99	0.99	0.99	0.99	0.97
62.5 °C (333.5 K)	R2	0.97	0.99	0.99	0.97	0.88	0.97	0.98	0.96	0.96	0.90
	R	0.99	1.00	1.00	0.99	0.94	0.99	0.99	0.98	0.98	0.95
80 °C (349 K)	R2	0.90	0.94	0.94	0.90	0.92	0.90	0.92	0.96	0.96	0.89
	R	0.95	0.97	0.97	0.95	0.98	0.95	0.96	0.98	0.98	0.94

Comparison of experimental and different model simulation results of excess adsorption isotherms of ScCO2 adsorption at the temperature of 62.5 °C (333.5 K) from Sihe coal mine; units of excess adsorption capacity are cm3/g (a) and mmol (b), respectively.

As shown in Figures –8 along with data in Table , most of the adsorption models can describe the variational characteristics of the excess adsorption capacity of ScCO2, and the simulation degree for the excess adsorption capacity of ScCO2 at a relatively low temperature is higher than that at a relatively high temperature. At each temperature, the modeled results at low pressure are superior to the modeled results at high pressure. As shown in Figures –8, the modeled values of excess adsorption capacity deviate from the experimental values at a certain value of equilibrium pressure, and the trend becomes more obvious with the increase of the experimental pressure; the simulation accuracy in Table also demonstrates this point, that is, that the regression coefficients R2 and the correlation coefficients R of the simulation formula decrease with increase of the experiment temperature. There is an inflection point of the excess adsorption capacity when the equilibrium pressure is 8.13 MPa, the first value beyond the critical pressure 7.38 MPa. When the equilibrium pressure exceeds 7.38 MPa, the modeled results start to deviate from the experimental data and the deficiency increases with increased pressure. Based on 1, in the L, T, LF, EL, and DBET models, the excess adsorption capacity is a monotonous increasing function of equilibrium pressure. The excess adsorption capacity of ScCO2 should always increase as the pressure increases, and no inflection points exist for the L, T, LF, EL, and DBET models. The excess adsorption capacities of ScCO2 can show inflection points for the TL, D–R, D–A, TBET, and OK models, and this means that these models are capable of modeling excess adsorption capacity of ScCO2. According to Figures –8, not all adsorption models can model the excess adsorption capacity of ScCO2 across all pressures and temperatures, especially high temperatures and pressures.

To analyze the validity of the adsorption models at low and high pressures, the Sihe sample at a temperature of 80 °C was chosen as an example. Figures and 10 demonstrate the comparison of the experimental and modeled results with equilibrium pressure less than or equal to 8.13 MPa and greater than 8.13 MPa, respectively. The R2 and R values of the regression values are listed in Table .

Figure 9

Comparison of experimental and different model simulation results of excess adsorption isotherms of ScCO2 adsorption with the equilibrium pressure below 8.13 MPa and at the temperature of 80 °C (349 K) from Sihe coal mine; units of excess adsorption capacity are cm3/g (a) and mmol (b), respectively.

Figure 10

Comparison of experimental and different model simulation results of excess adsorption isotherms of ScCO2 adsorption with the equilibrium pressure beyond 8.13 MPa and at the temperature of 80 °C (349 K) from Sihe coal mine; units of excess adsorption capacity are cm3/g (a) and mmol (b), respectively.

Table 8

Simulation Degree of Different Models for Excess Adsorption Capacity of ScCO2 from the Sihe Sample at Different Equilibrium Pressures and Temperatures of 80 °C (349 K)

		simulation results from different model
equilibrium pressure (MPa)	simulation degree	L model	T model	LF model	EL model	TL model	DBET model	TBET model	D–R model	D–A model	OK model
≤8.13	R2	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.98
	R	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.99
>8.13	R2	0.91	3.8 × 10–3	0.95	0.91	0.06	0.96	0.94	0.66	0	0.05
	R	0.96	0.06	0.97	0.96	0.25	0.98	0.97	0.81	0	0.21

As shown in Figures and 10 and Table , when the equilibrium pressure is less than or equal to 8.13 MPa, the modeled results agree well with the experimental data for the excess adsorption capacity of ScCO2. When the equilibrium pressure is greater than 8.13 MPa, the results from most of the adsorption models agree reasonably with the experimental data. In contrast, the T, D–A, TL, and OK models have more deviations than the other adsorption models.

Based on analysis of Figures and 5, the absolute adsorption capacity of ScCO2 is higher than the excess adsorption capacity of ScCO2. To simulate the absolute adsorption capacity of ScCO2, Figure presents a comparison of the experimental and modeled results of the adsorption capacity of ScCO2 with different models at the temperature of 80 °C for the Sihe sample. The R2 and R of different models are listed in Table .

Figure 11

Comparison of experimental and different model simulation results of absolute adsorption isotherms of ScCO2 adsorption at the temperature of 80 °C (349 K) from Sihe coal mine; units of absolute adsorption capacity are cm3/g (a) and mmol (b), respectively.

Table 9

Simulation Degree of Different Models for Absolute Adsorption Capacity of ScCO2 from the Sihe Sample at the Temperature of 80 °C (349 K)

		simulation results from different model
temperature	simulation degree	L model	T model	LF model	EL model	TL model	DBET model	TBET model	D–R model	D–A model	OK model
80 °C	R2	0.93	0.97	0.98	0.93	0.87	0.93	0.98	0.61	0.50	0.81
	R	0.96	0.98	0.99	0.96	0.93	0.97	0.99	0.78	0.71	0.90

As shown in Figure and Table , most of the adsorption models have relatively high precision for the absolute adsorption capacity of ScCO2. However, there is relatively larger deviation for the D–R and D–A models. Because of the model assumptions and functional properties, the absolute adsorption capacities of ScCO2 show a turning point when the TL, D–R, D–A, TBET, and OK models are adopted, which is inconsistent with the characteristics of increasing absolute adsorption capacity of ScCO2 with the increase of equilibrium pressure.

To analyze the difference between the absolute adsorption capacity of CO2 at low equilibrium pressure and that at high equilibrium pressure, a sectionalized simulation for the absolute adsorption capacity of ScCO2 is shown in Figures and 13. Table presents the R2 and R of the regression results for various models and pressures.

Figure 12

Comparison of experimental and different model simulation results of absolute adsorption isotherms of ScCO2 adsorption with the equilibrium pressure below 8.13 MPa and at the temperature of 80 °C (349 K) from Sihe coal mine; units of absolute adsorption capacity are cm3/g (a) and mmol (b), respectively.

Table 10

Simulation Degree of Different Models for Absolute Adsorption Capacity of ScCO2 from the Sihe Sample at Different Equilibrium Pressures and Temperatures of 80 °C (349 K)

		simulation results from different model
equilibrium pressure (MPa)	simulation degree	L model	T model	LF model	EL model	TL model	DBET model	TBET model	D–R model	D–A model	OK model
≤8.13	R2	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.98
	R	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	0.99
>8.13	R2	0.96	0.97	0.99	0.96	0.97	0.99	0.99	0.98	0	0.05
	R	0.98	0.98	1.00	0.98	0.98	1.00	1.00	0.99	0	0.21

As shown in Figures and 13 and Table , most of the adsorption models have great precision for modeling absolute ScCO2 capacity, but the D–A model is not suitable for modeling absolute adsorption.

Based on the above analysis, most of the adsorption models can be reasonably used to model the excess and absolute adsorption capacities of ScCO2. It was found that these models are applicable for low pressure (≤8.13 MPa). A good match of the modeled and experimental results does not mean that the modeled results are valid; the model parameters obtained by a simulation must be analyzed further, and the suitability of the adsorption model must be thoroughly evaluated and assessed.

Comparison and Model Screening for ScCO2 Sorption

An appropriate adsorption model should meet the following criteria: (1) the regressed parameter must have physical significance; (2) the modeled results must be in accordance with the adsorption characteristics of ScCO2 for deep coal seams; (3) the modeling precision should be high enough for accurate prediction.

Based on the above criteria, in comparing the 10 adsorption models in the previous analyses, the regressed modeling parameters VL, PL, ninf, KL, Kb, n, P0, Vm, C, Vb, D, and Γ0 must all have positive values. Moreover, n in the exponential function, which appears in the T, LF, EL, TBET, and D–A models, must be a positive nonzero integer.

The results for the simulation parameters with different adsorption models for the excess adsorption capacities of ScCO2 from the Sihe sample at the different temperatures are summarized in Table .

Table 11

Results for Simulation Parameters with Different Models for Excess Adsorption Capacity of ScCO2 from the Sihe Sample at Different Temperatures

		temperature					temperature
adsorption model	parameter	45 °C	62.5 °C	80 °C	adsorption model	parameter	45 °C	62.5 °C	80 °C
L model	VL	31.05	27.32	22.37	DBET model	Vm	–0.01	–0.08	–0.06
	PL	0.43	0.74	0.58		C	2376.37	341.22	359.24
TL model	ninf	2.50 × 10–3	2.60 × 10–3	2.20 × 10–3		P0	–0.43	–0.74	–0.58
	KL	3.07	5.28	5.57	TBET model	Vm	102.40	61.72	81.05
T model	VL	29.41	25.37	21.46		C	–25.82	12.38	–15.76
	Kb	0.36	0.41	0.31		P0	–0.06	0.18	–0.09
	n	110.90	4.17	5.74	D–A model	V0	29.56	25.73	22.18
LF model	VL	29.40	25.36	21.43		D	0.09	0.14	0.17
	Kb	2.40 × 10–15	0.30	0.06		n	2	2	2
	n	41.62	3.47	4.43	D–R model	V0	29.65	25.77	22.27
EL model	VL	0.98	0.67	0.58		D	0.47	0.14	0.18
	Kb	74.05	55.02	66.48	OK model	Γ0	1.7 × 10–3	1.8 × 10–3	1.2 × 10–3
	n	–1.94	–1.95	–1.95			571.87	510.13	678.77

As shown in Table , the parameter n simulated by the EL model and the parameters Vm and P0 simulated by the DBET model are less than 0 and thus have no physical significance; therefore, the EL and DBET models are not suitable to simulate the excess adsorption capacity of ScCO2. In addition, the parameter VL in the EL model for the different coal samples is obviously abnormal. When the TBET model is used to simulate the excess adsorption capacity of ScCO2, the parameters C and P0 are less than 0 for the Sihe sample at temperatures of 45 and 80 °C and thus have no physical significance. These results show that the stability of the TBET model is poor when it is used to simulate the excess adsorption capacity of ScCO2 for a deep coal seam. Based on the above analyses, the L, TL, T, LF, D–A, D–R, and OK models are effective and can be used to model the adsorption isotherms of the excess adsorption of ScCO2 in the scope of the whole equilibrium pressure range for deep coal seams.

Table summarizes the results for the regression parameters with different adsorption models for the excess adsorption capacities of ScCO2 from the Sihe samples at a temperature of 80 °C and different ranges of equilibrium pressure.

Table 12

Results for Simulation Parameters with Different Models for Excess Adsorption Capacity of ScCO2 from the Sihe Sample at the Temperature of 80 °C (349 K) and Different Ranges of Equilibrium Pressure

		equilibrium pressure				equilibrium pressure
adsorption model	parameter	<8.13 MPa	>8.13 MPa	adsorption model	parameter	≤8.13 MPa	>8.13 MPa
L model	VL	32.84	18.64	DBET model	Vm	–0.07	610.93
	PL	2.68	–1.34		C	4697.61	–0.03
TL model	ninf	2.00 × 10–3	8.00 × 10–3		P0	–2.37	7.54
	KL	4.31	59.68	TBET model	Vm	31.40	12.67
T model	VL	30.43	20.57		C	3.85	–2.83
	Kb	0.34	15.49		P0	1.06	1.71
	n	1.20	76.52	D–A model	V0	24.50	20.56
LF model	VL	30.95	19.99		D	0.35	–4.28 × 10–4
	Kb	0.38	–0.01		n	1	0
	n	1.12	3.41	D–R model	V0	24.50	21.11
EL model	VL	0.13	–0.35		D	0.23	0.13
	Kb	94.80	39.38	OK model	Γ0	2.00 × 10–3	2.30 × 10–3
	n	–1.99	–2.04			484.74	309.88

Based on Table , when the sectionalized simulation for the excess adsorption capacity of ScCO2 is adopted, most of the parameters lose physical significance, such as PL in the L model, Kb in the LF model, VL and n in the EL model, Vm, C, and P0 in the DBET model, C in the TBET model, and D in the D–A model. In addition, VL in the EL model is obviously abnormal. When the equilibrium pressure is lower than 8.13 MPa, most of the adsorption models have reasonable accuracy in modeling the excess adsorption capacity of ScCO2, except the EL and DBET models. However, when the equilibrium pressure is higher than 8.13 MPa, most of the adsorption models are not applicable to describe the excess adsorption capacities of ScCO2, except the TL, T, D–R, and OK models. Above all, the TL, T, D–R, and OK models are effective and can be used to simulate the excess adsorption capacity of ScCO2 when sectionalized modeling for this capacity is adopted.

Table demonstrates the results for the simulation parameters with different adsorption models for the absolute adsorption capacities of ScCO2 from the Sihe sample at a temperature of 80 °C under different ranges of equilibrium pressure.

Table 13

Results for Simulation Parameters with Different Models for Absolute Adsorption Capacity of ScCO2 from the Sihe Sample at the Temperature of 80 °C (349 K) and Different Ranges of Equilibrium Pressure

		equilibrium pressure					equilibrium pressure
adsorption model	parameter	0–20 MPa	<8.13 MPa	>8.13 MPa	adsorption model	parameter	0–20 MPa	≤8.13 MPa	>8.13 MPa
L model	VL	58.03	44.45	276.65	DBET model	Vm	2.43	0.04	6.76
	PL	8.31	4.34	99.78		C	–25.56	–1079.90	1.66
TL model	ninf	–0.01	3.90 × 10–3	–3.40 × 10–3		P0	–10.53	–4.35	38.41
	KL	–77.68	7.11	–33.51	TBET model	Vm	–27.77	17.63	–22.59
T model	VL	15.39	90.71	6.14 × 108		C	0.89	8.38	0.84
	Kb	0.11	0.25	1.48 × 10–8		P0	–1.34	2.74	–1.54
	n	–1.13	0.48	0.12	D–A model	V0	31.03	29.19	36.12
LF model	VL	12.96	67.09	14.92		D	2.2 × 10–3	0.48	–9.69 × 10–4
	Kb	–4.56	0.17	–9.31		n	0	1	0
	n	–0.40	0.73	–0.62	D–R model	V0	33.93	28.45	28.65
EL model	VL	1.06	0.49	1.00		D	0.24	0.30	–1.08
	Kb	6.57	20.97	2.76	OK model	Γ0	2.27 × 10–2	6.03 × 10–3	–1.28 × 10–3
	n	–1.96	–1.98	–1.99			55.45	216.47	–1733.24

As shown in Table , when the equilibrium pressure varies from 0 to 20 MPa, the parameters ninf and KL in the TL model, n in the T model, Kb and n in the LF model, VL and n in the EL model, C and P0 in the DBET model, and Vm and P0 in the TBET model are all less than 0 and thus lose physical significance. In addition, the parameter VL in the EL model is obviously abnormal. According to the above analysis, the L model, D–A model, D–R model, and OK model are effective and can be used to model the adsorption isotherms of the absolute adsorption of ScCO2 for the whole pressure range.

Based on Table , when the equilibrium pressure is less than or equal to 8.13 MPa, parameters such as n in the EL model and C and P0 in the DBET model are all less than 0 and lose their physical significance. In addition, the parameters VL in the T model and VL in the EL model are obviously abnormal when the equilibrium pressure is less than or equal to 8.13 MPa. Therefore, the L model, TL model, LF model, TBET model, D–A model, D–R model, and OK model are effective in modeling the absolute adsorption capacity of ScCO2 when the equilibrium pressure is lower than 8.13 MPa. However, when the equilibrium pressure is higher than 8.13 MPa, a portion or all of the parameters in all adsorption models lose physical significance. In this work, the linear simulation, exponential simulation, logarithmic simulation, power function simulation, and polynomial simulation were conducted when the equilibrium was higher than 8.13 MPa. Figure shows the modeled results from the linear simulation, exponential simulation, logarithmic simulation, power function simulation, and polynomial simulation for the absolute adsorption capacity of ScCO2.

Figure 14

Simulation results of absolute adsorption isotherms of ScCO2 adsorption using the linear function (a,b), the exponential function (c,d), the logarithmic function (e,f), the power function simulation (g,h), the polynomial function (i,j) with the equilibrium pressure beyond 8.13 MPa and at a temperature of 80 °C (349 K) from Sihe coal mine; units of absolute adsorption capacity adopted by cm3/g and mmol, respectively.

Figure shows that the linear simulation, exponential simulation, logarithmic simulation, power function simulation, and polynomial simulation all have good precision; the R2 values are 0.973, 0.9872, 0.9282, 0.9576, and 0.9959 respectively. The simulation results suggest that these five types of functions all can meet the needs for simulation of the absolute adsorption capacity of ScCO2 when the equilibrium pressure is higher than 8.13 MPa. However, the results for R2 show that the polynomial simulation, exponential simulation, and linear simulation are superior to the logarithmic simulation and power function simulation.

All selected models in this paper are nonlinear, so R2 and R cannot be used as effective standards for evaluating the superiority of the models. In this paper, the standard error S (eq ) and the residual sum of squares SSE (eq ) are defined to evaluate the simulation effectiveness of the model simulations. Smaller S and SSE indicate higher model accuracywhere S is the standard error, SSE is the residual sum of squares, n is the number of data points, and V and Ve are the experimental value and simulated value of the adsorption capacity of each pressure spot, respectively.

According to eqs and 13, the units of the excess adsorption capacity in the TL model and OK model were converted to the same units of the excess adsorption capacity in the other adsorption models. The values of S and SSE for the seven selected adsorption models were calculated for the excess adsorption capacity of ScCO2; the results are shown in Table .

Table 14

Results for S and SSE on Seven Adsorption Models for Excess Adsorption Capacity of ScCO2 at Different Temperatures from the Sihe Sample

	L model		TL model		T model		LF model		D–A model		D–R model		OK model
temperature (°C)	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE
45	1.34	14.37	2.10	35.41	0.92	6.70	0.92	6.70	1.08	9.32	1.07	9.14	2.50	49.09
62.5	1.22	16.32	2.88	91.06	0.70	4.92	0.80	5.12	0.64	4.49	0.64	4.48	2.43	65.01
80	1.88	46.01	1.85	44.49	1.41	25.81	1.43	26.48	1.23	19.51	1.22	19.44	2.09	56.65

As shown in Table , when the experimental temperature was 45 °C, for the Sihe sample, the order of superiority of the seven types of adsorption model for the excess adsorption capacity of ScCO2 is as follows: T model = LF model > D–R model > D–A model > L model > TL model > OK model. When the experimental temperature for the Sihe sample was 62.5 °C, the order of superiority of the seven types of adsorption models for excess adsorption capacity of ScCO2 is as follows: D–R model > D–A model > T model > LF model > L model > OK model > TL model. When the experimental temperature for the Sihe sample was 80 °C, the order of superiority for the seven types of adsorption model for the excess adsorption capacity of ScCO2 is as follows: D–R model > D–A model > T model > LF model > TL model > L model > OK model.

To verify the above results, the Yuwu sample was taken as a further example; the results of S and SSE for the different adsorption models for the excess adsorption capacity of ScCO2 at different temperatures are shown in Table .

Table 15

Results for S and SSE on Seven Adsorption Models for Excess Adsorption Capacity of ScCO2 at Different Temperatures from the Yuwu Sample

	L model		TL model		T model		LF model		D–A model		D–R model		OK model
temperature (°C)	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE
45	0.77	4.69	2.26	40.72	0.67	3.55	0.67	3.64	0.54	2.37	0.54	2.36	2.00	31.92
62.5	0.90	8.02	0.90	8.19	0.60	3.60	0.614	3.74	0.35	1.20	0.34	1.17	2.47	60.97
80	1.06	14.63	1.65	35.23	0.69	6.12	0.72	6.684	0.43	2.39	0.39	1.93	1.81	42.68

As indicated in Table , for this sample, the order of the superiority of the seven types of the adsorption model for the excess adsorption capacity of ScCO2 is as follows: D–R model > D–A model > T model > LF model > L model > TL model > OK model, when the experimental temperature from the Yuwu sample was different.

Based on a combination of Tables and 15, the D–R and D–A models had the best precision during the simulation of the excess adsorption capacity of ScCO2 for the whole equilibrium pressure range. The T and LF models had moderate precision among the seven adsorption models, and the L, TL, and OK models had relatively low precision. Of these seven adsorption models, the D–R, D–A, TL, and OK models all can represent the inflection point of the excess adsorption capacity of ScCO2. Therefore, the D–R and D–A models are the optimal adsorption models for simulation of the excess adsorption capacity of ScCO2 for the whole equilibrium pressure range.

Table shows the results of S and SSE for the four selected adsorption models for the excess adsorption capacity of ScCO2 at a temperature of 80 °C and at different ranges of equilibrium pressure.

Table 16

Results for S and SSE on Four Adsorption Models for Excess Adsorption Capacity of ScCO2 from the Sihe Sample at the Temperature of 80 °C (349 K) and Different Ranges of Equilibrium Pressure

	TL model		T model		D–R model		OK model
equilibrium pressure (MPa)	S	SSE	S	SSE	S	SSE	S	SSE
≤8.13	0.15	0.17	0.08	0.04	0.28	0.47	1.28	9.89
>8.13	0.89	5.49	0.52	1.90	0.30	0.65	1.35	12.69

As shown in Table , when the equilibrium pressure was less than or equal to 8.13 MPa, the order of priority of the four types of adsorption model in the simulation of the excess adsorption capacity of ScCO2 is as follows: T model > TL model > D–R model > OK model. The order of priority for the four types of adsorption model in the simulation of the excess adsorption capacity of ScCO2 when the equilibrium pressure was beyond 8.13 MPa is as follows: D–R model > T model > TL model > OK model. Moreover, the results for the priority of the four adsorption models are in accordance with the adsorption characteristics of ScCO2 under different ranges of equilibrium pressure. Given the above, the T, TL, and D–R models are the optimal adsorption models for the sectionalized simulation of the excess adsorption capacity of ScCO2 under different scopes of equilibrium pressure.

Table shows the results of S and SSE for the four selected adsorption models in the simulation of the absolute adsorption capacity of ScCO2 at the temperature of 80 °C and across the whole equilibrium pressure range. Table shows the results of S and SSE for the seven selected adsorption models for the absolute adsorption capacity of ScCO2 at the temperature of 80 °C and equilibrium pressure of less than or equal to 8.13 MPa.

Table 17

Results for S and SSE on Four Adsorption Models for Absolute Adsorption Capacity of ScCO2 from the Sihe Sample at the Temperature of 80 °C (349 K) and Whole Range of Equilibrium Pressure

	L model		D–A model		D–R model		OK model
equilibrium pressure	S	SSE	S	SSE	S	SSE	S	SSE
0–20 MPa	3.10	125.18	8.21	875.28	7.26	685.28	5.34	370.60

Table 18

Results for S and SSE on Seven Adsorption Model for Excess Adsorption Capacity of ScCO2 from the Sihe Sample at the Temperature of 80 °C (349 K) and Equilibrium Pressure of Less Than or Equal to 8.13 MPa

	L model		TL model		LF model		TBET model		D–A model		D–R model		OK model
equilibrium pressure	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE	S	SSE
≤8.13 MPa	0.20	0.24	0.45	1.19	0.02	3.30 × 10–3	0.02	2.4 × 10–3	0.21	0.27	0.77	3.60	1.55	14.69

As shown in Table , when the equilibrium pressure is the whole pressure with a range of 0–20 MPa, for the Sihe sample at a temperature of 80 °C, the order of superiority of the four types of adsorption model for the absolute adsorption capacity of ScCO2 is as follows: L model > OK model > D–R model > D–A model. Moreover, the results for the order of priority of the four adsorption model are in accordance with the adsorption characteristics of ScCO2 under different ranges of equilibrium pressure. When the equilibrium pressure is less than or equal to 8.13 MPa, the order of superiority of the seven types of adsorption model for the absolute adsorption capacity of ScCO2 is as follows: TBET model > LF model > L model > D–A model > TL model > D–R model > OK model, again for the Sihe sample at the temperature of 80 °C.

According to the results in Table , the values of S and SSE from the TBET and LF models are far lower than those from the other adsorption models. Therefore, the TBET and LF models are the optimal adsorption models for simulation of the absolute adsorption capacity of ScCO2 when the equilibrium pressure is less than or equal to 8.13 MPa. When the equilibrium pressure is higher than 80 °C, the linear simulation, exponential simulation, logarithmic simulation, power function simulation, and polynomial simulation can be used to simulate the absolute adsorption capacity of ScCO2.

Conclusions

This article investigates the sorption characteristics of ScCO2 for deep coal seams of the SQB, China. Ten different adsorption models were considered to model the excess and absolute adsorption capacities of ScCO2 under various temperatures and pressures. The optimal adsorption models were selected by parametric comparison and analyses based on the standard error and the residual sum of squares. The conclusions can be summarized as follows:

The excess adsorption capacity of ScCO2 has a common turning decline point at different pressures under different temperatures. The absolute capacity of ScCO2 always increases with the increase of injection pressure. It is higher than the excess adsorption capacity of ScCO2 at each equilibrium pressure.

Most of the adsorption models can describe adsorption characteristics and have good agreement with the experimental results when the pressure is less than 8.13 MPa for excess and absolute adsorption capacities. When the pressure is greater than 8.13 MPa, deviations of the modeled results are observed for most of the models.

The analytical results of the adsorption model parameters reveal that there is an obvious difference in the validity of the different adsorption models for the excess adsorption capacity and the absolute adsorption capacity of ScCO2. The L, TL, T, LF, D–A, D–R, and OK models are effective in the simulation of adsorption isotherms for the excess adsorption of ScCO2 in the scope of the whole equilibrium pressure range. The TL, T, D–R, and OK models are effective when sectionalized simulation is adopted. In representation of the absolute adsorption isotherms of ScCO2, the L, D–A, D–R, and OK models are effective in the scope of the whole equilibrium pressure. The L, TL, LF, TBET, D–A, D–R, and OK models are effective when the equilibrium pressure is lower than or equal to 8.13 MPa. All adsorption models lose physical significance when the equilibrium pressure is higher than 8.13 MPa.

The calculation results from the standard error S and the residual sum of squares SSE show that the D–R model and D–A model are the optimal adsorption models in the simulation of the excess adsorption capacity of ScCO2 with the condition of the whole equilibrium pressure range. The T, TL, and D–R models are the optimal adsorption models in the simulation of the excess adsorption capacity of ScCO2 in the selected adsorption model when the equilibrium pressure is divided into two sections at the point of 8.13 MPa. In the simulation of the absolute adsorption capacity of ScCO2, the TBET model and LF model are the optimal adsorption models for selection when the equilibrium pressure is less than or equal to 8.13 MPa. The linear simulation, exponential simulation, logarithmic simulation, power function simulation, and polynomial simulation all have good precision and can be used when the equilibrium pressure is beyond 8.13 MPa.