Insights into carbon dioxide sequestration into coal seams through coupled gas flow-adsorption-deformation modelling

Hywel Thoms ,Min Chen,b,*

a Geoenvironmental Research Centre,Cardiff School of Engineering,Cardiff University,Queen’s Buildings,The Parade,Newport Road,Cardiff,CF24 3AA,UK

b Key Laboratory of Marine Geology,Tongji University,Shanghai,200092,China

Keywords: CO2 geological storage Coal seam Adsorption Desorption hysteresis

ABSTRACT Injecting carbon dioxide (CO2) into coal seams may unlock substantial carbon sequestration potential.Since the coal acts like a carbon filter,it can preferentially absorb significant amounts of CO2.To explore this further,desorption of the adsorbed gas due to pressure drop is investigated in this paper,to achieve an improved understanding of the long-term fate of injected CO2 during post-injection period.This paper presents a dual porosity model coupling gas flow,adsorption and geomechanics for studying coupled processes and effectiveness of CO2 sequestration in coals.A new adsorption-desorption model derived based on thermodynamics is incorporated,particularly,the desorption hysteresis is considered.The reliability of the proposed adsorption-desorption isotherm is examined via validation tests.It is indicated that occurrence of desorption hysteresis is attributed to the adsorption-induced pore deformation.After injection ceases,the injected gas continues to propagate further from the injection well,while the pressure in the vicinity of the injection well experiences a significant drop.Although the adsorbed gas near the well also decreases,this decrease is less compared to that in pressure because of desorption hysteresis.The unceasing spread of CO2 and drops of pressure and adsorbed gas depend on the degree of desorption hysteresis and heterogeneity of coals,which should be considered when designing CO2 sequestration into coal seams.

1.Introduction

It is well-known that global warming can affect changes in global climate pattern(Abbass et al.,2022;Masson-Delmotte et al.,2022).It is reported that the globally-averaged temperatures is 0.99°C warmer than the middle twentieth century mean (NASA,2017).This environmental concern is mainly due to the significant emission of greenhouse gases into atmosphere.The greenhouse gases include carbon dioxide (CO2),methane (CH4) and nitrogen oxide (NO),and some manufactured gases like chlorofluorocarbons (CFCs) (Al-Yasiri and Géczi,2021).According to Mavor et al.(2002)and Ritchie et al.(2020),CO2emissions are the primary driver of global climate change.It is found that the CO2concentration in the atmosphere has rose significantly from 280 ppm in 1750 to 410 ppm in 2020 over last two centuries (Ali et al.,2022;Yoro and Daramola,2020).Therefore,reduction of CO2emission into atmosphere is a major aspect of mitigation of global warming effects.

Many initiatives have been proposed to reduce CO2emissions,including utilisation of carbon-free renewable energy sources (e.g.wind,solar),CO2capture and storage(CCS)in geological formations(Wei et al.,2023).Among these means,CCS has been broadly recognised as a potential technique to mitigate anthropogenic CO2emissions.There are some primary CO2geological sequestration sinks including depleted oil and gas reservoirs,saline aquifers,basaltic rocks and coalbeds (Tomi? et al.,2018).Among them,coal seams are significant because of their huge reserves and collocation with industrial scale CO2emission sources like power generation plants.Since the CO2adsorption capacity is higher than CH4in coals,existing coalbed methane(CBM) can be displaced using CO2and increase the gas recovery,known as enhanced coalbed methane(CO2-ECBM)recovery(Asif et al.,2022;Godec et al.,2014;Kuang et al.,2023).On the one hand,the life of CBM fields can be extended,on the other hand,CBM production can also offset the cost of CO2storage.Many pilot trials of CO2-ECBM have been completed or are currently underway or planned,such as San Juan Fairway ECBM project in USA (Reeves et al.,2003),RECOPOL pilot trial in Poland (van Bergen et al.,2006),Fenn Big Valley and Mannville pilot tests in Canada (Yang et al.,2023),Qinshui test in China (Wong et al.,2007) and Yubari test in Japan (Fujioka et al.,2010).

Naturally fractured coal is generally characterized by dual porosity model,i.e.almost uniformly spaced natural fractures(cleats)and porous coal matrices(see Fig.1a)(Hosking et al.,2020).Generally,gas migration in coals occurs at three processes:injected CO2firstly leaks into cleat system from injection well.And then the CO2diffuses into coal matrices and adsorbs onto the pore surface(Chen et al.,2019).Fig.1b represents the transport process of CO2in coals.The gas migration in cleat network is mainly controlled by coal permeability.Numerous experimental studies have been performed for exploring the change in coal permeability during gas transport(e.g.Pan et al.,2010;Wang et al.,2018a;Yao et al.,2023;Zhang et al.,2019).Similar to other fractured rocks,the coal permeability is stress dependent,showing an exponential relationship between the effective stress and permeability.In addition,the gas adsorption/desorption induced coal swelling/shrinkage can also lead to significant change in coal permeability (e.g.Meng and Li,2017;Pan and Connell,2012;Seidle and Huitt,1995;Wierzbicki et al.,2014).Various permeability models have been developed to capture the changes in permeability,details were presented in(Pan and Connell,2012).Although modelling permeability has incorporated the influences of both effective stress and swelling/shrinkage,the changes in either stresses or strains were superposed to calculate the total change in stresses or strains.These permeability models only hold based on an assumption that change in stress or strain due to fluid pressures is unrelated to that in coal swelling/shrinkage induced stress or strain.Most experimental tests on coal swelling/shrinkage were performed under non constrain conditions,leading to an overestimate compared to in situ stress conditions (Gu and Chalaturnyk,2006).Besides,the in situ stresses or strains of coal seams are dynamic during gas injection,which is challenge to experimental measurements.

Fig.1.(a) Schematic diagram of multi-scale pore structure of coals and (b) Gas transport process in coals.

Adsorption onto the pore surface of coal matrices is considered to be the primary gas retention mechanism of coal seams,which is differ significantly from conventional gas reservoirs (Busch and Gensterblum,2011).The gas adsorption behaviour in coals is impacted by some controllable factors including pressure,temperature,gas types,coal rank,moisture content (Chattaraj et al.,2016;Zhang et al.,2016).For example,because of smaller molecular size and coal pore structure,CO2shows a much higher adsorption affinity compared to CH4and N2(Strapoc,2007).Gas adsorption is negatively affected by temperature and moisture content.Gas retention mechanism in coals is primarily a physical sorption due to weak van der Waals force of attraction;this implies that adsorbed gases can be released from coals when conditions for adsorption vary.However,many experimental studies shown that gas desorption is generally not a fully reversible,the adsorption isotherm is different from the desorption isotherm.This phenomenon is known as desorption hysteresis(e.g.Bell and Rakop,1986;Wang et al.,2014;Zhou et al.,2020).However,most of current work focused on gas adsorption behaviour.For CO2storage in coal reservoirs,in addition to gas adsorption,gas desorption will also occur after injection event stops,since the pressure will decline with continuous propagation further (Chen et al.,2023;Wang et al.,2014).Understanding desorption hysteresis behaviour is of significance to evaluate storage efficiency of injected CO2in coal seams.

In addition to desorption hysteresis scenario,the coal reservoir heterogeneity is also an important factor influencing the long-term fate of sequestrated CO2.Coal heterogeneity effect has been considered in many studies.For example,the work by ?zgen Karacan and Okandan (1999) and Tan et al.(2018) demonstrated the effect of coal heterogeneity on CBM recovery,the homogenization assumption may cause large errors.In spite of the significance of heterogeneity effect,few attempts have made to explore the heterogeneity effects on CO2storage.This is another important issue this work attempts to address.

The objective of this work is to present an effective model for studying the gas flow and storage behaviour in heterogeneous coal seams based on our previous studies(Chen et al.,2022a,2023).The uniqueness of this work includes:

(1) A coupled gas flow-adsorption/desorption-geomehcanics model for CO2sequestration is presented,in which the adsorption hysteresis is considered.

(2) The coupled processes and long-term storage effectiveness of CO2in coals with different degrees of hysteresis are analysed.

(3) Coal heterogeneity effect on long term effectiveness of CO2storage in coals is also considered in this work.

The following is outline of this work:the adsorption-desorption isotherm based on thermodynamics is derived in Section 2.In Section 3,the development of a numerical model coupling gas flow,adsorption and deformation behaviour is detailed.Validation tests for examining model reliability are shown in Section 4.Section 5 presents the mechanism for gas desorption hysteresis is revealed and the temporal-spatial evolutions of pressure and adsorbed CO2during injection and post-injection periods.Conclusions are summarized in Section 6.

2.Adsorption-desorption model development

Coal is considered to be composed of inter-linked polymer of a certain molecular weight,along with a structure formed by aggregations of aromatic macro-molecular chains(Ward and Suárez-Ruiz,2008).The coal matrices have different size pores,which provide a much large internal surface for gas residence(see Fig.1a).According to Chen et al.(2023),the pore surface of coals is energetically heterogeneous,different adsorption sites are contained.The patchwise model can be employed for representing the topography of adsorption sites whereby the heterogeneous surface is separated into different patches,each patch has the same interaction energy level (Ng et al.,2017),as shown in Fig.2.

Fig.2.Schematic illustration of energetically heterogeneous surface conceptualized as patchwise topography via grouping the sites of the same energy of interaction with the adsorbate together in the same patch.

Therefore,each patch can be considered to be a homogeneous surface (Do,1998;Ng et al.,2017),the revised Langmuir kinetics model can be used for describing adsorption kinetics (Do and Wang,1998),expressed as

whereCsiis the adsorbed amount at each patch;CLiis the local adsorption capacity atith patch;kaiandkdiare the rate constants;EaiandEdiare the activation energies for adsorption and desorption,respectively;pis the pressure;Tis the temperature;andRis the universal gas constant.

where,Ei=Edi-Eaiis the difference between adsorption and desorption energy for a given patch,and θiis the fraction of local adsorption uptake.

The total fractional surface coverage θtis expressed in the following form:

whereEis the variable of integration.

By invoking the condensation approximation,θ in Eq.(4) reduces to a Heaviside step function (Panczyk and Rudzinski,2002):θ（E）=0 whenE＜Ec;and θ（E）=1 whenE≥Ec,in whichEcis the critical energy level of the adsorbate molecule.

Therefore,Eq.(4) reduces to

In the case of patchwise topography,F（E）in Eq.(5) represents adsorption energy distribution function.Quasi-Gaussian distribution has been successfully applied to characterize the energy distribution of adsorption sites(Ng et al.,2017;Panczyk and Rudzinski,2002).In this study,it is also employed to capture the adsorption on energetically heterogeneous solid surfaces,written as

whereE0is the mathematical expectation,andcis the standard deviation.

Inserting Eq.(6) into Eq.(5) and integrating over available adsorption sites produce

Application ofEc=-RTln（Kp）allows equation above to become(Dobruskin,1998):

Under isothermal condition,if define=n,Eq.(8) can be expressed in the form of Langmuir-Freundlich isotherm:

It is can be seen From Eq.(9) that Langmuir isotherm is a particular form of Langmuir-Freundlich isotherm,it is obtained by definingn=1.

For gas desorption,due to hysteresis scenario,the desorption isotherm generally deviates from adsorption isotherm.Also,when developing desorption isotherm,the following boundary conditions should be considered (see Fig.3):

Fig.3.Schematic representation of states M, A and D for desorption isotherm development: State M is the adsorption state where desorption initiates,state D is the experimentally measured desorption state,and state A and state D′ corresponds to the hypothetical fully reversible desorption state.Black,yellow,purple and green arrows indicate adsorption isotherm,desorption isotherm for irreversible adsorption,fully reversible desorption and experimental desorption isotherm.

(1) At stateM,depressurization begins,desorption isotherm is intersected with adsorption isotherm,and the adsorption amounts at both isotherms are identical;

(2) There is no adsorbed gas when pressure drops to zero;

(3) If adsorption is completely irreversible,the adsorption amount is constant although pressure decreases;

(4) The desorption isotherm should coincide with sorption isotherm if the adsorption is fully reversible;and

(5) Desorption curve is dependent on the initial state where depressurization begins.

Considering three different adsorption energy statespA,pDandpM,as shown in Fig.3,the adsorption sites energy differences from statepAto statepDand from statepMto statepDare

The ratio of ΔEcADto ΔEcMDdefines an index (HI):

HIcan be used to quantify the degree of hysteresis.Sander et al.(2005) defines a similar thermodynamic index of irreversibility(TII) to evaluate the degree of hysteresis.

After rearrangement,Eq.(11) becomes

Substituting Eq.(12) into Eq.(9) and replacingpDwithpallow desorption isotherm to be expressed as

Eq.(13) still takes the form Langmuir-Freundlich isotherm,it satisfies the conditions mentioned above.For example,the parameterPMreveals that the desorption curve depends on the initial pressure.Completely reversible adsorption process can be achieved via definingHIto be 0.

3.Modelling CO2 sequestration in coals

As mentioned above,naturally fractured coal is usually characterized as dual porosity system,gas migration processes include fracture network flow,diffusion in coal matrices and adsorption onto pore surface of coal matrices.This section will present a coupled flow-adsorption-geomechanics model to represent gas migration processes in coals.In the following sections,the governing equations are presented.

3.1.Gas transport

The mass balance equation of gas flow is expressed as (Chen et al.,2019;Cui et al.,2022):

wherecα is gas concentration;φαis porosity;qα is flow fluxes;Rα is the sink/source term;Γαis the mass exchange rate between fracture continuum and matrix continuum;?is the gradient operator;and m,f denote fracture continuum and matrix continuum,respectively.

The flux terms are expressed as

where vα is the flow velocity,it is expressed using Darcy’s law as

whereKα is the coal permeability,μ is the gas viscosity,andpα is the gas pressure.The permeability model development is detailed in Appendix A.

Considering the real gas law,the gas pressure can be given as

whereZα is the gas compressibility factor.Peng-Robinson equations of state or PR-EoS is used for calculation of gas compressibility factor in this work (Peng and Robinson,1976).

Since gas adsorption only occurs in coal matrices,which acts as the sink/source for matrix continuum,expressed as

where ρsis the density of coal.

It is assumed that the gas transfer between the matrix and fracture is driven by the difference of concentration,written as(Chen et al.,2019)

where τ is the diffusion time (Liu et al.,2015).

3.2.Coal deformation

Considering dual poroelastic theory,the effective stress is expressed as (Chen et al.,2019;Pao and Lewis,2002):

where σ is the total stress tensor,σ′is the effective stress tensor,I is a vector with IT=（1,1,1,0,0,0）and（1,1,0）in three-and twodimensions problems.βm=K/Km-K/Ksand βf=1-K/Kmare the Biot’s coefficients of the matrix and fracture,respectively;K=EY/3（1-2v）,is the bulk modulus,in whichEYis the Young’s modulus and v is Poisson’s ratio;andKm=EYm/3（1-2v）,is the modulus of coal matrix withEYmbeing Young’s modulus of the coal matrix andKsis the modulus of solid constituent.

The stress-strain constitutive relation is defined as

where D is the elastic stiffness tensor,and εeis the elastic strain vector.

The total strain can be expressed as

where ε is the total strain vector,and εsis the sorption-induced volumetric strain.

The strain-displacement relation is written as

where u is the displacement vector,and B is the straindisplacement matrix.

The swelling strain is considered to be linearly related with total adsorbed amount (e.g.Cui et al.,2007):

where εLis the volumetric strain coefficient of coals.

3.3.Numerical approach

In this study,the aforementioned theoretical formulation is implemented into the in-house computer code,which has been gradually developed (e.g.Thomas and He (1997);Hosking et al.(2017);Chen et al.(2022b).In this computer code,the Galerkin weighted residual method is employed to spatially discretize the governing equations and an implicit mid-interval backward-difference time-stepping algorithm is used for temporal discretization.Details can be found in Chen et al.(2022b).All the simulations in following section are completed using this in-house code.

4.Model validation against experimental data

This section presents a model validation exercise for examining the its reliability to predict gas adsorption behaviour in coals.The experimental data collected from published work (Dutta et al.,2011;Weishauptová et al.,2004) is used as benchmarks.More validation tests have been included in our previous work,for example,on unsaturated flow,coal permeability evolution,coal deformation and hydraulic-mechanical coupling (Chen et al.,2022a,2022b).Weishauptová et al.(2004) measured the equilibrium adsorption behaviour of CH4in bituminous coal samples(coal A and coal B)and brown coal(coal C)using the gravimetric method.Coal A and coal B were from Upper Silesian coal basin and coal C from North Bohemian basin,respectively.All measurements were carried out at temperature of 298 K.Dutta et al.(2011) conducted experimental measurements of CH4and CO2adsorption on bituminous coal samples using manometric method,and the sorption isotherms of CH4and CO2were obtained.Here,the experimental results of on Bogra and Kenda coal samples in Dutta et al.(2011)were collected as benchmarks for validation exercises.

Table 1 presents the model parameters for validation against benchmarks from Weishauptová et al.(2004) and Dutta et al.(2011),which were obtained by matching the experimental data.Values of model parametersnandHIranges from 0.793 to 0.983 and from 0.2 to 0.8,respectively,which fall within the range from 0 to 1.The comparisons between model predictions and the data published by Weishauptová et al.(2004)and Dutta et al.(2011)for pure CO2and CH4are ploted in Figs.4 and 5,from which the good agreements can be observed,demonstrating the reliability of the model.

Table 1Parameters for validation against experimental data (Weishauptová et al.,2004;Dutta et al.,2011).

Fig.4.Comparison between model predictions and experimental data on CH4 adsorption/desorption on coal samples by Weishauptová et al.(2004).

Fig.5.Comparison of between model predictions and experimental data on (a) Bogra coal samples and (b) Kenda coal samples.

5.Numerical simulations of CO2 sequestration in coal seams

5.1.Simulation setup

Depleted coal reservoirs have been recognised as a target formation for geological CO2storage (Reisabadi et al.,2022).This subsection designs a set of numerical simulations to unlock the mechanisms for CO2storage in depleted reservoirs.The twodimensional (2D) region of 400 m × 400 m with a depth of 400 m is considered with a CO2injection at the centre.Considering the symmetry,only a quarter of domain is considered in the simulation(Fig.6).It is assumed there is no CO2in coal initially.The initial vertical and horizontal stresses are 9 MPa and 6.3 MPa,respectively.Constant volume condition is used as boundary condition for coal deformation.A zero-flux boundary is used for gas flow.CO2is continuously injected at 6 MPa and injection ceases after 1 year.The simulation runs for 20 years.This simulation time is selected based on 5-year post-injection monitoring of stored CO2carried out by Mito and Xue (2011),which showed that the formation pressure became gradually stable from 1 years after injection stop.To ensure the long-term fate of injected CO2,the simulation time is extended in this work.Four analysis points are set to show the coupled process of CO2in coal seams:P1(10,10),P2(30,30),P3 (50,50),P4 (100,100).Table 2 lists the material properties for numerical simulations,which are chosen from Chen et al.(2023).

Table 2Parameters for the numerical simulation.

Fig.6.Schematic diagram of model domain and boundary conditions.

5.2.Results and discussions

5.2.1.Mechanism for desorption hysteresis

Fig.7 shows that site energy distributions under given conditions,which are calculated using Eqs.(6) and (13).It can be observed that mean site energy,E0,can be increased due to gas-coal interaction.Compared to site energy distribution for adsorption isotherm,the sites with medial and higher binding energy experience an increasing trend after coal-gas interaction,while low energy sites show a significant drop.Burhan et al.(2019) and Li et al.(2019) have reported that adsorption energy is negatively correlated with pore size,this implies that the size of some pores becomes small due to gas-coal interaction.This change in pore structure revealed here is similar to laboratory observations by e.g.Wang et al.(2018b),Cheng et al.(2021)and Geng et al.(2022).It is believed that the alteration of pore structure can be ascribed to pore deformation and structural rearrangement as a result of gas adsorption(Larsen,2004).An increase in smaller size pores leads to an increase in adsorption sites with higher binding energy.Consequently,desorption requires more activation energy,which is generated by a larger gas pressure drop,this is why the desorption hysteresis occurs.

Fig.7.Site energy distribution function F(E) and cumulative uptake θt (given that pM=6 MPa).

Fig.8.Pressure distribution in the coal seam after 1 year,2 years,5 years,10 years,15 years and 20 years.

Fig.9.Adsorbed gas concentration distribution in the coal seam after 1 year,2 years,5 years,10 years,15 years and 20 years.

5.2.2.Evolutions of pressure,adsorbed CO2 and permeability

Figs.8 and 9 show spatial distributions of gas pressure and adsorbed gas concentration at different times.The injected CO2moves outward in a radial pattern from the injection well and disperses within the coal seam,the pressure and adsorbed gas concentration distribute uniformly around the wellbore.After injection ceases (1 year),the injected gas propagates continuously,leading to drop in pressure in the vicinity of injection well.Because of pressure drop,adsorbed gas will desorb and adsorbed gas concentration also undergoes a decrease.In particular,the drop in pressure and adsorbed CO2is most significant in the first year after injection stops,as shown in Fig.10.The pressure near injection well decreases from 6 MPa to 1 MPa,in contrast,the decrease in adsorbed CO2concentration is less significant due to desorption hysteresis,which decreases from about 68 kg/m3to 46 kg/m3.As time increases,the decreases of pressure and adsorbed CO2concentration slow down.For example,the pressures near well are 0.55 MPa,0.38 MPa and 0.27 MPa after 5 years,10 years and 20 years,respectively.The adsorbed gas concentration drops to 37 kg/m3,32 kg/m3and 28 kg/m3,as shown in Fig.10a.

Fig.10.(a) Evolution of pressure and adsorbed gas concentration near injection well,(b) pressure distribution,(c) adsorbed gas concentration distribution and (d) permeability distribution along the diagonal after 1 year,2 years,5 years,10 years,15 years and 20 years.

After injection stop,pressure and adsorbed CO2concentration within the region far from injection well can still experience a little increase due to continuous gas spread,as shown in Fig.10b and c.The gas pressure front arrives at approximately 93 m away from wellbore,after 20 years,it reaches about 197 m from wellbore,as shown in Fig.10b.Nevertheless,the gas spread slows down as time goes.For example,the gas pressure front arrives at 148 m,170 m,and 180 m after 5 years,10 years and 10 years,respectively.This is because:(1)as the distance from the injection well grows,the area over which the gas spreads also expands;and (2) the pressure is almost identical in the area where CO2reaches,which leads to drop in the gas pressure gradient as time goes.

Fig.10d shows permeability distribution along the diagonal at different times.It can be observed that variation of coal permeability is contrary to that of adsorbed CO2.This is because CO2adsorption-induced swelling causes an increase in stresses within coal seam.The more CO2is adsorbed,the larger increase in stress is.The permeability is stress dependent,thus,it experiences a larger drop in the area near injection well.After injection stop,the desorption of CO2occurs as injected CO2continues to propagate further,which can lead to shrinkage of coal seams and reduction of stress of coal seams,therefore,the coal permeability can rebound in the area closed to injection well during post injection period,as shown in Fig.10d.

Fig.11 presents the temporal evolutions of pressure and adsorbed CO2concentration of monitoring points P1-P4.It is shown that the gas pressure and adsorbed CO2concentration within a 50-m range from the injection well begin to decrease immediately once injection ceases.The closer the monitoring point is to injection well,more rapidly the pressure and adsorbed CO2concentration drop.After 20 years,the gas pressure is almost the same in the region closed to wellbore.However,the difference of adsorbed gas concentrations between monitoring points is obvious since the desorption characteristics of gas in coals depends on the pressure at which pressure drop initiates (see Fig.12).When the initialized pressure is larger,the drop in adsorbed gas concentration is rapider once injection ceases.From Fig.12,we can observe that when the initialized pressure for desorption are different,the amounts of residual gas in coal are different although the gas pressure drops to the same value.Chen et al.(2023b) believed that a higher initial pressure marks the start of desorption,leading a greater portion of intermediate binding energy sites to transition into high binding energy sites.Consequently,under higher pressure condition,despite a more considerable pressure decrease,fewer adsorbed gas molecules are released when the starting pressure for desorption is higher,as shown in Fig.12.

Fig.11.Pressure and adsorbed gas concentration evolution at monitoring points P1-P4: (a) Pressure and (b) adsorbed gas concentration.

Fig.12.Desorption isotherms for different initialized pressures.

Fig.13.Comparison of pressure evolutions at monitoring points P1-P4 between different degrees of hysteresis.

Fig.14.Comparison of adsorbed gas concentration evolutions at monitoring points P1-P4 between different degrees of hysteresis.

5.2.3.Influence of desorption hysteresis

Due to the significance of adsorption hysteresis,the effect of degree of hysteresis is analysed in this study,which is achieved through defining another two different hysteresis indicesHI=0.6,0.9.Figs.13 and 14 present the comparisons of pressure and adsorbed gas concentration evolutions for different degrees of hysteresis at monitoring points P1-P4.For stronger degree of desorption hysteresis,the pressure drop after injection stops is more significantly and rapidly,however,the adsorbed gas concentration shows an opposite changing pattern.There is a significant drop in adsorbed gas concentration when degree of hysteresis is less.The reason behind this scenario is that when the degree of desorption hysteresis intensifies,the number of available adsorption sites containing higher binding energy increases.Consequently,a larger pressure decrease is required for desorption of adsorbed CO2,rendering it difficult for adsorbed CO2to desorb and return to the free phase.Meanwhile,the free phase CO2can continue to propagate further,leading to a drop in the concentration of free phase CO2in the region.As a result,the gas pressure in the region decreases more significantly,while the concentration of adsorbed CO2remains relatively higher.It can be inferred that because of substantial drop in pressure,the spread of CO2will become slower,and it might even cease when significant desorption hysteresis of CO2is present.This suggests that coal seams exhibiting strong desorption hysteresis are advantageous for the long-term sequestration of CO2.

5.2.4.Influence of reservoir heterogeneity

The coal reservoir is highly heterogeneous,therefore,one objective of present work is to show the heterogeneity effects on CO2storage in coal seams.Here,the non-uniform permeability distribution is considered to show the impact of coal heterogeneity in flow conductivity.Fig.15 shows the logarithmic distribution is used for generation of random permeability field used in simulation with a mean value of 1 ×10-15m2and variance of 4 ×10-30,other material properties are still assumed to be the same in the simulation domain.Figs.16 and 17 present pressure and adsorbed CO2concentration distributions during injection and post-injection periods of operations.Compared to the homogeneous case (see Figs.8 and 9),distributions of pressure and adsorbed CO2are nonuniform.The injected gas firstly flows into zone where the permeability is higher,leading to higher adsorbed gas concentration.

Fig.15.Permeability field.

Fig.16.Pressure distribution in the heterogeneous coal seam after 1 year,2 years,5 years,10 years,15 years and 20 years.

Fig.17.Adsorbed gas concentration distribution in the heterogeneous coal seam after 1 year,2 years,5 years,10 years,15 years and 20 years.

Particularly,the spread of injected CO2in coal seams when considering heterogeneity effect is slower than that under assumption of reservoir homogeneity.Fig.18 shows the pressure and adsorbed CO2distribution along the diagonal.It can be seen that the gas front only reaches at distance of about 76 m and 155 m from injection well after 1 year and 20 years,respectively,which is smaller than that (93 m and 197 m) for homogeneous case (see Fig.10).This implies that the heterogeneity effect on gas transport within coal seams is significant.It is worth pointing out that the random permeability field may be simplified,although the heterogeneity effects can be observed from the simulation results,more attempts to reservoir heterogeneity effect using advanced geostochastic methods like Kriging distribution should be made in future research work for engineering applications.

Fig.18.Pressure and adsorbed gas concentration distribution along the diagonal of heterogeneous domain at different times: (a) Pressure and (b) adsorbed gas concentration.

5.2.5.Implications for CO2 storage in coal seams

Understanding the coupled processes is important for geological CO2sequestration.To this end,this study presents a coupled flowadsorption-geomechanics model,particularly,the desorption hysteresis is considered.It offers an effective approach to estimate the CO2leakage during injection period and continuous migration after injection cease.These results can provide certain guidance for design and management of CO2injection into coal seams.For example,it facilitates pressure selection for CO2injection when the amount of injected CO2is identified.The distance between injection well and enough reservoir area should be considered for long term safety of CO2storage since the injected CO2will continue to spread after injection stops.The effect of reservoir heterogeneity should not be ignored when designing the geological CO2storage,advanced geostochastic methods like Kriging distribution can be used for accurate representation of reservoir heterogeneity.

6.Conclusions

To unlock the sustained effectiveness of CO2storage into coal reservoirs,this paper firstly develops a new adsorption-desorption isotherm of gases in coals with considering desorption hysteresis.Particularly,a hysteresis index,which is applied to quantify the degree of hysteresis,is derived based on thermodynamics.And then the developed adsorption-desorption model is incorporated into a numerical model of coupled gas flow and deformation behaviour.The ability of the proposed model is demonstrated through validation tests against laboratory experiments.The temporal-spatial evolutions of pressure and adsorbed CO2during injection and post-injection periods of operations are investigated.The major observations include:

(1) Adsorption induced pore deformation is the mechanism behind desorption hysteresis.There is more pores with smaller size after adsorption,this leads to an increase in adsorption sites with higher binding energy,the release of adsorbed gas requires greater activation energy generated by a larger decrease in gas pressure.

(2) Injected gas continues to propagate after injection stop.Gas pressure near the injection well experiences a significant drop after injection stop,which causes a drop in the pressure difference in the domain.In comparison,the differences in adsorbed CO2concentration in the domain are obvious due to desorption hysteresis.

(3) The continuous propagation of injected CO2within coal seams and drops of pressure and adsorbed gas as time increases are associated with the degree of desorption hysteresis and heterogeneity of coal seams.The stronger degree of hysteresis is,the more significant drop in pressure near injection well,but the drop of adsorbed gas concentration is less.The spread of gas in heterogeneous coal seams is obviously slower compared to the homogeneous case,thus,the heterogeneity effect on gas flow should be considered when designing CO2geological sequestration.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The research was conducted as part of the “Establishing a Research Observatory to Unlock European Coal Seams for CO2Storage (ROCCS)” project (Grant No.899336).The work of the second author is also sponsored by Shanghai Pujiang Program(Grant No.23PJ1412600).The financial support is also gratefully acknowledged.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2023.11.004.