Swelling of Coal in Response to CO2 Sequestration …...Swelling/shrinkage coefficients have been reported in different units by different authors. Seidle and Huitt (1995) calculated

Swelling of Coal in Response to CO2Sequestration for ECBM and Its Effect on

Fracture PermeabilitySaikat Mazumder, SPE, Amit Karnik, SPE, and Karl Heinz Wolf, SPE, Delft U. of Technology

SummaryThe “swelling” of coal by a penetrant refers to an increase in thevolume occupied by the coal as a result of the viscoelastic relax-ation of its highly crosslinked macromolecular structure. Projectsrelating to CO2 sequestration in coal seams suffer a serious setbackin terms of injectivity loss resulting from the swelling of coal.Volumetric swelling associated with CO2 sorption on coal has asignificant influence on the fracture porosity and permeability ofthe coal. Two coal samples differing in rank were used for volu-metric strain measurements. With CO2, the high-rank Selar Cor-nish coal showed a maximum volumetric strain of 1.48% corre-sponding to an average pore pressure of 13 MPa. A matrix swell-ing coefficient (Cm) of 1.77×10−4 MPa−1 was calculated for thisSelar Cornish coal. The low-rank Warndt Luisenthal coal exhibitedhigher strain of 1.6%, and a matrix swelling coefficient (Cm) of8.98×10−5 MPa−1 was calculated. The rank dependence of swell-ing holds true in this set of experiments. Repeat volumetric strainmeasurement on the same Warndt Luisenthal coal core showshigher volumetric strain values for all pressure steps. A volumetricstrain of 1.9% corresponding to a mean pore pressure of 14 MPawas measured. This confirms the process of sequential swelling.

A unique feature of this work is that real-time permeabilitymeasurements were done under unconstrained conditions. Perme-abilities were measured, reducing the pore pressure from 16 to 1MPa at constant flow rate. Although measured permeability in-creased with increasing pore pressure under unconstrained swell-ing, in-situ permeability will actually decrease because of fractureclosure in a constrained coal. To validate the permeability swellingrelationship, both permeability measurements under unconstrainedconditions and volumetric strain measurements were used.

IntroductionMaturation of coalbed methane (CBM) production operations insome basins, the emergence of injection schemes for enhancedcoalbed methane (ECBM), and carbon sequestration of greenhousegases has led to renewed focus on the behavior of coalbed reser-voir properties under these conditions.

Cleat permeability of coal is the most important parameter forcoalbed methane production. Being normal to the bedding planeand orthogonal to each other, the face and butt cleats in coal seamsare usually subvertically oriented. Thus, changes in the cleat per-meability are primarily controlled by the prevailing effective hori-zontal stresses that act across the cleats, rather than the effectivevertical stress, defined as the difference between the overburdenstress and pore pressure (Harpalani and Chen 1997). Coal swellingaccompanying CO2 sorption would decrease the permeability ofthe coal as the volume increase is compensated within the frac-ture porosity.

Field evidence suggests that the well injectivity has indeeddeclined at early stages of CO2 injection. It has been reported thaton a unit of pressure basis, CO2 is adsorbed in higher concentrationby coal than by CO2. A medium-rank coal can hold approximately22m3 of CO2 per ton of coal and the double amount of CO2

(Mazumder and Wolf 2003), whereas on a unit of concentrationbasis, CO2 causes more swelling than CH4 (i.e., 20 cm3/g of CO2

causes more swelling than 20 cm3/g of CH4) (Pekot and Reeves2002). This differential swelling behavior would have extremeconsequences for field-injection projects. It may lead to elevatedinjection pressures, causing uncontrolled fracturing of the reservoirbeyond a certain pressure. The detrimental effect of matrix swell-ing on cleat permeability is envisaged in this work. Also, therelationships between concentration, strain, pressure, and swellingof coal matrix are studied.

A series of volumetric swelling experiments by Chikatamarlaet al. (2004) using N2, CH4, CO2, and H2S, were carried out onCanadian coals to access the permeability damage.

Swelling/shrinkage coefficients have been reported in differentunits by different authors. Seidle and Huitt (1995) calculated theswelling coefficient, assuming the swelling to be proportional tothe amount of gas sorbed and relating the sorbed gas to pressure bythe Langmuir equation. The strain in the coal caused by the me-chanical deformation was deducted from the obtained “sorption”strain, and this value was then used to calculate the swelling co-efficient. The concept of mechanical strain in coals is explainedlater in this article. Seidle and Huitt (1995) reported the swellingcoefficient in dimensions of microstrain–ton/Scf.

Other authors have calculated the shrinkage/swelling coeffi-cients after Levine (1996) by using a Langmuir-type equation.They assume that the shrinkage/swelling coefficient is a measureof strain with a change in pressure. This was assumed because thepressure vs. strain curve follows the trend of an isotherm. Thevalues reported by all other authors are in dimensions of MPa−1.The swelling coefficients reported are all from experiments con-ducted on coal core or plugs. Table 1 lists the swelling and shrink-age coefficients for CO2 and CH4 reported up-to-date by vari-ous authors.

Equipment Design

The equipment was designed according to the work plan of theexperiments. Therefore, it is necessary to explain the work scheme:

1. Determine the mechanical compliance of the coal core as afunction of mean pore pressure using helium. The effective stress(Peff) was kept constant while changing the pore pressure. Effec-tive stress or effective pressure is the difference between the out-side mechanical pressure and the pore pressure.

2. Determine the absolute swelling of coal with CO2 as a func-tion of the mean pore pressure and constant Peff. To establish thematrix swelling effect alone, the mechanical effect measured fromStep i has to be substracted.

3. Estimate and establish the dependence of permeability onmean CO2 pore pressure. The effect of permeability variationcaused by change in Peff is removed by keeping the effectivepressure (Peff) constant over the whole course of the experiment.

The uniqueness of these experiments, using large cores, makesthe design of the setup complex. A high-pressure corefloodingsetup was constructed. The pressure cell can reach a maximumconfining pressure of 50 MPa. The confining pressure, which canbe otherwise stated as the outside mechanical stress, was exertedby means of hydraulic oil. During the course of the experiment,this confining pressure was controlled manually so as to set therequired effective stress. For each pressure step, the expected pore

Copyright © 2006 Society of Petroleum Engineers

Original SPE manuscript received for review 25 March 2005. Revised manuscript received24 November 2005. Paper SPE 97754 peer approved 17 January 2006.

390 September 2006 SPE Journal

pressure was calculated, and then the confining pressure was addedmanually by means of a pressure-actuated valve to keep the effec-tive stress (Peff) constant throughout the course of the experiment.The confining pressure was applied on the coal core inside a rub-ber sleeve. To prevent the gas from diffusing through the rubbersleeve, a lead foil was wrapped around the coal core. To simulatedownhole conditions, the temperature in the pressure cell wasmaintained at 45°C. The sample diameter is 72 mm. The length ofthe core varied from sample to sample. For the first experiment, ahigh-rank coal core of 268 mm in length was used, and for thesecond and third experiments, a low-rank coal core of 154 mm inlength was used. To avoid mechanical end effects on the corepermeability, two si-perm plates are fixed at either ends of thecore. The injection and production tubings were attached to the endplates. These si-perm plates have a porosity of 33% and a perme-ability of 10−13 m2. The schematic of the setup is shown in Fig. 1.

Strain gauges were attached on the sample surface to measurethe sorption-induced volumetric strain in the coal. The procedurefollowed is explained in the following section. The strain mea-surements were stored, through an amplifier and a data acquisitionsystem, into a computer. A mechanical displacement transducer(LVDT) measured the axial changes in the sample dimensionthroughout the course of the experiment.

A reference vessel outside the reactor was used to feed the gas.The gas was charged to this reference vessel by an ISCO pump.Then the gas was boosted into the reference cell to get the required

pressures. Time was needed to stabilize the temperature in thereference cell.

Permeability measurements were carried out during the experi-ment with each decreasing pressure step. The ISCO pump wasused to inject the gas at a constant rate. The average of the injec-tion and production pressure was taken as the core pressure for thecalculation of the permeability. A digital flowmeter unique to mea-sure CO2 flow was used at the production end to monitor the flowrate. When no change in flow rate was observed over a period of1 hour, the flow was considered to be stable. Usually, the flowstabilized between 12 and 30 hours after the start of injection.Considering the fact that the desorbing gas was also contributingto the production stream, up to a maximum of 48 hours was givenfor the flow to stabilize. At the production end, a backpressurevalve was used to control the flow out. CO2 was used to measurethe permeability.

Sample Description and PreparationThe samples used for these experiments were from the SouthWales coal field (Selar Cornish) in the U.K. and the WarndtLuisenthal coal field in Germany. The details of the samples areshown in Table 2. The samples selected were quite diverse in theirrank and internal properties.

First, a part of the coal core surface, smoothed free of cleats,was selected. If needed, the representative surface was polished.So that the strain gauges did not come off the surface because of

Fig. 1—Schematic of the entire setup.

391September 2006 SPE Journal

the shear force of the rubber sleeve, grooves approximately 2 mmdeep were made. The groove surfaces were also polished. Thebonding area was cleaned with industrial tissue paper or clothsoaked in a small quantity of chemical solvent such as acetone. Itwas cleaned until a new tissue or cloth came away completely freeof coal particles. If the surface is left uneven, the strain gauges willnot adhere properly to the surface. Then the adhesive to be used forfixing the strain gauges on the coal surface was prepared. Theadhesive was applied evenly on both surfaces (i.e., on the straingauge surface as well as the coal surface). A polyethylene sheetwas placed onto it and pressed down on the gauge for approxi-mately 10 minutes. Connectors were positioned at a distance of 3to 5 mm from the gauge. The junction area was soldered for boththe gauge leads and the connecting terminals. To connect the ex-tension, the lead wires were soldered to the connecting terminals.Two strain gauges were axially oriented, and the two others wereradially oriented on the core surface. Copper wires of sufficientlength were soldered to the terminals of each of these straingauges. A groove was made along the length of the core, and thewires were guided through this groove. All the grooves were thenfilled with a mixture of coal puff and the adhesive. This furtherprevented the strain gauges from being sheared off the surfaceduring the experiment.

The strain gauges were of the rosette type (TML-PC-10), witha gauge factor of 2.07. The strain gauges had an accuracy of+/–2%. The gauge factor can be defined as follows:

k =�R�R

�. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

�R/R is indicated by specifying the Poisson’s ratio of the testspecimen. The gauges were connected to a (1/4) Wheatstonebridge, whose aplifier output is given by

� =4Aop

k�BA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

With this arrangement, the axial and radial strain in the coalsample caused by swelling induced by the sorption of CO2 wasmeasured. The directional placements of the strain gauges weredone so as to measure the two horizontal strains (strain parallel tothe bedding plane). Because the natural fracture system in coal(cleats) is disposed perpendicular to the bedding plane, it is thehorizontal strain that is involved in permeability change takingplace because of the swelling of the coal matrix.

Sorption-Induced AbsoluteSwelling ExperimentsThe setup was designed to measure volumetric strain caused bychanges in sorbed gas concentration while keeping the net stresson the coal sample constant. The tests start with a complex pro-cedure of mounting the coal core sample in a rubber sleeve andbuilding it in the high-pressure cell (leak-free). The sample cellwas connected to a vacuum pump for at least a week to eliminateany form of residual gas or moisture. Prior to the start of theexperiment, strain gauges were calibrated for temperature variations.

A mechanical compliance test with helium is almost compul-sory at the start. Helium was injected in the coal in 20-bar steps ofincreasing pressure up to 160 bar. The effective pressure (Ppore–Pann) was kept constant throughout the experiment. The pressurewas reduced in a similar way. Each injection cycle ended after anequilibriation time of 30 minutes. This test was done to measurethe void volume of the setup and to estimate the mechanical com-

pliance coefficient of the coal (Seidle and Huitt 1995). Helium wasselected because of its nonsorbing nature to the coal surface. Thus,the measured strain with helium is solely caused by the mechanicalcompression of the solid coal resulting from the change in pressure.

The next set of experiments were done to determine the abso-lute swelling of coal with CO2 as a function of the mean porepressure and constant Peff. Here, CO2 was used instead of helium.The CO2 sorption experiment was carried out at 45°C. The con-fining pressure was maintained on the sample with hydraulic oil.The pore pressure, Ppore, was increased in increments of 20 baruntil the end pressure of 160 bar was reached. After each pressurestep, an equilibration time of 4 to 7 days was given. Over the entirecourse of the experiment, the effective pressure, Peff, was keptconstant. Measurements are made for the strain in the system.Three experiments were performed, one with the Selar Cornishcoal and two with the Warndt Luisenthal coal. The third experi-ment was a repetition of the second experiment. At the end of eachexperiment, the core was built out, the length of the sample mea-sured, and the integrity of the coal checked. For all three experi-ments, the position of the strain gauges was checked for slip, butwas found to be intact. No independent evidence of deformationwas recorded.

Data Analysis. The axial and the radial strains were obtained fromthe strain gauges fixed on the sample. Strain-gauge response fromthe repeat Warndt Luisenthal experiment is shown in Fig. 2. As-suming isotropic swelling, we have

�volumetric = �x + 2�y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

Following the helium injection, the volumetric strain responseof the coal sample was used to calculate the mechanical com-pliance coefficient (Cp). Cp is defined as the strain change withcorresponding change in pressure and is primarily caused bygrain compression.

Cp =d�

dP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

Methane and carbon dioxide sorption data can be modeledusing the empirical form of the Langmuir isotherm model (Levine1996). Therefore, an equation having the same mathematical formas the Langmuir equation was used in this study to fit the sorptionstrain data theoretically, as depicted in the next section.

Fig. 2—Volumetric strain response for the Selar Cornish coalfollowing helium injection.


�s = �max

P

P + P�

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

�max and P� were estimated by best fitting a linearized form ofEq. 5 where �/P is plotted against �. The slope of this linearizedform is equal to 1/P� and the y-intercept is equal to �max/P�.Matrix swelling coefficient is a measure of the strain change withthe corresponding change in pressure.

Cm =d�

dP=

��max P��

�P� + P�2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

The coefficient derived from this equation has the unit of MPa−1,which quantifies the change in volumetric strain per unit pressure.

Results and Discussion. The first part of the experiment is amechanical compliance test for the coal core samples by injectinghelium in pressure steps of 20 bar and continuously monitoring thestrain. The sample was considered to be in equilibrium if the strainremained constant for more than 30 minutes. Because helium is notsorbed onto coal, no swelling of the coal matrix occurs, and theentire strain observed is because of the compression of the coalmatrix by the increasing gas pressure. The mechanical compliancetest results are shown in Figs. 3 and 4. The linearity of the com-pression with pressure is quite evident. This effect is subtracted toget the volumetric strain because of the sorption of CO2. Themechanical compliance coefficient (Cp) for the Selar Cornish andthe Warndt Luisenthal coal were calculated to be −5.0×10−4

MPa−1 and −1.0×10−4 MPa−1, respectively. Various values of Cp

have been reported by various authors. This holds true because Cp

is a rank-dependent property of coal. For the same sample, Cp ispressure-dependent, but while comparing different samples, Cp isrank-dependent as well.

In the second series of experiments with CO2 injection, werecognized a combined effect of grain compression and matrixswelling. The volumetric strain results from the three experimentsare shown in Figs. 5 through 7. The effect of swelling was singledout by subtracting the mechanical effects. As can be seen from thevolumetric strain results, matrix swelling is more dominant. Fig. 5shows the experimental and the theoretical volumetric strain mea-surements of the Selar Cornish coal. During this experiment, theeffective pressure (Peff) was kept constant at 4 MPa. With CO2, theSelar Cornish coal showed a maximum volumetric strain of 1.48%corresponding to an average pore pressure of 13 MPa. A matrixswelling coefficient (Cm) of 1.77×10−4 MPa−1 was calculated fromthis experiment. Similarly, the experimental and theoretical volu-metric strain measurements of the Warndt Luisenthal coal areshown in Figs. 6 and 7. Fig. 7 shows a repeat experiment, con-ducted on the same coal sample as the experiment shown in Fig. 6.The low-rank Warndt Luisenthal coal exhibited a higher strain ofaround 1.6% compared to the high-rank Selar Cornish. Thus, therank dependence of swelling holds true for this set of experiments.The repeat Warndt Luisenthal experiment shower higher volumet-ric strain values for all pressure steps. A maximum volumetricstrain of 1.9% corresponding to a mean pore pressure of 14 MPawas measured. This confirms that the process of sequential swell-ing is in accordance with the observation, as suggested by Bodilyet al. (1989). Sequential swelling confirms the highly crosslinkedmacromolecular nature of coal. It also suggests that the swelling ofcoal by all nonpolar gases such as CO2 and CH4 is caused by thedispersion force interaction between the gas and the coal macro-molecular network. The crosslinks broken at the first place are notcompletely reformed upon removal of the sorbent leading to in-cremental strains, as shown in the repeat experiment. Sequentialswelling is proposed to explain the incremental strain observedfrom the repeat experiment. More experiments are presently beingconducted to prove the fact.

Fig. 3—Volumetric strain response for the Warndt Luisenthalcoal following helium injection.

Fig. 5—Experimental and theoretical strain for WarndtLuisenthal coal core experiment.

Fig. 6—Experimental and theoretical strain for repeat WarndtLuisenthal coal core experiment.

Fig. 4—Experimental and theoretical strain for Selar Cornishcoal.


The matrix swelling coefficients (Cm) from the two WarndtLuisenthal experiments are 8.98×10−5 MPa−1 and 7.92×10−5

MPa−1, respectively. The matrix swelling coefficients for the low-and high-rank coal differ by an order of magnitude. For all threeexperiments, the actual value of Cm varied, and was lower forgas pressures greater than 4 MPa and higher for gas pressureslower than 4 MPa. This was also reported by George and Barkat(2001). For the Selar Cornish coal, an end strain of −0.45% wasmeasured, and for the Warndt Luisenthal coal an end strain of−0.92% was measured.

The curvy nature of the experimental strains are probably at-tributable to short equilibration times or the heterogeneity in thecoal. Fig. 2 demonstrates the strain change with time for the repeatWarndt Luisenthal experiment. Inertinite rich bands in the core docontribute to the volume, but do not adsorb the same as the brightvitrinite bands. Fig. 2 shows that reaching equilibrium in terms ofstrain measurement over all individual strain gauges was not pos-sible. But the criterion for continue doing the next step was basedon the equilibration of the pressure over time. When the change inpressure was observed to be less than 0.01 MPa over 12 hours, theexperiment was ready for the next step. Moreover, the nonequi-librium in the strain measurement (Fig. 2) is only observed in onepair of axial and radial strain measurements, which were coupledtogether at one particular point on the coal core. Considering thescale of the samples it is quite possible that a particular location onthe coal surface cannot be absolutely free of micro/meso cleats.The presence of such minor fractures will obviously affect theequilibrium strain measurements. The bad fit between the theoret-ical and the experimental strain may otherwise suggest that aLangmuir-type model is not enough to describe the process. Amore mechanistic model is needed for this purpose.

The swelling experiments show that the transport process incoal is complex. The similarities in structure between coal andglassy polymers have led to the application of theories of sorptionbehavior of polymers to coals. During diffusive transport at low ormoderate temperatures, as gas enters the macromolecular networkof coal, the network density decreases. It results in an increase ofthe large molecular chain motions (Peppas and Ritger 1987). Thisincrease of the gas concentration of the network can be consideredas an effective decrease of the glass transition temperature. Struc-tural changes induced during this process include swelling, micro-cavity formation, and primary-phase transition requiring rear-rangements of each chain segment. Such changes are dominated byrelaxational phenomenon.

The diffusion of gas into glassy polymers may vary betweentwo analytically treatable extremes. If the diffusion is controlled bythe concentration gradient between the center and the outside ofthe particle, the diffusion mechanism is Fickian. The diffusion inglassy polymers often does not fit the Fickian diffusion model.Alfrey et al. (1966) presented a second limiting case for sorption.Here, the rate of transport is entirely controlled by molecular re-laxation. This type of transport mechanism is designated as Case IItransport. Thomas and Windle (1982) proposed that the rate-

controlling step at the penetrant front is the time-dependentmechanical deformation of the glassy polymer in response tothe thermodynamic swelling stress. A stress-driven anomalous dif-fusion process of CO2 in coal has been discussed by Mazumderet al. (2006).

Effect of Matrix Swelling on Fracture Porosityand PermeabilityThe coal matrix is heterogeneous and is characterized by twodistinct porosity systems: micropores and macropores. Themacroporosity in coal consists of the cleats. It is a well-defined anduniformly distributed network of natural fractures. The cleat sys-tem can be subdivided into continous face and discontinous buttcleats, which terminate at intersections with the face cleat.

Cleat permeability is recognized as the most important param-eter for coalbed methane production. Being normal to the beddingplane and orthogonal to each other, the face and butt cleats in coalseams are usually subvertically oriented. Changes in cleat perme-ability are primarily controlled by the prevailing effective horizon-tal stress that acts across the cleats.

The impact of increasing triaxial stress on permeability of coalsamples has been investigated by a number of researchers (Som-erton et al. 1975; Durucan and Edwards 1986). Experimental mea-surements indicate that permeability of coal decreases exponen-tially with increasing effective stress (Peff) (McKee et al. 1987).

The permeability of the cleat structure in coal changes because:1. The phase relative permeability effects, whereby the degree

of saturation will affect the gas and water relative permeabilities ofthe reservoir.

2. The permeability varies by a change in the effective stresswithin the seams. The effective stress tends to close the cleats andreduce permeability. It is likely that the permeability is relatedparticularly to the “effective horizontal stress” (Gray 1987) acrossthe cleats because these appear to conduct the most seam fluids.The “effective normal stress” is referred to as the total stress nor-mal to the cleat minus the fluid pressure within the cleat. Underfield disposition, the “effective normal stress” can also be termedas the “effective horizontal stress” (Shi and Durucan 2003) be-cause the cleat system is subvertically oriented to the beddingplane and its subdivisions are orthogonal to each other. Underthese circumstances, the permeability variations brought about byvariations in fluid pressures are anisotropic, depending on the na-ture, frequency, and direction of the cleats. Such opening andclosing of the cleats is also likely to change the phase relativepermeabilities and capillary pressures within the coal.

3. The permeability varies because of shrinkage while methaneis being desorbed, or swelling while carbon dioxide is being in-jected. This aspect of permeability variation is being dealt with.

The test procedure in the laboratory involved confining a 20-cm-long and 7-cm-diameter coal core sample under a number ofisotropic stress levels in the cell and injecting carbon dioxidethrough the sample at a steady pressure until the flow came toequilibrium. Twelve to 48 hours were required to reach equilib-rium. Because gas pressure varied across the sample, the averageof the two end gas pressures was used in the calculation of theeffective stress. The equation below was used to calculate the corepermeability (Gray 1987).

k =2qP0L�

A�Pi2 − Po

2�. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

The permeability measurements were conducted on the SelarCornish and the Warndt Luisenthal coal core samples. The coalsamples used had high cleat density. At the end of the absoluteswelling measurements with CO2, when the coal core reachedequilibrium at pressures greater than 14 MPa, the permeabilitymeasurements were carried out at each step of decreasing pressure.For all measurements, the cell was kept at a constant temperatureof 45°C. As shown in Fig. 1, the pressure vessel is a biaxial cellwhere the coal core is placed inside a rubber sleeve. The effectivestress during the entire experiment was maintained around 4 MPafor the Selar Cornish coal and around 6 MPa for the Warndt

Fig. 7—Strain change with time for repeat Warndt Luisenthalcoal core experiment.


Luisenthal sample. After the stress stabilized, the injection of CO2

was performed with the ISCO pump at a constant rate. A digitalmass flowmeter specially calibrated for CO2 was used to measurethe flow on the production end. To keep the downstream pressureconstant and to create a pressure gradient, a backpressure valvewas used. The flow measurements for a particular pressure stepwere only used when all equilibrium conditions were satisfied.Performing the first permeability measurement at higher pressureensured that the coal core sample equilibrated both in terms of itssorption capacity and of sorption-induced swelling. This arrange-ment does allow the coal to swell to its maximum under the re-spective mean pore pressure and the applied effective stress, andthis can be better referred to as unconstrained swelling. The swell-ing of coal matrix caused by injection results in a change in thecleat porosity and, therefore, the cleat permeability. Under idealfield conditions, the coal seam is not allowed to swell beyond itsboundaries in both the vertical and horizontal directions. The com-plete effect of volumetric strain will thus be translated in terms ofreduction in cleat porosity.

Results and Discussion. The results of the permeability measure-ments in the laboratory are shown in Figs. 8 and 9. Under stress,both the coal samples have extremely low initial permeability inthe range of 0.01 md. The slight variation in the effective stress(Peff) at lower pressures was unavoidable. Because the coal corewas free to swell inside the pressure cell (unconstrained swelling),the measured permeability is higher at higher mean pore pressure,and vice versa. This whole process of free swelling in the labora-tory in comparison to constrained swelling in the field is analogousto thermal expansion (Shi and Durucan 2003). A hollow steel pipesubjected to thermal expansion encounters an increase in its freevolume, which is analogous to an increase in the cleat porositywith increasing swelling in our case. Stress-strain relationships forcoal as a thermoelastic porous medium are described by Shi andDurucan (2003). They have modeled this process by which theyhave replaced the thermal expansion term with an analogous swell-ing term.

To understand why the permeability of the coal core increasewith increasing pore pressure (Ppore) while the effective stress iskept constant is a question of understanding what swelling stress(�sw) is. Swelling stress is defined as the pressure of an element ofcoal matrix saturated with the adsorbent (CO2/CH4/N2) avoiding atthe same time deformation. The very definition makes it clear thatthe measurement, or measurement methodology of swelling stress,is not a matter to be easily accomplished. From the viewpoint ofthermodynamics, swelling stress represents a kind of energy. In thecase of free swelling (unconstrained laboratory conditions), it turnsout to be a volume change. Swelling stress only occurs in the caseof constrained swelling. The concept of swelling stress is shown inFig. 10. Considering a deformed domain, a process of back com-paction can be visualized to understand the swelling stress. With

the present experimental setup, a case of free swelling will resultin a volume change (dV). This volume change will see an incre-mental rise in the annular pressure (Pann) of the cell. But becausethe system is set so as to keep the effective stress (Peff) constant,some of the oil from the annular space will drain out.

There are two sets of experimental data to validate a relationshipbetween permeability and swelling: permeability measurements un-der unconstrained conditions, and volumetric strain measurements.

Using the experimentally determined permeability measure-ments under unconstrained conditions (Figs. 8 and 9) and assum-ing that permeability varies with porosity as follows,

knew

kinitial= � �new

�initial�3 �1 − �initial�

2

�1 − �new�2, . . . . . . . . . . . . . . . . . . . . . . . . . (8)

changes in cleat porosity were calculated. The increase in coalcleat porosity because of unconstrained swelling is considered tobe equal to the decrease in cleat porosity under field conditionswith constrained swelling. The resulting decrease in the cleat po-rosities is shown in Figs. 11 and 12. This assumption is valid whenthe total volume of coal (matrix and cleats) remains constant withinjection of CO2. With the decrease in cleat porosity calculated andwith a set of three different initial porosity values, the permeabilityvariation under constrained condition was determined. Althoughsignificant advances have been made, it is still difficult to measure

Fig. 8—Experimentally determined variation in permeability forSelar Cornish coal as a result of matrix swelling under uncon-strained conditions. Fig. 9—Experimentally determined variation in permeability for

Warndt Luisenthal coal as a result of matrix swelling under un-constrained conditions.

Fig. 10—Concept of swelling stress.


cleat porosity accurately because of the very small volume ofcleats in a core. For that reason, a range of three different initialcleat porosity values between 0.1 and 1.0% was used to estimatethe change in permeability with sorption-induced swelling. Theresulting variations in permeability are shown in Figs. 13 and 14.For all initial porosity cases, the porosity attains negative values,because the initial permeability of the sample is very low. This hasalso been reported by Zutshi and Harpalani (2004) with a match-stick model.* Under laboratory conditions, the negative perme-ability can be explained as the flow, which takes place through thecoal matrix and can no longer be considered as a fracture or cleatflow. Model-generated negative permeability and porosity lacksany physical meaning. But this retains the essence of the swelling-induced injectivity problem. Negative permeability and negativeporosity values indicate near-zero porosity and permeability atthose pressures. This problem can be anticipated at field-scaleinjection projects in low-permeability coal. Thus, injecting under anear-zero permeability condition results into very high bottomholepressures, which exceeds the fracture breakdown limit, resulting inpropagation of uncontrolled fractures.

With the second set of data on volumetric strain measurementsand following the procedure described by Harpalani and Chen(1992, 1995, 1997), changes in cleat porosity and permeability, asa result of changing volumes of the coal matrix, were calculated.This procedure, by using the matchstick model (Reiss 1980), isbriefly described next. The increase in coal matrix volume causedby swelling was considered equal to the decrease in cleat aperture(b) as shown in Fig. 15, assuming that the the total volume of coalremains constant upon injection of CO2. Assuming a matchstickgeometry, where a1=a2, the initial geometry (�initial) is given by

2b/a. The change in matrix dimension depends on the change inpressure and the swelling behavior of coal:

�a = alm�P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)The new cleat porosity can thus be written as

�new =2�b − �a�

�a + �a�. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10)

Substituting the value of �a, the porosity ratio can be written as:

�new

�initial=

1 − �2lm�P��initial�

�1 + lm�P�. . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

Using estimates for initial porosity and the experimental hori-zontal strain, pressure-dependent cleat porosity can be estimatedand compared to the experimentally derived porosity change.Moreover, the change in cleat porosity by swelling will change thecleat permeability. Similar to the case just presented, the ratio ofthe modified cleat permeability can be written as:

knew

kinitial=

�1 − �2lm�P��initial��3

�1 + lm�P�. . . . . . . . . . . . . . . . . . . . . . . . . . (12)

The variations in permeability as a function of the intial poros-ity for both the Selar Cornish and Warndt Luisenthal coal coreabsolute swelling experiments are shown in Figs. 16 and 17. Thepermeability variations for both the experiments have been workedout for three different porosity situations as shown in the figures.As expected, the permeability in all three situations decreases tozero. However, these results showing a decrease in permeabilityare caused by a change in matrix volume alone. In our experi-ments, the effective stress (Peff) was kept constant. Under true fieldconditions, the injection of CO2 would also result in a simulta-neous decrease in the Peff, which would result in an increase in thecleat permeability and would thus counter a part of the permeabil-ity reduction attributable to volume increase.* Personal communication with Harpalani, 2005.

Fig. 12—Variation in fracture porosity for Warndt Luisenthalcoal as a result of matrix swelling under constrained condi-tions.

Fig. 14—Variation in permeability for Warndt Luisenthal coal asa result of matrix swelling under constrained conditions.

Fig. 11—Variation in fracture porosity for Selar Cornish coal asa result of matrix swelling under constrained conditions.

Fig. 13—Variation in permeability for Selar Cornish coal as aresult of matrix swelling under constrained conditions.


ConclusionsThe major conclusion of this experimental study is that injection ofCO2 in coal seams results in volumetric swelling. This injectionhas a profound effect on the fracture porosity and permeability ofthe coal. The rank dependence of swelling was established byperforming experiments with two coal samples differing in rank.Sequential swelling of coal holds true and is in line with compar-ing the coal structure with that of glassy polymers. With the per-ception of swelling in coal, the transport process should be dealtwith in much detail. Decrease in permeability caused by change inmatrix volume was studied under constant effective stress condi-tions. This suggests that CO2 injection in coal seams could resultin serious injectivity problems near the wellbore.

Nomenclaturea � the initial cleat spacing, mA � cross-section area, cm2

Aop � amplifier output, voltsAz � amplification, ×1000 in this case

Cm � swelling coefficient, MPa−1

Cp � mechanical compliance coefficient, MPa−1

k � permeability, mdK � gauge factor, −lm � change in dimension of the cleat matrix in the

horizontal direction per unit pressureL � length of the core, m

Pann � annular pressure, MPaPeff � effective stress, MPa

Pi � injection pressure, MPaPpore � pore pressure, MPa

P0 � production pressure, MPaP� � corresponds mathematically to the “Langmuir

pressure” and represents the pressure at which the coalhas attained 50% of its maximum strain. The lower thevalue of P�, the steeper the sorption curve at lowpressures.

�P � change in the gas pressureq � flow rate, m3/sR � gauge resistance, �

�R � resistance variation� � mechanical strain, %

�max � corresponds mathematically to the “Langmuir volume”and represents the theoretical maximum strainapproached asymptotically at infinite pressure

�s � linear sorption strain at pressure P� � viscosity, Pa�s

�B � bridge supply, volts�sw � swelling stress, MPa

� � porosity, −f � fracture porosity, −

m � matrix porosity, −

AcknowledgmentsThis work was funded by the EU-funded CO2 sequestration projectRECOPOL and the Dutch CATO program. At the very onset, wewould like to thank Professor Harpalani and Hans Bruining fortheir valuable input. They have been instrumental in solving ourdoubts, which have been basic at times. We would like to extendour gratitude once again to both of them for being patient andinspiring us to walk on this path, which was arduous at times. Ourspecial thanks also go to Henk van Asten, Leo Vogt, Arnold Mul-ders, Paul Vermeulen, and Kees van Beek for their technical sup-port. The experimental work would not have been possible withouttheir help.

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Fig. 15—Matrix and cleat geometry for a matchstick model.

Fig. 16—Theoretically calculated permeability variation as a re-sult of matrix swelling for Selar Cornish coal from matchstickmodel.

Fig. 17—Theoretically calculated permeability variation as a re-sult of matrix swelling for Warndt Luisenthal coal from match-stick model.


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SI Metric Conversion Factorscp × 1.000 E–03* � Pa.sft × 3.048 E–01* � m

md × 9.869 233 E–04 � �m2

psi × 6.8948 E–03* � MPa

*Conversion factor is exact

Saikat Mazumder is presently working for Shell Intl. E&P as asenior reservoir engineer specializing in coalbed methane andenhanced coalbed methane. He has 8 years of experience,both in operations and research. Amit Karnik is presently work-ing as a production technologist for Royal Dutch Shell (NAM).He holds a Masters degree in petroleum engineering from theDelft U. of Technology in The Netherlands. Karl Heinz Wolf is adistinguished faculty member in the Dept. of Geotechnologyat the Delft U. of Technology. He leads the ECBM researchteam at Delft and was instrumental in providing key input andsupervision for this work.


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Swelling of Coal in Response to CO2 Sequestration …...Swelling/shrinkage coefficients have been reported in different units by different authors. Seidle and Huitt (1995) calculated