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One of the approaches suggested for sequestering CO2 is by injecting it in coal-bed methane. (CBM) reservoirs. Despite its potential importance for CO...
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Ind. Eng. Chem. Res. 2004, 43, 2887-2901

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Overview of Laboratory and Modeling Studies of Carbon Dioxide Sequestration in Coal Beds Theodore T. Tsotsis,† Hiren Patel,† Babak Fayyaz Najafi,† Deepti Racherla,† Mark A. Knackstedt,‡ and Muhammad Sahimi*,† Department of Chemical Engineering, University of Southern California, 925 Bloom Walk, HED-216, Los Angeles, California 90089-1211, and Research School of Physical Sciences and Engineering, Department of Applied Mathematics, The Australian National University, Canberra, Australia

One of the approaches suggested for sequestering CO2 is by injecting it in coal-bed methane (CBM) reservoirs. Despite its potential importance for CO2 sequestration, to our knowledge, CO2 injection in CBM reservoirs for the purpose of sequestration has not been widely studied. Furthermore, a key element missing in most of the existing studies is the comprehensive characterization of the CBM reservoir structure. CBM reservoirs are complex porous media because in addition to their primary pore structure, generated during coal formation, they also contain a variety of fractures, which may potentially play a key role in CO2 sequestration because they generally provide high permeability flow paths for both CO2 and CH4. In this paper, we present an overview of our ongoing experimental and modeling efforts, which aim to investigate the injection, adsorption, and sequestration of CO2 in CBM reservoirs, the enhanced CH4 production that results, and the main factors that affect the overall operation. We describe the various experimental techniques that we utilize and discuss their range of application and the value of the data generated. We conclude with a brief overview of our modeling efforts aiming to close the knowledge gap and fill the need in this area. Introduction Fossil fuels are the main source of anthropogenic CO2, a major player in the “greenhouse” effect.1 One of the approaches suggested for sequestering CO2 is by injecting it in coal-bed methane reservoirs (CBMR). In doing so, one displaces CH4 gas in these reservoirs, which can then be utilized as an energy source. The advantage of this approach over other storage/sequestration options is that the value of CH4 produced helps to alleviate partly or wholly the sequestration costs.2 The gases found in CBMR were generated during the conversion of plant materials into coal and are either adsorbed on the coal surface or condensed in the coal pores. CH4 is the major component (∼95%), and other gases include C2H6, CO2, N2, He, H2, and H2S (all collectively known as natural gas). Most of the CH4 found in CBMR is in the sorbed state. Its amount, which can be significant, is determined by the confining pressure and the surface area within the coal micropores, which reportedly ranges from 20 to 200 m2/g3 (controversy still exists, however, on how one properly measures coal surface areas; see the discussion that follows). Because of their significant storage capacities, CBMR can potentially produce more CH4, and also sequester more CO2, than conventional gas reservoirs of comparable size at the same temperature and pressure.4 The worldwide CO2 sequestration potential of CBMR is very significant, ranging from 225 up to 964 Gt of CO2.1 CBMR are complex porous media. In addition to the primary coal pore structure generated during coal formation, they also contain various fractures, which * To whom correspondence should be addressed. Tel.: 213740-2064. Fax: 213-740-8053. E-mail: [email protected]. † University of Southern California. ‡ The Australian National University.

play a key role in CO2 sequestration in CBMR because they provide high permeability flow paths for both CO2 and CH4. There are four types of fractures found in CBMR.5 They include (i) faults and shear zones, (ii) extension- and compression-related joints, (iii) mininginduced fractures, and (iv) the coal cleat system. Of these, cleats, likely, play the most important role during CBM CO2 sequestration. Two types of cleats are found in coal: the primary cleats (face cleats) and the secondary cleats (butt cleats).6 The face cleats, which control the flow of CO2 and CH4 from and/or to the injection/ production wells, usually form an interconnected network; the butt cleats control transport of gases between the micropores and the face cleats. Factors determining cleat spacing and size are thought to be coal rank, petrographic composition, mineral matter content, and stress/strain history.6,7 However, a comprehensive literature search reveals only a few studies to date devoted to the detailed characterization of the cleat fracture system.8-10 Uncertainty exists, for example, about the cleat porosity (thought to range between 0.1 and 1%), cleat spacing, and even cleat aperture (thought to range between 100 nm and 100 µm).6 Another complication in the study of CO2 sequestration in coal beds results from the fact that CBMR also contain water, in addition to natural gas. The moisture content varies with coal rank, for example, 75-90% in peat, 30-50% in lignite, 7-10% in highly volatile bituminous, and 1-5% in lowly volatile bituminous.10 There are four types of coal moistures.10 They include (i) free or adherent moisture, retained in the pore structure in a free state (not bonded to coal), (ii) inherent or bed moisture, physically adsorbed in the micropores, (iii) chemically bound moisture of decomposition, organically associated within the coal molecules and progressively released during coalification, and (iv)

10.1021/ie0306675 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/04/2004

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water of hydration, associated with the inorganic constituents of coal. Of these, the most important during sequestration are the adherent moisture, which affects gas permeability, and the inherent moisture, which interferes with gas adsorption. In addition, when CO2 is dissolved in water, it forms carbonic acid, which reduces the pH. Increased acidity may result in coal mineral dissolution and potentially in secondary precipitation of carbonate minerals.1 For laboratory studies involving CBMR samples, reproducing and maintaining the same amounts of moisture as those found under field conditions remain key challenges. The displacement of CH4 by CO2, key during CO2 sequestration in CBMR, results from three processes: (i) adsorption/desorption of the two gases in the coal matrix; (ii) diffusion in the matrix toward the cleats; (iii) flow through the cleats and eventually the larger coal fractures. Most of the gases reside in the coal micropores, which have diameters ranging from 0.4 to 2 nm and low permeability.11 The cleats, on the other hand, have much higher permeability but adsorb little CH4. Traditionally, CH4 production from CBMR happens as a result of pumping the gas out of the reservoir through the natural or induced fracture system. When CO2 or other gases (e.g., N2) are used to produce CH4 from the coal bed (a process known as ECBM), they are injected under high pressure through a series of wells and displace CH4 out of the reservoir. CO2 is more adsorptive in coal than CH4, and because it displaces CH4, it is itself sequestered. The CO2-ECBM process for CO2 sequestration is defined as CO2-ECBM/sequestration1 (ECBM/S). Efforts to model and simulate CH4 production from coal beds, either by conventional techniques or by ECBM or ECBM/S, use double-porosity (DP) models12-14 representing the CBMR as a uniform porous matrix with a network of embedded fractures. The flow to and from the production/injection wells is assumed to occur only through the fracture system, typically represented by a cubic network. In the coal matrix, the gases are assumed to be transported by Fickian diffusion. Though potentially useful at some level, the DP models fail to capture key aspects of the ECBM/S process.2,13 There are a number of reasons for that. (1) The fracture and pore networks have complex and multiscale structures; fractures, as an example, develop over a wide range of scales, and the coal matrix itself is not necessarily disconnected and isolated, as assumed in the DP model. (2) The pores of the CBMR, where CH4 and CO2 are adsorbed, have subnanometer dimensions; conventional Fickian diffusion theory with constant diffusivity may not be applicable. In fact, the few data available on CH4 diffusivity in coal samples indicate an exponential dependence of diffusivity on CH4 partial pressure.9 Such observations are in line with experimental observations with other carbonaceous microporous materials, e.g., carbon molecular sieve membranes.15-17 How CH4 and CO2 diffuse and adsorb in microporous carbons, particularly under high-pressure sub- and supercritical conditions, is a key research area in our group and the topic of recent publications;18-24 considerable progress is being made here, but more remains to be learned. (3) DP models of CBMR typically fail to account for the swelling/deformation of the coal matrix, which may occur during pressure drawdown, when CO2 is injected into and CH4 desorbs out of the reservoir; these phe-

nomena may result in the closure of some of the fractures.25 Depending on the pressure of CO2 and the temperature of the coal bed, the potential is there, at sufficiently high pressures and temperatures, for the coal matrix to even make a transition from a glasslike to a rubberylike state.1 Deformation of CBMR cores has been measured in the laboratory,7,26 and variations in their effective permeability caused by injection of CO2 have been reported in field studies.25 Though the causes and implications of this behavior for ECBM/S are still being debated, there is a clear need for additional experimentation. There is now evidence6,27,28 that tectonic fracturing processes lead to the creation of fracture networks with multiscale, self-similar characteristics. For flow and transport in such reservoirs, the Darcy permeability and the transport coefficients are generally not constant but vary with the distance from the source (well); local formulations, used previously for CBMR, are inadequate for describing the transport processes. The complexity of such phenomena in fractured reservoirs requires the development of more elaborate models than the DP approaches and validation of these models with measurements so that they can be used for both local and regional studies. Our group has previously developed a network model of pores with rough surfaces29 that successfully models the effect of surface roughness on adsorption, flow, and diffusion through a porous medium; we have also carried out extensive simulations of transport and sorption in microporous carbon systems.18-24 These are important components of a comprehensive CO2 injection based ECBM model currently under development. There are several aspects of CO2 sequestration in CBMR that make it a unique problem. As noted previously, the reservoir consists of pore and fracture networks with a heterogeneous morphology, each with a multiscale hierarchical structure; this has two important implications. One is that CO2 and CH4 adsorption is different from that in a conventional reservoir. The second implication is that the CBMR is drained in a qualitatively different manner from that predicted from cubic fracture networks, commonly used in the DP models. Other factors that complicate the study of CO2 sequestration in CBMR is that the coal matrix itself, as previously noted, may deform as a result of CO2 injection and CH4 desorption and that the transport of CH4 and CO2 in the micropores may be non-Fickian. In the study of CO2 injection, all of these factors must be accounted for. Recent success in modeling petroleum reservoirs using multiscale models of fractures and pores30,31 suggests that similar approaches may be more appropriate for modeling the ECBM, in general, and CO2 sequestration in CBMR, in particular. Despite its potential importance for CO2 sequestration, to our knowledge, CO2 injection in CBMR for sequestration has been studied by only a few groups, with only a limited number of peer-reviewed literature reports.1,32-34 The emphasis in the earlier investigations was on increasing CH4 production rather than on CO2 sequestration.35-37 Most recently, studies are beginning where CO2 sequestration is the objective. Since 1995, Burlington Resources has been performing a large-scale ECBM/S field study in the Allison Unit of the San Juan Basin in Northern New Mexico.38 Four CO2 injection wells and nine CH4 recovery wells have been utilized. The field tests have been successful, in that they have

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indicated enhanced production of CH4 and CO2 sequestration, though the physicochemical phenomena occurring at the site remain poorly understood. A smaller scale field study was carried out in Alberta Canada in the Fenn Big Valley,39 in which CO2 was sequestered in a highly volatile bituminous coal seam. The initial phase, which was recently completed, has evaluated the feasibility of injecting CO2 (but also N2 and flue gas) and producing CH4 at a rate twice as much as the gas injected. A larger field test is in the planning stages.1 A ECBM/S project was also initiated in Nov 2001 in the Silesian Coal Basin in Poland by an international consortium of companies. Once all the infrastructure is in place, injection of CO2 will be carried out for 18 months.40 Similar field studies are also planned in Australia, Japan, and China.1 A key element missing in most of these studies is meaningful characterization of the CBMR structure. Without such structural information, it is difficult to predict (i) how much CO2 can be sequestered in the CBMR, (ii) how much CH4 can be produced due to CO2 injection, and (iii) how the morphology of a CBMR affects CO2 sequestration. Furthermore, to date, no attempt has been made to combine modern ideas involving realistic models and geostatistical concepts with computer simulations and experiments of CO2 injection into a CBMR and its sequestration therein. To fill this knowledge gap and need in the area, our group has initiated a study of the injection of CO2 in CBMR, its adsorption and sequestration there, and the enhanced CH4 production that results from the CO2 injection, as well as the factors that affect the overall operation. We carry out this study collaboratively with Dr. David Morse of the Illinois State Geological Survey (ISGS), who provides the coal cores for us. At the coal matrix (micro-, meso-, and macropores) and cleat fracture length scales, the study involves laboratory investigations with CBMR cores. The focus of these studies are on (i) the understanding of the core’s structure, (ii) its transport and sorption characteristics, and (iii) its behavior under CO2 sequestration-relevant conditions. The primary goal of this paper is to outline the methodology and techniques developed and utilized to address these technical challenges and key issues for this length scale. As previously noted, a major challenge that one faces when modeling ECBM/S is the presence of multiple and widely varying length scales. In modeling of phenomena in systems that contain several disparate length scales, multiscale modeling approaches must be utilized that involve use of the results of one series of computations (beginning with the smallest length scale) as input to the next and larger length scale. In every stage of this modeling endeavor, emphasis should be on validation of this sequential, multiscale modeling approach with experimentation. A brief outline of the modeling methodology for the CBMR samples is presented at the end of this paper. Extending the multiscale modeling methodology beyond the coal matrix/cleat/fracture length scales (e.g., CBMR modeling) is rather straightforward; the key challenge, however, is developing the methodology and techniques for generating a set of experimental field data at these length scales comparable with those generated in the laboratory. In what follows, we first describe the experimental methodology. We categorize the techniques into three groups: (i) Those that are aimed at understanding the

CBM core structure. (ii) Those that are used in the measurement of transport and sorption characteristics. (iii) Those whose focus is on the CBM core behavior under CO2 sequestration conditions. We discuss briefly the key features of each technique, the importance of the data generated, the means of their interpretation, and the information they provide for the multiscale modeling methodology. We conclude the paper by providing a brief outline of the modeling methodology. Experimental Aspects Experimental Details. The data presented in this paper are for two coal cores extracted at different depths from a single well (Clark well 1, in Illinois) as part of the ISGS CBM testing program during 2001 and 2002. The first core sample was extracted at the depth of 824824.9 ft from what is known as the Lower Seelyville coal seam, while the second sample was extracted at a depth of 587 ft from what is known as the Jamestown coal seam. All of the available information from ISGS about these cores are shown in Table 1. Upon receipt of these cores from ISGS, they were placed in hermetically sealed plastic bags to limit exposure to room conditions, until the point at which they were utilized in laboratory experiments. The main part of each core (after being machined carefully into the required shape) was utilized in the simulated CO2 sequestration and the permeability experiments. Smaller fragments of each core were utilized in the other characterization studies. The emphasis in this part of our studies (with the exception of the technique of perporometry; see the discussion below) is on establishing the baseline with dry CBM samples, and, therefore, no effort was made to reconstitute the moisture content of the original coals. During the application of the flow perporometry technique, we utilized the simpler approach for wetting the cores recommended by the ASTM procedure for the technique itself rather than the more elaborate ASTM procedure for reconstituting moisture in coal samples.41 Understanding the CBM Core Structure. The challenge here is the multiple length scales characterizing the CBM coal structure. In the laboratory, one can analyze up to the cleat length scale of the CBM cores. Unfortunately, no technique can, alone, provide a complete characterization of the pore structure. We have utilized, as a result, a number of different techniques. They include (i) physical adsorption of probe gases, (ii) flow perporometry, (iii) optical and scanning electron microscopy (SEM), and (iv) high-resolution X-ray CT (HRXCT) microimaging. In what follows, the key characteristics of each technique and some of the data generated are discussed. 1. Adsorption of Single Probe Gases. Two different probe gases are used in our investigations, namely, N2 adsorption at 77 K and CO2 adsorption at 273 K. Both gases are relevant to CO2-ECBM, with CO2 being a key important probe gas because one would like to probe the microporous region potentially accessible by CO2 during sequestration. N2 adsorption, beyond its practical importance in ECBM, also provides the baseline pore-size distribution (PSD) to compare with the PSD based on CO2 adsorption. Of importance is to be able to operate the sorption/desorption apparatus down to very low pressures, to be able to probe the microporous (10003). The series of projections is reconstructed with an algorithm based on the Feldkamp technique44 to generate a 3-D density map. HRXCT generates 3-D images of CBM reservoir samples with potentially a resolution of less than 1 µm and allows the identification of the macropore and fracture networks; these images can then be used for computing the absolute and relative permeabilities,45 which are required for matching twophase flows (see the discussion below). Figure 8 shows a series of cross-sectional images for the CBM Seelyville core analyzed at the ANU facility. On the top of each image, key observations are noted. Obvious from these cross sections is the presence of a persistent complex

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Figure 6. SEM pictures of a single spot on the Seelyville sample at different magnifications: 500×, 5K×, 15K×, and 30K× (top left, top right, bottom left, and bottom right, respectively).

Figure 7. Schematic of the HRXCT microimaging apparatus.

macropore and cleat fracture network. In addition, they indicate that the CBM sample’s matrix is highly nonuniform with many mineralized regions (a complete movie of all the data generated by this particular CBM core sample can be accessed at www.usc.edu/dept/che/ disordered.media/). The distinct advantage of the HRXCT technique is that it provides 3-D information with unparalleled resolution, compared to what conventional optical and electron microscopy techniques (see the discussion above) using serial sectioning of samples provide; in addition (and this is key for the analysis of the CBM core samples), it is a nondestructive technique as opposed to serial sectioning of CBM samples. After the phases (pores and the coal matrix) have been identified, one can generate 3-D visualizations of the pore space and, if present, different density phases. Using the image of the porous sample, its effective flow and transport properties are computed.45,46 This is done, using finite-element or finite-difference techniques, by

discretizing the transport equations and superimposing the appropriate grid on the 3-D image, hence avoiding any approximation regarding the shape or size of the pores. Hence, the effective flow and transport properties of the CBM samples are predicted directly from microtomographic images. This technique also allows one to illustrate the local transport paths within a porous structure, an experimentally intractable problem, thus providing insight into the pore-scale mechanism of flow and transport. The computations are ongoing and results will be presented in future publications. Flow, Sorption, and Simulated Sequestration Experiments. To study the transport/sorption characteristics and to carry out simulated CBM reservoir CO2 sequestration experiments, we have constructed a new experimental apparatus (for further details, see ref 47). At the heart of the experimental system is a stainless steel autoclave capable of withstanding pressures up to 140 bar, which is placed inside a temperature-controlled oil bath. The CBM sample is placed in this autoclave. The way the CBM sample is positioned within the autoclave depends on the types of experiments to be carried out. For adsorption/desorption experiments of single gases and mixtures, the sample is placed inside the autoclave, whose excess volume is filled with inert quartz beads. The sample is then exposed to relevant gases at predetermined intervals and sequences. The composition of the inlet gas stream and the inlet pressure are controlled using mass flow controllers and back-pressure regulators, respectively. Water can be

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Figure 8. HRXCT images. Other details are shown in the figure.

added by a syringe pump to saturate the incoming gas, if measurements are to be made with moisture-reconstituted cores. The flow of emitted gases exiting the autoclave is monitored with a mass flowmeter, and its composition is continuously analyzed with a mass spectrometer. Alternatively, the sorption characteristics can be measured in a static fashion, during which a certain amount of gas is metered into the autoclave and is allowed to equilibrate with the core sample at a given pressure and temperature. The procedure is then repeated until the CBM core sample no longer appears to be adsorbing any gas, manifested by the autoclave pressure changing by less than 0.0345 bar at its

predetermined level for a period of more than 8 h (the same procedure is also followed for loading the core sample with methane prior to the initiation of the simulated CO2 sequestration experiment). Figure 9 shows single gas adsorption measurements for both CH4 and CO2 at 30 °C, measured by the static technique for the Jamestown core sample after it had been placed in the autoclave and prior to its utilization for a series of simulated CO2 sequestration experiments (see the discussion of these experiments below). Before initiation of each series of adsorption experiments, the core was evacuated overnight (for at least 14 h). We report in Figure 9 the total amounts of gas that the CBM core

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Figure 9. Adsorption isotherms for (*) methane and ([) carbon dioxide.

sample uptakes (the amount of gas injected minus the amount corresponding to the dead volume in the autoclave, pipes, valves, etc.) rather than the Gibbs excess sorbed volumes because the Gibbs approach has been shown to lead to very spurious results (negative excess sorbed volumes) with CO2 and CH4 uptake by coal cores.41 Note that the CO2/CH4 sorption separation factor for the Jamestown core averages ∼1.93, in agreement with measurements with a number of other coals.32-34,39,41 However, the sorption measurements with moisture-reconstituted Jamestown coal cores by ISGS48 are significantly smaller (∼60%) than those measured by us. Such disagreements are not uncommon, however, between dry and moisture-reconstituted coal samples.41,49,50 As previously noted, coal seams are relatively fixed volume systems, in which the coal is confined and not allowed to freely swell.1 To simulate these conditions, for the measurement of the flow characteristics but also for the sorption and simulated CO2 sequestration experiments reported here (see below), the core is embedded in a high-temperature epoxy matrix. To accomplish this, a piece of the original CBM core is carefully machined into a cylinder and the epoxy coating (typically 1/4 in. in thickness) is applied to the whole core with the exception of the top and bottom surfaces. When the epoxy cures (a multistep preparation approach is followed to ensure that the epoxy during the curing step does not infiltrate the core from its sides), the top and bottom surfaces are machined flat, if needed. An additional thick coating of epoxy is then placed to seal the sample bottom. A cylindrical channel (whose diameter is smaller than the diameter of the core sample) is then carefully drilled through the epoxy bottom layer and about 2 mm deep into the core’s bottom surface. A stainless steel tubing is then placed through this channel and just below the core bottom surface and is affixed with additional epoxy to seal it to the epoxy layer at the base. We believe that this experimental coal core design, in addition to providing better constraint and support at the base of the core sample, especially during flow experiments and simulated CO2 sequestration experiments in the presence of a pressure gradient, also represents more faithfully in the laboratory the phenomena occurring during CO2-ECBM. Coal seams are generally anisotropic, characterized by a permeability tensor, with estimated field permeabilities in one direction being often 5-10 times smaller or larger than those measured in the vertical direction.6,51 During the flow experiments, the pressures at the top and bottom of the coal surfaces are independently controlled, and the flow rate of the gas exiting the core is measured. 1. Flow Experiments. For measuring the flow characteristics of CBM cores, various gases (He, CH4, and CO2) are allowed to pass through the core, while

Figure 10. (a) Helium flow vs average pressure: (2) HE1; (O) HE2; (*) HE3. (b) Carbon dioxide flow vs average pressure: (2) CO1; (O) CO2; (*) CO3. Table 2. Chronology of Experiments Done with the Seelyville Coal Seam Sample month

experiment series no.

Dec ’02 Dec ’02 Dec ’02 Jan ’03

CO1 HE1 SEQ1 CO2a

Jan ’03 Jan ’03 Jan ’03 Feb ’03

CO2 HE2 SEQ2 CO3a

Feb ’03 Feb ’03 Feb ’03 Mar ’03

CO3 HE3 SEQ3 CO4

type of experiment done CO2 flow experiment after preconditioning He flow experiment after preconditioning simulated CO2 sequestration experiment CO2 flow experiment without sample preconditioning CO2 flow experiment after preconditioning He flow experiment after preconditioning simulated CO2 sequestration experiment CO2 flow experiment without preconditioning CO2 flow experiment after preconditioning He flow experiment after preconditioning simulated CO2 sequestration experiment CO2 flow experiment after preconditioning

maintaining the downstream pressure constant and varying the upstream pressure (during the flow measurements, the pressure gradient ranges from 3.45 to 31.03 bar). Prior to the initiation of the flow experiments, the core sample is appropriately conditioned. For the experiments reported here, for example, the core prior to each experiment is evacuated overnight (at least 14 h) at 400-450 mTorr at 90 °C. Before the flow experiment is started, the heater is turned off, while the sample continues to be evacuated for an additional 4 h. The flow experiments were initiated by exposing the sample to the appropriate gas at the preselected temperature. For the experiments reported here, the low-pressure side was kept at 4.45 bar, while the highpressure side was changed at 3.45 bar intervals. For each experimental point, we waited for at least 4 h before making the final measurement. Figure 10a shows the He flow data, measured at room temperature (∼2223 °C) on three different occasions, spread over a period of 3 months, for the Seelyville core sample. Note that the reproducibility of the data is rather satisfactory. Table 2 indicates all of the various experiments this particular coal core sample underwent throughout the same 3-month period. Figure 10b shows the flow data of the same core measured on three different occasions using CO2 as the test gas and following the same

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Figure 11. CO2 flow during the first 4 h of the extended time experiment.

experimental conditions and protocol and sample conditioning as with the He permeability experiments. There is substantial scatter in the flow data that are generated during these three series of experiments. We attribute this behavior to coal matrix swelling due to the presence of CO2. The changes that occur to the sample by swelling are reversible, however. Note, for example, that the HE1 experiment took place after the CO1 experiment, the HE2 experiment took place after the CO2 experiment, and the HE3 experiment took place after the CO3 experiment. It was realized subsequent to the completion of the CO2 flow experiments shown in Figure 10b, that the 4 h allotted to each experimental point, though satisfactory for the He flow experiments, was not quite sufficient enough for the system to equilibrate during the CO2 flow experiments. Figure 11 shows the first 4 h of an extended time experiment measuring the CO2 flow with the same core sample during which the upstream pressure was set at 28.59 bar while the downstream pressure was kept constant at 25.14 bar. Though the CO2 flow had appeared to have reached a steady state within the first 4 h of the experiment, in fact slow changes did continue to occur even after 75 h, with the CO2 flow changing, albeit very slowly. (By the time the experiment in Figure 11 was initiated, the core sample in the autoclave had undergone irreversible changes; the corresponding He permeability of the core at that point was severalfold higher than that reported in Figure 10a. We have found that small cracks accidentally developing in laboratory size CBM cores have a significant impact on the permeability, which may explain the broad range of permeability values reported in the literature for various core samples.) The results of Figures 10 and 11 point out the importance of incorporating into the model the effect of CO2 on the core flow properties. Other investigators have also previously reached similar conclusions;13 certainly, this remains an area where additional fundamental understanding is needed, and it remains under active study by our group. In the section on modeling, we describe the approach for analysis of the flow data in the context of CO2-ECBM multiscale model development. To establish a connection between what has been reported in the literature and the flow data reported here, we briefly outline an analysis based on Darcy’s law. Assuming effectively 1-D flow in the laboratory CBM core, Darcy’s law, as it applies locally to compressible fluids, is expressed as

QSC ) -

TSCAck dP P PSCTZcµ dZ

(2)

where k is the absolute permeability in darcy, µ is the fluid viscosity in cP, Ac is the local sample area, T is the temperature, Zc is the compressibility factor, TSC

Figure 12. (a) QSC/∫PP12(P/Zcµ) dP vs 1/Pave for helium: (*) HE1; (2) HE2; (O) HE3. (b) QSC/∫PP12(P/Zcµ) dP vs 1/Pave for carbon dioxide: (*) CO1; (2) CO2; (O) CO3.

and PSC are the standard temperature and pressure, respectively, dP/dZ is the pressure gradient in the direction of flow, and QSC is the output flow rate measured at standard conditions. Assuming that the permeability stays constant, then Darcy’s law predicts that

QSC kTSC ) ) constant LdZ P dP P T SC P2 Z µ 0 A c c

∫

P1

∫

(3)

where P1 and P2 are the upstream and downstream pressures, respectively, and L is the sample thickness. Figure 12 shows a plot of QSC/∫PP21(P/Zcµ) dP vs 1/Pave for both the He and CO2 data (µZc for He stays virtually constant for the region of pressures investigated here; however, it varies substantially for CO2 and, therefore, the term should stay within the integral; in our calculations, we have used the PRO/II software to calculate the compressibility factor and viscosity for both He and CO2.) Note from Figure 12 that eq 3 is not applicable to either He or CO2 and QSC/∫PP21(P/Zcµ) dP seems to vary by a factor of 2.23 for He and a factor of 7.9 for CO2 over the pressure range investigated (these changes are, however, substantially lower than what has been reported for unconstrained coal cores9,10). Though these changes may be attributable to other effects (like violation of the nonslip condition52,53 due to surface flow and diffusion), they may also result from the flexible nature of coal, which responds to both stress and swelling and shrinking due to the sorption phenomena. 2. Simulated CO2 Sequestration Experiments. The same experimental apparatus is also utilized to study CBM core behavior during CO2 sequestration. For these experiments, a piece of the Jamestown core sample was machined carefully into a cylinder with a diameter of 5.1 cm and a length of 17 cm. It was then embedded in a high-temperature epoxy following the procedure previously described. Prior to initiating these experiments, the core is first conditioned under appropriate conditions, by typically evacuating overnight

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Figure 13. Methane loading curve.

Figure 14. Methane (]) and carbon dioxide (b) volume fractions vs dimensionless exit volume of gas.

at room temperature for at least 14 h. Then, following the same protocol as that utilized for the adsorption experiments under static conditions, the autoclave is pressurized at a certain pressure with CH4; the autoclave inlet is then closed, and the core is allowed to equilibrate in the CH4 atmosphere until it no longer appears to adsorb CH4, manifested by the autoclave pressure changing by less than 0.0345 bar for a period of more than 8 h. The autoclave is then loaded with additional CH4, and the procedure is repeated for many cycles until the core completely saturates with methane at the desired pressure and temperature. The pressure profile during loading of the Jamestown core sample at 28.59 bar is shown, for example, in Figure 13. Once the sample is completely saturated with CH4, the CO2 sequestration experiment begins. With the existing experimental system, one can control the pressure downstream of the core (if it is encased in an epoxy matrix as in the permeability experiments) and either the CO2 injection rate or the pressure upstream of the core. As the CO2 flows into the core, the exit gas stream’s flow rate and composition are continuously measured. From these values, one calculates the individual flow rates of CH4 and CO2 that exit the core. Sequestration experiments can also be run with free-standing core samples, or samples encased in various sleeves in order to apply confining pressures different from the core gas pressure, to simulate other stress profiles likely to be encountered under field conditions.1 Figure 14 shows the data from a simulated CO2 sequestration experiment with the Jamestown core sample after it had been loaded with CH4 in the experiment of Figure 13. In this experiment, carried out at room temperature (22-23 °C), the downstream and upstream pressures were kept constant at 25.14 and 28.59 bar, respectively. In Figure 14, the composition of the exit stream is shown as a function of the dimensionless exit volume of gas, which is defined as the volume of gas exiting the autoclave divided by the amount of methane gas that was uptaken by the sample prior to the initiation of the simulated CO2 sequestration experiment; the latter is calculated on the basis of the total amount of methane loaded into the autoclave minus the methane volume corresponding to the “dead

Figure 15. (a) Methane and carbon dioxide volume fractions and methane recovery vs dimensionless exit volume of gas. (b) Dimensionless sequestered amount of carbon dioxide vs dimensionless exit volume of gas.

space” in the autoclave, pipes, valves, etc. As expected, a high initial flow rate of methane is observed, followed by a gradual decrease and breakthrough of carbon dioxide, showing the complete flushing phenomenon commonly observed during the ECBM process. The experiment of Figure 14 was repeated after reconditioning of the core sample and reloading with methane with a high degree of repeatability, indicative of the ability of the core sample to reversibly recover its structure after it had been subjected to the methane loading and the flushing-out cycle. Figure 15a shows another simulated CO2 sequestration experiment, in which the downstream core pressure was kept constant in the range of 28.59-28.93 bar and the CO2 injection rate was set equal to 86.8 sccm. To carry out this experiment, after the core is loaded with methane under static conditions at 28.59 bar, the exit valve is opened and, simultaneously, a constant methane flow is initiated at a rate of 101.28 sccm. After the upstream and downstream pressures are stabilized, the methane flow is replaced with the CO2 flow. This simulated sequestration experiment is more reflective of the field tests and provides critical data that one can utilize to fine-tune the multiscale CO2-ECBM models. In addition to the gas composition in Figure 15a, we plot the dimensionless methane recovery ratio, which is defined as the percent ratio of the methane volume exiting the autoclave divided by the total amount of methane injected in the autoclave (note that 18.9% of this amount corresponds to the dead volume). For the experiment in Figure 15a, at the point when the experiment was terminated at a dimensionless exit volume of gas value of 7.82, the methane recovery ratio was equal to 54.3%, which corresponds to 44.4% of the methane gas volume originally adsorbed by the sample. This is a somewhat higher recovery ratio than that reported in prior simulated laboratory sequestration experiments,10 reflecting perhaps the different experimental conditions and the coal cores utilized. Shown in Figure 15b is the dimensionless sequestered amount of CO2 (defined as the ratio of CO2 injected minus the

Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 2899

amount exiting the autoclave divided by the total amount of methane originally injected in the autoclave). At the point the experiment was terminated, its value was 0.91, which upon subtraction of the dead volumes for both methane and carbon dioxide gives a value of 1.95 molecules of CO2 that are sequestered in the core for every molecule of methane that is produced. This is in very good agreement with the sorption experiments of Figure 9. Modeling CO2 Sequestration in CBMR As already noted, one of the key challenges that one faces when modeling CO2 sequestration in CBMR is the presence of multiple and widely varying length scales. To investigate the phenomena that occur, our plan involves utilizing a sequential multiscale modeling method. Here, beginning with the smallest length scale of the problem, the results of one series of computations are used as the input to the next (larger) up the lengthscale hierarchy, hence passing information from the finer to the coarser scales. Currently, the emphasis is on applying and validating the approach with the laboratory CBM cores. Extending the modeling methodology beyond this length scale (e.g., CBMR modeling) is rather straightforward mathematically; the challenge here lies, however, in generating a set of experimental data at these length scales comparable with those generated with the laboratory cores. Interpreting the experimental data in a manner appropriate for the multiscale methodology is a key step. As an example, large macropores and cleat fractures can be obtained from the HRXCT images (see Figure 8); the same images can be used to compute the absolute (and relative) permeabilities of the core samples, to match the experimental permeabilities, and to serve as a useful check of our overall effort. The technique we use for carrying out such computations is novel. As mentioned above, it involves first laying out a 3-D finite-element (or finite-differences) grid on the 3-D images, then identifying macropore, cleat fracture, and solid matrix areas, and solving for the effective permeabilities, by solving the Stokes equation without needing to make assumptions regarding the shape and/or sizes of the macropores and cleat fractures. CO2 sequestration in CBMR is the outcome of a complex series of events, involving transport through the macropore and cleat fracture networks, diffusion through the mesopore and micropore regions of the coal matrix, and adsorption of CO2 onto (or desorption of CH4 from) the surface of the micropores. Macropore cleat fractures and the coal matrix itself represent distinct classes of transport paths, in the sense that each has its own distinct characteristics. We have shown previously54,55 that transport in a disordered medium with multiple families of transport paths is distinctly different from that in a porous medium with only one type of transport path. Consider first diffusion, which is simpler to simulate than both diffusion and flow. Because we use networks of cleat fractures and pores to represent the core, our model utilizes a set of discrete equations of the following form:

∂Ci ∂t

)

Dij [Cj(t) - Ci(t)] + EiCi(t)

∑j l

ij

where Ci(t) is a 2-D column vector, the sth component

of which gives the concentration of the gas at time t in path s at network site i. By “path” here we mean either the macropore and cleat fracture or the coal matrix pore networks, which are very different. Dij is a matrix whose elements are the diffusivities in the paths between sites i and j. The exchange matrix Ei gives the rate of diffusive exchange between the different transport paths at site i. lij is the length of the path (fracture or pore) between i and j. The multiscale modeling methodology approach consists of (1) generating the fracture and coal matrix networks based on the experimental data and (2) solving eq 4 for the coupled networks. For the macropore and cleat fracture transport paths, one needs no assumptions regarding the shapes and sizes. For the coal matrix paths, the data available (probe gas physisorption and flow perporometry) do not provide for direct imaging. Techniques developed by our group and others, on the other hand, allow determination of the PSD of the pore network and its connectivity. At the nanopore lengthscale continuum, descriptions of sorption and transport are no longer valid. In our ongoing efforts, we are developing nonequilibrium molecular dynamic techniques to describe transport in the presence of concentration gradients in microporous carbonaceous porous media and membranes18-23 coupled with semiempirical statistical mechanics descriptions of multicomponent sorption phenomena.24 In reality, CO2 sequestration in CBM cores involves, in addition to diffusion, sorption of CO2 (and desoprtion of CH4) and two-phase flow of water, CH4, and CO2. Equation 4, as a result, is much more involved. The basic approach, however, is similar in that one utilizes the coupled networks generated as described previously, and the effective values of the various flow and transport properties measured and/or computed to study twophase flow, transport, and sorption in the CBM cores. The complexity is compounded by the CO2 pressure dependence of permeabilities. Understanding the effect of sample deformation/swelling on flow and sorption properties remains, as a result, a key focus of our overall research effort, whose ultimate objective is the development of an experimentally validated simulator for predicting the amounts of CO2 sequestered and the CH4 produced. Conclusions We have presented here an overview of our ongoing experimental and modeling studies of a process termed CO2-ECBM/S, which involves sequestering CO2 by injecting it in CBMR. In doing so, one displaces the methane gas that is stored in these reservoirs, which can then be utilized as a clean form of energy. The advantage of this approach over other long-term storage/ sequestration options is that the value of the methane gas produced may help to alleviate partly or wholly the CO2 separation and sequestration costs. The process faces a number of key technical hurdles, however. Most of these relate to the structure of the CBMR themselves, which are very complex porous media and which in addition to the coal matrix structure generated during coal formation, they also contain a variety of fractures, which may potentially play a key role in CO2 sequestration because they provide high-permeability flow paths for both CO2 and CH4. Despite its potential importance, ECBM/S has, so far, been studied by only a few groups. Furthermore, until

2900 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004

recently, the emphasis in these investigations was on increasing CH4 production rather than on CO2 sequestration. A key element missing in most of these studies is a meaningful characterization of the CBMR structure that, as noted in the paper, is characterized by the presence of multiple and widely varying length scales. Our own experimental methodology, described above, involves using a number of techniques which aim (i) to characterize and understand the CBM core structure, (ii) to measure its flow and sorption characteristics, and (iii) to study its behavior under simulated CO2 sequestration conditions. We briefly described the various techniques and discussed the importance of the data generated, means to interpret them, and useful information they provide in the context of the design of the ECBM/S. As far as the modeling of these phenomena is concerned, the challenge one faces is the need to include the effect of several disparate length scales; our approach uses a multiscale modeling technique that involves, beginning with the smallest length scale of the problem, using the results of one series of computations as input to the next and larger length scale. The emphasis in every stage of this modeling endeavor is on applying and validating this sequential multiscale modeling approach with experimentation. The emphasis in this paper is principally on “dry” CBM cores. In field applications of the CO2-ECBM/S process, the water present in the coal matrix’s mesoporous and macroporous regions, and in the cleat fractures, may interfere with both the sorption and flow characteristics. The experimental methodology described here can be conveniently adapted to allow one to condition the samples in situ with H2O at various temperature and pressures, to examine the sorption and flow behavior of wet (at various saturation levels) samples and to measure the absolute and relative permeabilities. The results of such studies will be presented in future reports. Acknowledgment We are grateful to the U.S. Department of Energy for providing the funding for this study. We also thank Dr. David Morse of the Illinois Geological Survey, who kindly provided us with the coal cores and other useful information. Nomenclature Ac ) sample surface area (cm2) Ci(t) ) concentration vector Dij ) matrix of diffusivities Ei ) exchange matrix k ) permeability (d) P ) pressure (atm) in eq 2 PSC ) standard pressure (1 atm) ∆P ) pressure drop (Pa), in eq 1 QSC ) gas flow at standard conditions (sccm) rP ) radius of a cylindrical-shaped pore (m) t ) time (s) T ) system temperature (K) TSC ) standard temperature (273.15 K) Z ) sample length (cm) Zc ) compressibility factor Subscript SC ) standard conditions

Greek Symbols µ ) viscosity (cP) γ ) surface tension at the liquid/air interface (N/m) θ ) contact angle (deg)

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Received for review August 14, 2003 Revised manuscript received December 30, 2003 Accepted January 5, 2004 IE0306675