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Effects of coal composition and fabric on porosity, sorption capacity and gas flow properties in Western… Adeboye, Oyeleye Oluwafemi 2011

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EFFECTS OF COAL COMPOSITION AND FABRIC ON POROSITY, SORPTION CAPACITY AND GAS FLOW PROPERTIES IN WESTERN CANADA SEDIMENTARY BASIN COALS  by  Oyeleye Oluwafemi Adeboye B.Sc. (Honours), The University of Regina, 2008  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in  THE FACULTY OF GRADUATE STUDIES (Geological Sciences)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  February 2011  ©Oyeleye Oluwafemi Adeboye, 2011  ABSTRACT Porosity, methane sorption capacity, diffusivity and permeability of a suite of vitriniterich coals from the Horseshoe Canyon and Mannville formations of the Western Canada Sedimentary Basin were investigated. Coal rank ranges from subbituminous to medium volatile bituminous, equilibrium moisture is between 2.32%-23.75%, and ash is up to 72% although < 20% on average. Total coal porosity estimated using mercury porosimetry and helium pycnometry is between 4.4% and 18%. Helium pycnometry porosity is higher than mercury porosimetry porosity because the smaller molecular diameter of helium allows it to access coal pores which are inaccessible to mercury at test pressures. Greater vitrinite content is generally correlated with higher coal total pore area due to the abundant microporosity in vitrinite. Coal methane sorption capacity is up to 23.5 cc/g on a moisture equilibrated basis and is up to 40.4 cc/g for dry coals. Moisture equilibrated and dry coals sorb differently due to competition for adsorption sites in coal between methane and moisture. No relationship is observed between sorption capacity and coal rank or between maceral content and sorption capacity because of the narrow rank and maceral composition of the samples studied. Permeability was investigated on crushed coals and plugs with crushed permeability not exceeding 1.79∙10-2 md while plug permeability is up to 0.9 md. Average diffusivity is estimated to be around 10-11 to 10-12 m2/s. Coal matrix properties influence crushed permeability. Inertinite-rich coals have higher matrix permeability and diffusivity because of the greater macro- and meso- porosity of ii  inertinite. Plug permeability is dependent on coal matrix properties and the presence of fractures on tested plugs. Coals with better developed fractures are more permeable than coals with poorly developed fractures at the same effective stresses. Probe gas type influences plug permeability. Helium permeability measurements are higher than permeability measured with methane or nitrogen. Permeability difference with probe gas is attributed to a combination of different probe gas molecule size, relative swelling effects of probe gas on coal and associated changes at in-situ stress during tests. Understanding the reasons for permeability variations in coals will help in more focused coal bed methane exploration and development.  iii  PREFACE The idea for this research project was conceived by Dr. R. Marc Bustin and he was also responsible for sourcing the samples used in this study. Some of the equipment used to carry out the experiments were built by Dr. R. Marc Bustin and his previous graduate students and are housed at the department of Earth and Ocean Sciences, University of British Columbia. The software used to process the data was also written solely or in part by Dr. R. Marc Bustin. All experiments, data analyses, data interpretation and the preparation of this manuscript were carried out by Oyeleye Adeboye, with conceptual, scientific and editorial guidance provided by Dr. R. Marc Bustin. Troubleshooting of experimental equipment during the course of this project was carried out with assistance from Dr. R. Marc Bustin, Dr. Gareth Chalmers and in-house machine shop staff of the department of Earth and Ocean Sciences, University of British Columbia. All experiments were carried out at the department of Earth and Ocean Sciences, The University of British Columbia, Vancouver.  iv  TABLE OF CONTENTS ABSTRACT ...................................................................................................................................................... ii PREFACE ....................................................................................................................................................... iv TABLE OF CONTENTS ..................................................................................................................................... v LIST OF TABLES ............................................................................................................................................ vii LIST OF FIGURES ......................................................................................................................................... viii ACKNOWLEDGEMENTS ................................................................................................................................ ix 1  2  INTRODUCTION .....................................................................................................................................1 1.1.  Western Canada Sedimentary Basin introduction ........................................................................1  1.2.  Thesis structure .............................................................................................................................4  Porosity of Western Canada Sedimentary Basin coals .........................................................................6 2.1.  Introduction ..................................................................................................................................6  2.2.  Coal matrix and fracture porosity and previous work on coal porosity .......................................6  2.3.  Factors affecting coal porosity ......................................................................................................9  2.3.1.  Coal rank (both normal rank progression and igneous intrusion rank effects) ........................9  2.3.2.  Maceral content of coal ..........................................................................................................10  2.3.3.  Nature of probe material ........................................................................................................11  2.4.  3  Methods of estimating and characterizing coal porosity............................................................11  2.4.1.  Mercury porosimetry ..............................................................................................................12  2.4.2.  Gas pycnometry ......................................................................................................................13  2.5.  Adsorption methods and surface area in coals...........................................................................15  2.6.  Sample origin, sample preparation, experimental methodology and equipment .....................19  2.7.  Results and discussions ...............................................................................................................22  2.8.  Conclusions .................................................................................................................................34  GAS SORPTION PROPERTIES OF WESTERN CANADA SEDIMENTARY BASIN COALS ............................36 3.1.  Introduction ................................................................................................................................36  3.2.  Sample origin, sample preparation, experimental methodology and equipment .....................37  3.3.  Results and discussions ...............................................................................................................40  3.4.  Conclusions .................................................................................................................................47  4 EFFECTS OF PROBE GAS, COAL COMPOSITION AND COAL FABRIC ON COAL PERMEABILITY AND DIFFUSIVITY IN THE WESTERN CANADA SEDIMENTARY BASIN ..................................................................49 4.1.  Introduction ................................................................................................................................49  4.2.  Permeability, absolute permeability, effective permeability and relative permeability ............51  v  4.3.  Fick’s law, Darcy’s law and gas movement in coals ....................................................................52  4.4.  Coal fracture permeability vs. Coal matrix permeability ............................................................54  4.5.  Factors affecting coal permeability .............................................................................................54  4.5.1.  Coal matrix shrinkage and cleat compression.........................................................................55  4.5.2.  Effective stress ........................................................................................................................57  4.5.3.  Gas slippage (Klinkenberg) effect............................................................................................58  4.6.  The pulse decay technique for estimating coal permeability .....................................................59  4.7.  Sample origin, sample preparation, experimental methodology and equipment .....................62  4.8.  Results and discussion.................................................................................................................67  4.8.1.  Diffusivity.................................................................................................................................67  4.8.2.  Matrix permeability .................................................................................................................74  4.8.3.  Coal plug permeability ............................................................................................................81  5.9 5  Conclusions .................................................................................................................................90  CONCLUSIONS AND FUTURE WORK ....................................................................................................92 5.1.  Conclusions .................................................................................................................................92  5.2.  Future work .................................................................................................................................94  REFERENCES ................................................................................................................................................96 APPENDICES ..............................................................................................................................................105 Appendix 1: Mercury porosimetry traces .................................................................................................106 Appendix 2: Methane adsorption isotherms ............................................................................................139  vi  LIST OF TABLES Table 2.1: Coal sample rank and Formations of origin for coal sample suite investigated in this study ............................................................................................................................................. 20 Table 2.2: Maceral content for coal sample suite investigated in this study ............................... 21 Table 2.3: Comparison of coal bulk density values obtained via Hg-immersion and Hgporosimetry .................................................................................................................................. 23 Table 2.4: Comparison of coal skeletal density values obtained via He-pycnometry and Hgporosimetry .................................................................................................................................. 24 Table 2.5: Coal porosity obtained from helium pycnometry and mercury porosimetry ............. 25 Table 2.6: Total pore area of coal determined from mercury porosimetry................................. 27 Table 2.7: Comparison of total coal pore area determined from mercury porosimetry with rank and coal vitrinite content ............................................................................................................. 30 Table 3.1: Coal sample rank and formations of origin for coal sample suite investigated in this study ............................................................................................................................................. 39 Table 3.2: Maceral composition for coal sample suite investigated in this study ....................... 40 Table 3.3: Langmuir volumes and Langmuir pressures for sample suite (Moisture equilibrated coal basis) ..................................................................................................................................... 44 Table 3.4: Dry vs. moisture equilibrated sorption parameters for select coals ........................... 45 Table 4.1: Coal sample rank and formations of origin for coal sample suite investigated .......... 65 Table 4.2: Maceral composition for coal sample suite investigated in this study ....................... 66 Table 4.3: Average diffusivity and Langmuir volumes for coals studied ...................................... 70 Table 4.4: Diffusivity comparison across different basins ............................................................ 71 Table 4.5: Comparison of isorank samples showing maceral effects on average coal diffusivity 73 Table 4.6: Properties of coal subset used to investigate effects of moisture on coal diffusivity 74 Table 4.7: Effects of moisture on average coal diffusivity ........................................................... 74 Table 4.8: Coal matrix permeability from helium pycnometry .................................................... 78 Table 4.9: Comparison of isorank samples showing maceral effects on coal matrix permeability ...................................................................................................................................................... 80 Table 4.10: Comparison of permeability obtained from different gases ..................................... 87  vii  LIST OF FIGURES Figure 1.1: Locations of coal-bearing formations in Alberta (From the Alberta Geological Survey) ........................................................................................................................................................ 3 Figure 1.2: Stratigraphy of coal-bearing formations in Alberta (From the Alberta Geological Survey) ............................................................................................................................................ 4 Figure 2.1: Trend of coal macro- and micro-porosity with increasing coal rank (modified from Levine, 1993)................................................................................................................................. 10 Figure 2.2: Schematic of a pycnometer (From Cui et al., 2009) ................................................... 15 Figure 2.3: Type I isotherm produced from methane sorption on coal ....................................... 16 Figure 2.4: Total pore area of coal vs. coal vitrinite content for all samples ............................... 29 Figure 2.5: Total pore area of coal vs. coal inertinite content for all samples ............................. 31 Figure 2.6: Total pore area of coal vs. coal vitrinite content for subbituminous A rank samples 31 Figure 2.7: Total pore area of coal vs. coal vitrinite content for high volatile bituminous C samples ......................................................................................................................................... 32 Figure 2.8: Total pore area of coal vs. coal vitrinite content for high volatile bituminous B samples ......................................................................................................................................... 32 Figure 2.9: Relationship between helium pycnometer coal porosity and mean random vitrinite reflectance .................................................................................................................................... 34 Figure 3.1: Differential Langmuir volume vs. equilibrium moisture content ............................... 45 Figure 3.2: Coal rank vs. Langmuir volume (on a moisture equilibrated basis) ........................... 46 Figure 3.3: Coal vitrinite content vs. Langmuir volume (on a moisture equilibrated basis) ........ 46 Figure 3.4: Coal inertinite content vs. Langmuir volume (on a moisture equilibrated basis) ...... 47 Figure 4.1: Natural coal fracture system (modified from Harpalani and Schraufnagel, 1990) .... 49 Figure 4.2: Two-step process involved in CBM transport (modified from Harpalani and Schraufnagel, 1990) ...................................................................................................................... 53 Figure 4.3: Schematic diagram of pulse decay permeability set up for measuring coal permeability (modified from Cui et al., 2009) .............................................................................. 61 Figure 4.4: Average coal diffusivity vs. vitrinite content of coal .................................................. 71 Figure 4.5: Average coal diffusivity vs. inertinite content of coal ................................................ 72 Figure 4.6: Average coal diffusivity vs. mean random vitrinite reflectance of coal (coal rank) ... 72 Figure 4.7: Coal matrix permeability vs. vitrinite content of coal ................................................ 77 Figure 4.8: Coal matrix permeability vs. inertinite content of coal .............................................. 79 Figure 4.9: Coal matrix permeability vs. mean random vitrinite reflectance of coal (coal rank) 79 Figure 4.10: All coal plug samples tested at all effective stresses ............................................... 82 Figure 4.11: EEC sample................................................................................................................ 83 Figure 4.12: Leyejn sample ........................................................................................................... 84 Figure 4.13: 9R sample ................................................................................................................. 84 Figure 4.14: HW sample................................................................................................................ 85 Figure 4.15: Leye prop .................................................................................................................. 85 Figure 4.16: NR#7 sample ............................................................................................................. 86 Figure 4.17: Fracture height definition ......................................................................................... 86 Figure 4.18: Coal permeability vs. fracture height ....................................................................... 87  viii  ACKNOWLEDGEMENTS This thesis was written as part of the requirements for a Master of Science degree in Geological Sciences undertaken from September 2008 to February 2011 at the Department of Earth and Ocean Sciences, University of British Columbia, Vancouver. I would like to express sincere gratitude to Dr. R. Marc Bustin for his overall guidance throughout the course of this M.Sc. project and his help in strengthening the thesis. The author would also like to thank Dr. Stuart Sutherland and Dr. Kurt Grimm for their helpful comments and advice over the course of the project. Financial support throughout the course of the entire project from Dr. R. Marc Bustin is gratefully acknowledged. I am grateful for the helpful comments and insights provided by Dr. Gareth Chalmers and Mr. Venkat Murthy Pathi during the course of my M.Sc. program as well as for the assistance rendered by the various lab assistants who helped out with some aspects of sample preparation during the course of this work. Appreciation is also due to the various professors and fellow graduate students here at the department of Earth and Ocean Sciences, UBC with whom I interacted during the course of my M.Sc. program, I am thankful for the many friendships forged with these esteemed colleagues. Finally, I would like to thank my parents for their unwavering support in every undertaking of mine including during the course of this M.Sc. program.  ix  1 INTRODUCTION 1.1.  Western Canada Sedimentary Basin introduction  The western Canada Sedimentary Basin (WCSB) is a petroleum rich basin which extends from the Yukon and North West Territories to north east British Columbia and into the United States. This Basin also encompasses areas in the Canadian provinces of Alberta and Saskatchewan as well as the southern part of the province of Manitoba. Creaney and Allan (1990) state that the WCSB contains approximately 1.75 trillion barrels of crude oil and Beaton et al. (2006) report that there is around 142 trillion cubic feet of conventional gas reserves and potential resources held within the WCSB. In addition to the abundant petroleum resources of the WCSB, coal resources of the WCSB are vast and the WCSB is estimated to contain around 90% of Canada’s total coal resources of immediate interest; an amount in excess of 5900 million tonnes of coal (Cameron and Smith, 1991; Cross and Bowlby, 2006; BP statistical review of world energy, 2010). The province of Alberta is the major production centre for oil and natural gas from the WCSB. It is estimated that there is 100-550 trillion cubic feet (2.28∙1012 m3 to 1.56∙1013 m3) of potential gas resources held within Alberta’s vast coal deposits (Beaton et al., 2006). With declining production from conventional gas reservoirs already acknowledged in the WCSB coupled with rising domestic and international demand for clean burning natural gas, attention has turned increasingly to unconventional gas resources such as gas shales and coal bed methane to make up for declining production from a basin that supplies over 90% of Canada’s total gas output and about 15% of total US gas consumption (National Energy Board, 2003;  1  Russum and Botterill, 2006; King, 2008; National Energy Board, 2010a and 2010b). The United States Energy Information Administration (2010) projects that tight gas, shale gas and coal bed methane (CBM) sources will provide about 63% of total domestic natural gas production in Canada by the year 2035. Hence an investigation into factors which impact coal bed methane exploitation potential of WCSB coals as undertaken in this study is necessary. Coal bed methane, the subject of the present study, is considered an unconventional gas resource of the continuous gas accumulation type. Law and Curtis (2002) define unconventional gas resources as regionally pervasive gas accumulations which occur independently of structural and stratigraphic traps while Schmoker (2002) describes continuous gas accumulations as those gas accumulations that exist independently of the water column and which do not owe their existence to the buoyancy of gas in water. The major formations of interest for CBM production in Alberta are the Paskapoo and Scollard formations (which contain the Ardley coal zone), the Horseshoe Canyon Formation, the coal-bearing Belly River Group and the Mannville Formation (Figures 1.1 and 1.2). The coals studied for this research project are mainly from the Horseshoe Canyon Formation with some samples from the Mannville Formation. Deeper Mannville Formation coals have higher gas contents than their Horseshoe Canyon counterparts but the Mannville Formation coals are not as permeable as coals of the shallower Horseshoe Canyon Formation and hence are currently less exploited. Estimates of potential CBM resources available from the major individual coal formations in Alberta have been reported by Beaton et al. (2006). Low coal permeability as an obstacle to CBM resource development from Alberta’s vast coal deposits has been highlighted by several authors (e.g., Johnson and Flores, 1998; Beaton et 2  al., 2006 and others) consequently; this study investigated factors which influence the permeability of coals in the WCSB, the results of which are presented in this thesis.  Figure 1.1: Locations of coal-bearing formations in Alberta (From the Alberta Geological Survey 1) 1  Retrieved from: http://www.ags.gov.ab.ca/graphics/cbm/CBM_intro/Coal_CBM_Potential_large.jpg on Sept. 6, 2010  3  Figure 1.2: Stratigraphy of coal-bearing formations in Alberta (From the Alberta Geological Survey 2)  1.2.  Thesis structure  This thesis is divided into five chapters. There is an introductory chapter (chapter 1) and a conclusion (chapter 5). There are three individual body chapters which detail various aspects of the research project carried out as part of this overall research. These three body chapters  2  Retrieved from: http://www.ags.gov.ab.ca/GRAPHICS/CBM/CBM_intro/figure_5_strat_col.jpg on Sept. 6, 2010  4  are prepared as standalone manuscripts which can be read independently of the rest of this thesis. Chapter 2 discusses coal porosity of Western Canada Sedimentary Basin coals and the factors which influence coal porosity on the samples tested from this basin. This chapter also includes an overview of the available literature on coal porosity. Chapter 3 presents gas sorption properties of Western Canada Sedimentary Basin coals and the factors on which the observed sorption capacity of these coals are dependent. Chapter 4 presents permeability of Western Canada Sedimentary Basin coals and factors which influence coal permeability in the western Canada Sedimentary Basin.  5  2 Porosity of Western Canada Sedimentary Basin coals 2.1.  Introduction  Although coal porosity has been extensively studied, there is a shortage of studies on the porosity of Canadian coals, especially coals of the Western Canada Sedimentary Basin (WCSB). The increasing importance of the gas resources held within the coals of the WCSB as a source of clean and abundant domestic energy necessitates a proper study of the porosity characteristics of these coals because coal porosity controls coal surface area and thus coal gasin-place. Furthermore, the potential to sequester CO2, along with resultant associated enhancement of coal bed methane production in some of the WCSB coals makes an overview of coal porosity in the WCSB timely. The current study investigated porosity of vitrinite-rich subbituminous to medium volatile bituminous coals from the Horseshoe Canyon, Mannville and Mesaverda (USA) formations using helium pycnometry and mercury porosimetry.  2.2. Coal matrix and fracture porosity and previous work on coal porosity Porosity in coal has been defined as the proportion of the total volume of a coal that can be occupied by water, helium or some similar probe molecule (Levine, 1993). Porosity in coal matrix and porosity in coal attributed to the presence of fractures are recognized. Coal matrix porosity is any porosity present in coal which is not associated with coal cleats, fractures or joints. Coal matrix porosity is almost entirely within the micropore realm (i.e., pores of 2 nm and less) and is the reason why coal has a high surface area (Parkash and Chakrabartty, 1986). 6  Fracture porosity in coals consists primarily of the network of natural fractures called cleats which form from the natural process of coalification (Ting, 1977; Close, 1993; Laubach et al., 1998). Fracture porosity is important in coals because it is usually through this network of cleats that economic production of gases from coal is dependent. Fracture porosity is usually in the macropore realm (thus pores of 50 nm and greater in size) and if the coal has any free gas, it is within these fractures and in larger pores that such free gas is held. Gamson et al. (1993) have reported the presence of fracture porosity, matrix porosity and phyteral porosity in coals based on scanning electron microscopy. These authors indicate that fracture porosity is primarily associated with bright coals although microfractures are also observed in maceral fragments from dull coals. Matrix and phyteral porosity are associated with dull coals that are composed of plant fragments or coals that contain a heterogeneous mixture of macerals. There is a large body of published work on coal and coal properties in the literature. A very early published article on coal porosity by Weller (1959) presented results of a study on sediment compaction and stated that coal is reduced in volume by compression and elimination of pore space and loss of substance as a result of maturation. Weller (1959) concluded erroneously that “coal is essentially non-porous”. Porosity in coal is classified as macroporosity, mesoporosity or microporosity. Sing et al. (1985) defined macropores as pores with widths exceeding 50 nm (5.0∙10-8 m), mesopores as those pores with widths between 2 nm and 50 nm (2.0∙10-9 m and 5.0∙10-8 m) and micropores as those pores that have widths not exceeding about 2 nm (2.0∙10 -9 m).  7  Thomas and Damberger (1976) examined the relationship between coal rank and porosity and surface area of Illinois coals. These authors concluded among other things that coal has a very fine pore structure. Walker (1981) reported that coals possess significant porosity with a major fraction of this porosity residing in micropores for coals of most ranks. Walker (1981) also states that the values of surface area and pore volumes of coal are not unique properties but instead are dependent upon the molecular probe used and the conditions under which measurements are made. Toda and Toyoda (1972) described the application of mercury porosimetry in characterizing Japanese coals. Spitzer (1981) gives a synopsis of mercury porosimetry and its application in characterizing the pore structure of coals. Huang et al. (1995) have submitted findings based on gas pycnometry and its applicability to characterizing the pore structure of coal. Tricker et al. (1983) studied coal porosity using neutron scattering methods and they indicate that the use of these methods allows detection of closed coal pores, something which some of the other methods employed in characterizing coal porosity are not capable of. Gan et al. (1972) and Parkash and Chakrabartty (1986), from their efforts in characterizing coal porosity and surface area using adsorption methods, point out that surface areas of coals calculated using carbon dioxide adsorption are higher than those obtained using nitrogen (even on the same samples). These workers link this difference in surface areas obtained from the two different gases to the molecular sieve characteristic of coal. Clarkson and Bustin (1996) also report from their work on characterizing coal micropores using adsorption methods that coal micropore capacity and monolayer volumes measured at low  8  pressures generally increase with increasing vitrinite content and they attribute this increase to the large number of micropores that are present in vitrinite. Mahajan (1984) provides a general and concise overview of the different methods available for coal characterization.  2.3.  Factors affecting coal porosity  Examined below are the various factors which affect coal porosity. These factors include coal rank, maceral content of coal, nature of the probe and the method used to investigate the magnitude of coal porosity.  2.3.1. Coal rank (both normal rank progression and igneous intrusion rank effects) Coal rank plays a great role in determining porosity. Initially, low rank coals have a high porosity composed mostly of macropores (up to 75% porosity in peat according to Levine, 1993). As physical and chemical coalification proceeds, micropores dominate at higher rank levels (Gan et al., 1972). Physical compaction leads to closure of the macropores which dominated at earlier rank intervals while expulsion of volatile matter from the coal due to various chemical reactions which take place during coalification result in the formation of micropores which are dominant at higher rank intervals. Figure 2.1 shows the relative proportion of coal macropores and coal micropores with respect to coal rank.  9  Figure 2.1: Trend of coal macro- and micro-porosity with increasing coal rank (modified from Levine, 1993) Igneous intrusions accelerate the normal rank progression of coals hence these intrusions will accelerate coal porosity changes which take place with increasing coal maturation if they are present in the vicinity of a coal.  2.3.2. Maceral content of coal Porosity varies with coal maceral content. Consequently, a coal composed entirely of more porous macerals should, all other things being equal, be more porous than those coals composed predominantly of less porous macerals. Examples of these more porous macerals are the inertinite group of macerals fusinite and semifusinite which are formed due to paleo-fires (Stach et al., 1982; Levine, 1993) and in which porosity change very little with rank (i.e., a semifusinite at low rank has about the same porosity as a semifusinite at high rank). This is in  10  contrast to vitrinite which is not as porous at lower ranks but which becomes successively more microporous with increasing maturation due to the loss of volatile matter. Clarkson and Bustin (1996) report that the high micropore volumes observed in a vitrinite-rich coal sample was due to an enhancement of micropore capacity associated with increasing coal maturity and work by Adeboye (2008) also reports greater enhancement of vitrinite porosity, as compared to that of inertinite, at high coal maturity intervals.  2.3.3. Nature of probe material The nature of the molecule used to investigate coal porosity can affect results. Smaller probe molecules (for example, helium) are able to access most pores available in coal and this greater pore access results in higher porosity estimates. Larger probe molecules (mercury for instance) are unable to access all the available pore sizes in coal due to their large size and as such give a lower estimate of coal porosity. This phenomenon, the molecular sieve effect of coal, has been described by a number of authors including Gan et al. (1972), Walker (1981), Mahajan (1984), Parkash and Chakrabartty (1986), Rodrigues and Lemos de Sousa (2002), Prinz and Littke (2005), Chalmers and Bustin (2007) amongst others. The effects of probe molecule size on coal porosity estimates are also demonstrated in the present study and are discussed later.  2.4.  Methods of estimating and characterizing coal porosity  Various methods for estimating coal porosity are described in the literature. Some of these methods include fluorescence microscopy (e.g., Soeder, 1990), small angle x-ray scattering and small angle neutron scattering (e.g., Tricker et al., 1983; Radlinski et al., 2004), mercury porosimetry (e.g., Spitzer, 1981) and gas pycnometry (e.g., Huang et al., 1985). The 11  methods discussed in some detail here are mercury porosimetry and gas pycnometry. A brief mention of adsorption methods with respect to determining coal surface area is also made.  2.4.1. Mercury porosimetry Spitzer (1981) gives an overview of mercury porosimetry and its application to the characterization of coals while Giesche (2006) gives a detailed overview of the general method of mercury porosimetry. Mercury porosimetry involves forcing mercury into coal pores under successively higher pressures. Mercury is forced into the pores present in coal under this method because of the non-wetting nature of mercury hence without application of an external force, mercury will not invade the pores present in the coal. The mercury porosimetry experiment is conducted in two steps after evacuation of gases from the sample is completed. The first low pressure step involves introducing mercury into the coal samples at pressures up to 206.84 KPa (30 psi). The second high pressure step forces mercury into the sample at pressures up to 413.69 MPa (60,000 psi). The mercury porosimetry experiment gives information about the total accessible pore area of the coals, coal bulk and skeletal densities and the porosity of the coals. Mercury porosimetry has advantages of being a very common method of determining porosity and pore size distribution of coals although the toxicity of mercury is a drawback. Coal samples investigated using this technique need to be dry. Due to the microporous nature of coals, the technique of mercury porosimetry will underestimate porosity because this method is only able to access pore throats which are 3 nm (3.0∙10-9 m) or greater. There is also the possibility that intergranular space will be counted as part of the total porosity present in coals thus great care must be taken when utilizing this 12  method to characterize coal porosity. Webb (2001) has published a paper on how to correct for this problem by discarding the portion of the results which are within the grain size of the investigated samples.  2.4.2. Gas pycnometry A pycnometer is a vessel whose volume is known precisely (Webb, 2001). In the method of gas pycnometry, a probe gas at constant temperature is expanded into another vessel of known volume containing a pre-weighed amount of sample whose density (and consequently, porosity) is to be determined. The reference vessel (a vessel of known volume) and the sample vessel (which contains the sample of unknown porosity) are sealed and the probe gas is allowed to come into equilibrium between both reference vessel and sample vessel. The volume of the sample is then calculated using the ideal gas law written as:  Where P is the pressure of the gas; V is the volume; n is the amount of substance; R is the gas constant; and T is the temperature. Once the volume of the sample has been obtained from the pycnometer, its porosity, skeletal density and permeability can be calculated (Huang et al., 1995). The percentage value of porosity is calculated by subtracting the inverse of the skeletal density of the test sample from the inverse of its bulk density and then multiplying the result first by the bulk density and then multiplying the value arrived at by one hundred (see equation 2.2). Bulk density values for the test sample are obtained either from mercury immersion or mercury porosimetry prior to analyzing the sample in the gas pycnometer.  13  Where SD is skeletal density and BD is bulk density of coal sample. Helium is the most common gas used in gas pycnometers because of its low adsorption affinity, its inert nature and its small molecular size (Franklin, 1949; Gan et al., 1972). Gan and his co-workers however caution that based on X-ray studies with anthracites some microporosity is not accessible to the helium atom and as such even helium would underestimate the true porosity of some microporous, high rank coals. The use of nitrogen as an alternative probe gas to helium in gas pycnometry has been discussed in the literature (for example Rodrigues and Lemos de Sousa, 2002; Saha et al., 2007) and readers are referred to these articles for exhaustive treatment of nitrogen gas pycnometry. The greatest advantage of using the gas pycnometer method to characterize coal porosity is its ability to probe into the micropore size range of coals thus giving a value of total coal porosity which is a better estimate of the true total porosity of the coal being studied. The limits of the pores which a gas pycnometer will detect are determined by the size of the probe gas and consequently this method is very useful when characterizing microporous solids such as coals. Another advantage of gas pycnometry is that, unlike some other techniques (such as mercury porosimetry), there are no toxic materials being handled when this method is being utilized thus allowing for a safer work area. The helium pycnometer utilizes helium expansion to determine the skeletal density, porosity and permeability of crushed coal samples (Cui et al., 2009). Figure 2.2 shows the schematic of a typical pycnometer. In figure 2.2, Pr and Ps are pressures in the reference cell and sample cell respectively while Vr and Vs are reference cell volume and sample cell volume respectively. Valves 1 and 3  14  are for venting gas from the reference cell and sample cell respectively while valve 2 allows for gas to pass from the reference cell to the sample cell.  Figure 2.2: Schematic of a pycnometer (From Cui et al., 2009)  2.5.  Adsorption methods and surface area in coals  Adsorption is defined as the enrichment of one or more components in an interfacial layer (Gregg and Sing, 1982; Sing et al., 1985). The adsorbable gas during the process of adsorption is known as the adsorptive while the solid surface upon which adsorption of the gas takes place is called the adsorbent. Various isotherm types are recognized: types I, II, III, IV, V, VI (Byrne and Marsh, 1995; Sing, 1995). Coal, as is typical for most microporous solids, yields a type I isotherm (figure 2.3). According to Sing (1995), microporous solids have a large internal surface area.  15  Figure 2.3: Type I isotherm produced from methane sorption on coal A number of different equations have been proposed to model the behaviour of gas molecules being sorbed onto a solid. These equations include the Langmuir equation, the Brunauer-Emmett-Teller (BET) equation, the Dubinin-Radushkevitch (D-R) equation and the Dubinin-Astakhov (D-A) equation. According to Marsh (1987), both the Langmuir and BET equations predict a value of adsorptive monolayer coverage from which surface area values can be calculated while the D-R and D-A equation predict a micropore volume. Surface areas of coals are usually calculated from N2 adsorption at 77 K (-196.15°C) or CO2 adsorption at 298 K (24.85°C) using the BET and D-R equations respectively. According to Mahajan (1984), problems associated with the use of N2 adsorption at 77 K include activated diffusion effects which lead to N2 molecules being unable to penetrate coal micropores and shrinkage of some coal micropores at the low analytical temperatures at which this procedure is carried out. Carbon dioxide adsorption at 298 K helps to overcome the deficiencies of N2 16  adsorption because the minimum dimension of the CO2 molecule is smaller than that of N2 (3.3 Ǻ vs. 3.64 Ǻ respectively) and due to the higher temperature at which CO2 adsorption takes place, the kinetic energy of CO2 molecules exceed those of N2 molecules at 77 K thus rates of diffusion of CO2 into coal micropores is significantly higher and as a result, a more realistic value for coal surface area is obtained when CO2 is utilized. An introduction of the various equations used to model adsorption isotherms are given below. Gregg and Sing (1982), Marsh (1987), Parkyns and Quinn (1995) and, Stoeckli (1995) provide excellent overviews of the various adsorption methods for studying porosity in coals and carbons and the advantages and disadvantages of each method. The Langmuir equation is written as:  Where V is volume of gas adsorbed, VL is Langmuir volume, the monolayer adsorption capacity of the coal under investigation, PL is Langmuir pressure, the pressure at half the Langmuir volume (Langmuir, 1918). According to Byrne and Marsh (1995), surface areas can be obtained from the Langmuir equation using Avogadro’s number and a projected area of the adsorbate molecule. The Brunauer-Emmett-Teller (BET) equation is written as:  Where V is volume (at STP) of gas adsorbed at pressure P, P o is the liquefaction pressure of the adsorbate used at experimental temperature, C is a constant related to adsorption energy and Vm is the volume of gas required to form a monolayer on the solid surface. The value of Vm is obtained from the experimental data. A plot of the left hand side of the equation 17  against P/Po is linear at values of between 0.05-0.35 (which corresponds approximately to monolayer coverage) with the intercept and slope being 1/VmC and (C-1)/VmC respectively. The surface area of the adsorbent is calculated from Vm, the area occupied by a single gas molecule, Avogadro’s number and the molar volume of the gas (Thomas and Damberger, 1976). The BET equation was devised to improve the Langmuir model and to take into account multilayer adsorption, something which the Langmuir equation does not account for (Byrne and Marsh, 1995). The Dubinin-Radushkevich (D-R) equation is written as:  The Dubinin-Astakhov (D-A) equation is written as:  Where Wo is total micropore volume, W is volume of adsorptive in porosity at relative pressure Po/P, k is characterization parameters of pore size (energy) distribution of adsorbent and β is adsorbate affinity coefficient, R is the gas constant and T is absolute temperature (Marsh, 1987). The D-R equation differs from the Langmuir and BET equations because it is not based on a model process to describe physical adsorption of gases rather it takes into account energies of adsorption (Byrne and Marsh, 1995). Byrne and Marsh (1995) provide more detailed explanations on the underlying assumptions and differences of the various adsorption equations briefly discussed here.  18  2.6. Sample origin, sample preparation, experimental methodology and equipment Thirty two coal samples mostly from the Western Canada Sedimentary Basin were investigated for their porosity characteristics (table 2.1). Twenty samples are from the Horseshoe Canyon Formation (WCSB), nine samples are from the Mannville Formation (WCSB) and 3 samples are from the Mesaverda Formation of Colorado, USA. Coal rank reported in table 2.1 is based on mean random reflectance in oil of fifty discrete vitrinite grains per coal sample. Sample preparation for vitrinite reflectance adhered to standard methods as prescribed in ASTM D2797 (1980) and ASTM D2798 (1980). Three hundred grains per coal sample were counted in order to characterize the maceral composition of the individual coal samples. Bustin (1991) has reported that unlike the prescribed standard methods for characterizing coal macerals (i.e. ASTM D2799, 1980), accuracy does not increase significantly after counting more than two to three hundred grains per coal sample. The range of counted points suggested by Bustin (1991) is also less tedious than the minimum one thousand points required to be counted under the ASTM method (ASTM D2799, 1980). Maceral contents for the coals are shown in table 2.2. All coal samples used in these experiments were crushed to a size range of 0.6 mm to 0.8 mm (20-30 mesh). Mercury porosimetry was carried out using 1-1.5 g of coal that was dried overnight in an oven set to 110°C. The mercury porosimetry experiments involve forcing mercury into the sample at pressures up to 413 MPa (60,000 psi). These experiments were conducted on a Micromeritics Autopore IV 9520 apparatus. The Autopore IV 9520 covers the pore diameter range from about 3.6∙10-4 m (360 µm) to about 3∙10-9 m (0.003 µm) with progressively smaller pores being intruded at higher pressures. 19  Table 2.1: Coal sample rank and Formations of origin for coal sample suite investigated in this study Sample # Mean random reflectance (%) Coal rank Formation S1 0.37 Lignite/Subbituminous C Horseshoe Canyon S2 0.53 Subbituminous A Horseshoe Canyon S3 0.47 Subbituminous B Horseshoe Canyon S4 0.64 High Volatile Bituminous C Horseshoe Canyon S5 0.67 High Volatile Bituminous C Horseshoe Canyon S6 0.71 High Volatile Bituminous B Horseshoe Canyon S7 0.59 Subbituminous A Horseshoe Canyon S8 0.66 High Volatile Bituminous C Horseshoe Canyon S9 0.58 Subbituminous A Horseshoe Canyon S10 0.57 Subbituminous A Horseshoe Canyon S11 0.58 Subbituminous A Horseshoe Canyon S12 0.55 Subbituminous A Horseshoe Canyon S13 0.61 Subbituminous A Horseshoe Canyon S14 0.63 High Volatile Bituminous C Horseshoe Canyon S15 0.60 Subbituminous A Horseshoe Canyon S16 0.75 High Volatile Bituminous B Horseshoe Canyon S17 0.74 High Volatile Bituminous B Horseshoe Canyon S18 0.72 High Volatile Bituminous B Horseshoe Canyon S19 0.73 High Volatile Bituminous B Horseshoe Canyon S20 1.07 High Volatile Bituminous A Horseshoe Canyon S21 0.67 High Volatile Bituminous C Mannville S22 0.71 High Volatile Bituminous B Mannville S23 0.58 Subbituminous A Mannville S24 0.55 Subbituminous A Mannville S25 1.47 Medium Volatile Bituminous Mannville S26 0.67 High Volatile Bituminous C Mannville S27 0.61 Subbituminous A Mannville S28 0.88 High Volatile Bituminous A Mannville S29 0.52 Subbituminous A Mannville S30 0.63 High Volatile Bituminous C Mesaverda (USA) S31 0.61 Subbituminous A Mesaverda (USA) S32 0.64 High Volatile Bituminous C Mesaverda (USA)  20  Table 2.2: Maceral content for coal sample suite investigated in this Sample Vitrinite Liptinite Inertinite Mineral Matter # (%) (%) (%) (%) S22 65 0 31 3 S21 78 0 22 0 S26 79 0 20 1 S1 84 0 8 8 S27 84 0 15 1 S18 85 0 14 1 S23 85 0 14 0 S32 86 0 11 3 S5 87 0 13 0 S10 87 0 10 2 S17 87 0 13 0 S20 89 0 10 1 S29 89 0 10 0 S4 90 0 8 2 S8 91 0 9 0 S16 91 0 9 0 S28 91 0 9 0 S25 92 0 7 0 S9 93 0 6 1 S6 94 0 5 1 S12 95 0 4 2 S11 96 0 4 0 S19 96 0 3 1 S24 96 1 3 0 S30 97 0 3 0 S31 97 0 3 0 S2 98 0 1 1 S3 98 0 2 0 S13 98 0 2 0 S14 98 0 2 0 S15 98 0 2 0 S7 99 0 1 0  study Total (%) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100  21  2.7.  Results and discussions  Graphical relationships between mercury intrusion pressure and cumulative pore area in coal as well as the relationship between intrusion pressure and average diameter of intruded coal pores are presented in Appendix 1. All samples possess a great amount of macro-and meso-porosity. Coal bulk density values obtained from mercury porosimetry and from mercury immersion are presented in table 2.3. The mercury immersion technique involved immersing a solid coal sample into a known mass of mercury and then weighing the combined mass of mercury and coal (Archimedes’ principle). The bulk density of the solid coal is then calculated from these two numbers. Measurements were repeated three times per coal sample and averaged in order to arrive at the values listed in table 2.3. The mercury porosimetry technique was described in an earlier section of this paper and readers are referred there for full details about this method. The bulk density values obtained from mercury porosimetry and via mercury immersion are similar for individual samples. The discrepancies observed in results from both methods may be due to the different states of coal samples utilized in each method. Solid coal samples are employed in the mercury immersion technique while crushed coal samples are used in the mercury porosimetry experiments. The presence of non-coal contaminants (i.e. mineral matter) in the solid coal samples used for mercury immersion may also be a contributing factor to the differences observed in measured bulk density for some of the coal samples tested. The results for tests of coal skeletal density are presented in table 2.4. Skeletal density values were obtained from both helium pycnometry and mercury porosimetry. There is good agreement between both methods of obtaining coal skeletal density. 22  Coal porosity results from both helium pycnometry and mercury porosimetry are displayed in table 2.5. Table 2.3: Comparison of coal bulk density values obtained via Hg-immersion and Hgporosimetry Sample Mercury immersion bulk density Mercury porosimeter bulk density # (g/cc) (g/cc) S1 1.45 1.33 S2 1.32 1.28 S3 1.38 1.25 S4 1.51 1.26 S5 1.30 1.26 S6 1.30 1.16 S7 1.32 1.22 S8 1.39 1.19 S9 1.43 1.35 S10 1.43 1.27 S11 1.31 1.41 S12 1.43 1.33 S13 1.37 1.21 S14 1.38 1.19 S15 1.43 1.25 S16 1.28 1.19 S17 1.28 1.27 S18 1.38 1.45 S19 1.38 1.38 S20 1.47 1.32 S21 1.23 1.17 S22 1.88 1.88 S23 1.23 1.12 S24 1.23 1.19 S25 1.46 1.82 S26 1.50 1.31 S27 1.28 1.29 S28 1.28 1.20 S29 1.28 1.25 S30 1.54 1.44 S31 1.34 1.26 S32 1.26 1.20  23  Table 2.4: Comparison of coal skeletal density values obtained via He-pycnometry and Hg-porosimetry Sample Helium pycnometer skeletal density Mercury porosimeter skeletal density # (g/cc) (g/cc) S1 1.51 1.50 S2 1.46 1.49 S3 1.39 1.39 S4 1.41 1.44 S5 1.41 1.46 S6 1.70 1.39 S7 1.39 1.42 S8 1.46 1.45 S9 1.52 1.51 S10 1.45 1.47 S11 1.72 1.68 S12 1.56 1.57 S13 1.38 1.40 S14 1.38 1.39 S15 1.44 1.48 S16 1.35 1.34 S17 1.51 1.49 S18 1.68 1.69 S19 1.47 1.61 S20 1.50 1.49 S21 1.37 1.38 S22 2.18 2.12 S23 1.36 1.36 S24 1.32 1.44 S25 2.07 2.07 S26 1.51 1.51 S27 1.49 1.49 S28 1.34 1.32 S29 1.37 1.42 S30 1.73 1.70 S31 1.44 1.45 S32 1.39 1.41  24  Table 2.5: Coal porosity obtained from helium pycnometry and mercury porosimetry Sample Helium pycnometer porosity Mercury porosimeter porosity # (%) (%) S19 7.5 6.0 S29 8.9 7.1 S3 9.9 4.8 S24 9.9 7.4 S5 10.5 7.7 S28 10.6 4.5 S4 10.9 6.3 S1 11.6 5.8 S9 11.6 6.0 S16 11.8 5.0 S25 11.8 5.9 S7 12.0 8.3 S2 12.2 8.7 S20 12.2 4.7 S10 12.4 7.7 S13 12.5 6.7 S31 12.6 8.0 S26 13.0 7.8 S27 13.2 7.8 S14 13.3 6.5 S15 13.6 8.9 S18 13.7 7.4 S32 13.7 10.3 S22 13.8 6.3 S21 14.6 9.2 S12 14.9 7.7 S6 15.1 7.5 S17 16.0 6.1 S30 17.0 9.8 S23 17.7 9.5 S11 17.8 10.4 S8 18.8 4.4 Coal porosity values obtained from helium pycnometry are higher than those obtained from mercury porosimetry as shown in table 2.5. This is because the helium molecule is smaller than the mercury molecule (molecular diameter of helium is 2.6∙10-10 m vs. 3.14∙10-10 m for mercury) and also because the mercury porosimetry method is unable to detect porosity 25  smaller than about 3 nm (3.0∙10-9 m) in the coals. Coal is highly microporous and possesses abundant micropores of less than 2 nm and hence, the mercury porosimetry technique will underestimate coal porosity because it does not account for very fine coal mesopores with widths around 3 nm and coal micropores with widths less than 3 nm. This is particularly true for vitrinite-rich coals such as those studied here since vitrinite is mainly microporous (Walker, 1981; Clarkson and Bustin, 1996) hence the higher coal porosity values obtained from helium pycnometry versus coal porosity obtained from mercury porosimetry (see table 2.5). Results of investigation into total pore areas of the examined coals obtained from mercury porosimetry are presented in table 2.6. As seen from table 2.6, total coal pore area ranges from 12.08 m2/g to 49.04 m2/g.  26  Table 2.6: Total pore area of coal determined from mercury porosimetry Sample Total pore area (m2/g) # S22 12.08 S20 12.13 S25 12.95 S17 16.62 S16 19.65 S28 20.26 S8 20.92 S1 23.03 S3 23.37 S9 26.37 S18 27.78 S29 28.02 S19 30.12 S4 30.3 S10 30.82 S26 31.46 S23 32.63 S27 32.92 S13 33.41 S12 33.58 S2 34.38 S14 34.38 S5 34.42 S21 34.49 S24 35.19 S11 35.2 S6 36.77 S31 40.74 S15 41.24 S30 42.61 S7 43.46 S32 49.04 These coal total pore area results are consistent with those of other workers (Gan et al., 1972; Thomas and Damberger, 1976; Clarkson and Bustin, 1996; etc) who have stated that coals posses a high internal surface area and this property is the reason why coals are able to sorb a great amount of gas. Relationships, if any, between total pore area of coal and maceral 27  content of coal were investigated and results are presented in figures 2.4 and 2.5 respectively. Although there is no overall relationship observed in figures 2.4 and 2.5 between total coal pore area versus coal vitrinite and inertinite content respectively, in isorank subsets of the data (as in figures 2.6, 2.7 and 2.8 and table 2.7) coal total pore area increases with increasing vitrinite content. Sample S22, with the lowest vitrinite content of the entire sample suite (65% vitrinite) only has a total pore area of 12.08 m2/g in contrast to samples which have higher vitrinite contents for example, sample S6 (94% vitrinite, and of the same rank as S22) which has a total pore area of 36.77 m2/g. An examination of isorank subsets (figures 2.6, 2.7 and 2.8) of the sample suite presented in table 2.7 indicate that there is a general trend of increasing total pore area with increasing coal vitrinite content (for example, samples S2 and S29; S9 and S10; S12 and S24, etc in the subbituminous A rank, S22 and S18 in the high volatile bituminous B rank, S30 and S4 in the high volatile bituminous C rank, S28 and S20 in the high volatile bituminous A rank, see table 2.7). Some samples with higher vitrinite contents however have lower total pore areas (for example samples S32 and S8 in the high volatile bituminous C rank interval, S17 and S18 in the high volatile bituminous B rank, etc). This observation is possibly a result of the increasing microporous nature of vitrinite as coal rank increases coupled with the limitations of the mercury porosimeter which is only able to access coal pores of 3 nm (3∙10-9 m) and greater. Also supporting this observation of increasing vitrinite microporosity as rank increases is the observation that total pore area of the coals generally decreases after peaking in the high volatile bituminous C rank (sample S32, 49.04 m2/g total pore area with vitrinite content of 86%) with the most mature sample (sample S25, medium volatile bituminous rank) only having a total pore area of 12.95 m2/g even though it has a vitrinite content of 92%. These observations of vitrinite-rich coals having greater total pore areas than less vitrinite-rich coals 28  and the observed general decrease in total coal pore area with increasing rank confirms results of other authors (for example, Levine, 1993; Clarkson and Bustin, 1996, etc.) that the large internal pore (surface) areas seen in coals are a result of the very microporous nature of vitrinite. Investigations on coal microporosity via CO2 estimation of surface area (Mahajan, 1984) could be carried out on the higher maturity samples in order to fully characterize the total pore areas of these vitrinite-rich, microporous samples. 55.00 50.00  Total pore area (m2/g)  45.00 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 55  60  65  70  75  80  85  90  95  100  % Vitrinite Figure 2.4: Total pore area of coal vs. coal vitrinite content for all samples  29  Table 2.7: Comparison of total coal pore area determined from mercury porosimetry with rank and coal vitrinite content Sample # Total pore area (m2/g) % Vitrinite Rank S1 23.03 84 Lignite/Subbituminous C S3 23.37 98 Subbituminous B S29 28.02 89 Subbituminous A S2 34.38 98 Subbituminous A S12 33.58 95 Subbituminous A S24 35.19 96 Subbituminous A S10 30.82 87 Subbituminous A S9 26.37 93 Subbituminous A S11 35.2 96 Subbituminous A S23 32.63 85 Subbituminous A S7 43.46 99 Subbituminous A S15 41.24 98 Subbituminous A S13 33.41 98 Subbituminous A S27 32.92 84 Subbituminous A S31 40.74 97 Subbituminous A S14 34.38 98 High volatile bituminous C S30 42.61 97 High volatile bituminous C S4 30.3 90 High volatile bituminous C S32 49.04 86 High volatile bituminous C S8 20.92 91 High volatile bituminous C S5 34.42 87 High volatile bituminous C S21 34.49 78 High volatile bituminous C S26 31.46 79 High volatile bituminous C S6 36.77 94 High volatile bituminous B S22 12.08 65 High volatile bituminous B S18 27.78 85 High volatile bituminous B S19 30.12 96 High volatile bituminous B S17 16.62 87 High volatile bituminous B S16 19.65 91 High volatile bituminous B S28 20.26 91 High volatile bituminous A S20 12.13 89 High volatile bituminous A S25 12.95 92 Medium volatile bituminous  30  60.00  Total pore area (m2/g)  50.00  40.00  30.00  20.00  10.00  0.00  0  5  10  15  20  25  30  35  % Inertinite Figure 2.5: Total pore area of coal vs. coal inertinite content for all samples 50 45 R² = 0.6786  Total pore area (m2/g)  40 35 30 25 20 15 10  5 0 82  84  86  88  90  92  94  96  98  100  % Vitrinite Figure 2.6: Total pore area of coal vs. coal vitrinite content for subbituminous A rank samples  31  60  Total pore area (m2/g)  50 40  30 20  10 0 70  75  80  85  90  95  100  % Vitrinite Figure 2.7: Total pore area of coal vs. coal vitrinite content for high volatile bituminous C samples 40 35  Total pore area (m2/g)  R² = 0.6415 30 25 20 15 10 5 0 80  82  84  86  88  90  92  94  96  98  % Vitrinite Figure 2.8: Total pore area of coal vs. coal vitrinite content for high volatile bituminous B samples There is no relationship observed between coal porosity and coal rank determined from mean random vitrinite reflectance (figure 2.9). Other authors (for example Thomas and 32  Damberger, 1976; Levine, 1993) have however examined the effects of coal rank on coal porosity and conclude that coal porosity is initially very high at the lowest maturity levels (with up to 75% of the porosity being in the macropore range according to Levine, 1993) and this initial high porosity declines continuously until it reaches a minimum at mid-rank levels (around medium volatile bituminous rank according to Levine, 1993) after which there is an increase in coal porosity (with greater proportions of coal porosity at these higher rank regions belonging to the micropore size range according to Gan et al., 1972). The relationship between coal rank and coal porosity described by Thomas and Damberger (1976) and Levine (1993) were not observed in the current study because of the narrow rank interval represented by the samples studied (sample suite span a rank interval from subbituminous C to medium volatile bituminous rank). Effects of coal maceral content on porosity were not investigated in this study because the coals studied are mainly vitrinite-rich. It is pertinent to note that other authors (e.g. Levine, 1993 and Clarkson and Bustin, 1996) have studied the effects of coal maceral content on coal porosity and concluded that vitrinite-rich coals are more microporous than their inertinite-rich counterparts which tend to have their porosity concentrated in macropores and mesopores. The conclusions put forth by Levine (1993) and Clarkson and Bustin (1996) while not explicitly tested in the present study is somewhat confirmed due to the higher coal porosity values obtained from helium pycnometry since helium is able to penetrate the significant microporosity present in coals (especially vitrinite-rich coals according to the aforementioned authors) while mercury is unable to access coal microporosity due to its larger size.  33  20 18  Porosity (%)  16 14 12 10 8 6 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  Mean random vitrinite reflectance (%) Figure 2.9: Relationship between helium pycnometer coal porosity and mean random vitrinite reflectance  2.8.  Conclusions  Vitrinite-rich subbituminous to medium volatile bituminous coals from the Horseshoe Canyon and Mannville formations (WCSB) and Mesaverda Formation (USA) have been studied in order to characterize their porosity using the methods of mercury porosimetry and helium pycnometry. Total porosity of the coals ranged from 7.5% to 18.8% as estimated from helium pycnometry while the method of mercury porosimetry yielded porosity of between 4.4% and 10.4% for the studied coals. This difference in measured porosity is attributed to the smaller kinetic diameter of the helium molecule thus allowing it to penetrate coal pores which are smaller than 3 nm, the pore size limit beyond which the mercury porosimetry method is no longer applicable. The presence of significant microporosity in coals, especially in vitrinite-rich coals, is inferred by the higher porosity values obtained from helium pycnometry and this fact  34  should be considered when characterizing coal porosity otherwise an incomplete picture of the total porosity present in the coals being studied will be obtained. Total pore area of these coals range from 12.08 m2/g to 49.04 m2/g as estimated from mercury porosimetry. The data indicates that there is an increase in total coal pore area with increasing vitrinite content. This increase is due to the greater microporosity of vitrinite. Relationships between coal porosity and coal rank deduced from mean vitrinite reflectance measurements were also investigated and results from this study suggests that there is no observable relationship between these parameters. The absence of any observable trends between coal porosity and coal rank is attributed to the narrow rank interval of the samples studied.  35  3 GAS SORPTION PROPERTIES OF WESTERN CANADA SEDIMENTARY BASIN COALS 3.1.  Introduction  The presence of gas in coals has long been recognized and is a consequence of the coalification process that generates gas and results in high surface area of coal organic matter. Gas present in coal initially was viewed as a hazard in coal mining operations (Patching, 1970) however, gas stored in coal (called coal bed methane or natural gas from coal) is now recognized as a valuable and important source of clean energy which is rapidly becoming a more important part of the energy mix due to dwindling production from conventional gas sources (Flores, 1998; Law and Curtis, 2002). Initial investigations on coal bed methane production were spurred by a tax holiday funded by the United States government in the 1970s (Law and Curtis, 2002). Gas is stored in coals mainly by the process of physical adsorption a process involving weak intermolecular attraction as a result of van der Waals and electrostatic forces (Yee et al., 1993). Sing (1995) gives a concise overview of the chemistry of physical adsorption of gases by porous solids. Storage of gas in coal via adsorption is possible due to the presence of significant microporosity in coals which in turn results in coal possessing a large surface area which consequently allows a great amount of gas to be sorbed in a small volume of coal (Patching, 1970). As a result of this observation, a variety of workers have published results showing increase in coal gas sorption capacity with increasing coal vitrinite content however, results of the present investigation do not appear to support this widely held premise. This chapter investigates methane sorption capacity (Langmuir volume) of vitrinite-rich subbituminous to medium volatile bituminous coals from the Horseshoe Canyon, Mannville and 36  Mesaverda (USA) formations using a volumetric adsorption apparatus. Relationships between coal methane sorption capacity and coal moisture content, coal rank and coal maceral composition respectively were also investigated.  3.2. Sample origin, sample preparation, experimental methodology and equipment Samples used to estimate coal methane sorption capacity were crushed to a size of between 0.6 mm and 0.8 mm (20-30 mesh). These samples were then brought to equilibrium moisture at 97% relative humidity and 30°C (303.15 K) using a solution of K2SO4 as per the standard ASTM method D1412 (1980). Helium void volumes were measured for each moisture equilibrated coal following which methane adsorption isotherms were measured. The sorption isotherm experiments were carried out at a temperature of 30°C (303.15 K) and at pressures up to 9 MPa. Thirteen individual pressure steps were successively measured during each individual adsorption isotherm experiment viz.: 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 7, 8 and finally 9 MPa. Adsorption isotherms were also measured on select coals dried overnight in a vacuum oven at temperatures not exceeding 80°C (353.15 K) using the volumetric method. It has been reported by several authors in the literature that exposing coals to very high temperatures causes a change in the structure of the coals especially at lower ranks (Evans, 1973; Suuberg et al., 1993; Song et al., 1994; Miknis et al., 1996). Sorption isotherm data obtained in the current study were fit using Langmuir’s equation (Langmuir, 1918). The Langmuir equation is written as:  37  Where V is volume of gas adsorbed, VL is Langmuir volume- the monolayer adsorption capacity of coal, PL is Langmuir pressure, the pressure at half the Langmuir volume (Langmuir, 1918). The volumetric adsorption isotherm experimental set up is used in this study and has been described by several workers including Mavor et al. (1990) and Siemons and Busch (2007) amongst others. Table 3.1 shows the rank and formations of the samples studied while maceral composition of the studied coals are presented in table 3.2. A total of thirty two coal samples were studied. Twenty samples are from the Horseshoe Canyon Formation, nine samples are from the Mannville Formation and 3 samples are from the Mesaverda Formation of Colorado, USA. The coals range in rank from subbituminous C to medium volatile bituminous rank. The coals studied are vitrinite-rich with some minor inertinite and very little mineral matter and liptinite (tables 3.1 and 3.2). Coal rank reported in table 3.1 is based on the mean random reflectance in oil of fifty discrete vitrinite grains per coal sample. Sample preparation for vitrinite reflectance adhered to standard methods described in ASTM D2797 (1980) and ASTM D2798 (1980). Three hundred distinct grains per coal sample were counted in order to characterize the maceral composition of the individual coals. Bustin (1991) has reported that unlike the prescribed standard methods for point counting coal macerals (i.e. ASTM D2799, 1980), accuracy does not increase significantly after counting more than two to three hundred points per coal sample. The number of points prescribed by Bustin (1991) is also less tedious than the minimum one thousand points required to be counted under the ASTM D2799 (1980) method.  38  Table 3.1: Coal sample rank and formations of origin for coal investigated in this study Sample # Mean random reflectance (%) Coal rank S1 0.37 Lignite/Subbituminous C S2 0.53 Subbituminous A S3 0.47 Subbituminous B S4 0.64 High Volatile Bituminous C S5 0.67 High Volatile Bituminous C S6 0.71 High Volatile Bituminous B S7 0.59 Subbituminous A S8 0.66 High Volatile Bituminous C S9 0.58 Subbituminous A S10 0.57 Subbituminous A S11 0.58 Subbituminous A S12 0.55 Subbituminous A S13 0.61 Subbituminous A S14 0.63 High Volatile Bituminous C S15 0.6 Subbituminous A S16 0.75 High Volatile Bituminous B S17 0.74 High Volatile Bituminous B S18 0.72 High Volatile Bituminous B S19 0.73 High Volatile Bituminous B S20 1.07 High Volatile Bituminous A S21 0.67 High Volatile Bituminous C S22 0.71 High Volatile Bituminous B S23 0.58 Subbituminous A S24 0.55 Subbituminous A S25 1.47 Medium Volatile Bituminous S26 0.67 High Volatile Bituminous C S27 0.61 Subbituminous A S28 0.88 High Volatile Bituminous A S29 0.52 Subbituminous A S30 0.63 High Volatile Bituminous C S31 0.61 Subbituminous A S32 0.64 High Volatile Bituminous C  sample suite Formation Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Mannville Mannville Mannville Mannville Mannville Mannville Mannville Mannville Mannville Mesaverda (USA) Mesaverda (USA) Mesaverda (USA)  39  Table 3.2: Maceral composition for coal sample suite investigated in this study Sample # Vitrinite (%) Liptinite (%) Inertinite (%) Mineral Matter (%) Total (%) S22 65 0 31 3 100 S21 78 0 22 0 100 S26 79 0 20 1 100 S1 84 0 8 8 100 S27 84 0 15 1 100 S18 85 0 14 1 100 S23 85 0 14 0 100 S32 86 0 11 3 100 S5 87 0 13 0 100 S10 87 0 10 2 100 S17 87 0 13 0 100 S20 89 0 10 1 100 S29 89 0 10 0 100 S4 90 0 8 2 100 S8 91 0 9 0 100 S16 91 0 9 0 100 S28 91 0 9 0 100 S25 92 0 7 0 100 S9 93 0 6 1 100 S6 94 0 5 1 100 S12 95 0 4 2 100 S11 96 0 4 0 100 S19 96 0 3 1 100 S24 96 1 3 0 100 S30 97 0 3 0 100 S31 97 0 3 0 100 S2 98 0 1 1 100 S3 98 0 2 0 100 S13 98 0 2 0 100 S14 98 0 2 0 100 S15 98 0 2 0 100 S7 99 0 1 0 100  3.3.  Results and discussions  Results of adsorption isotherm experiments (Langmuir volume and Langmuir pressure) for the thirty two coal samples are presented in table 3.3. Coal Langmuir volumes are between 5.6 cc/g and 23.5 cc/g on a moisture equilibrated coal basis (table 3.3). Also shown in table 3.3 40  is the equilibrium moisture content for each coal sample investigated in this study. Equilibrium moisture contents range from 2.3% to 23.8% for the samples studied. Joubert et al. (1973, 1974) and Yee et al. (1993) have reported that moisture in coal beyond the equilibrium moisture content of such coal does not affect the adsorption capacity of coal. Table 3.4 shows comparative results between adsorption isotherm parameters (Langmuir volume and Langmuir pressure) measured on moisture equilibrated coal basis versus on dry coal basis for selected coals from the entire sample suite. Coal Langmuir volume is between 9.8 cc/g to 40.4 cc/g for the dry coals (table 3.4). Results presented in table 3.4 indicate that Langmuir volumes of dry coals are higher than moisture equilibrated Langmuir volumes of the same coals for all samples investigated except one (S28). The results of lower amounts of sorbed gases on moist coals seen in the present study (samples S1, S24, S7, S21, S6, S22 and S25 as presented in table 3.4) is consistent with other published works which indicate that water and gas molecules compete for available adsorption sites in coal thus resulting in lower amounts of adsorbed gases on moist coals (Joubert et al., 1973; Joubert et al., 1974; Yang and Saunders, 1985; Levy et al., 1997; Van Bergen et al., 2009). Sorption of gas and water in coal both take place via physical adsorption hence there is competition between water and gas molecules for available adsorption sites in coal (Yee et al., 1993). The deviation from increased gas sorption on dry coal seen for sample S28 (table 3.4) is perhaps because the moisture present in this sample is held in coal pores which are unavailable for methane sorption. It is possible that this may be caused by pore throats which are narrower than the diameter of the methane molecule and this would explain why the amount of gas sorbed on both the dry and moisture equilibrated coal are the same. Figure 3.1 is a plot of the difference between dry and moist coal Langmuir volumes versus equilibrium moisture content of coal. Figure 3.1 supports 41  the fact that gas molecules and water molecules compete for available adsorption sites on coal as seen by the increase in difference between volumes of gas adsorbed on dry coals versus moist coals with respect to increasing equilibrium coal moisture content. There is no trend observed between coal sorption capacity (Langmuir volume) and coal rank determined from vitrinite reflectance in the present study (figure 3.2). This is attributed to the narrow rank interval spanned by the entire suite of studied coals (coals investigated here fall into the rank range between subbituminous C and medium volatile bituminous rank). Yee et al. (1993) describe a trend of decreasing gas sorption on lower rank coals which bottoms out at around high volatile bituminous A rank then followed by increasing gas sorption on coals at higher rank intervals. The observations of Yee et al. (1993) are not recorded in the current study. Chalmers and Bustin (2007) suggest a trend of increasing gas sorption capacity in high rank coals as a result of increasing microporosity in coals. This trend of increasing sorption capacity at high coal ranks is also not observed in the current study possibly due to the relatively low maturity level of the highest rank coals studied (high to medium volatile bituminous rank). Results of comparisons between coal maceral content (coal vitrinite and inertinite content) and coal sorption capacity (Langmuir volume) on a moisture equilibrated basis are displayed in figures 3.3 and 3.4. No trends are observed between coal maceral content and coal sorption capacity in the studied coals even when isorank subsets of the entire sample suite are examined. This is attributed to the narrow compositional range of the studied coals as all the coals investigated in the present study are vitrinite-rich and have between 65%-99% vitrinite content. Yee et al. (1993) conclude from their literature review of factors which influence gas sorption on coals that there is no consistent trend observed between gas sorption capacity in 42  coal and coal maceral content and results of the present study appear to support this lack of correlation between coal maceral content and coal sorption capacity. Other workers (Crosdale and Beamish, 1993; Lamberson and Bustin, 1993; Crosdale et al., 1998, etc) have reported findings which indicate that increasing coal vitrinite content enhances coal sorption capacity due to the microporous nature of vitrinite. The results of the current work presented in figures 3.3 and 3.4 does not support this. Work using only dry coals may help clarify this matter.  43  Table 3.3: Langmuir volumes and Langmuir pressures for sample suite (Moisture equilibrated coal basis) Sample Equilibrium As received Langmuir As received Langmuir Rank # Moisture (%) volume (cc/g) pressure (MPa) Lignite/Subbituminous S1 11.4 11.1 7.9 C S3 13.9 13.5 12.3 Subbituminous B S29 9.5 22.8 13.2 Subbituminous A Subbituminous A S2 12.7 8.6 5.9 Subbituminous A S24 7.8 18.2 9.1 Subbituminous A S12 11.9 14.2 16.8 Subbituminous A S10 12.8 11.1 8.3 Subbituminous A S23 10.5 15.9 7.9 Subbituminous A S11 13.4 10.5 13.6 Subbituminous A S9 11.5 8.9 6.1 Subbituminous A S7 14.6 10.4 7.6 Subbituminous A S15 15.0 9.8 8.1 Subbituminous A S31 10.3 13.3 9.6 Subbituminous A S13 13.4 11.2 6.1 Subbituminous A S27 11.4 11.2 5.8 S14 13.7 13.2 10.2 High vol bituminous C High vol bituminous C S30 9.0 10.5 6.1 High vol bituminous C S32 10.3 23.5 18.6 High vol bituminous C S4 13.8 9.5 7.5 High vol bituminous C S8 11.7 21.3 19.3 High vol bituminous C S21 23.8 15.9 6.1 High vol bituminous C S26 8.2 10.9 6.0 High vol bituminous C S5 12.4 10.3 5.9 S6 13.7 9.7 11.1 High vol bituminous B High vol bituminous B S22 5.7 5.6 8.9 High vol bituminous B S18 13.2 5.6 7.2 High vol bituminous B S19 9.4 12.6 9.1 High vol bituminous B S17 11.4 14.3 4.5 High vol bituminous B S16 2.3 20.5 5.3 High vol bituminous A S28 2.5 19.1 5.9 High vol bituminous A S20 3.8 13.7 5.9 Medium volatile S25 4.5 8.6 12.6 bituminous  44  S1 S24 S7 S21 S6 S22 S28 S25  35  Differential Langmuir volume (cc/g)  Sample #  Table 3.4: Dry vs. moisture equilibrated sorption parameters for select coals Dry Moisture Dry Moisture equilibrated Equilibrium Langmuir equilibrated Langmuir Langmuir pressure Coal rank moisture volume Langmuir volume pressure (MPa) (%) (cc/g) (cc/g) (MPa) 21.2 11.1 3.5 7.9 SubBit C 11.4 26.4 18.2 2 9.1 SubBit A 7.8 40.4 10.4 3.6 7.6 SubBit A 14.6 29.7 15.9 3 6.1 HiVolBit C 23.8 27.4 9.7 3.1 11.1 HiVolBit B 13.7 9.8 5.6 3.5 8.9 HiVolBit B 5.7 19.1 19.1 2.2 5.9 HiVolBit A 2.5 11.3 8.6 5.3 12.6 MedVolBit 4.5  30 R² = 0.4463 25  20 15 10 5 0 0  5  10  15  20  25  Equilibrium moisture (%) Figure 3.1: Differential Langmuir volume vs. equilibrium moisture content  45  25  Langmuir volume (cc/g)  20  15  10  5  0 0  0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  Mean random vitrinite reflectance in oil (%) Figure 3.2: Coal rank vs. Langmuir volume (on a moisture equilibrated basis)  As received Langmuir volume (cc/g)  25  20  15  10  5  0 55  60  65  70  75  80  85  90  95  100  % Vitrinite Figure 3.3: Coal vitrinite content vs. Langmuir volume (on a moisture equilibrated basis)  46  As received Langmuir volume (cc/g)  25  20  15  10  5  0 0  5  10  15  20  25  30  35  % Inertinite Figure 3.4: Coal inertinite content vs. Langmuir volume (on a moisture equilibrated basis)  3.4.  Conclusions  Vitrinite-rich subbituminous to medium volatile bituminous coals from the Horseshoe Canyon and Mannville formations (WCSB) and Mesaverda Formation (USA) have been examined in order to describe their methane sorption properties. Langmuir volume of coals on a moisture equilibrated basis ranged from 5.6 cc/g to 23.5 cc/g while coal Langmuir volume is between 9.8 cc/g to 40.4 cc/g on a dry coal basis. The difference in estimated coal methane sorption capacity between moisture equilibrated and dry coals is a result of the competition for available adsorption sites on coal between methane gas molecules and water molecules. Sorption of methane and water on coal both occur by the process of physisorption hence why competition for available adsorption sites on coal exists between methane and water molecules. Dry coals sorb more gas than moisture equilibrated coals because adsorption sites occupied by water are open and are able to sorb gas in dry coals. 47  No trends exist between coal sorption capacity and coal rank deduced from mean random vitrinite reflectance in oil for the studied coals. The lack of an apparent relationship between coal rank and coal sorption capacity is ascribed to the narrow rank interval of the coals studied. Similarly, no relationship exists between coal maceral content (vitrinite and inertinite content of coals) and coal methane sorption capacity. The lack of correlation between coal composition and coal methane sorption capacity (coal Langmuir volume) is a result of the narrow maceral compositional range of the coal samples studied; a great majority of the coals studied are vitrinite-rich hence this compositional similarity may be the reason for the lack of any observable trend between coal maceral composition and coal sorption capacity in the current study. The investigation of coal methane sorption capacity helps with coal bed methane reserves assessment by elucidating potential maximum gas-in-place volumes for the studied coals.  48  4 EFFECTS OF PROBE GAS, COAL COMPOSITION AND COAL FABRIC ON COAL PERMEABILITY AND DIFFUSIVITY IN THE WESTERN CANADA SEDIMENTARY BASIN 4.1.  Introduction  Permeability is a critical property that needs to be determined for successful development of resources (e.g., oil, gas, and water) stored in porous subsurface rocks. Two permeability systems are recognized in coal. Coal matrix permeability is attributed to flow paths that are 2 nm (2.0∙10-9 m) and lower in size (micropores as defined by Sing et al., 1985) while fracture permeability is due to coal cleats and fractures, flow paths with sizes generally greater than 50 nm (5.0∙10-8 m, macropores according to Sing et al., 1985). Coal matrix permeability is negligible therefore permeability due to the presence of coal cleats and fractures is the major avenue for producing gas stored in coal seams (Harpalani and Schraufnagel, 1990). The natural fractures observed in coals and coal matrix micropores are depicted in figure 4.1.  Figure 4.1: Natural coal fracture system (modified from Harpalani and Schraufnagel, 1990) 49  Natural gas from coals and other low permeability reservoirs (e.g., shales) have become increasingly important energy sources due to declining production from conventional gas reservoirs and the increasing demand for cleaner sources of energy consequently, a study of coal permeability in the Western Canada Sedimentary Basin (WCSB) is essential and an understanding of coal permeability in the WCSB as reported in subsequent sections will lead to optimized coal bed methane exploration and development. This chapter presents results of a study on coal flow properties (permeability and diffusivity) of vitrinite-rich, subbituminous to medium volatile bituminous coals from the Horseshoe Canyon and Mannville formations of the Western Canada Sedimentary Basin. Both solid coal plugs and coal samples crushed to between 0.8 mm-0.6 mm (20-30 mesh) were investigated in the current study. Permeability of crushed coal ranges from 7.18∙10-5 md to 1.79∙10-2 md whereas coal plug permeability is between 0.02 md to 0.9 md. Average diffusivity of crushed coal is estimated to be on the order of 10-11 to 10-12 m2/s. This difference of up to four orders of magnitude between crushed and coal plug permeability is attributed to different stress conditions during sample testing and the enhancing influence of coal cleats and coal fractures on coal plug permeability. The permeability of crushed coal is influenced by coal matrix properties including maceral content and micro fabric. The coals with greatest amount of inertinite have the greatest matrix permeability and diffusivity due to the greater macro- and meso- porosity of inertinite. Increasing effective stress, with all other factors kept constant, leads to a decrease in coal plug permeability. This reduction in coal plug permeability with increasing effective stress is attributed to the closure of permeability pathways due to shrinkage of coal at high effective stress levels.  50  The impact of probe gas type on coal plug permeability was investigated using the gases helium, nitrogen and methane. Helium permeability measurements on coal plugs are higher than coal plug permeability measured with methane and nitrogen. This disparity in permeability is attributed to a combination of different probe gas molecule size, relative swelling effects of probe gas on coal and associated changes at in-situ stress during tests.  4.2. Permeability, absolute permeability, effective permeability and relative permeability Permeability is defined as the ability of a rock to transmit fluids without changing the structure of the rock or causing a displacement of its components (Bend, 2007). The SI unit of permeability is m2 although Darcy and millidarcy units are common in the petroleum literature (1 md = 10-15 m2). Coal permeability is almost always in the millidarcies (md) range. Amyx et al. (1960, as cited by Saites, 2005) defined 1 Darcy as follows: “a porous medium has a permeability of one Darcy when a single-phase fluid of one centipose viscosity that completely fills the voids of the medium will flow through it under conditions of viscous flow at a rate of one cubic centimetre per second per square centimetre cross-sectional area under a pressure or equivalent hydraulic gradient of one atmosphere per centimetre”. Absolute permeability is defined when a reservoir contains only one fluid. Absolute permeability is independent of fluid properties but is a function of the porous medium. When a reservoir contains more than one fluid, an effective permeability term is employed and the interaction between the different fluids affects the permeability of the reservoir. Effective permeability is always less than absolute permeability. Relative permeability is the ratio of the effective permeability of a given fluid at a given saturation to absolute permeability at 100% 51  fluid saturation expressed as a percentage or as a decimal. In a single fluid system, the relative permeability of the single fluid present is 1.0 (Clark, 1960; Bend, 2007).  4.3.  Fick’s law, Darcy’s law and gas movement in coals  According to several authors (e.g., Patching, 1970; Harpalani and Schraufnagel, 1990; Ayers, 2002, etc) movement of gas through coals is a two step process (figure 4.2). The first step entails desorption of adsorbed gas and occurs through the process of diffusion within the coal micropores. The gas desorption step is governed by Fick’s law which is stated as:  Where m is the mass flow rate, D is the diffusion coefficient and C is the concentration gradient. Once the desorbed gases reach the coal matrix-coal cleat interface via diffusion, the subsequent travel of such gases through the coal fracture system to the producing well is governed by Darcy’s law which is defined as:  Where v is the velocity vector, k is the permeability tensor, µf is the fluid viscosity, P is pressure gradient, ρf is fluid density and g is acceleration due to gravity.  52  Figure 4.2: Two-step process involved in CBM transport (modified from Harpalani and Schraufnagel, 1990) Gamson et al. (1993) argue that flow of methane through coal may not be a simple two step process as generally assumed. These workers propose a four step process between diffusion in the coal micropores and laminar flow in coal fractures. The four steps proposed by Gamson and his co-workers are: 1)  Diffusion from and through the micropores to microfractures and cavities  2)  Diffusion/flow(?) through microfractures and cavities partly blocked by  diagenetic minerals; due to the presence of diagenetic minerals, these authors propose that gas movement through coal at this level is likely to involve both diffusion and flow depending on the size of the pore space remaining after infilling. 3)  Flow through open, unmineralized microfractures and cavities to the  cleat via a process involving Darcy’s laminar flow. 4)  Laminar movement of gas through cleats.  53  These authors state that the rate of gas movement through coal would be dependent upon the size, continuity and connectivity of microfractures and cavities present in coals and which have a size of between 0.05-20 μm (5.0∙10-8 m to 2.0∙10-5 m).  4.4.  Coal fracture permeability vs. Coal matrix permeability  The permeability of the natural fracture network in coals (the cleat system) is generally considered to control the magnitude of coal bed methane production (Dhir et al., 1991). The coal cleat system consists of the face and butt cleats (see figure 4.1). The face cleat is defined as the better developed fracture set and is usually more continuous and pervasive throughout a coal seam while the butt cleat is less well developed, less continuous and usually terminates at contact with the face cleat. The more extensive nature of the face cleat gives it a larger area of contact with the coal matrix, which has negligible permeability, thus allowing the face cleat to drain a wider area of the seam. In effect, the face cleat direction is generally assumed to be the maximum permeability direction in most coal seams. The bulk of the gas found in coal seams is stored within the coal matrix (up to 98% of total gas stored in coal is held within the coal matrix according to Harpalani and Schraufnagel, 1990). It follows then that the coal matrix acts as the origin of the gas which is eventually evacuated through the more permeable cleats and fractures which are present in coals.  4.5.  Factors affecting coal permeability  Examined below are some of the various factors which affect coal permeability. The factors examined include coal matrix shrinkage and cleat compression, effective stress and the gas slippage (Klinkenberg) effect.  54  4.5.1. Coal matrix shrinkage and cleat compression Bustin (1997) states that for coals and other low permeability reservoirs, the matrix compressibility (or matrix shrinkage) is equally as important as fracture closure in determining stress sensitivity and associated permeability changes in these reservoirs. Gas production from coals results in a decrease in fluid pressure in the producing coals and this leads to a shrinkage of the coal matrix (since methane adsorption onto coals leads to a swelling of the coals as reported by various workers including Patching, 1970). Coal matrix shrinkage considered solely leads to about a 12 times increase in coal permeability according to Bustin (1997). Harpalani and Schraufnagel (1990) also indicated that methane desorption from coals leads to a shrinkage of the coal matrix which in turn widens coal fracture openings that serve as flow paths for gas transport in coals. This widening of gas flow paths consequently results in the observed increase in coal permeability witnessed upon gas desorption from coals. Harpalani and Schraufnagel (1990) further state that the enhancement in coal permeability resulting from coal matrix shrinkage is greater than coal permeability reduction caused by increasing effective stress in the Australian coals they studied. Palmer and Mansoori (1996) explain that desorption of methane (via production of a coal bed methane reservoir) results in matrix shrinkage which causes an opening of coal cleats and a consequent increase in coal permeability hence, the effects of coal matrix shrinkage and cleat compression influence coal permeability in opposite directions. The impact of these opposing effects of matrix shrinkage and cleat compression on coal permeability is confirmed by permeability rebound phenomenon observed at lower pressures in producing coal bed methane wells and might have implications for enhanced coal bed methane recovery using CO2 injection (Zulkarnain, 2005).  55  Harpalani and Chen (1997) report that at gas pressures greater than 1.7 MPa, the effects of coal matrix shrinkage resulting from volumetric strain plays a more important role in influencing coal permeability than the Klinkenberg effect (which is only of great influence at pressures lower than 1.7 MPa). These authors further submit that the change in permeability associated with matrix shrinkage is linearly proportional to coal volumetric strain which itself is linearly proportional to the amount of gas desorbed (thus, change in permeability of coal is a linear function of the amount of gas being desorbed from such coal). Harpalani and Chen (1997) also suggest that it might be possible to estimate the permeability variation of a coal associated with matrix shrinkage from the sorption isotherm of such coal provided some estimate of a constant of proportionality (called “A”) is available. The relation suggested by Harpalani and Chen (1997) for purposes of estimating permeability associated with matrix shrinkage is:  Where: ∆k is change in permeability, Vdes is the volume of gas desorbed and A is a constant. A matrix shrinkage coefficient was also proposed by Harpalani and Chen (1997). These authors define the shrinkage coefficient as the rate of change of coal matrix volume with change in gas pressure of a desorbing gas. The shrinkage coefficient is defined as follows: m m  Where Cm* is the shrinkage coefficient, Vm is the matrix volume and dP is the change in applied pressure at both internal and external surfaces.  56  4.5.2. Effective stress Jones (1975) investigated the effects of increased net overburden pressures on rock fractures using both fabricated core and reservoir core. The fabricated samples were made from Portland cement and plaster of Paris while Carthage marble, Smackover limestone and Ellenburger dolomite were the rock samples studied. The assumption underlying the experiment by Jones (1975) was that confining pressure applied uniformly in all direction in the lab mimics in-situ conditions where the effective stress experienced by reservoir rocks is due to the difference between overburden and pore pressures. Jones (1975) discovered from his experiments that there is a linear relationship between the cube root of permeability and the logarithm of confining pressure. Jones (1975) also reports two orders of magnitude reduction in permeability with increase in confining pressure. Harpalani and Schraufnagel (1990) state that changes in effective stress within coal seams affect relative permeability of such seams. According to Harpalani and Schraufnagel (1990), there is a pore pressure decrease associated with gas desorption from coals and which consequently leads to increase in effective stress. The rise in effective stress causes the coal matrix to shrink and also leads to the progressive closure of coal fractures (the main gas flow paths in coals) thereby resulting in reduced coal permeability. Palmer and Mansoori (1996) state that naturally fractured formations (e.g. coal) are sensitive to changes in effective stress hence during drawdown of a coal bed methane reservoir by primary production, effective stress increases and coal permeability decreases due to cleat compression. Bustin (1997) concluded based on investigations of Australian coals that a two fold increase in effective stress causes a six fold decrease in permeability. The results of Bustin  57  (1997) are in general agreement with published results by Jones (1975) who noted a decrease in permeability of reservoir carbonates with increase in confining pressure.  4.5.3. Gas slippage (Klinkenberg) effect The gas slippage effect was first reported by Klinkenberg (1941) who observed variations in permeability with pressure when gases are used as the flowing fluid in permeability experiments. Klinkenberg did not notice these permeability variations when nonreactive liquids (e.g. brine) are used instead of gases during experiments. These permeability variations are ascribed to gas slippage, a phenomenon that occurs during gas flow in capillary tubes. The gas slippage effect (Klinkenberg effect) becomes significant when the porous medium possesses small pores and the gases are at low pressures. Consequently, measured permeability within the porous medium is higher than the actual permeability (thus considered on its own, the slippage effect also leads to an increase in permeability in coals). Under conditions where the gas slippage effect holds true, the measured gas permeability is described thus:  Where k is the measured gas permeability, k0 is the absolute permeability of the medium, Pm is mean gas pressure and b is the Klinkenberg coefficient. Harpalani and Chen (1997) report that the value of b is different for various gases but the value of K0 is constant (since absolute permeability of a porous medium is independent of the property of the gas flowing through it rather, it is a function of the structure of the porous medium). The value of K however, changes since it depends on both the structure of the porous medium and also on the gas flowing through it. 58  Klinkenberg (1941) submits that slippage occurs when the mean free path of molecules in the gas is of similar scale to the flow conduit therefore gas is not stationary at the walls of the conduit and slippage occurs while Saites (2005) reports that increase in measured permeability due to gas slippage is a result of a velocity component arising from molecular motion being superimposed on the gas flow. Harpalani and Chen (1997) state that gas slippage results in about a 5 times increase in coal permeability when considered solely although the gas slippage effect is important only at pressures of around 1.7 MPa and below. The observation by Harpalani and Chen (1997) that gas slippage is only important at low pressures is a confirmation of earlier work by Somerton et al. (1975) who report that the Klinkenberg effect disappears at higher flowing pressures and for media with permeabilities above about 20 md.  4.6.  The pulse decay technique for estimating coal permeability  The pulse decay technique involves applying a small pore pressure to one end of a sample and then monitoring the overall pressure vs. time behaviour of the sample as the pore fluid moves through the sample from the upstream reservoir to the downstream reservoir (Walls, 1982). Jones (1997) and Saites (2005) report that the pulse decay method allows for effective laboratory measurements of permeability in porous materials that have very low permeability (e.g. coals, shales, etc) on the order of 0.1 md to 0.01 μd using either a liquid or a gas over very short time periods. Permeability is measured on cylindrical plugs cut from the porous material of interest (in the present study, coals) under the pulse decay technique. The dimensions (diameter, length and mass) of the coal plug is measured and recorded then the coal plug is confined axially by a rubber jacket or some other suitable material and then inserted into a core holder 59  after which it is saturated fully with the probe fluid. The probe fluid is then made to flow through the jacketed sample and the flow rate through the porous test material and the pressure drop across the sample are monitored and recorded. Murthy Pathi (2008) summarized the pulse decay method for determining shale permeability based on an equipment earlier described by Jones (1997). The testing equipment has a core holder, a rubber membrane inside the core holder acts as a pressurization chamber for the hydraulic fluid which supplies the confining pressures under which permeability measurement is carried out. The core holder is connected to both an upstream and a downstream reservoir of known volumes (Vu and Vd respectively in figure 4.3). A differential pressure transducer measures the pressure difference between the upstream and downstream reservoirs (Pu and Pd in figure 4.3). Two absolute pressure transducers are also present in the set up, one each at the upstream and downstream reservoir to measure pressures at both these reservoirs. A probe gas is passed through the sample end plate to supply the pore pressure while a computer connected to the entire apparatus is used to record all of the data which is periodically collected during the experiment. Figure 4.3 is a schematic of the pulse decay experiment.  60  Figure 4.3: Schematic diagram of pulse decay permeability set up for measuring coal permeability (modified from Cui et al., 2009) Jones (1997) and Murthy Pathi (2008) described the pulse decay method for shales and other rocks but the process is very similar for estimating coal permeability hence very little modifications to the experimental set up and procedures took place when coal permeability was estimated using this technique in the course of the present study. Jochen et al. (1994) report several methods used for field forecasting of transient and longer-term permeability of coalbeds. These methods include conventional well test analysis using well pressures and single phase flow rates to evaluate the reservoir around the well, an analysis method for pressure transient testing in coal bed wells based on a pseudopressure function that uses an adsorption isotherm and relative permeability relations for that specific reservoir and finally, reservoir simulations which are used to match the production history and pressure from coal bed methane reservoirs and which are used to estimate reservoir permeability. These field methods are expensive and results are not generated as quickly as the 61  laboratory pulse decay method. These field methods also involve more complex procedures when compared with the laboratory pulse decay method which is a relatively straight forward technique.  4.7. Sample origin, sample preparation, experimental methodology and equipment The procedures for laboratory pulse decay permeability measurements reported here for coals are similar to those reported by Murthy Pathi (2008) for estimating shale permeability using the pulse decay technique. A suitable plug is first obtained by re-coring from a coal core using a diamond drill bit. The plug is then cut and polished with the end face normal to the core axis. The plug sample is then placed in the Hoek cell (Figure 4.3) between two pistons. Desired confining pressure is applied via a hydraulic pump which is part of the experimental set up. The confining pressure applied usually corresponds to desired reservoir conditions. With valves 1, 2 and 3 (as in figure 4.3) open, gas is flowed through the system after which valves 2 and 3 (in figure 4.3) are closed and the system is allowed to come to equilibrium. The entire system is allowed to equilibrate for a period of about seven hours in the present study. After achieving equilibrium, the differential pressure transducer is set to zero and valve 2 is opened. Opening up of valve 2 creates a pressure gradient between the upstream and downstream reservoirs. This pressure differential is then monitored along with both the upstream and downstream pressures. As the experiment proceeds, the upstream pressure decreases while the downstream pressure increases. The experimental set up is automated, and as a result, once an experiment is finished, the computer terminates the experiment. Experiments were run at different confining pressures with pore pressure kept constant in the current study in order to determine the stress sensitivity of the coals being investigated. Pore pressure increase or decay 62  depends on fluid viscosity, sample pore volume, sample compressibility and fluid compressibility (Brace et al., 1968; Lin, 1977; Hsieh et al., 1981; Trimmer 1982; Jones, 1997; Murthy Pathi, 2008). Samples used to estimate coal diffusivity were crushed to a size of between 0.6 mm and 0.8 mm (20-30 mesh). These samples were subsequently brought to equilibrium moisture at 97% relative humidity and 30°C (303.15 K) using a solution of K2SO4 as per the standard ASTM method D1412 (1980). Helium void volumes were estimated for each coal sample following which methane adsorption isotherms were determined for these moisture equilibrated coals at a temperature of 30°C (303.15 K) and at pressures up to 9 MPa using a volumetric adsorption isotherm set up (which has been described by Mavor et al., 1990 and Siemons and Busch, 2007 for example). Thirteen individual pressure steps are successively measured during an adsorption isotherm experiment thus: 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 7, 8 and finally 9 MPa. Adsorption isotherms were also measured on select coals dried overnight in a vacuum oven at temperatures not exceeding 80°C (353.15 K). Exposing coals to high temperatures causes a change in the structure of the coals especially at lower ranks (Evans, 1973; Suuberg et al., 1993; Song et al., 1994; Miknis et al., 1996) and hence a temperature lower than 80°C (353.15 K) was used here. The sorption isotherms obtained were fit using the Langmuir equation (Langmuir, 1918). The Langmuir equation is written as:  Where V is volume adsorbed, VL is Langmuir volume- the monolayer adsorption capacity of coal, PL is Langmuir pressure, the pressure at half the Langmuir volume (Langmuir, 1918)  63  Coal rank and formations of the samples studied are presented in table 4.1 while table 4.2 shows the maceral composition of the studied coals. Majority of the studied coals are from the Horseshoe Canyon Formation (thirty samples) while nine samples are from the Mannville Formation. Three coal samples from the Mesaverda Formation of Colorado, USA are also included in the studied suite. The coals range in rank from subbituminous C to medium volatile bituminous rank (table 4.1). The coals are vitrinite-rich coals with some minor inertinite and very little mineral matter and liptinite (table 4.2). Coal rank reported in table 4.1 is based on mean random reflectance in oil of fifty distinct vitrinite grains per coal sample. Sample preparation for vitrinite reflectance adhered to standard methods as prescribed in ASTM D2797 (1980) and ASTM D2798 (1980). Three hundred grains per coal sample were counted in order to characterize the maceral composition of the individual coals. Bustin (1991) has reported that unlike the prescribed standard methods for characterizing coal macerals (i.e. ASTM D2799, 1980), accuracy does not increase significantly after counting more than two to three hundred grains per coal sample. The range of counted points suggested by Bustin (1991) is also less tedious than the minimum one thousand points required to be counted under the ASTM method (ASTM D2799, 1980).  64  Table 4.1: Coal sample rank and formations of origin for coal sample suite investigated Sample # M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27 M28 M29 M30 M31 M32 M33 M34 M35 M36 M37 M38 M39 M40 M41 M42  Mean random reflectance (%) 0.37 0.53 0.47 0.64 0.67 0.71 0.59 0.66 0.58 0.57 0.58 0.55 0.61 0.63 0.60 0.75 0.74 0.72 0.73 1.07 0.68 0.65 0.65 0.64 0.65 0.61 0.59 0.57 0.61 0.63 0.67 0.71 0.58 0.55 1.47 0.67 0.61 0.88 0.52 0.63 0.61 0.64  Coal rank Lignite/Subbituminous C Subbituminous A Subbituminous B High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous B Subbituminous A High Volatile Bituminous C Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A High Volatile Bituminous C Subbituminous A High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous A High Volatile Bituminous B High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C Subbituminous A Subbituminous A Subbituminous A Subbituminous A High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous B Subbituminous A Subbituminous A Medium Volatile Bituminous High Volatile Bituminous C Subbituminous A High Volatile Bituminous A Subbituminous A High Volatile Bituminous C Subbituminous A High Volatile Bituminous C  Formation Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Horseshoe Canyon Mannville Mannville Mannville Mannville Mannville Mannville Mannville Mannville Mannville Mesaverda (USA) Mesaverda (USA) Mesaverda (USA)  65  Table 4.2: Maceral composition for coal sample suite investigated in this study Sample #  Vitrinite (%)  Liptinite (%)  Inertinite (%)  M32 M31 M36 M1 M37 M18 M33 M42 M5 M10 M17 M20 M39 M4 M8 M16 M38 M35 M9 M6 M12 M25 M11 M19 M23 M28 M34 M22 M24 M40 M41 M2 M3 M13 M14 M15 M26 M27 M29 M30 M7 M21  65 78 79 84 84 85 85 86 87 87 87 89 89 90 91 91 91 92 93 94 95 95 96 96 96 96 96 97 97 97 97 98 98 98 98 98 98 98 98 98 99 99  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  31 22 20 8 15 14 14 11 13 10 13 10 10 8 9 9 9 7 6 5 4 5 4 3 4 4 3 3 3 3 3 1 2 2 2 2 2 2 2 2 1 1  Mineral matter (%) 3 0 1 8 1 1 0 3 0 2 0 1 0 2 0 0 0 0 1 1 2 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0  Total (%) 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100  66  4.8.  Results and discussion  4.8.1. Diffusivity Diffusivity (or diffusion coefficient) is a constant of proportionality between mass flux due to diffusion and concentration gradient of the diffusing species. The SI unit of diffusivity is m2/s although units of cm2/s are also seen in the literature (for example Sevenster, 1959). In this study, coal diffusivity was estimated from adsorption isotherm data obtained from moisture equilibrated coals using the method explained in detail by Cui et al. (2009). Averaged coal diffusivity results and Langmuir volumes for each coal sample are presented in table 4.3. A total of thirty two coal samples ground to between 0.6 mm and 0.8 mm (20 and 30 mesh) were tested in order to determine coal diffusivity. Coal diffusivity for the studied coals falls within the range of 10-11 to 10-12 m2/s (table 4.3), values in line with some of the published work on coal diffusivity from other basins (e.g. Smith and Williams, 1984; Charriere et al., 2010). Table 4.4 shows a comparison of diffusivity results from the present study and those of Smith and Williams (1984) and Charriere et al. (2010). The differences in diffusivity values obtained in these three studies are attributed to the heterogeneous nature of coal although the reported diffusivity values are still similar in magnitude. Relationships between average coal diffusivity, coal maceral (vitrinite and inertinite) content and coal rank as deduced from mean random vitrinite reflectance values were investigated and results are presented in figures 4.4, 4.5 and 4.6. No overall trend exists between average coal diffusivity (on a moisture equilibrated basis) and maceral content neither is any overall trend found for coal diffusivity and coal rank. The lack of observable overall trends between coal rank and coal diffusivity and coal maceral content and coal diffusivity may 67  be due to the narrow rank range of the coals studied or the lack of an overall trend could be a consequence of the narrow maceral composition of the coals studied (the coals studied are mostly vitrinite-rich). When isorank subsamples of the entire sample suite are observed however, samples containing a greater proportion of inertinite (with other factors kept constant) generally had higher average as received diffusivity than their more vitrinite-rich counterparts (for example, samples M41 vs. M13, M37 vs. M33, M15 vs. M7 and M10 vs. M9 in the subbituminous A rank; M40 vs. M14, M42 vs. M4, M31 vs. M36 and M5 vs. M8 in the high volatile bituminous C rank; M32 vs. M6, M18 vs. M16, and M17 vs. M19 in the high volatile bituminous B rank and M20 vs. M38 in the high volatile bituminous A rank; see table 4.5). Higher diffusivity observed in coals with higher inertinite contents is attributed to the greater meso- and macro-porosity of inertinite which enhances gas diffusivity. This is consistent with results published by Laxminarayana and Crosdale (2002) who found effective diffusivity rates measured for dull (inertinite-rich) coals are higher than those measured on bright (vitrinite-rich) coals. While greater coal inertinite content generally enhances coal diffusivity, this is not true in every sample (for example samples M12 vs. M34, M33 vs. M11 and M37 vs. M41 in the subbituminous A rank; M4 vs. M14, M36 vs. M42 and M5 vs. M40 in the high volatile bituminous C rank; M16 vs. M6 in the high volatile bituminous B rank; see table 4.5). The reasons for this deviation from the observed enhanced diffusivity with greater coal inertinite content are unclear but perhaps the gas content of coals is a contributing factor. It is observed from table 4.5 that the coals with higher proportions of vitrinite which had higher average diffusivity than isorank inertinite-rich coals also had higher Langmuir volumes hence the greater amount of gas present in these vitrinite-rich coals resulted in their higher diffusivity values. 68  The effect of moisture on coal diffusivity was explored in the present study and results are presented in table 4.7. In order to conduct this investigation, a subset of the coals used in this study were selected to provide variety in coal rank and coal composition and properties of the selected coals are shown in table 4.6. These samples were subsequently put in a vacuum oven set not to exceed 80°C (353.15 K) overnight in order to drive off coal surface moisture while ensuring that there is no damage to the coal structure (Evans, 1973; Suuberg et al., 1993; Song et al., 1994; Miknis et al., 1996). In all the coals studied, dry coal diffusivity is higher than coal diffusivity estimated from moisture equilibrated coals; the presence of moisture in coal reduces coal diffusivity by up to an order of magnitude in the studied coals (see table 4.7). The observed reduction in diffusivity of moisture equilibrated coals is because the moisture held within coal pores competes with gas for storage sites in coals (Van Bergen et al., 2009) and hence leads to reduction in both amount of gas stored in coals and in available spaces for the gas held within the coal to diffuse out of the coal. Dry coals also have higher sorbed gas content as a result of having more open porosity in which to sorb gas therefore this higher sorbed gas content of dry coals contributes to the higher average diffusivity observed for dry coals. Laxminarayana and Crosdale (2002) report in their study on Australian coals that diffusivity decreases with increasing coal maturation as a result of increasing microporosity of coals at higher ranks. This trend was not observed in the current study perhaps as a result of the narrow rank interval of the coals studied and also the general low maturity of the samples which were investigated (the highest rank coal in the present study is of medium volatile bituminous rank).  69  Table 4.3: Average diffusivity and Langmuir volumes for coals studied Langmuir volume (cc/g) Average moisture equilibrated diffusivity Sample # (on a moisture equilibrated coal (m2/s) basis) -11 5.6 M18 3.94∙10 -11 5.6 M32 6.73∙10 -11 8.6 M2 2.26∙10 -11 8.6 M35 1.36∙10 -11 8.9 M9 1.26∙10 -11 9.5 M4 2.14∙10 -11 9.7 M6 5.74∙10 -11 9.8 M15 2.67∙10 -11 10.3 M5 2.47∙10 -11 10.4 M7 2.31∙10 -11 10.5 M11 3.00∙10 -11 10.5 M40 3.15∙10 -11 10.9 M36 2.54∙10 -12 11.1 M1 8.73∙10 -11 11.1 M10 3.82∙10 -11 11.2 M13 2.26∙10 -11 11.2 M37 2.11∙10 -11 12.6 M19 1.61∙10 -11 13.2 M14 2.28∙10 -11 13.3 M41 2.39∙10 -11 13.5 M3 1.40∙10 -11 13.7 M20 7.03∙10 -11 14.2 M12 1.23∙10 -11 14.3 M17 3.06∙10 -11 15.9 M31 3.47∙10 -11 15.9 M33 1.81∙10 -11 18.2 M34 1.77∙10 -11 19.1 M38 1.24∙10 -11 20.5 M16 1.95∙10 -11 21.3 M8 2.30∙10 -11 22.8 M39 2.48∙10 -11 23.5 M42 4.23∙10  70  Table 4.4: Diffusivity comparison across different basins Author(s) Basin/coals examined Diffusivity (m2/s) This study (2011)  Horseshoe Canyon and Mannville coals of WCSB  ≈10-11  Charriere et al. (2010)  High volatile bituminous coals of Lorraine Basin, NE France  ≈10-12  Smith and Williams (1984)  Anthracites from Madrid, NM; Pittsburgh bituminous and Fruitland subbituminous coals; all USA  ≈10-10  Vitrinite (%) 60  65  70  75  80  85  90  95  100  Average diffusivity (m2/s)  1.00E-10  1.00E-11  1.00E-12  Figure 4.4: Average coal diffusivity vs. vitrinite content of coal  71  Inertinite (%) 0  5  10  15  20  25  30  35  Average diffusivity (m2/s)  1.00E-10  1.00E-11  1.00E-12  Figure 4.5: Average coal diffusivity vs. inertinite content of coal  Mean Random Vitrinite Reflectance (%) 0.2  0.4  0.6  0.8  1  1.2  1.4  1.6  1.00E-10  1.00E-11  1.00E-12  Figure 4.6: Average coal diffusivity vs. mean random vitrinite reflectance of coal (coal rank)  72  Table 4.5: Comparison of isorank samples showing maceral effects on average coal diffusivity Lang. Sample Diffusivity % % % Mineral Vol. Rank 2 # (m /s) Vitrinite Inertinite matter (cc/g) 11.1 M1 8.73∙10-12 84 8 8 Lignite/Subbituminous C -11 13.5 M3 1.40∙10 98 2 0 Subbituminous B -11 22.8 M39 2.48∙10 89 10 0 Subbituminous A -11 8.6 M2 2.26∙10 98 1 1 Subbituminous A -11 14.2 M12 1.23∙10 95 4 2 Subbituminous A -11 18.2 M34 1.77∙10 96 3 0 Subbituminous A -11 11.1 M10 3.82∙10 87 10 2 Subbituminous A -11 8.9 M9 1.26∙10 93 6 1 Subbituminous A -11 10.5 M11 3.00∙10 96 4 0 Subbituminous A -11 15.9 M33 1.81∙10 85 14 0 Subbituminous A 10.4 M7 2.31∙10-11 99 1 0 Subbituminous A -11 9.8 M15 2.67∙10 98 2 0 Subbituminous A -11 11.2 M13 2.26∙10 98 2 0 Subbituminous A -11 11.2 M37 2.11∙10 84 15 1 Subbituminous A -11 13.3 M41 2.39∙10 97 3 1 Subbituminous A -11 13.2 High volatile bituminous C M14 2.28∙10 98 2 0 -11 10.5 High volatile bituminous C M40 3.15∙10 97 3 0 -11 9.5 High volatile bituminous C M4 2.14∙10 90 8 2 -11 23.5 High volatile bituminous C M42 4.23∙10 86 11 3 -11 21.3 High volatile bituminous C M8 2.30∙10 91 9 0 -11 10.3 High volatile bituminous C M5 2.47∙10 87 13 0 -11 15.9 High volatile bituminous C M31 3.47∙10 78 22 0 -11 10.9 M36 2.54∙10 79 20 1 High volatile bituminous C -11 9.7 High volatile bituminous B M6 5.74∙10 94 5 1 -11 5.6 High volatile bituminous B M32 6.73∙10 65 31 3 -11 5.6 High volatile bituminous B M18 3.94∙10 85 14 1 -11 12.6 High volatile bituminous B M19 1.61∙10 96 3 1 -11 14.3 High volatile bituminous B M17 3.06∙10 87 13 0 -11 20.5 M16 1.95∙10 91 9 0 High volatile bituminous B -11 19.1 M38 1.24∙10 91 3 0 High volatile bituminous A 13.7 M20 7.03∙10-11 89 10 1 High volatile bituminous A 8.6 Medium volatile M35 1.36∙10-11 92 7 0 bituminous  73  Table 4.6: Properties of coal subset used to investigate effects of moisture on coal diffusivity Sample # Vitrinite (%) Liptinite (%) Inertinite (%) Mineral matter (%) Coal rank M1  84  0  8  8  Subbituminous C  M7  99  0  1  0  Subbituminous A  M34  96  1  3  0  Subbituminous A  M31  78  0  22  0  High Volatile Bituminous C  M6  94  0  5  1  High Volatile Bituminous B  M32  65  0  31  3  High Volatile Bituminous B  M38  91  0  9  0  High Volatile Bituminous A  M35  92  0  7  0  Medium Volatile Bituminous  Sample # M1  M7 M34 M31 M6 M32 M38 M35  Table 4.7: Effects of moisture on average coal diffusivity Moisture equilibrated diffusivity Dry diffusivity (m2/s) Coal rank (m2/s) 1.11∙10-11 8.73∙10-12 Subbituminous C -10 -11 2.04∙10 2.31∙10 Subbituminous A -11 -11 4.31∙10 1.77∙10 Subbituminous A -10 -11 1.29∙10 3.47∙10 High Volatile Bituminous C -10 -11 1.09∙10 5.74∙10 High Volatile Bituminous B -10 -11 1.61∙10 6.73∙10 High Volatile Bituminous B -11 -11 1.26∙10 1.24∙10 High Volatile Bituminous A -11 -11 1.98∙10 1.36∙10 Medium Volatile Bituminous  4.8.2. Matrix permeability Coal matrix permeability was estimated from helium pycnometry data obtained from coals crushed to between 0.6 mm-0.8 mm (20-30 mesh) on an as received basis using the method discussed by Cui et al. (2009). Results are shown in table 4.8. A total of forty two coal samples were investigated and estimated coal matrix permeability is between 10-2 to 10-5 md as shown in table 4.8. Relationships between coal matrix permeability and coal rank (obtained from mean random vitrinite reflectance in oil) and coal maceral composition (inertinite and vitrinite contents of coals) are presented in figures 4.7, 4.8 and 4.9. There is lack of a strong overall 74  relationship between coal matrix permeability and coal vitrinite and inertinite content for the coals studied. This may be a consequence of the narrow rank range of the coals studied for this project or the lack of an observable overall trend may be due to the narrow compositional variations in the maceral content of the coals studied (the coals studied are all vitrinite-rich consequently there is very little differences in maceral content between all the coals). When isorank coal samples are compared however, samples containing a greater proportion of inertinite (all other factors being equal) have higher matrix permeability than samples which contain a greater amount of vitrinite as seen from samples M2 vs. M7, M9 vs. M12 and M37 vs. M33 (subbituminous A rank); M40 vs. M30, M23 vs. M22, M5 vs. M4 and M31 vs. M6 (high volatile bituminous B rank); M19 vs. M21, M16 vs. M6 and M18 vs. M17 (high volatile bituminous B rank) in table 4.9. Higher matrix permeability observed in coals with greater proportion of inertinite is attributed to the greater meso- and macro-porosity of inertinite macerals, an observation corroborated by Laxminarayana and Crosdale (2002). It should be noted that Clarkson and Bustin (1997), in their study on the variation of coal permeability with lithotype and maceral composition of some Canadian coals, conclude that there is a general increase in permeability with increasing coal vitrinite content. The divergence in results between those of the current study and those of Clarkson and Bustin (1997) might be because coal samples crushed to between 0.6 mm-0.8 mm were investigated to determine coal matrix permeability in the current study while Clarkson and Bustin (1997) determined bulk permeability from coal core. The coals examined in the present study are also from different coal formations than those looked at by Clarkson and Bustin (the present study looks at coals from the WCSB in Alberta, particularly coals of the Horseshoe Canyon and Mannville formations while Clarkson and Bustin 75  (1997) examined medium volatile bituminous coals from the Elk Valley coalfields, Mist Mountain Formation and Gates Formation). Clarkson and Bustin (1997) also utilized a different method to determine coal permeability than the method utilized in the present study. Laxminarayana and Crosdale (2002) state that mineral matter acts as a higher permeability pathway for gas flow through coals hence, the presence of more mineral matter in a coal sample could also account for increased matrix permeability in these mineral matter containing samples (see table 4.9). Some samples with greater proportion of vitrinite have high matrix permeabilities than their isorank inertinite-rich counterparts (for example samples M41 vs. M29 and M10 vs. M39, subbituminous A rank; M8 vs. M25, high volatile bituminous B rank; M18 vs. M32, high volatile bituminous C rank and M38 vs. M20, high volatile bituminous A rank; all from table 4.9). The reasons for this deviation are unclear but perhaps may have to do with the type of vitrinite present in these coals since different vitrinite types have different proportions of macropores, mesopores and micropores. No relationship exists between coal rank (mean random vitrinite reflectance) and coal matrix permeability for the samples studied (figure 4.9). This lack of an overall trend is attributed to the narrow rank interval of the sample suite examined for this project.  76  Vitrinite (%) 60  65  70  75  80  85  90  95  100  Coal matrix permeability (md)  1  0.1  0.01  0.001  0.0001  0.00001  Figure 4.7: Coal matrix permeability vs. vitrinite content of coal  77  Table 4.8: Coal matrix permeability from helium pycnometry Sample # M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27 M28 M29 M30 M31 M32 M33 M34 M35 M36 M37 M38 M39 M40 M41 M42  Coal matrix permeability (md) 2.46∙10-4 6.36∙10-3 1.39∙10-3 7.18∙10-5 2.11∙10-3 2.90∙10-4 2.44∙10-4 3.39∙10-4 1.08∙10-3 5.83∙10-5 1.49∙10-2 7.63∙10-4 1.46∙10-5 8.01∙10-4 6.38∙10-5 3.96∙10-4 6.78∙10-3 7.66∙10-3 5.41∙10-4 1.15∙10-4 2.47∙10-4 2.97∙10-3 5.21∙10-3 4.92∙10-4 1.31∙10-3 2.90∙10-4 7.55∙10-4 5.15∙10-3 4.83∙10-3 3.74∙10-4 3.03∙10-3 7.60∙10-3 7.93∙10-4 2.40∙10-4 1.79∙10-2 2.47∙10-3 6.79∙10-3 2.64∙10-4 1.97∙10-3 5.96∙10-3 1.20∙10-3 2.83∙10-3  78  Inertinite (%) 0  5  10  15  20  25  30  35  Coal matrix permeability (md)  1  0.1  0.01  0.001  0.0001  0.00001  Figure 4.8: Coal matrix permeability vs. inertinite content of coal  Coal matrix permeability (md)  Mean random reflectance (%) 0.20  0.40  0.60  0.80  1.00  1.20  1.40  1.60  1.00E+00  1.00E-01  1.00E-02  1.00E-03  1.00E-04  1.00E-05  Figure 4.9: Coal matrix permeability vs. mean random vitrinite reflectance of coal (coal rank)  79  Table 4.9: Comparison of isorank samples showing maceral effects on coal matrix permeability Sample # M1 M3 M39 M2 M12 M34 M10 M28 M9 M11 M33 M7 M27 M15 M13 M26 M29 M37 M41 M14 M30 M40 M4 M24 M42 M22 M23 M25 M8 M5 M31 M36 M21 M6 M32 M18 M19 M17 M16 M38 M20 M35  Matrix permeability (md) 2.46∙10-4 1.39∙10-3 1.97∙10-3 6.36∙10-3 7.63∙10-4 2.40∙10-4 5.83∙10-5 5.15∙10-3 1.08∙10-3 1.49∙10-2 7.93∙10-4 2.44∙10-4 7.55∙10-4 6.38∙10-5 1.46∙10-5 2.90∙10-4 4.83∙10-3 6.79∙10-3 1.20∙10-3 8.01∙10-4 3.74∙10-4 5.96∙10-3 7.18∙10-5 4.92∙10-4 2.83∙10-3 2.97∙10-3 5.21∙10-3 1.31∙10-3 3.39∙10-4 2.11∙10-3 3.03∙10-3 2.47∙10-3 2.47∙10-4 2.90∙10-4 7.60∙10-3 7.66∙10-3 5.41∙10-4 6.78∙10-3 3.96∙10-4 2.64∙10-4 1.15∙10-4 1.79∙10-2  % Vitrinite  % Inertinite  84 98 89 98 95 96 87 96 93 96 85 99 98 98 98 98 98 84 97 98 98 97 90 97 86 97 96 95 91 87 78 79 99 94 65 85 96 87 91 91 89 92  8 2 10 1 4 3 10 4 6 4 14 1 2 2 2 2 2 15 3 2 2 3 8 3 11 3 4 5 9 13 22 20 1 5 31 14 3 13 9 9 10 7  % Mineral matter 8 0 0 1 2 0 2 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 3 0 0 0 0 0 0 1 0 1 3 1 1 0 0 0 1 0  Coal rank Lignite/Subbituminous C Subbituminous B Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A Subbituminous A High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous C High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous B High Volatile Bituminous A High Volatile Bituminous A Medium Volatile Bituminous  80  4.8.3. Coal plug permeability Permeability of coal plugs was determined by pulse decay permeametry with helium, nitrogen and methane employed as probe gases. Water was used as a lubricant in drilling coal plugs from coal cores as air drilling of coals did not yield useful plugs. Visual observation of the plugs were carried out in order to account for and describe any visible mineralization, fractures, cleats and other fabric present on the coal plug. A total of twenty nine samples were tested for this portion of the research project and the permeability data obtained was corrected for adsorption in the case where the probe gas used is adsorbed onto coal (i.e. in the case of methane and nitrogen gases). Figure 4.10 shows a plot of permeability versus effective stress for all samples at all effective stress levels. As evident from figure 4.10, there is no clear overall trend observed between effective stress and coal plug permeability however, examination of individual coal plugs tested over a range of effective stress levels show exponential decline in plug permeability with increasing effective stress. Results showing permeability decrease with increasing effective stress for select individual coal plugs are presented in figures 4.11 through 4.16.  81  Effective stress (psi) 0  500  1000  1500  2000  2500  3000  3500  Coal plug permeability (md)  9.00E-01 9.00E-02 9.00E-03 9.00E-04 9.00E-05  9.00E-06 9.00E-07 9.00E-08 9.00E-09  Figure 4.10: All coal plug samples tested at all effective stresses The degree of the exponential decrease in coal plug permeability with increasing effective stress (as shown in figures 4.11-4.16) ranges from fair (figure 4.14, R2 value of 0.45) to very strong (figure 4.12, R2 value of 0.96). Other samples (figures 4.11, 4.13, 4.15 and, 4.16) have R2 values in the 0.75-0.78 range, which shows a reasonable level of correlation between increasing effective stress and decreasing coal plug permeability. The trend of decreasing coal permeability with increase effective stress observed in the present study has been described and reported in the literature by several authors including Somerton et al. (1975), Harpalani and McPherson (1984), McKee et al. (1988), Siriwardane et al. (2009), Pini et al. (2009), Liu et al. (2010), Pan et al. (2010), etc. The reason for declining coal plug permeability with increasing effective stress is the shrinkage of the coal matrix under progressively greater effective stress which results in closure of cleats, fractures and other coal permeability pathways which were hitherto open and allowed gas passage at lower effective stresses. This reasoning has been 82  argued by different authors in the field (e.g., Weller, 1959; Somerton et al., 1975; Bustin, 1997; Siriwardane et al., 2009; Pan et al., 2010, etc). Relationships between coal plug permeability and fracture height (fracture height as estimated in the current study is depicted in figure 4.17) were examined. No overall trend is observed between fracture height and coal plug permeability (figure 4.18). The magnitude of coal fractures does not affect coal permeability except when the fractures or cleats are sufficiently large enough to be interconnected and consequently enhance gas movement in the coals thereby resulting in higher permeability (e.g., Somerton et al., 1975; Huy et al., 2010, etc).  Effective stress (psi) 0  500  1000  1500  2000  2500  3000  3500  Permeability (md)  1.00E+00  1.00E-01 R² = 0.7827  1.00E-02  1.00E-03  Figure 4.11: EEC sample  83  Effective pressure (psi) 0  500  1000  1500  2000  2500  3000  Permeability (md)  1.00E+00  1.00E-01 R² = 0.9606  1.00E-02  Figure 4.12: Leyejn sample  Effective stress (psi) 0  500  1000  1500  2000  2500  Permeability (md)  1.00E-05  1.00E-06  R² = 0.7485  1.00E-07  1.00E-08  Figure 4.13: 9R sample  84  Effective stress (psi) 1000  1200  1400  1600  1800  2000  2200  2400  2600  2800  Permeability (md)  1.00E+00  1.00E-01  R² = 0.4445  1.00E-02  Figure 4.14: HW sample  0  500  Effective stress (psi)  1000  1500  2000  2500  3000  Permeability (md)  1.00E+00  R² = 0.7652 1.00E-01  1.00E-02  Figure 4.15: Leye prop 85  6.00E-01  Permeability (md)  5.00E-01 4.00E-01 3.00E-01 R² = 0.7651  2.00E-01 1.00E-01 0.00E+00  0  500  1000  1500  2000  2500  3000  Effective stress (psi) Figure 4.16: NR#7 sample  Figure 4.17: Fracture height definition  86  Fracture height (mm) 0  5  10  15  20  25  30  35  40  Permeability (md)  1.00E+00  1.00E-01  1.00E-02  1.00E-03  1.00E-04  1.00E-05  Figure 4.18: Coal permeability vs. fracture height  Table 4.10: Comparison of permeability obtained from different gases Test Probe Gas Permeability (md) Test 1  Helium  0.88  Test 2  Nitrogen  0.58  Test 3  Methane  0.84  Test 4  Methane  1.06  Test 5  Nitrogen  0.84  Test 6  Helium  1.29  Test 7  Nitrogen  0.72  Test 8  Methane  0.87  Test 9  Helium  0.94  Results of investigations into the effects of probe gas specie on measured coal plug permeability are presented in table 4.10. Previous studies (for example, Van Bergen et al., 2009; Pan et al., 2010; Siriwardane et al., 2010; etc) have reported that there are differences in 87  measured coal permeability when various gases are used. In the present study, the gases used to test this premise are helium, nitrogen and methane. In order to investigate the effect of probe gas specie on measured coal plug permeability, a sample of coal was selected and multiple tests were run in sequence using the gases helium, nitrogen and methane in different orders to investigate the effects of gas type and exposure order to coal. Furthermore, the selected sample was kept at constant effective stress of 500 psi (3447.38 KPa) throughout the various experimental sequences in order to ensure that only the effects of probe gas type on measured permeability was being determined. From table 4.10, it is seen that permeability of coal measured with helium gas is higher than that measured with either nitrogen or methane irrespective of the order in which the gases are tested. Higher coal permeability with helium gas is attributed to the small size of the helium molecule (molecular diameter of 2.6∙10-10 m) which allows it to flow through permeability pathways unavailable to the larger molecules of nitrogen (3.7∙10-10 m) and methane (3.8∙10-10 m) respectively. Helium also does not cause swelling of coal and therefore, the permeability measured with helium is assumed to be more representative for the tested coal. The lowest permeability is obtained when nitrogen is used as the test gas. This may be due to the size of the nitrogen molecule and its interaction with coal. Nitrogen results in less coal swelling than methane (Rodrigues and Lemos de Sousa, 2002). Consequently, hitherto closed permeability pathways present in coal are not opened up by nitrogen induced coal swelling. Rather, the slight swelling of coal caused by nitrogen results in closure of some previously opened flow paths thus resulting in the low permeability values measured on the tested coal with nitrogen gas. The molecular size of nitrogen (3.7∙10-10 m) is also very similar to the molecular size of methane (3.8∙10-10 m) and as such, even the smaller size of the nitrogen 88  molecule does not compensate for the blockage of previously opened flow paths brought about by the slight coal swelling induced by nitrogen. Permeability measured with methane is lower than permeability measured with helium gas but higher than the permeability measured with nitrogen in all instances as seen from table 4.10. This may be attributed to the swelling of coal caused by methane which would lead to the opening up of some previously closed coal permeability pathways. Rodrigues and Lemos de Sousa (2002) have reported that methane causes irreversible swelling of coals which increases coal volume and this coal volume increase, and the associated opening up of hitherto closed coal permeability pathways it causes, perhaps explains the higher permeability measured with methane gas. Pan et al. (2010) report from their investigations on Australian coals that permeability measured using methane is lower than permeability measured using helium. They attribute this finding partly to the Klinkenberg effect and partly due to swelling of coal caused by interaction of coal with methane which leads to reduction in open flow pathways especially when the coal is confined. The findings of Pan et al. (2010) showing that helium coal permeability is higher than methane coal permeability are validated by results of the current study. Further work on the effects of various probe gases (especially methane and nitrogen) on coal permeability are required to conclusively prove why there are differences in measured permeability on the same coal sample when different probe gases are utilized.  89  5.9  Conclusions Vitrinite-rich subbituminous to medium volatile bituminous coals from the Horseshoe  Canyon and Mannville formations of the Western Canada Sedimentary Basin have been studied in order to characterize their diffusivity and permeability. Both crushed coals and solid coal plugs were used to investigate coal diffusivity, matrix permeability and coal plug permeability. Average diffusivity of crushed coals is on the order of 10-11 m2/s to 10-12 m2/s, permeability of crushed coals was found to be between 7.18∙10-5 md to 1.79∙10-2 md and coal plug permeability was up to 0.09 md. The difference of up to four orders of magnitude between crushed coal permeability and coal plug permeability is the result of permeability enhancement by fractures present in coal plugs. Coal plug permeability declined exponentially with increasing effective stress and this exponential permeability decline is attributed to coal matrix compression and resulting closure of coal permeability pathways (fractures and cleats) at high effective stresses. No relationship was observed between fracture height and coal plug permeability. The reason for this lack of relationship is because interconnectivity of coal cleats and fractures not coal fracture magnitude (in this case, cleat height) is responsible for coal permeability enhancements even at high effective stress levels. Greater coal inertinite content enhances coal diffusivity and coal matrix permeability measured on crushed coals while higher coal vitrinite content adversely affects coal diffusivity and crushed coal permeability. The increase in coal matrix permeability and coal diffusivity observed in inertinite-rich coals is a result of the greater proportion of macro- and meso-pores which are present in inertinite and which consequently result in higher crushed coal diffusivity and permeability in inertinite-rich coals versus their vitrinite-rich counterparts. No trends are observed between coal rank and crushed coal permeability or coal diffusivity perhaps as a 90  result of the narrow rank range of the coals studied. Crushed coal permeability is determined at atmospheric pressure therefore this parameter is not indicative of in-seam conditions however it gives an indication of coal matrix permeability and is useful for comparative purposes. The impact of probe gas type on coal plug permeability was also investigated and helium permeability measurements were generally higher than plug permeability determined with methane and nitrogen. This disparity in permeability is attributed to a combination of different probe gas molecule size, relative swelling effects of probe gas on coal and associated changes at in-situ stress during tests. Knowledge of coal permeability and its relationship with coal fabric would help in more focused exploration for and exploitation of CBM resources in a basin as this knowledge could help locate production sweet spots.  91  5 CONCLUSIONS AND FUTURE WORK 5.1.  Conclusions  The porosity, methane sorption characteristics, diffusivity and permeability of vitriniterich coals from the Horseshoe Canyon and Mannville formations of the Western Canada Sedimentary Basin in Alberta have been investigated. The effects of coal properties (coal rank, coal maceral composition) and test methods and conditions (effective stress, probe gas type) on these characteristics were studied and from this work, the following conclusions can be drawn: 1)  Crushed coal samples provide a means of comparative assessment for  coal micro characteristics such as coal matrix diffusivity, matrix permeability and gas sorption capacity while coal plugs provide a means of assessing reservoir characteristics such as permeability and transmissivity of the gas stored within coal matrix. 2)  Total porosity of the studied coals range from 7% to 18% as estimated  from helium pycnometry while mercury porosimetry yielded porosity of between 4% and 10% for the same coals. The difference in estimated coal porosity using helium and mercury indicate that coals have significant microporosity accessible to the smaller helium molecule but which is inaccessible to mercury as a result of its larger kinetic diameter. The higher surface tension of mercury also contributes to the lower coal porosity estimates obtained from mercury porosimetry. 3)  Total pore area of the examined coals range from 12.08 m2/g to 49.04  m2/g as estimated from mercury porosimetry. The data indicates that there is an increase in total coal pore area with increasing vitrinite content. This increase in total pore area with higher vitrinite content is due to the abundant microporosity of vitrinite. 92  4)  Langmuir volume of the studied coals on a moisture equilibrated basis  ranged from 5.6 cc/g to 23.5 cc/g while coal Langmuir volume is between 9.8 cc/g to 40.4 cc/g for dry coals. The difference in estimated methane sorption capacity between moisture equilibrated and dry coals is due to the competition for available adsorption sites on coal between methane gas molecules and water molecules. 5)  No relationship exists between coal sorption capacity and coal rank.  Similarly there is no correlation between coal composition and coal methane sorption capacity (coal Langmuir volume) for moisture equilibrated coals. The lack of observable trends is attributed respectively to the narrow rank range and very similar maceral composition of the studied coals. 6)  Average diffusivity of crushed coals is on the order of 10-11 m2/s to 10-12  m2/s while permeability of crushed coals is between 7.18∙10-5 md to 1.79∙10-2 md whereas coal plug permeability is up to 0.09 md. 7)  Coal plug permeability declines exponentially with increasing effective  stress. This permeability decline is attributed to coal matrix compression and resulting closure of coal fractures and cleats at high effective stresses. 8)  There is no relationship between coal fracture height and coal plug  permeability. The reason for this lack of relationships between fracture height and coal plug permeability is because interconnectivity of cleats and fractures not fracture magnitude (in this case fracture height) is responsible for coal permeability enhancements even at high effective stress levels. 9)  Greater coal inertinite content enhances coal diffusivity and crushed coal  permeability while higher vitrinite content adversely affects coal diffusivity and crushed 93  coal permeability. The increase in coal diffusivity and crushed permeability observed in coals with higher inertinite is a result of the greater meso- and macro- porosity of inertinite. 10)  No relationship is observed between coal rank and crushed coal  permeability or coal diffusivity possibly as a result of the narrow rank range of the studied coals. 11)  Coal plug permeability measured using helium gas is generally higher  than plug permeability determined with methane and nitrogen. The disparity in permeability is attributed to a combination of different probe gas molecule size, relative swelling effects of probe gas on coal and associated changes at in-situ stress during tests.  5.2.  Future work  Further research is needed to determine if there is variability in crushed coal permeability with probe gas type. Permeability variation with various probe gases (helium, nitrogen and methane) was observed with coal plugs in this study. Further investigations on the reasons behind permeability variations with probe gas type on coal plugs is necessary in order to fully understand the causes and effects of various probe gases on coal permeability. Investigations of coal porosity and coal methane sorption capacity using coal samples from the Horseshoe Canyon and Mannville formations which span the entire rank interval from lignite to anthracite should be conducted as this will help to conclusively explore the relationships between coal rank and these coal properties. This investigation was started in the present study, albeit using coals of a narrower rank interval (lignite to medium volatile bituminous rank). Further investigations on coal permeability both on coal plugs and crushed 94  coals as well as crushed coal diffusivity using coals with very heterogeneous maceral compositions should be conducted especially with coals that have high liptinite content in order to study the effects of liptinite on fluid transport properties of coals. 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L., 1984: Diffusion models for gas production from coal: determination of diffusion parameters; Fuel, vol. 63, pg. 256- 261 Soeder, D. J., 1990: Applications of fluorescence microscopy to study of pores in tight rocks; AAPG bulletin, vol. 74, pg. 30-40 Somerton, W. H., Soylemezoglu, I. M. and Dudley, R. C., 1975: Effect of stress on permeability of coal; International journal of rock mechanics and mining sciences & geomechanics abstracts vol. 12, pg. 129-145  102  Song, C., Saini, A. K. and Schobert, H. H., 1994: Effects of drying and oxidation of Wyodak Subbituminous coal on its thermal and catalytic liquefaction. Spectroscopic characterization and products distribution; Energy & fuels, vol. 8, pg. 301-312 Spitzer, Z., 1981: Mercury porosimetry and its application to the analysis of coal pore structure; Powder technology, vol. 29, pg. 177-186 Stach, E., Mackowsky, M.-Th., Teichmuller, M., Taylor, G. H., Chandra, D. and Teichmuller, R., 1982: Stach’s textbook of coal petrology, 3rd edition. Gebruder Borntraeger, 535pp. Stoeckli, H. F., 1995: Characterization of microporous carbons by adsorption and immersion techniques in Patrick, J. W. (editor), Porosity in carbons; characterization and applications; Halsted press, New York, 331pp. Suuberg, E. M., Otake, Y., Yun, Y. and Deevi, S. C., 1993: Role of moisture in coal structure and the effects of drying upon the accessibility of coal structure; Energy & fuels, vol. 7, pg. 384-392 Thomas, J., and Damberger, H. H., 1976: Internal surface area, moisture content and porosity of Illinois coals: variations with coal rank; Illinois state geological survey circular 493, 38pp. Ting, F. T. C., 1977: Origin and spacing of cleats in coal beds; Journal of pressure vessel technology, Transactions of the ASME, vol. 99, pg. 624-626 Toda, Y. and Toyoda, S., 1972: Application of mercury porosimetry to coal; Fuel, vol. 51, pg. 199-201 Tricker, M. J., Grint, A., Audley, G. J., Church, S. M., Rainey, V. S. and Wright, C. J., 1983: Application of small-angle neutron scattering (SANS) to the study of coal porosity; Fuel vol. 62, pg. 1092-1096 Trimmer, D., 1982: Laboratory measurements of ultralow permeability of geologic materials; Review of scientific instruments, vol. 53, pg. 1246-1254 United States Energy Information Administration’s International energy outlook 2010 retrieved from: http://www.eia.doe.gov/oiaf/ieo/highlights.html Van Bergen, F., Spiers, C., Floor, G. and Bots, P., 2009: Strain development in unconfined coals exposed to CO2, CH4 and Ar: Effect of moisture; International journal of coal geology, vol. 77, pg. 43-53 Walker Jr., P. L., 1981: Microporosity in coal: its characterization and its implications for coal utilization; Philosophical transactions of the royal society of London. Series A, vol. 300, #1453, pg. 65-81  103  Walls, J. D., 1982: Effects on pore pressure, confining pressure and partial saturation on permeability of sandstones; Unpublished Ph.D. dissertation submitted to Stanford University, USA, Oct. 1982, 112 pp. Webb, P. A., 2001: Volume and density determinations for particle technologists; Micromeritics instrument corp., 16pgs. Weller, J. M., 1959: Compaction of sediments, AAPG Bulletin, vol. 43, pg. 273-306 Yang, R. T. and Saunders, J. T., 1985: Adsorption of gases on coals and heat-treated coals at elevated temperature and pressure: 1. Adsorption from hydrogen and methane as single gases; Fuel, vol. 64, pg. 616-620 Yee, D., Seidle, J. P. and Hanson, W. B., 1993: Gas sorption on coal and measurement of gas content in B.E. Law and D. D. Rice (editors), Hydrocarbons from coal: AAPG Studies in geology #38, pg. 203-218 Zulkarnain, I., 2005: Simulation study of the effect of well spacing, effect of permeability anisotropy and effect of Palmer and Mansoori model on coalbed methane production; Unpublished M.Sc. thesis submitted to Texas A and M University, USA, Dec. 2005, 120pp.  104  APPENDICES  105  Appendix 1: Mercury porosimetry traces  106  Sample S1 Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  25 R² = 0.9267  20  15  10  5  0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1  1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S2 107  Intrusion pressure vs. Cumulative pore area 40  Cumulative pore area (m2/g)  35 30  R² = 0.9197  25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  108  Sample S3 Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  25  20 R² = 0.9321 15  10  5  0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  109  Sample S4 Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  35 30 R² = 0.9228 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000  10000 1000 100 10 1  1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S5 110  Intrusion pressure vs. Cumulative pore area 40  Cumulative pore area (m2/g)  35 R² = 0.9261  30 25 20 15 10  5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  111  Sample S6 Intrusion pressure vs. Cumulative pore area 40 Cumulative pore area (m2/g)  35 R² = 0.9243  30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Itrusion pressure (psi)  112  Sample S7 Intrusion pressure vs. Cumulative pore area 50  Cumulative pore area (m2/g)  45 40 R² = 0.9199  35 30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  113  Sample S8 Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  25 R² = 0.9327  20  15  10  5  0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S9 114  Intrusion pressure vs. Cumulative pore area 30  Cumulative pore area (m2/g)  25 R² = 0.9334 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diamtre (nm)  100000 10000 1000 100 10  1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  115  Sample S10 Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  35 30 R² = 0.9313 25 20 15 10 5 0 0  10000  20000  30000 40000 50000 Intrusion pressure (psia)  60000  70000  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  116  Sample S11 Intrusion pressure vs. Cumulative pore area 40  Cumulative pore area (m2/g)  35 R² = 0.9653  30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S12 117  Intrusion pressure vs. Cumulative pore area 40  Cumulative pore area (m2/g)  35 R² = 0.9252  30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  118  Sample S13 Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  40 35 R² = 0.9233 30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S14 119  Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  40 35 R² = 0.9135 30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10  1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S15  120  Intrusion pressure vs. Cumulative pore area 45  Cumulative pore area (m2/g)  40 R² = 0.9307  35 30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S16 121  Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  25 R² = 0.9536  20  15  10  5  0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S17  122  Intrusion pressure vs. Cumulative pore area 18  Cumulative pore area (m2/g)  16 R² = 0.9471 14 12 10  8 6 4 2 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S18  123  Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  30 25 R² = 0.9163 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000  10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  124  Sample S19 Intrusion pressure vs. Cumulative pore area 35  Cumulative pore area (m2/g)  30 R² = 0.9373  25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S20 125  Intrusion pressure vs. Cumulative pore area 14 R² = 0.94 Cumulative pore area (m2/g)  12 10 8 6  4 2 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S21  126  Intrusion pressure vs. Cumulative pore area 40 Cumulative pore area (m2/g)  35 R² = 0.9475  30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S22  127  Intrusion pressure vs. Cumulative pore area 14  Cumulative pore area (m2/g)  12  R² = 0.9359  10 8 6 4 2 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S23  128  Intrusion pressure vs. Cumulative pore area 35  Cumulative pore area (m2/g)  30 R² = 0.9462 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S24  129  Intrusion pressure vs. Cumulative pore area 40  Cumulative pore area (m2/g)  35 R² = 0.9267  30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  130  Sample S25 Intrusion pressure vs. Cumulative pore area 14 R² = 0.9686  Cumulative pore area(m2/g)  12 10 8  6 4 2 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  131  Sample S26 Intrusion pressure vs. Cumulative pore area 35  Cumulative pore area (m2/g)  30 R² = 0.9402  25 20  15 10 5 0 0  10000  20000  30000 40000 Intrusion pressure (psia)  50000  60000  70000  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S27 132  Intrusion pressure vs. Cumulative pore area 35  Cumulative pore area (m2/g)  30 R² = 0.926 25 20 15  10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10  1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S28  133  Intrusion pressure vs. Cumulative pore area 25  Cumulative pore area (m2/g)  20 R² = 0.9436 15  10  5  0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Mean pore diametre vs. Intrusion pressure  Mean pore diametre (nm)  1000000 100000 10000  1000 100 10 1 1  10  100 1000 Intrusion pressure (psi)  10000  100000  Sample S29  134  Intrusion pressure vs. Cumulative pore area 30 R² = 0.9351  Cumulative pore area (m2/g)  25  20 15 10 5 0 0  10000  20000  30000 40000 Intrusion pressure (psia)  50000  60000  70000  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (nm)  1000000 100000 10000 1000 100 10  1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S30  135  Intrusion pressure vs. Cumulative pore area 45 Cumulative pore area (m2/g)  40 R² = 0.9197  35 30 25 20 15 10 5 0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre 1000000  Mean pore diametre (nm)  100000 10000 1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S31  136  Intrusion pressure vs. Cumulative pore area 45 40 Cumulative pore area (m2/g)  R² = 0.9165 35 30 25 20 15  10 5  0 0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametre (psi)  1000000 100000 10000  1000 100 10 1 1  10  100  1000  10000  100000  Intrusion pressure (psi)  Sample S32  137  Intrusion pressure vs. Cumulative pore area  Cumulative pore area (m2/g)  60 50 R² = 0.9357 40 30  20 10 0  0  10000  20000  30000  40000  50000  60000  70000  Intrusion pressure (psia)  Intrusion pressure vs. Mean pore diametre  Mean pore diametere (nm)  1000000 100000 10000 1000 100  10 1 1  10  100 1000 Intrusion pressure (Psi)  10000  100000  138  Appendix 2: Methane adsorption isotherms  139  Sample S1  140  Sample S2  141  Sample S3  142  Sample S4  143  Sample S5  144  Sample S6  145  Sample S7  146  Sample S8  147  Sample S9  148  Sample S10  149  Sample S11  150  Sample S12  151  Sample S13  152  Sample S14  153  Sample S15  154  Sample S16  155  Sample S17  156  Sample S18  157  Sample S19  158  Sample S20  159  Sample S21  160  Sample S22  161  Sample S23  162  Sample S24  163  Sample S25  164  Sample S26  165  Sample S27  166  Sample S28  167  Sample S29  168  Sample S30  169  Sample S31  170  Sample S32  171  

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