EXPERIMENTAL INVESTIGATION OF ENHANCED COAL BED METHANE RECOVERY

Transcription

1 EXPERIMENTAL INVESTIGATION OF ENHANCED COAL BED METHANE RECOVERY A REPORT SUBMITTED TO THE DEPARTMENT OF PETROLEUM ENGINEERING OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE By Sameer Parakh July 2007

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3 I certify that I have read this report and that in my opinion it is fully adequate, in scope and in quality, as partial fulfillment of the degree of Master of Science in Petroleum Engineering. Prof. Margot Gerritsen (Principal Advisor) iii

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5 Abstract Enhanced coal bed methane recovery involves simultaneous adsorption-desorption, diffusion and convection phenomena in the coal beds which can structurally be divided into matrix and cleats. This complex mechanism in a one-dimensional system is described by a non-linear, hyperbolic differential equation. Extensive work has been performed to solve the system analytically by method of characteristics. Solutions for binary, ternary and quaternary mixtures consisting of single and two-phase systems show the effects of component adsorption, volatility and injection gas composition on the solution profiles. This thesis presents a systematic approach of conducting experiments for performing onedimensional slim tube displacement for enhanced coal bed methane recovery. The purposes of the experimental studies are to understand the reservoir mechanisms of CO 2 and N 2 injection into coal beds, demonstrate the practical effectiveness of the ECBM and sequestration processes and the engineering capability to simulate them, and to validate the analytical results and conclusions. Single phase experiments are first conducted to investigate methane recovery by injection of pure and mixed gases. A tracer test is then conducted with non-adsorbing gases to find the dispersion coefficient of gases in coal tube. The result is useful to perform numerical simulations for the single phase systems. Two-phase investigations are further performed to validate the analytical results for different injection gas compositions. The experimental results are in good agreement with the analytical solutions. The calculation of dispersion coefficient is validated by both experimental and theoretical models and its application in the numerical simulation drives the spatially and temporally refined solutions to match with the dispersed experimental results. Two-phase v

6 experiments confirm the analytical theory for saturated and under-saturated systems and also show the presence of a degenerate shock in the solution profile for mixture injection. vi

7 Acknowledgments I am highly indebted to my advisors Prof. Lynn Orr and Prof. Margot Gerritsen for their role as an excellent guide during my graduate studies at Stanford University. The unique experience of working with two experts in the fields of analytical and computational modeling was highly rewarding during my research work. I would like to thank them for their encouragement and patience shown to me for doing challenging experiments. I would also like to thank Prof. Anthony R. Kovscek for helping me design my experimental setup and for his constant technical support. I am thankful to Dr. Tom Tang, Dr. Louis Castanier, and Aldo Rossi for helping me build my experimental setup. I would also like to acknowledge the support of Mohamed Hassam from CMG for helping me build the simulation model. I would like to thank the SUPRI-C group for financially supporting my graduate study and research. A special thanks to all the colleagues in the department for making my stay at Stanford a memorable one. Finally, I would like to thank my grandparents, my parents and my sisters who have been a constant source of inspiration for me. vii

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9 Table of Contents Abstract v Acknowledgments... vii Table of Contents... ix List of Tables... xi List of Figures...xiii 1. Introduction Current usage and energy recovery statistics of coal Technology in energy recovery from coal: Enhanced Coal Bed Methane Recovery CO 2 sequestration and ECBM Analytical modeling for enhanced coal bed methane recovery Theory of ECBM Recovery Flow characteristics in coal The physics of coal bed methane recovery Physics of the enhanced coal bed methane recovery process Experimental Design Study of coal characteristics Slim tube configuration Flow rate determination Single phase experiments Binary displacement Determination of dispersion coefficient Ternary displacement with mixture injection Two-phase experiments Ternary displacement with pure CO 2 injection Quaternary displacement with mixture injection One-dimensional numerical simulation Operating Procedure Results, Discussion and Material Balance Results for pure CO 2 injection for methane displacement Results for pure N 2 injection for methane displacement ix

10 5.3. Results for dispersion experiment Results for methane displacement by injection of a mixture of N 2 and CO Comparison of the single phase experiments with different injection gases Results for displacement of water and methane by pure CO 2 injection Results for displacement of water and methane by mixture injection Effects of saturated and under saturated initial conditions and comparison with analytical solutions Numerical study of ECBM recovery Simulation of methane displacement by pure CO Simulation of methane displacement by pure N Simulation of methane displacement by mixture of CO 2 and N Conclusions Nomenclature.65 References..68 Appendix A. Individual Components of Experimental Setup B. Porosity Measurement Data C. Permeability Measurement Data D. Simulation Data File x

11 List of Tables Table 3-1: Operating conditions for single phase experiments Table 3-2: Analytical vs realistic K values (Seto, 2007) Table 3-3: Operating conditions for two-phase experiments Table 4-1: Method setup for running sequences in the GC Table 5-1: Material balance calculations for pure CO 2 injection Table 5-2: Material balance calculations for N 2 injection Table 5-3: Material balance calculations for mixture injection in single phase system Table 5-4: Material balance calculations for water injection in methane saturated coal.. 51 Table 5-5: Material balance for mixture injection in water + methane saturated coal Table 5-6: Material balance for CO 2 capture in saturated and under-saturated systems Table 5-7: Discretization parameters for dispersion experiment Table 5-8: Discretization parameters for pure CO 2 injection in methane saturated coal.. 59 Table 5-9: Discretization parameters for pure N 2 injection in methane saturated coal Table 5-10: Discretization parameters for mixture injection in methane saturated coal.. 60 Table B: Porosity measurement data Table C: Permeability measurement data xi

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13 List of Figures Figure 1-1: Coal resources in the continental United States (Britannica)... 2 Figure 1-2: Fractions of methane production from various coal basins in the US (Smith, 2003)... 3 Figure 1-3: Schematic of Enhanced Coal Bed Methane Recovery project (Seto, 2007)... 4 Figure 2-1: Adsorption-desorption isotherm for gases on coal (Tang. et al. 2005) Figure 2-2: Relative permeability curves for gas-water system in coal packing (Chaturvedi, 2006) Figure 3-1: Powder River Basin coal in raw (a) and crushed (b) forms Figure 3-2: Coal particles at 20X (a) and 50X (b) magnification Figure 3-3: Single particles at 50X magnification Figure 3-4: Effect of injection velocity on residual trapping (Hill, 1949) Figure 3-5: Analytical results for injection of mixture of CO 2 and N 2 (50-50) for methane displacement (Zhu, 2003) Figure 3-6: Schematic diagram of experimental setup for the single phase systems Figure 3-7: Schematic diagram of the experimental setup for the two phase systems Figure 3-8: Analytical results for injection of mixture of CO 2 and N 2 (60:40) for twophase displacement (Seto, 2007) Figure 4-1: Gas cylindrical bomb (a) and pressure gauge (b) Figure 4-2: Methane injection in coal tube Figure 5-1: Total production rate for pure CO 2 injection Figure 5-2: Composition profile at tube outlet for pure CO 2 injection Figure 5-3: Component molar rates for pure CO 2 injection Figure 5-4: Cumulative moles produced for pure CO 2 injection Figure 5-5: Fractional molar recovery of methane for pure CO 2 injection Figure 5-6: Comparison of composition profiles of experimental (a) and analytical (b) solutions for pure CO 2 injection Figure 5-7: Total production rate for pure N 2 injection xiii

14 Figure 5-8: Composition profile at tube outlet for pure N 2 injection Figure 5-9: Component molar rates for pure N 2 injection Figure 5-10: Cumulative moles produced for pure N 2 injection Figure 5-11: Methane recovery for pure N 2 injection Figure 5-12: Comparison of composition profiles of experimental (a) and analytical (b) solutions for pure N 2 injection Figure 5-13: Helium fraction in the produced gas Figure 5-14: Measurement of dispersion coefficient Figure 5-15: Composition profiles for CO 2, N 2 and methane for mixture injection Figure 5-16: Total production rate for mixture injection in single phase system Figure 5-17: Production profiles for mixture injection Figure 5-18: Methane recovery for mixture injection in single phase system Figure 5-19: Comparison of composition profiles of experimental (a) and analytical (b) solutions for mixture injection in single phase systems Figure 5-20: Experimental results for Methane recovery by different injection gases Figure 5-21: Experimental results for total production rate with different injection gases Figure 5-22: Experimental results for methane production rate by different injection gases Figure 5-23: Composition profile for CO 2 injection in coal with methane and water saturation Figure 5-24: Fractional water production for CO 2 injection in methane and water saturated coal Figure 5-25: Comparison of experimental (a) and analytical (b) results for pure CO 2 injection in water + methane saturated system Figure 5-26: Injection and production profiles for water injection Figure 5-27: Production profiles for water injection in methane saturated coal Figure 5-28: Composition profile of exit gases for mixture injection Figure 5-29: Injection and production profiles Figure 5-30: Water and methane recovery for mixture injection in two-phase system xiv

15 Figure 5-31: Comparison of experimental (a) and analytical (b) results for mixture injection in water + methane saturated system Figure 5-32: Comparison of experimental (a) and analytical (b) solutions for saturated and under-saturated systems Figure 5-33: Composition profiles of CO 2 in saturated and undersaturated systems Figure 5-34: Convergence test for dispersion experiment Figure 5-35: Effect of increasing the numerical diffusion Figure 5-36: Composition profile for dispersion experiment Figure 5-37: Simulation and experimental comparisons for pure CO 2 injection Figure 5-38: Simulation and experimental comparisons for pure N 2 injection Figure 5-39: Simulation and experimental comparisons for mixture injection Figure A-1: Gas Chromatograph Figure A-2: Schematic of the valve and column configuration inside the GC Figure A-3: Overall setup for single phase experiments Figure A: The different pieces of the experimental setup xv

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17 Chapter 1 1. Introduction In reservoir engineering terms, coal beds are naturally fractured, low-pressure, watersaturated reservoirs, where most of the gas is retained in the micro-pore structure of the coal by physical adsorption. A reservoir is that portion of the coal seam that contains gas and water as a connected system. Thus coal serves as a reservoir and a source rock, containing relatively pure methane. The mechanisms governed by coupled convective, adsorptive and dispersive phenomena in coal are currently being studied for enhanced recovery of methane from coal as well as from CO 2 sequestration point of view. Analytical modeling and numerical simulations have been performed for one-dimensional transport of single phase (Zhu, 2003) and multi-phase (Seto, 2007) multi-component mixtures in coal, utilizing the method of characteristics solutions for non-linear hyperbolic equations, as outlined in Orr (2007). Analytical solutions to convection dominated displacements provide insight into the interplay of flow, phase behavior and sorption in ECBM processes. It shows that adsorption of CO 2 onto the coal reduces the propagation velocity of the CO 2 front, delaying breakthrough time of CO 2 at the production well thereby allowing for more CO 2 to be sequestered per amount of methane produced. The study also concludes that if pure CO 2 is injected, pure methane is produced until breakthrough of the injected CO 2. Displacement of methane by N 2 occurs via a partial pressure reduction. Volume change as methane desorbs results in a faster recovery of methane, though the produced gas is now a mixture of N 2 and methane. Apart from these analytical models, laboratory experiments have also been performed in a coal pack for single phase flow studies by Tang, Jessen and Kovscek, reflecting many of the proposed analytical solutions. In practice, most of the coal beds are initially saturated with both methane and water, changing the flow regime from single phase to multi-phase flow and for which the analytical studies need validation and that is the prime motivation to continue the laboratory investigations for recovery of methane from coal under 1

18 saturated (mostly methane) and under-saturated (mostly water) conditions. The goal of this study is to generate a suite of laboratory data that probes the transport of multicomponent mixtures through coal. This is achieved by performing one-dimensional slim tube displacement experiments using different injection and initial conditions. The initial conditions consist of both saturated and under-saturated coal and various injection conditions consist of pure and mixed gas injections of CO 2 and N 2. This data suite is then useful for validation of the assumptions made in analytical modeling, the model itself and finally the results and conclusions from these models and solution methods. The data also provides useful information about the amount of CO 2 that can be trapped after performing these experiments and are therefore also useful for CO 2 sequestration processes Current usage and energy recovery statistics of coal In 1996, the Energy Information Agency (EIA) estimated the coal resources to a depth of 6000 ft in the US to be almost 60 trillion tons with about 90% or 54 trillion tons being unmineable. Coal has been mined to a depth of 3000 ft, below which is the zone of deep unmineable coal. This zone can be effectively utilized for methane production and/or CO 2 storage. Figure 1-1 provides a map of the major coal basins in the U.S. (lower 48 states). Figure 1-1: Coal resources in the continental United States (Britannica) 2

19 Coal bed gas is primarily composed of hydrocarbons from methane to butane. The absolute concentration of each hydrocarbon varies from coal to coal. However, methane is usually the major constituent (88-98 %) with the higher hydrocarbons and CO 2 present in smaller volumes. Marine shales are often found at the roof of coal beds. These shales serve as an excellent sealing material to prevent methane from migrating away from the coal seam as it accumulates in the coal. The coal beds hold both water and methane trapped inside the pores of the coal. There has been an active exploration for coal bed gas in the US due to the federal tax incentive for its production. Between 1986 and 1990 new gas well completions went from 400 to 1600 per year. Progress in Coal Bed Methane (CBM) technology, such as improved geological knowledge and well completion practices, led to more exploration and more efficient production. Improved drilling practices also played a major role in increased CBM production. The volume of methane available in the major coal basins in the US has been estimated by several sources. Gunter et al. (1997) estimated CBM resources in the US in the range of 275 to 650 TCF. The US CBM proved reserves for 2000 were estimated at 15.7 TCF out of which US CBM production for 2001 was 1.56 TCF. The distribution of CBM production between different parts of US for 2004 is shown in figure 1-2. Global CBM resources have been estimated to range from TCF. Figure 1-2: Fractions of methane production from various coal basins in the US (Smith, 2003) 3

20 1.2. Technology in energy recovery from coal: Enhanced Coal Bed Methane Recovery Primary recovery methods of methane by depressurization of coal beds yield only 30-40% of methane in place and generally produce large volume of water at the same time. By injecting gas in the reservoir, pressure can be maintained and a sustained recovery can be achieved (figure 1-3). Flue gases are easily available near coal fired power plants which can be injected to enhance the recovery of methane. Figure 1-3: Schematic of Enhanced Coal Bed Methane Recovery project (Seto, 2007) Every and Del Osso (1972) found that methane is effectively removed from crushed coal by flowing a stream of CO 2 at ambient temperature through the coal. Enhanced Coal Bed Methane (ECBM) recovery is defined as the process of injecting a gas or a mixture of gases into a coal seam with the purpose of enhancing the desorption of CBM and increasing the recovery of methane from the coal. Chaback et al. (1996) simulated the effects of injecting pure nitrogen, pure CO 2 and dry flue gas composed of 15% CO 2 and 85% N 2 on production as well as modeling primary production. They reported almost a 100% increase in the recovery of methane by injecting these gases with the production profile dependent on the composition of the injection gas. 4

21 Laboratory investigations have been performed by Tang et al. (2005) for flow of methane, CO 2 and N 2 in coal under the influence of adsorption. Adsorption-desorption isotherms for Powder River Basin coal were generated by conducting experiments on a one foot long coal pack. These experiments established preferential adsorption of CO 2 on coal over methane and methane over nitrogen. Porosity and permeability measurements were also done by helium expansion experiments. Recovery factors of more than 94 % of the original gas in place (OGIP) were reported. Also, another interesting outcome of this study was to show the ability of coal to separate N 2 from CO 2 owing to preferential adsorption of CO 2. Reproduction of binary behavior, for displacement of methane by pure CO 2 or pure N 2, was characterized as excellent. The dynamics of ternary system, in which methane was displaced by injecting mixtures of varying compositions of CO 2 and N 2, was predicted with less accuracy due to reasons owing to multi-component sorption and geomechanical effects from coal shrinkage and swelling. Experimental results for both dry and water saturated samples have been reported by Fulton et al. (1980). They concluded that a cyclic CO 2 injection - gas production technique was the most effective way of recovering the adsorbed methane from coal samples. Their work did not include the effects of injecting other gases like N 2 or mixed gases. The above experimental observations are the motivation to continue the research with further extensions to the work done by Tang et al. (2005) and Fulton et al. (1980). Laboratory investigations are extended from binary and ternary, single phase flow to multi-component, multi-phase flow CO 2 sequestration and ECBM Coal seam sequestration with simultaneous recovery of natural gas is a particularly appealing way of addressing the rise in atmospheric concentration of CO 2. This technology has the potential of offsetting the costs of capture, compression, transportation and storage of CO 2 by producing natural gas. Other options may include storage of CO 2 in active or depleted oil and gas fields through enhanced oil recovery (EOR), in deep 5

22 saline aquifers, gas-rich shales, methane hydrate formations, salt caverns, or in the ocean. Among the possible scenarios for long term storage of CO 2, those techniques that offer production of a by-product such as natural gas or petroleum are expected to be first commercially practiced sequestration technologies. Also, the deep, unmineable coal seams are convenient sinks because they are widespread and exist in many of the same areas as large fossil-fuel fired power plants. The observation that some coal bed gas can be high in CO 2 content is a particularly pertinent observation relative to the use of coal beds as a sequestration sink for CO 2. It has been shown by numerical modeling (Hesse et al., 2007) that in some instances CO 2 can safely remain in coal for geologically significant time periods. This storage may be affected as CO 2 can be transported away from coal by dissolution in water. Studies have also been done (Garduno et al., 2003) for storage of CO 2 in coal beds with high water salinity. Because the water salinity significantly reduces CO 2 solubility, sequestration in coal is favored. On the basis of the assumption that two moles of CO 2 are adsorbed onto coal for every mole of methane released, the global CO 2 storage capacity of coal beds was estimated to be 150 Giga tons of CO 2 (Smith et al. 2003). For low-rank coals, including lignite, the adsorption capacity for CO 2 may be as much as 10 times higher for CO 2 than methane. This report sheds light on the amount of CO 2 trapped in coal after performing ECBM experiments using a material balance of the participating components (Chapter 5) Analytical modeling for enhanced coal bed methane recovery The governing equations representing the transport of multi-phase multi-component mixture in coal beds are described by a system of nonlinear, hyperbolic and first-order differential algebraic equations under the assumptions of negligible capillary, diffusion, and dispersion effects. The Riemann problem, which is with the assumption of constant injection and initial conditions, can be solved analytically using the method of characteristic (MOC) as described in Orr (2007). The MOC solution leads to composition 6

23 paths composed of rarefactions (continuous solutions), shocks (discontinuous solutions) and/or zones of constant states which connect the initial and injection states. Analytical work was previously done to model polymer injection in Johansen and Winther (1989) but this work did not consider the volume change as components transferred between phases. Extensive work on analytical modeling of ECBM including volume change has been performed by both Zhu (2003) and Seto (2007). Their studies lead to the following important conclusions about the dynamics of multi-component injection and recovery in coal beds: Injection gas rich in N 2 leads to faster recovery of methane. A mixture of the two gases is produced at the outlet due to the presence of a rarefaction wave in the solution. The presence of the rarefaction is due to the injection gas being less adsorbing than the initial gas present in coal. Injection gas rich in CO 2 leads to a slower recovery of methane. As CO 2 is more adsorbing than methane, displacement of methane occurs through a shock and distinct banks of methane and CO 2 are produced. A decrease in local flow velocity occurs when CO 2 is adsorbed onto the coal surface. When mixtures of CO 2 and N 2 are injected into a coal bed, gas components are chromatographically separated based on relative adsorption strength and volatility. Displacement in under-saturated coal beds is slower than in saturated coals due to the additional volume change associated with a phase change shock. Thus, more CO 2 can be trapped in under-saturated conditions. In quaternary systems, if the adsorption and volatility of the initial gas in coal lies between those of the components of the injection gas mixture, a degenerate shock solution may be observed. This type of solution is found to appear for particular cases of injection gas composition richer in the more adsorbing component. 7

24 This report also throws light on the important findings of the analytical study by validating the above results by building experiments for binary, ternary and quaternary systems (sections 3.4 and 3.5). 8

25 Chapter 2 2. Theory of ECBM Recovery 2.1. Flow characteristics in coal Coal deposits are formed by rapid burial of organic and inorganic material called peat in sedimentary layers at depths ranging from few hundred feet to a depth of several thousand feet. A low oxygen environment is necessary for the coalification process to occur. Water present in peat is driven out by compaction caused by overburden, and material is converted into a sedimentary rock. Increase in pressure and temperature with increasing burial depth further compacts the system. Over a long period of time, these organic and inorganic materials are slowly converted to coal (Levine, 1993). The coalification process leads to physical and chemical changes in the subsurface and natural gas is generated as a by-product. Natural gas produced during this process ranges from 150 to 200 cm 3 per gram of coal, depending on the organic content of peat, temperature and pressure of burial and maturation time (Rice, 1993). The structure of coal bears a dual porosity character. It consists of a high permeability fracture network, formed by the inter-granular porosity, and a low permeability matrix, which is basically the intra-granular porosity. The majority of the gas is stored in the matrix (> 95%) in adsorbed state, while the fractures provide conduits for production by convection. Coals are classified according to their rank, which is a measure of thermal maturity and carbon content, with the higher rank coals being more mature with a higher carbon content. The main contribution to the convective flow in coal is from flow through the cleat spacing. The porosity and permeability in coal seams are direct functions of cleat spacing. Cleats are formed by matrix shrinkage (water loss) during the coalification process (Pollard and Aydin, 1988, Pollard and Fletcher, 2005) and their spacing is determined by 9

26 the overburden pressure, coal rank and composition. For any rank coal, cleat spacing decreases as bed thickness decreases. Higher rank coals have smaller cleat spacings than lower rank coals. Lignites have a cleat spacing close to 2 cm whereas different grades of bituminous coal have a wide range of cleat spacing varying from 0.25 cm in high volatile A-bituminous coal to 25 cm in the bituminous coal of Arkoma basin, Oklahoma (Close, 1993). Flow of gas from the matrix to the cleats is determined by the diffusion coefficient of the gas. The permeability of coal ranges from 2 md in Bowen basin, Australia coal to 1500 md in Green River, WY coal. Permeability is found to vary as gases adsorb onto and desorb from the coal surface (Lin, 2006). Gas adsorption and desorption from the matrix can cause swelling and shrinkage of the matrix respectively, thereby affecting the permeability The physics of coal bed methane recovery Coal exhibits dual porosity behavior in which gas is stored by sorption in the coal matrix and accounts for approximately 95-98% of the gas in the coal seam. The remaining gas is stored in the natural fracture, or cleats, either free or dissolved in water. Characterization of gas adsorption and desorption on different coals can be performed in laboratories. The relationship between the adsorbed gas concentration in the coal matrix and the free gas in the cleat is described in an adsorption isotherm. By reduction in pressure, gas desorbs from the matrix and diffuses to the cleat network from where it is produced by convective and/or dispersive flow. The diffusion process represents the flow of gas from an area of high concentration to an area of low concentration as described by Fick s Law. The free gas flow in cleat systems can be described by Darcy s Law. An extension to Darcy s Law is used in reservoirs with simultaneous flow of more than one fluid by considering the effective permeability of each flowing phase which is generally considered a function of the saturations. Thus, gas that is produced from coal is the result of desorption, diffusion and convection mechanisms. Two parameters play an important role in evaluating a CBM prospect: the total gas in place and reservoir gas deliverability. The total gas in place involves data obtained from a 10

27 variety of sources such as well logs, core testing and well/production testing. Volumetric and material balance calculations help in determining the total gas in place. Gas deliverability of a coal reservoir represents the ability of the reservoir to produce gas through a well or a system of wells with two-phase flow considerations. Wells produce significant quantities of water at the early stage, and once the drainage area of the coal well has been dewatered, water production becomes negligible. Because the gas is stored by sorption in the coal, a low bottom-hole pressure is required to recover a large amount of the original gas in place. The physical adsorption is reversed by lowering the partial pressure of adsorbed species. This is the first stage of primary depletion when water and some gas are produced. In this stage, gas and water flow at relatively constant rates until a pseudo steady state is reached. At the end of this stage, the well reaches its minimum bottom-hole pressure. A second stage begins at the pseudo steady state and is characterized by a decline in gas and water production rates. In this stage, water-relative permeability decreases, gas-relative permeability increases, and changes in gas desorption rates are observed. A third stage starts when the gas rate has peaked and water production is negligible. A mild gas production decline sets in and may be continued for years. This stage represents most of the economic life of a typical coal well. This whole process of primary recovery yields % recovery of the gas in place Physics of the Enhanced coal bed methane recovery process Gas injection methods have been employed in the petroleum industry as enhanced oil recovery techniques for a long time. ECBM recovery methods are a particular case of enhanced recovery by gas injection in which the liquid and gas phases consist of, respectively, water present initially in the cleats and methane and injected gases. The solid phase (coal) is also important as it determines the adsorption-desorption of gases and hence governs the mechanism of methane displacement. As injection proceeds, gas phase components dissolve in the liquid phase and liquid phase components vaporize in the gas phase depending on thermodynamic equilibrium. The liquid and vapor phases move under the head at flow velocities that depend on the relative permeabilities and viscosities. Multi-component mixtures can be modeled by the rigorous multicontact 11

28 miscible displacement via condensing and vaporizing gas drives as described in Orr (2007). ECBM production is a combination of the effects of adsorption-desorption, diffusion, convection and convective dispersion. Adsorption characteristics of injection gas influence the mechanism of methane displacement and hence the production profile. CO 2 has preferential adsorption on coal over methane as seen from figure 2-1. Figure 2-1: Adsorption-desorption isotherm for gases on coal (Tang. et al. 2005) When CO 2 is injected to displace methane, for every mole of methane desorbed, the number of moles of CO 2 getting adsorbed ranges from 2 to 10 depending on the rank of the coal. When N 2 is injected, desorption takes place by reduction in the partial pressure of methane. Gas injection helps in maintaining the reservoir pressure, so the production rates can be maintained for longer times and water production is also controlled, which helps in minimizing the adverse effects on the water table. ECBM recovery is controlled by a combination of gravity, capillary and viscous forces. The governing equations for the one-dimensional flow of gas into water saturated coal can be formulated under the assumptions of negligible hydrodynamic dispersion and molecular diffusion, negligible capillary and gravity effects and isothermal conditions. 12

29 The conservation equation for one-dimensional flow of N c components in N p phases with adsorption in porous media is written as N p φx ρ S j + (1 φ) ai + Adsorption ij j t j= 1 Accumulation N p x ρ u ij j j x j= 1 Convection = 0, i = 1.. N, c j = 1.. N p, (1) where φ is the porosity of the medium, x ij is the mole fraction of component i in phase j, j, S j, and u j are the molar density, saturation and local flow velocity of phase j respectively, and a i is the amount of component i adsorbed on per unit volume of coal. The latter is defined as a i ρ ρ V i r mi = Nc 1 + j= 1 B B j i p p j i, where p i is the partial pressure of component i, r is the mass density of coal bed, and V mi is the Langmuir constant at specified temperature B i for component i. Relative permeability functions for gas-water system on coal have been found experimentally by Chaturvedi (2006) and are shown in figure 2-2. Relative Permeability Krg Krw Water Saturation, Sw Figure 2-2: Relative permeability curves for gas-water system in coal packing (Chaturvedi, 2006) 13

30 Numerical methods can be used to solve these flow equations and the ECBM process can be simulated using commercial simulators. When using the standard first order upwind discretization for transport, numerical diffusion may overwhelm any physical diffusion present in the system. This may make it difficult to interpret the physics governing the transport and production profiles. To achieve sufficient accuracy, a high level of grid refinement is therefore required, which is generally computationally expensive for compositional systems. Analytical solutions for the equations with the aforementioned assumptions and under Riemann conditions can be useful in generating quick approximate solutions. The validity of the simplifying assumptions and consequently their conclusions can be investigated by performing laboratory experiments for onedimensional systems. Experiments also help in determining the feasibility of doing an ECBM process depending on the physical and thermodynamic properties of the initial system and the injection gas. The current work focuses on validating the analytical theory by conducting both the laboratory-scale experiments as well as numerical simulations for the multi-component, multi-phase flow for methane recovery from one-dimensional coal packs (sections ). 14

31 Chapter 3 3. Experimental Design The aim of the project is to design and conduct experiments in order to improve understanding of the governing mechanisms of enhanced coal bed methane recovery processes in one-dimensional systems. The experiments are also used to validate the simplifying assumptions made in the derivation of the analytical solutions for single and multi-phase multi-component systems given in Zhu (2003) and Seto (2007). The following sections describe the methodology of the experimental design Study of Coal Characteristics The coal used in the study is lignite quality coal from Powder River Basin, Wyoming (figure 3-1). It is ground into fine particles of size mesh and stored under vacuum to prevent its oxidation. Figure 3-1: Powder River Basin coal in raw (a) and crushed (b) forms The particle density of coal is measured to be 1466 kg/m 3. Because coal particles are compressible and adhesive, they show a wide range of size distribution as shown in figure

32 Figure 3-2: Coal particles at 20X (a) and 50X (b) magnification The crushed coal particles exhibit a dual porosity nature. The primary porosity is the void space between particles and the secondary porosity is the intra-granular porosity within the particles. A high magnification microscope image can capture the micro pores which form the secondary porosity in coal as shown in figure 3-3. Figure 3-3: Single particles at 50X magnification The adsorption and desorption characteristics of the coal was previously studied by Tang et al. (2005), and are reported to follow the Langmuir isotherm curve shown in figure 2-1. The coal surface is micro porous and it exhibits diffusion within particles. Fick s diffusion model applies to coal particles and the diffusivities are reported to be of the order of cm 2 /s. For the particle size under consideration this diffusivity leads to a diffusion time of seconds in a single particle (Crank, 1957) Slim tube configuration Because the analytical studies so far were for one-dimensional systems, a slim tube configuration is chosen. The length of the tube is chosen such that four pore volumes can be passed through the tube in a run time of 8 hrs with a flow rate of 0.5 cc/min. For a 16

33 standard stainless steel tube of outer diameter 3/8 and thickness 0.035, leading to an inner diameter of 0.77 cm and a cross-sectional area of cm 2, the length is calculated to be q * t 0.5*8* 60 l = = = cm = 3.18 m. 4 * A* φ 4 * * 0.4 As this is an approximate calculation, a slim tube of 3 m length is used to do the experiment. The experiment is to be done vertically in order to avoid gravity effects. In cases of large density difference between displacing and displaced fluid, gravity can be used to assist displacement by countering the viscous effects like fingering. The tube, being long for the height of laboratory, is bent at regular intervals in a zig-zag fashion Flow rate determination In multi-phase studies, the mobility ratio plays an important role in determining the sweep efficiency. In previous laboratory studies, several mechanisms were found to stabilize solvent fingering. Under appropriate conditions, gravity can prevent viscous fingers from forming. According to Hill (1949), solvent fingers will be completely dampened if the frontal advance rate v, is less than or equal to the critical rate v c given by 15 k ρ (760 *10 ) * (1000) * 9.8 * v c = g sinθ = cm / min, (2) 3 µ 10 where is the dip below horizontal, and are the density and viscosity differences, respectively, between the displacing and the displaced fluid, and k is the Darcy permeability of coal, which is discussed in chapter 5. As a very small tube is needed to satisfy this bound on the velocity, which does not allow the experiment to be conducted in a reasonable time, the injection is performed at a 17

34 higher rate. The resulting sweep inefficiency was studied by Hill (1949). His results are shown in figure 3-4 below. Figure 3-4: Effect of injection velocity on residual trapping (Hill, 1949) The estimated flow rate of 0.5 cc/min falls in the range of v/v c between 10 and 100 for which the residual saturation is between 10 and 20 percent of the pore volume Single phase experiments Solutions to the Riemann problem have been obtained analytically for single phase systems by Zhu (2003). The solutions obtained showed the presence of shocks and rarefactions in the solutions for injection of pure and mixed gases. A typical displacement is illustrated in figure 3-5. Experiments are conducted to validate the conclusions (discussed in section 1.5) of the above analytical study. Figure 3-6 shows the experimental setup for conducting single phase experiments. A brief description of different components of the experimental setup is presented in Appendix A. The following subsections discuss the different types of experiments conducted in this category. 18

35 Figure 3-5: Analytical results for injection of mixture of CO 2 and N 2 (50-50) for methane displacement (Zhu, 2003) Bubble Flow Meter Composition Profile GC 2-way BPR Valve 2 Methane saturated coal tube Pr Gauge 45 0 Gas Cylinder MFC Valve m Figure 3-6: Schematic diagram of experimental setup for the single phase systems 19

36 Binary displacement The analytical work focuses on two main types of injection gases for displacement of methane from coal. The first one is displacement with a more adsorbing and less volatile gas than methane and the second is displacement with a less adsorbing and more volatile gas than methane. These two experiments are conducted in the slim tube with two different injection gases, CO 2 and N 2. CO 2 is more adsorbing and less volatile than methane, whilst N 2 is less adsorbing and more volatile than methane. The operating conditions for these experiments are listed in table 3-1. The coal tube is initially saturated by injecting methane at a known pressure. Injection is done by controlling the rate at 25 cc/min at standard conditions and the production end is under pressure control with a back pressure regulator. The back pressure is generally set close to the pressure at which methane is initially injected in the coal. The back pressure is maintained high for two reasons. Firstly, it helps in avoiding methane desorption from matrix space, so only the methane from pore space is produced. Secondly, the pressure drop in the tube is small, so the adsorption-desorption profile near the inlet is not very different from that near the outlet of the tube Determination of dispersion coefficient The results obtained from the single phase binary displacements are in agreement with the analytical and numerical work done by Seto (2007) and Zhu (2003). They show the presence of shocks and rarefactions for the two different injection scenarios discussed in section The spread of the front at the outlet is due to adsorption and dispersion of gases in the coal pack. In the absence of adsorption, the spread of the front is an indication of the convective dispersion and can be used to determine the dispersion coefficient. An extra test is performed in which the tube is initially saturated with a nonadsorbing gas in order to remove the effects of adsorption and to understand the dispersion due to flow of gases in the pore space. Helium is known to be an inert gas with negligible adsorption on coal, so coal is initially saturated with helium at a low pressure and displacement is done with N 2. N 2 Injection is done from the bottom of the tube as it is 20

37 heavier than helium. The injection end is under rate control and the production end is under pressure control. The operating conditions are listed in table Ternary displacement with mixture injection Pure gases are not available at all the sites for performing ECBM, so a mixture of CO 2 and N 2 is tested as an injection gas to displace methane from coal tube in a displacement study of gas phase systems. CO 2 and N 2 are mixed in a piston cylinder in the ratio of 55:45, keeping in mind that the analytical results in Zhu (2003) and Seto (2007) are obtained for injection mixtures with 50:50 and 60:40 ratios of CO 2 and N 2 respectively. The mixture is injected at a constant rate with the back end of the tube maintained at a constant pressure. The operating conditions are listed in table 3-1. Table 3-1: Operating conditions for single phase experiments Initial Condition Injection Gas Injection Condition - Rate control (cc/min) Production Condition Pressure Control (psia) Standard Conditions Tube Pressure Methane at 440 psia Methane at 480 psia CO N Helium at 70 psia N Methane at 490 psia CO 2 + N 2 (55:45) Two-phase experiments Analytical work has been done by Seto (2007) to solve the two-phase Riemann problem for binary, ternary and quaternary systems with water as a mobile phase and component of each system. The binary and ternary results led to similar conclusions of shock solution 21

38 for more adsorbing gas injection, rarefaction solution for less adsorbing gas injection and chromatographic separation for mixture injection, as those obtained for the single phase analytical (Zhu, 2003) and experimental studies (section 3.4). Seto s results for quaternary systems, which are initially saturated with water and methane, are obtained for various compositions of the injection gas, which is composed of CO 2 and N 2. Validation of these analytical results and conclusions about comparisons of saturated and undersaturated systems is the motivation to extend the experimental work to two-phase systems. Two-phase experiments are conducted with an initial water saturation in the pore space and methane saturation in the matrix space and displacement is done for different injection conditions. The experimental setup for two-phase systems is shown in figure 3-7 and the details of the setup are discussed in Appendix A. Bubble Flow Meter Composition Profile GC 2-way Valve Water trap BPR Valve 2 Methane + water saturated coal tube Pr Gauge 45 0 Gas Cylinder MFC Valve m Figure 3-7: Schematic diagram of the experimental setup for the two phase systems 22

39 Ternary displacement with pure CO 2 injection This experiment is conducted in a horizontal coal tube by first saturating it with methane. Water is injected by constant pressure constraint from the inlet of the tube and the back end of the tube is maintained at the same pressure at which methane was injected. Water occupies the pore space by displacing methane. The matrix space is still occupied by methane in its adsorbed state. The operating conditions for this experiment are listed in Table 3-3. After saturating the tube to its initial condition, CO 2 is injected at a constant rate of 20 cc/min at standard conditions. The back end of the tube is maintained at a constant pressure of 525 psia and not 725 psia at which the tube was initially saturated with methane and water. This is because after the initial coal saturation at 725 psia, the tube pressure reduced to 525 psia in the absence of any leakage. This is possibly due to the dissolution of methane in water which reduced the pressure of the system Quaternary displacement with mixture injection Analytical results for quaternary systems are obtained for various sets of injection gas compositions. The fraction of CO 2 in the injection mixture of CO 2 and N 2 is increased from 0 to 1. A new composition path for certain injection gas compositions, depending on the initial and thermodynamic state of the tube, is reported. The analytical result for a 60:40 injection mixture of CO 2 and N 2 representing this analytical solution is shown in figure 3-8. Table 3-2: Analytical vs realistic K values (Seto, 2007) Analytical Real K N K CO K CH K WATER

40 Figure 3-8: Analytical results for injection of mixture of CO 2 and N 2 (60:40) for two-phase displacement (Seto, 2007) Figure 3-8 shows the presence of a degenerate shock from C-D which is a switch between two non-tieline paths. A degenerate shock is one where the velocities immediately upstream and downstream of the shock are equal to the shock velocity (Seto, 2007). This two-phase quaternary experiment is conducted to see if this degenerate shock can be seen in laboratory scale displacement in under-saturated coal by injection of a mixture of CO 2 and N 2. Even under same operating conditions, the results from experimental and analytical studies are not expected to resemble due to inconsistencies in the physical parameters. The analytical solutions are obtained for nonrealistic K values. The real K values of CO 2, N 2 and methane are much higher, while that of water is much lower as seen in table 3-2. Hence, in real the solubility of these gases in water is much lower. Therefore, the size of the two phase region is larger. So, the compositional features seen experimentally are expected to scale appropriately to the phase behavior of the system. Similar to the experiment in section 3.5.1, this experiment has initial coal tube saturated with water and methane. This experiment is conducted in a vertical tube with water 24

41 injection from the bottom of the tube at three different rates of 0.4, 0.1 and 0.05 cc/min. The injection profile of water is shown in figure 5-26-a. After saturating the tube to its initial condition, a mixture of CO 2 and N 2 in the ratio of 55:45 is injected from the top of the tube at constant rates of 12 cc/min (standard conditions) at the beginning, then 2 cc/min and then 4 cc/min at the end of injection period The mixture injection profile is shown in figure 5-29-a. The production end is controlled by the back pressure regulator at 300 psia (Due to pressure drop in the initial state of tube from 450 psia to 300 psia due to dissolution of methane in water). The operating conditions for this experiment are listed in Table 3-3. Table 3-3: Operating conditions for two-phase experiments Methane Injection (psia) Initial Condition Injection Injection Condition - Gas Rate control (cc/min) Injection Condition Water Injection Production Condition Standard Conditions Tube Pressure Production Condition Pressure Control (psia) 725 Pressure control 775 psia Pressure control 725 psia CO Variable rate control 0.4, 0.1, 0.05 cc/min Pressure Control 450 CO 2 + N 2 (55:45) 12, 2, , 0.1, One-dimensional numerical simulation Another way of validating the experimental results and also the analytical ones is by numerical simulations. 1-D, finite-difference simulations with a fully implicit scheme are performed using CMG s commercial compositional simulator GEM (2006). From the experiments, it is clear that physical dispersion (discussed in section 3.4.2) is infact 25

42 present in the system. But, since GEM does not allow it to be included, the physical dispersion is modeled by using the numerics. So, a systematic approach of simulating these systems with physical dispersion is followed. Using the experimental results, the governing dispersion coefficient and Peclet number can be estimated. They are further verified by analytical correlations (section 5.3). The Peclet number can be mimicked in the numerical experiments if upwind methods are used to discretize transport. For the standard first order upwind method (SPU) Lantz (1971) has shown that the numerical diffusion coefficient can be computed using 1 ξ τ Pe num = 1. (3) 2 ξ The spatial and temporal grid sizes can now be chosen such that the numerical Peclet number equals the estimated physical Peclet numer. The ratio τ / ξ must be taken so as to satisfy the standard stability criteria as also discussed in Orr (2007). 26

43 Chapter 4 4. Operating Procedure 1. Determination of porosity and permeability To find the porosity, a cylindrical bomb (figure 4-1-a) of 150 cc volume is pressurized with helium at a known pressure P 1. The coal tube is vacuumed for 24 hours and then connected with the bomb with a valve in between the two. The valve is opened and the final pressure P 2 in the gauge (figure 4-1-b) is noted. This pressure corresponds to the volume of bomb plus the pore volume of the coal tube plus any dead volume. The pore volume can be found by using the relation P 1 V1 = P T V T, (4) where V = V + V1 + V. (5) T Pore dead V1 = 150 cc, V dead = cc. P 1 and P T are read from the gauge, so V T and V pore are the only unknowns and can be found by solving equations (4) and (5). Several sets of these measurements are obtained and the data is tabulated in Appendix B. The porosity of the coal tube is found to be 44%. It should be noted that this porosity includes both the pore volume (roughly 34%) and the matrix porosity (roughly 10%) of the coal pack (Resnik, 1984). Figure 4-1: Gas cylindrical bomb (a) and pressure gauge (b) 27

44 Permeability is measured by performing simple Darcy experiments in the coal tube with helium gas. Four pore volumes of helium are passed through the coal tube. The injection and outlet pressures are observed and flow rate at the tube outlet is measured using the bubble flow meter. The Darcy permeability is defined as q * µ * l k =, (6) A* P where q is the measured flow rate, µ is the viscosity of helium, l is the tube length, A is the cross-sectional area of the tube and P is the pressure drop across the length of the tube. Several sets of this measurement are obtained and the data is tabulated in Appendix C. The permeability is found to be around 760 md. 2. Vacuuming coal tube After finding porosity and permeability or after doing one set of experiment, the tube is put to vacuum for atleast 24 hrs. The weight of tube should come to that prior to measuring porosity. 3. Purging coal tube with methane As some of the components always remain on the coal surface due to its adsorbent properties, the coal tube is purged with pure methane at high pressure after vacuuming and the composition of the outlet gases is monitored in the GC. Methane is passed till the chromatograph shows nearly100 % methane in the exit gas. 4. Injection of methane After purging the tube, methane injection is continued at the desired injection pressure for the experiment, with one end of the coal tube closed. The tube is weighed regularly in order to determine the amount of methane injected. Injection should be done for atleast hours even if the weight has stabilized. This is done in order to make sure that methane does not remain only in free state but also gets adsorbed on surface of the coal. 28

45 1.6 Methane injected (gms) Time (hrs) Figure 4-2: Methane injection in coal tube The volume of methane injected in the coal with time is shown in figure 4-2. This amount can vary slightly for each experiment due to error made in the injection pressure gauge and weighing balance. The injected methane is distributed in the coal pack both in the pore space in free form and in the matrix space in adsorbed form. The individual amounts can be computed by a material balance. The moles of methane present in the pore volume i.e. the inter-granular space can be written as n p P * V p =, (7) z * R * T where P is the injection pressure, V p is the inter-granular pore volume, z is the nonideality compressibility factor, R is the universal gas constant and T is the temperature. The remaining moles are in the adsorbed state in the matrix porosity which can be found by subtracting the moles in pore space, n p, from the total moles injected, which is found by weighing the tube. 5. Flow meter calibration The flow meter is calibrated for each different gas being injected. The flow meter being built for CO 2 does not need to be calibrated for CO 2 injection but needs calibration for N 2 injection and the mixture injection. 6. Setting the back pressure 29

46 Before connecting the BPR to downstream end of the tube, it is set to the regulated pressure as discussed in section 3.4 and 3.5, so that gas doesn t escape before injection begins after the BPR is connected to the coal tube. 7. Configuring the GC The valve and column settings are adjusted in a way that the GC is able to separate the components in the minimum possible time. Table 4-1 shows the setting for each experiment: Table 4-1: Method setup for running sequences in the GC Exp # Components Run time Columns used Valve setting Det temp Oven temp Carrier gas rate Retention time (mins) (mins) ( 0 C) ( 0 C) (ml/min) 1 CO 2 + C1 5.3 Plot Q T=0, V3 on T=5, V3 off He 4.8 CO C V2 always on 2 N 2 + C1 6.4 Mol Sieve T=0, V3 on T=0.1, V3 off ,65 He 4.8 N C1 4.1 V2 always off 3 He + N Mol Sieve T=0, V3 on T=0.1, V3 off H N He 1.78 V2 always off 4 CO 2 + N 2 + C Plot Q + Mol Sieve T=0, V3 on T=3.4, V2 on T=4.2, V2 off H CO N 2 7 C1 8.5 T=10, V3 off 5 CO 2 + N 2 + C1 + Water Plot Q + Mol Sieve T=0, V3 on T=3.4, V2 on T=4.2, V2 off T=10, V3 off H CO N 2 7 C1 8.5 A sequence table is set for automatic injections at regular interval which is analyzed using the above configuration table called as a method in the GC software ChemStation (2006). 8. Starting gas injection 30

47 Once the set up is completed, the gas cylinder is turned on and the injection pressure is adjusted automatically depending on the inlet flow rate and the back pressure. The injection end is under rate control by the mass flow controller (MFC). The production end is under pressure control by the back pressure regulator (BPR). The outlet valve of the tube is opened first to check if the pressure in the tube is still maintained to what it was saturated at. Then the inlet valve is opened for flow to begin in the tube. For water + methane saturated initial conditions, the gas injection is done from top of the tube. In that way gravity helps in preventing the fingering effect in a low viscosity fluid displacing a high viscosity fluid system i.e. a high mobility ratio system. 9. Measurements The following parameters are recorded during the injection period for the analysis and interpretation of results: Injection pressure. Gas production rate. Produced gas composition. Water production in case of methane + water saturated initial condition. 10. Ending the experiment Once all the injection gases have broken through and the flow rates have stabilized, the injection is stopped and the valves are closed to measure the tube weight. Steps 2 through 10 are repeated for the next experiment. 11. Conducting two-phase experiments After methane injection (step 4) at a known pressure, water is injected from the bottom of the tube using the water pump at a fixed rate or fixed pressure. The back pressure regulator is set at the end of the tube in order to avoid methane-escape by desorption. This ensures that methane is displaced only from the free space and is produced at the tube outlet. Once water sweeps through the tube, methane and water are co-produced and then 31

48 the water injection is stopped. Steps 5-10 are then conducted as in the single phase experiments. The produced water is trapped in the water-trap and is measured in step 9. 32

49 Chapter 5 5. Results, Discussion and Material Balance 5.1. Results for pure CO 2 injection for methane displacement Pure methane is initially injected in the coal tube at 450 psia to get the system at an initial condition saturated with methane. Pure CO 2 is injected to displace this methane present in both free state and adsorbed state. Methane is produced at the tube outlet and is followed by CO 2 production once the injected gas breaks through. Production of gases is monitored and recorded to do a material balance check and the results are analyzed to understand the displacement behavior of methane in coal by a more adsorbing gas. CO 2 is injected in the coal tube at 25 cc/min at standard conditions. Figure 5-1 shows that production rate of gases at the outlet of the tube is around 12 cc/min till the time CO 2 breaks through at the tube outlet. This is an indication of reduction in flow velocity due to preferential adsorption of CO 2 on coal over methane. As CO 2 is transported in the coal tube, for approximately three moles of CO 2 adsorbed, only one mole of methane is released, thereby leading to a reduction in volume and hence a decrease in velocity. As, the CO 2 front begins to appear at the tube outlet, the flow velocity increases. This is because after all the adsorption has taken place, the flow is purely convective, so the production rate comes to 25 cc/min which is also the injection rate. Figure 5-1: Total production rate for pure CO 2 injection. 33

50 Figure 5-2 shows the composition profiles of gases at the tube outlet vs pore volumes injected (PVI). It can be seen that CO 2 breaks through at around 2 PVI, which might seem non-intuitive because as per mass conservation, for flow in a porous medium, the injection gas should appear at the tube outlet after one pore volume is injected. But in this case as CO 2 gets adsorbed on coal, the volume of CO 2 in free space reduces, hence the need for more than one PVI to see the breakthrough. It can also be seen that CO 2 breaks through as a sharp front. This is because of the presence of a shock between the injection and the initial tie line. This is in agreement with the analytical result for displacement by an injection gas that is more adsorbing than the gas present initially. Figure 5-2: Composition profile at tube outlet for pure CO 2 injection Figure 5-3 shows the individual component molar flow rates at the producing end of the tube. By knowing the total volume flow rate and the composition of the production mixture, the component molar rate is computed from ideal gas law as n c = 6 6 PQx c * * Q *10 * xc 5 = = *10 Q * xc RT * 293 gmoles / min, (8) where P is the pressure at which composition is measured in Pa, Q is the total production rate in cc/min, x c is the mole fraction of the component c in the production mixture, R is the universal gas constant and T is the tube temperature in K. 34

51 Figure 5-3: Component molar rates for pure CO 2 injection Figure 5-4 shows cumulative production of the components at the tube outlet. The material balance is shown in table 5-1. It can be seen that almost all of the methane is produced by the time CO 2 breaks through. This also indicates that the CO 2 front moves very sharply inside the coal tube. Figure 5-4: Cumulative moles produced for pure CO 2 injection Table 5-1: Material balance calculations for pure CO 2 injection Gmoles Gms Amount of methane injected initially (measured) Methane present in pore space (34% by volume) (Calculated) Methane adsorbed in Matrix space (Calculated) Amount of methane produced (measured) Amount of CO 2 trapped in coal (measured)

52 Figure 5-5: Fractional molar recovery of methane for pure CO 2 injection It can be seen from figure 5-5 that 90% of the methane present initially in the tube is recovered at the time of CO 2 breakthrough. The over all recovery is 100% as can also be seen from the material balance check in table 5-1. A result of this single phase experiment of methane displacement by CO 2 in coal has been obtained analytically by Zhu (2003). Figure 5-6 shows a comparison of experimental and analytical results for methane and CO 2 composition paths with non-dimensional wave velocity. Figure 5-6 shows a good qualitative picture of the presence of a shock solution from both the results. The results do not match perfectly in quantitative sense due to differences in physical dispersion and adsorption of gases in the experimental and analytical work. The analytical work assumes no dispersion to be present in this study whereas the calculations in section 5.3 show a large physical dispersion. Figure 5-6: Comparison of composition profiles of experimental (a) and analytical (b) solutions for pure CO 2 injection 36

53 5.2. Results for pure N 2 injection for methane displacement Similar to the above experiment, pure methane is initially injected in the coal tube at 480 psia to get the tube to methane-saturated initial state. Pure N 2 is injected to displace this methane and the production of gases are monitored and recorded. N 2 is injected in the coal tube at 25 cc/min at standard conditions. Figure 5-7 shows that the production rate of gases at the outlet of the tube is around 32 cc/min till the time N 2 breaks through at the tube outlet. N 2 is more volatile and less strongly adsorbing than methane so it travels quickly through the system, causing methane to desorb earlier than when CO 2 is injected. From the adsorption isotherm (figure 2-1) it can be seen that more molecules of methane are desorbed for every molecule of N 2 getting adsorbed. So, volume is added to the flowing gas phase thereby increasing the flow velocity. As N 2 is produced at the tube outlet, the flow velocity gradually decreases to the injection velocity. Figure 5-7: Total production rate for pure N 2 injection Figure 5-8 shows the composition profiles of gases at the tube outlet for N 2 injection. It can be seen that N 2 breaks through at around 0.4 PVI, which gives an indication of an increase in local flow velocity in the tube. This is due to the fact that injected gas is seen at the outlet even before one pore volume is injected in the tube. This is just the reverse effect of pure CO 2 injection in which breakthrough occurs at 2 PVI. Also, another observation is that the N 2 front is highly dispersed as compared to the CO 2 front in figure 5-2. This also blends well with the analytical study which predicts that displacement of 37

54 more strongly adsorbing and less volatile components by less strongly adsorbing and more volatile components occurs through a continuous variation or a rarefaction wave. Figure 5-8: Composition profile at tube outlet for pure N 2 injection The molar rates of individual components is shown in figure 5-9. It can be seen that the rate of methane production is 1.3*10-3 gmoles/min for N 2 injection as compared to 5*10-4 gmoles/min for CO 2 injection case before breakthrough. As N 2 propagates faster through the tube, partial pressure of methane decreases, thereby leading to an early desorption and hence a higher production rate of methane. Figure 5-9: Component molar rates for pure N 2 injection Figure 5-10 shows the cumulative production of methane and it can be seen that even after N 2 breaks through, methane continues to produce. Hence there is a production of the binary mixture which needs separation facilities. 38

55 Figure 5-10: Cumulative moles produced for pure N 2 injection The overall recovery of methane is 97% at 3 PVI as seen from figure 5-11 representing the fractional recovery of methane for N 2 injection. 40 % of methane is recovered at the time of N 2 breakthrough unlike the 90 % recovery of methane at CO 2 breakthrough (figure 5-5). Figure 5-11: Methane recovery for pure N 2 injection The material balance calculations for N 2 injection are shown in table 5-2. Table 5-2: Material balance calculations for N 2 injection Gmoles Gms Amount of methane injected initially (measured) Methane present in pore space (34% by volume) (Calculated) Methane adsorbed in Matrix space (Calculated) Amount of methane produced (measured) Amount of N 2 trapped in coal (measured)

56 Figure 5-12 shows a comparison of the results from the analytical work of Zhu (2003) and the experimental work for methane displacement in coal by N 2. Again, the numerical values of breakthrough time and the extent of the dispersed front do not match but both the results are in agreement with the proposed theory of the presence of a rarefaction wave between the initial and injection tie lines for this kind of displacement. Figure 5-12: Comparison of composition profiles of experimental (a) and analytical (b) solutions for pure N 2 injection 5.3. Results for dispersion experiment The dispersed fronts seen in sections 5.1 and 5.2 led to the conduction of a tracer test in which the tube is initially saturated with helium which is then displaced with N 2. The composition profile is shown in figure Figure 5-13: Helium fraction in the produced gas 40

57 The dispersion coefficient K l is made up of the combined effects of molecular diffusion and fluid flow in the pore space. It can be calculated using a correlation given by Perkins and Johnston (1963) given as K D l 0 1 U * d p = , (9) F φ D 0 where D o is the molecular diffusion coefficient, U = cm/sec is the flow velocity, d p = cm is the particle diameter and 1 / F φ = 0. 7 (Perkins and Johnston, 1963). Rohling et al. (2007) reported a molecular diffusion coefficient of N 2 in helium, to be cm 2 /sec at ambient conditions. The molecular diffusion coefficient can be calculated at the tube pressure using P D o Constant (Perry and Green, 2007). So, D o at 70 psia is approximately cm 2 /sec and the dispersion coefficient, K l is thus found to be cm 2 /sec. The dispersion coefficient can also be calculated using the analytical theory as described in Orr (2007) as 1 Pe( ξ τ ) c = erfc 2, (10) 2 τ where c is the volume fraction of a component, ξ = x / L, τ = ut / φl and Pe = ul / φkl. The dispersion coefficient can be found by creating a plot in the arithmetic probability coordinates using c = erfc( b) 2. Taking the inverse of both sides, equation (10) becomes erfc 1 (2 c) = b. The argument on the right hand side can be evaluated atξ = 1, the core outlet, where the concentration is measured. Now (10) becomes 41

58 τ = * erfc (2c) Pe *. (11) τ So, plotting 2* erfc 1 (2 c) against 1 τ, the slope gives the Peclet number from which the τ dispersion coefficient can be deduced. Figure 5-14: Measurement of dispersion coefficient Using the slope of the plot in figure 5-14, a Peclet number of Pe = is found. The dispersion coefficient, K l is now found to be ul *300 K l = = = cm 2 /sec. φ Pe 0.44*106.2 The above experimental result is in agreement with the theoretical result suggested by Perkins and Johnston (1963). This dispersion coefficient is quite large and this is the reason for observing a more dispersed front than the analytical results Results for methane displacement by injection of a mixture of N 2 and CO 2 A mixture of CO 2 and N 2 in the ratio of 55:45 is injected in the coal tube which is initially saturated with methane at 490 psia. The production of gases is monitored and recorded to investigate the effects of this mixture injection for displacement of methane from coal. The composition profiles of the three components at the tube outlet as injection and production take place is shown in figure The analytical work predicts chromatographic separation of injection components as they propagate through the tube 42

59 which is evident in this result. N 2 breaks through at 1 PVI and it is produced along with methane. CO 2 adsorbs more on the coal than N 2 and methane, hence there is a late breakthrough at 2.1 PVI CO2 N2 C1 Gas Composition Time (PVI) Figure 5-15: Composition profiles for CO 2, N 2 and methane for mixture injection Figure 5-16 shows the total production rate of gases at the tube outlet measured with a rotameter. The profile has three characteristic zones (separated by green lines): first is the nitrogen dominated displacement where the production rate is around 21cc/min. After nitrogen sweeps through the whole length of the tube, the production rate decreases down to 17 cc/min. This is because the displacement is governed primarily by more adsorbing CO 2. Finally, after CO 2 also breaks through at 2.1 PVI, the displacement is governed purely by convection and the production rate is same as the injection rate. Figure 5-16: Total production rate for mixture injection in single phase system 43

60 Similar to pure gas injection, the production molar rates of individual components are calculated by applying the ideal gas law and then the cumulative production of gases in moles are calculated. The results are shown in figure Production Molar Rate (gmoles/min) 1.0E E E E E E Pore Volumes Injected Exp-C1 Exp-CO2 Exp-N2 Cumulative Moles produced (gmoles) Pore Volumes Injected Exp-C1 Exp-CO2 Exp-N2 Figure 5-17: Production profiles for mixture injection Figure 5-18 shows that 75% of the original methane in place is recovered by the time nitrogen breaks through and the overall recovery is 95%. Fractional Molar Recovery Pore Volumes Injected Figure 5-18: Methane recovery for mixture injection in single phase system The material balance calculations for the mixture injection are shown in table 5-3. Table 5-3: Material balance calculations for mixture injection in single phase system Gmoles Gms Amount of methane injected initially (measured) Methane present in pore space (34% by volume) (Calculated) Methane adsorbed in Matrix space (Calculated) Amount of methane produced (measured) Amount of (CO 2 + N 2 ) trapped in coal (measured)

61 A good qualitative comparison between the analytical (0.5 CO N 2, Zhu (2003)) and experimental (0.55 CO N 2 ) results can be seen in figure The experimental observations show a clear nitrogen bank being produced with methane and the shock solution for CO 2 composition as depicted in the analytical results. Figure 5-19: Comparison of composition profiles of experimental (a) and analytical (b) solutions for mixture injection in single phase systems 5.5. Comparison of the single phase experiments with different injection gases Figure 5-20: Experimental results for Methane recovery by different injection gases 45

62 Figure 5-20 shows the recovery profiles for the cases of pure CO 2, the mixture of CO 2 and N 2 (0.55 CO N 2 ) and pure N 2 injection to displace methane from the coal tube. It can be seen that as the CO 2 concentration in the injection gas increases, the rate of recovery decreases. The overall recovery varies from 95 % to 99 %. Figure 5-21: Experimental results for total production rate with different injection gases Figure 5-21 shows the total production rate at the tube outlet for the three cases. The total production rate is 12 cc/min in the pure CO 2 injection case before the break through of CO 2 where as in the pure N 2 injection case the total production rate is 32 cc/min before N 2 breaks through. In the mixture injection case, the production rate is 21 cc/min initially until N 2 breaks through and then reduces to 17 cc/min until CO 2 breaks through. The three results show that N 2, being less adsorbing than methane, passes quickly through the tube leading to reduction of partial pressure of methane and subsequent desorption and higher flow rate. On the other hand, the presence of CO 2 tends to slow down the front velocity. CO 2 is preferentially adsorbed on coal over methane so the volume flow rate decreases. Finally, after all the injection gases break through, the three profiles for production rates come to the same value as the injection rate which is 25 cc/min as seen in figure

63 Figure 5-22: Experimental results for methane production rate by different injection gases Figure 5-22 shows the methane production rate for the three cases. As explained above, it can be seen that the methane production rate decreases as the CO 2 fraction in the injection gas increases. Also, it is interesting to note the shape of fronts for the three cases. CO 2 injection leads to a sharper front (shock solution) where as N 2 injection leads to a smooth transition (rarefaction solution) Results for displacement of water and methane by pure CO 2 injection The production rate at the tube outlet is not measured in this case. Only the composition of the exit gases is measured with the gas chromatograph and is shown in figure Breakthrough of CO 2 occurs at 1.8 PVI. The figure also shows that the CO 2 moves as a sharp front. Almost all of the methane is recovered by the time CO 2 breaks through. Composition Time (PVI) CO2 C1 Figure 5-23: Composition profile for CO 2 injection in coal with methane and water saturation 47

64 Figure 5-24 shows the fractional water recovery. There was no production of water initially as the back pressure of the tube went below the controlled design pressure of 600 psia. As the pressure built up, water production started and a total of 35 % of the water was recovered from the tube. Fraction of water produced PVI Figure 5-24: Fractional water production for CO 2 injection in methane and water saturated coal Figure 5-25 shows a comparison of the analytical (Seto, 2007) and experimental results for gas phase compositions of methane and CO 2. The breakthrough times for both the cases are around 0.45 in terms of the dimensionless wave velocity. The experimental results show a more dispersed front than the analytical results due to the presence of physical dispersion discussed in section 5.3. Another reason is because the analytical results are obtained for nonrealistic K values and solubilities for the two-phase system as shown in table 3-2. Figure 5-25: Comparison of experimental (a) and analytical (b) results for pure CO 2 injection in water + methane saturated system 48

65 5.7. Results for displacement of water and methane by mixture injection The tube is initially saturated with methane. The amount of methane in the pore space and in the matrix is calculated as described before. Water is injected to displace the methane in the pore space. Methane in the matrix space remains adsorbed because the back pressure is maintained at the adsorption pressure of methane. This brings the system to its initial state. Water Injection Water Injected (cc) a injection production Time (mins) Water Produced (cc) Water Injected (cc) Time (PVI) b injection production Water Produced (cc) water injected (cc) c water injected cum gas produced time (mins) produced gas (gmoles) water injected (cc) d Time (PVI) water injected cum gas produced produced gas (gmoles) Figure 5-26: Injection and production profiles for water injection A total of gmoles of methane are injected in the tube initially and then water is injected at variable rates of 0.4, 0.1 and 0.05 cc/min at tube pressure. The variable injection rates can be seen in figure 5-26-a as a function of time. In figure 5-26-b water injection and production are plotted as a function of pore volumes injected so the effect of rate does not show up in the graph. Water is produced after 1 PVI, which is an indication 49

66 that water has swept all the pore space. It should be noted here that the pore space refers to inter-granular porosity (total porosity matrix porosity). After breakthrough, water is produced at the same rate as the injection rate, which is 0.05 cc/min. Methane is produced through out the water injection time as seen from figure 5-26-c. It can be seen that methane production rate is also affected by the water injection rate. As the water injection rate is decreased, the methane production rate also decreases. It can be seen from figure 5-27-a that as the water breaks through, the gas rate comes to zero sharply, also indicating the sharpness of water front in the tube. Gas Production Rate (cc/min) a gas pdn Rate water pdn Time (PVI) water pdn (cc) Fraction of methane produced Time (PVI) Figure 5-27: Production profiles for water injection in methane saturated coal b Figure 5-27-b shows the fraction of methane released from the tube as water is injected. 73% of the total methane in place is produced by water injection. This is the volume of methane which is calculated to be present in the pore space prior to water injection as shown in the material balance check in table 5-4. Because methane is produced only from the pore space, the produced volume also validates of the assumed porosity distribution between pore space and matrix space of 34% and 10 % respectively. Material balance calculations for water injection in methane-saturated tube are shown in table

67 Table 5-4: Material balance calculations for water injection in methane saturated coal Gmoles Gms Amount of methane injected 500 psia (measured) Methane present in pore space (34% by volume) (Calculated) Methane adsorbed in Matrix space (Calculated) Total methane left after pressure reduction to 420 psia due to connecting water pump Amount of methane produced (measured) Amount of water in the tube (= injected-produced-dead volume) (measured) Amount of methane left in the tube Gas Mixture injection Mixture of CO 2 and N 2 (0.55:0.45) is initially injected at a flow rate of 12 cc/min at standard conditions to displace the methane and water from the coal. No gas was produced for the first quarter of pore volume injected. This is because the pressure in the tube was lower than the designed back pressure. As the gases begin to produce, N 2 is detected in the exit gases (figure 5-28). The early breakthrough of N 2 may be because of the unstable displacement velocity. The mobility ratio for this system, with gas and water viscosities of the order of 0.01 cp and 1 cp respectively, is around 100. Due to this large mobility ratio there is fingering effect in the coal due to which N 2 flows quickly through the pores. Figure 5-28: Composition profile of exit gases for mixture injection 51

68 The injection rate is reduced to 2 cc/min after 0.8 pore volumes are injected and further increased to 4 cc/min after 1.5 PVI. The gas production rate is seen to follow the injection profile as seen in figure 5-29-a. Initially a high production rate is seen, then the rate decreases and finally increases up to the injection rate of 4 cc/min at standard conditions. a b Figure 5-29: Injection and production profiles The cumulative production is shown in figure 5-29-b. A large volume of N 2 is produced due to its early break through as seen in figure Methane is also produced with N 2, so needs to be separated from the mixture for commercial uses. Sharp changes are seen in the composition profiles due to changes in the injection rate. Figure 5-30: Water and methane recovery for mixture injection in two-phase system The overall recovery of methane is 100% and only 23% of original water is produced (figure 5-30). Low water production is likely caused by an unstable displacement front in the tube. So, from an ECBM point of view, a higher injection rate than the critical 52

69 velocity (determined in section 3.3) can still be a feasible approach as all the methane is still recovered. However, this large production comes at the cost of large injection volumes of CO 2 and N 2. Also, the produced gas is mostly a mixture of N 2 and methane, which need to be separated. Material balance calculations for mixture injection in a tube saturated with water and methane are shown in table 5-5. Table 5-5: Material balance for mixture injection in water + methane saturated coal Gmoles Gms Amount of water injected (measured) Amount of methane left in the tube (calculated) Amount of methane released (measured) Amount of water produced (measured) Amount of (CO 2 +N 2 ) trapped in coal (calculated) 2.05 Composition profiles for the four components are plotted for the experimental and the analytical study (Seto, 2007) in figure The experimental solutions are more dispersed than the analytical ones but it is interesting to note some of the common features. The analytical result shows the presence of a degenerate shock for this composition of the injection gas (Type III-C: 0.6 CO N 2 ). Two sharp peaks can be seen in the experimental results for N 2. One of them is possibly due to the degenerate shock. A shock solution for CO 2 can also be seen but as a more dispersed front which is due to the large dispersion coefficient calculated in section 5.3. The numerical values of solution compositions are different as the analytical study is done for non-real K values and solubility data of liquids and gases as shown in table

70 Figure 5-31: Comparison of experimental (a) and analytical (b) results for mixture injection in water + methane saturated system 5.8. Effects of saturated and under saturated initial conditions and comparison with analytical solutions Another important part of the analytical study done by Seto (2007) is the comparison between saturated and under saturated systems. Saturated systems are defined as the ones having significantly large volumes of methane trapped in coal (more than 30% of mixture on molar basis). Under-saturated systems are defined as ones in which less methane is available to be recovered (0.05% of mixture). In the experimental study, a similar comparison can be made between systems with a large quantity of methane (single phase systems with pure methane) referred to as saturated and the ones having a small volume of methane trapped in coal (methane (0.04%) + water saturated coal) referred to as under-saturated system. The analytical study proposes a banking behavior in the methane profile in under-saturated system. This is seen as the red curve in figure 5-32 in the methane profiles of both the analytical and experimental results. Also, the small leading shock in CO 2 profile is clearly visible in the experimental results in figure 5-32-a. Again, this is a good qualitative match but not a 54

71 quantitative assessment due to different parameters, mainly the K values (table 3-2) and the dispersion coefficient (section 5.3), used in the two studies. Figure 5-32: Comparison of experimental (a) and analytical (b) solutions for saturated and undersaturated systems Another result of comparison between saturated and under-saturated systems is from the CO 2 sequestration point of view. The analytical study proposes more CO 2 to be injected into the reservoir prior to the gas break through in under-saturated coals. Material balance check (table 5-6) for the pure CO 2 injection experiments in systems with and without water shows the same result. Figure 5-33 shows the composition profiles of the exit gases for the two systems. It should be noted that the under-saturated (with water) experiment was conducted at a higher pressure of 725 psia where as the saturated (without water/single phase) experiment was conducted at 450 psia. So, even though the saturated system shows a late break through of CO 2, the material balance check (table 5-6) shows that 27 % more CO 2 is injected in the under-saturated coal as compared to the saturated coal. 55

72 Figure 5-33: Composition profiles of CO 2 in saturated and undersaturated systems Table 5-6: Material balance for CO 2 capture in saturated and under-saturated systems Volume at tube pressure (cc) Volume at STD (cc) Unsaturated initial condition 720psia 4897 Saturated initial condition 450 psia Numerical study of ECBM recovery Numerical simulations are done to further validate the experimental and the analytical observations. As discussed in section 3.6, the dispersion experiment is simulated first by including some numerical diffusion in the discretization scheme. In case of no physical dispersion in the system, the converged solution should give a sharp front. As the numerical Peclet number is increased, the solution front gets sharper, which can be seen in figure

73 Figure 5-34: Convergence test for dispersion experiment The dispersed experimental solution seen in section 5.3 is obtained by matching the numerical diffusion to the physical dispersion. Starting from Pe = 1300, both the space and time discretization are coarsened while keeping d τ / dξ = 0.1. A good match is obtained for a numerical Peclet number of 200 (figure 5-35). The best fit straight line in figure 5-14 gave a Peclet number of 106. The discretization parameters are listed in table 5-7. Figure 5-35: Effect of increasing the numerical diffusion Table 5-7: Discretization parameters for dispersion experiment Peclet Number, Pe d τ / dξ Number of grid blocks x (m) t (min)

74 The match between experimental and numerical result for this discretization is shown in figure The data file for this simulation result is attached in Appendix D. Figure 5-36: Composition profile for dispersion experiment Following the same approach of including some numerical diffusion, other experiments are also simulated by using the fully implicit discretization method in the GEM simulator. The dual porosity model with matrix and fracture regions is used to simulate the actual flow in the coal tube. The adsorption parameters and PVT properties of the participating components are assigned and the coal properties like density and compressibility are assigned for the two regions Simulation of methane displacement by pure CO 2 The production rate shown in figure 5-37-a is matched by supplying the adsorption data (figure 2-1) to the simulator. Maximum adsorption of methane on coal is set to be gmol/kg of rock, maximum adsorption of CO 2 is set as 2.8 gmol/kg of rock and the inverse pressure parameter is 1.61*10-4 KPa -1. It should be noted that the simulation result is very sensitive to the adsorption data. The breakthrough time and the production rate are both directly related to the adsorption of the gas species. A more adsorbing injection gas leads to a late breakthrough and a slower production rate. Thus, the adsorption data influences the numerical solutions. 58

75 a b Figure 5-37: Simulation and experimental comparisons for pure CO 2 injection The spread of the front as seen in figure 5-37-b is matched by using a numerical Peclet number of 100. This also compares well with the physical Peclet number found as 106. The discretization parameters are listed in table 5-8. Table 5-8: Discretization parameters for pure CO 2 injection in methane saturated coal Peclet Number, Pe d τ / dξ Number of grid blocks x (m) t (min) Simulation of methane displacement by pure N 2 The production rate shown in figure 5-38-a is matched by supplying the adsorption data (figure 2-1) to the simulator. Maximum adsorption of methane on coal is set to be gmol/kg of rock, maximum adsorption of N 2 is set as gmol/kg of rock and the inverse pressure parameter is 1.61*10-4 KPa -1. The discretization parameters are listed in table 5-9. Table 5-9: Discretization parameters for pure N 2 injection in methane saturated coal Peclet Number, Pe d τ / dξ Number of grid blocks x (m) t (min)

76 It should be noted from table 5-9 that the number of grid blocks is brought down to 50 to match the dispersed front. The convergence study shows a Peclet number of around 1300 for the converged solution which corresponds to around 700 grid blocks. This indicates the significant amount of dispersion present in the system as discussed in section 5.3. Figure 5-38: Simulation and experimental comparisons for pure N 2 injection The numerical Peclet number for this case also matches very well with the physical Peclet number and the production data also matches well with the numerical result as shown in figure Simulation of methane displacement by mixture of CO 2 and N 2 The same adsorption parameters as in section and are supplied to the simulator for the ternary system of mixture injection. The discretization parameters are listed in table Table 5-10: Discretization parameters for mixture injection in methane saturated coal Peclet Number, Pe d τ / dξ Number of grid blocks x (m) t (min) In this case also, a significant numerical diffusion is present as the Peclet number is The numerical solution is in good agreement with the experimental results as seen in figure

77 Figure 5-39: Simulation and experimental comparisons for mixture injection 61

78 Chapter 6 6. Conclusions The experimental results are obtained for binary, ternary and quaternary systems and are compared with the analytical and the numerical results. The following conclusions can be drawn from the comparison of these results: 1. Significant dispersion is present in gas phase systems as shown in section 5.3. The dispersion coefficient is cm 2 /sec. The large dispersion in the tube leads to more dispersed front of the injection gases as compared to the analytical solutions. 2. As predicted in the analytical study, the displacement of methane by a more adsorbing gas occurs via a shock solution between the injection and the initial compositions. This can be seen in figure 5-2 where the composition change interval for methane and CO 2 lies within 0.3 pore volume injections. 3. As predicted in the analytical study, the displacement of methane by a less adsorbing gas occurs via a rarefaction wave between the injection and initial compositions. The composition profiles vary smoothly for both the components as seen in figure 5-8. The composition change interval for N 2 and methane lies in a 1.5 pore volume injection period. The comparison between the analytical and experimental work shown in figure 5-12 also shows the same characteristics of a rarefaction wave. 4. The solutions from the experimental results for the displacements by pure CO 2 and pure N 2 are more dispersed than the analytical solutions because of the large dispersion coefficient and nonrealistic K-values used in the analytical study. 62

79 5. Displacement of methane by a more adsorbing gas occurs slowly due to volume reduction. This can be seen in figure 5-1, where the production rate is smaller than the injection rate until CO 2 breaks through. 6. Displacement of methane by a less adsorbing gas occurs faster due to an increase in the volume. This can be seen in figure 5-7, where the production rate is larger than the injection rate till the time N 2 breaks through. 7. Displacement of methane by a mixture of gases (more adsorbing and less adsorbing than methane) shows three prominent stages of production (figure 5-16). The first stage is controlled by N 2 production at a rate depending on the concentration of N 2 in the injection mixture. Next stage is controlled by CO 2 production at a rate lower than the previous stage due to more adsorption of CO 2 than methane. The third stage is purely due to convection where the rate of production equals the injection rate. 8. Displacement by a more adsorbing gas is slower than the displacement by a less adsorbing gas and that by a mixture of the two occurs at a rate between the displacements by individual gases. This can be seen in figure 5-22 where the methane production rate for the three types of injection gases is shown. As CO 2 concentration in the injection gas increases, the production rate decreases. 9. Two-phase experiments should be conducted at a very small rate in order to have a stable front displacement. The early breakthrough of N 2 seen in figure 5-28 and low water production (figure 5-30) are a result of the unstable front. 10. The experimental results shown in figure 5-31, confirm the presence of a degenerate shock in the solution profile for the particular mixture injection in the two-phase system. This validates the analytical theory as suggested by Seto (2007). 63

80 11. A banking behavior in the methane composition profile and a small leading shock for the CO 2 profile for under-saturated systems are validated by experimental results for saturated and under-saturated systems as shown in figure More CO 2 is trapped when the initial state of coal is under-saturated as shown by material balance in table 5-6. So, under-saturated systems are better from CO 2 sequestration point of view. 13. Numerical models can be constructed to represent the actual physical dispersion in the coal by including numerical diffusion of the order of the actual dispersion present in the system. The numerical Peclet numbers are in good agreement with the physical dispersion and the solution profiles from the numerical models are in good agreement with the experimental results. 64

81 Nomenclature A : Cross Sectional area of coal tube a i : Amount of component i adsorbed on per unit volume of coal c : Volume fraction of a component D o : Molecular diffusion coefficient d p : Particle diameter g : Gravitational constant k : Permeability of coal packing K l : Dispersion coefficient in coal K rg : Gas relative permeability K rw : Water relative permeability l : Length of coal tube n p : Moles of methane in inter-granular porosity Pe : Peclet number p i : Partial pressure of component i q : Volume flow rate R : Universal gas constant S j : Saturation of phase j 65

82 T : Temperature of the coal tube u j : Local flow velocity of phase j U : Flow velocity in the tube v : Injection velocity V 1 : Volume of cylindrical bomb v c : Critical velocity for stable flow V dead : Dead volume of the coal tube V mi : Langmuir constant at specified temperature B i for component i V p : Volume of the inter-granular pore space V pore : Total volume of the pores in coal tube V T : Total volume of bomb + pore volume + dead volume x ij : Mole fraction of component i in phase j z : Non-ideality compressibility factor Greek Symbols ξ : Dimensionless distance τ : Dimensionless time : Dip angle below horizontal : Density difference between displacing and displaced fluid 66

83 : Viscosity difference between displacing and displaced fluid P : Pressure drop across length of the coal tube φ : Porosity of the medium j : Molar density of phase j r : Mass density of coal bed 67

84 References Britannica Encyclopedia, Inc. Online at Chabak, J., Yee, D., Volz, R. F., Seidle, J. P., Puri, R. : Method for Recovering Methane from Solid Carbonaceous Subterranean Formations, U.S. Patent (1996) Chaturvedi, T. : Spontaneous Imbibition and Wettability Characteristics of Powder River Basin Coal, Master s Report, Stanford University (2006). Online at ChemStation : Understanding Your ChemStation Gas Chromatograph Software User Manual Number G , Agilent Technologies (2006) Close, J. C. AAPG Studies in Geology: Natural Fractures in Coal. (1993) 38, Crank, J. : The Mathematics of Diffusion Oxford at the Clarendon Press, N.Y. (1957) Every, R. L., Dell osso, Jr., L., : A New Technique for the removal of methane from Coal, Canadian Mining and metallurgy Bulletin (March 1972) Fulton, P. F., Parente, C. A., Rogers, B. A., Shah, I., Reznik, A. A. : Laboratory Investigation of Enhanced Recovery of Methane from Coal by Carbon Dioxide Injection, paper SPE 8930 presented at the SPE/DOE Symposium on Unconventional Gas Recovery held in Pittsburg, PA, May

85 Garduno, J. L., Morand, H., Saugier, L., Ayers, W. B., McVay, D. A. : CO 2 Sequestration Potential of Texas Low-Rank Coals paper SPE presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, 5-8 October 2003 GEM : Generalized Equation-of-State Model Compositional Reservoir Simulator, Computer Modelling Group Ltd., Version (2006) Gunter, W. D., Genetzis, T., Rottenfuser, Richardson, R. J. H. : Deep coalbed methane in Alberta, Canada. A fuel resource with the potential of zero greenhouses gas emissions, Energy Conservation and Management (1997), 38, S: Hesse, M. A., Tchelepi, H. A., Cantwell, B. J., Orr, F. M., Jr. : Gravity currents in horizontal porous media: Transition from early to late self-similarity, J. Fluid Mechanics (2007), 577, Hill, S.: Channeling in Packed Columns, Chem. Eng. Sci. (1949) 1, No. 6, 247 Johansen, T., Tveito, A., Winther, R., Dahl, O. : Multicomponent Chromatography in a Two Phase Environment, SIAM J. Appl. Math. (1992) 52, no. 1, Lantz, R. B. : Quantitative Evaluation of Numerical Dispersion (Truncation Error), Soc. Pet. Eng. J. (1971) 11, 315 Levine, J. R. AAPG Studies in Geology: Coalification: The Evolution of Coal as a Source Rock and Reservoir Rock for Oil and Gas. (1993) 38,

86 Lin, W. : Gas Permeability of Coal Beds and Thermochemical Recovery of Viscous Oil, Master s Report, Stanford University (2006). Online at Orr, F. M., Jr. : Theory of Gas Injection Processes Tie Line Publications, Copenhagen, Denmark (2007). Perkins, T. K., Johnston, O. C., : A Review of Diffusion and Dispersion in Porous Media, Soc. Pet. Eng. J. (March 1963) Perry, R.H., Green, D.W.: Perry's Chemical Engineers'Handbook McGraw Hill Publication. Online at Pollard, D. D., Aydin, A. GSA Bulletin: Progress in Understanding Jointing Over the Past Century. (1988) 100, no. 8, Pollard, D. D., Fletcher, R. C. Fundamentals of Structural Geology. Cambridge University Press, Cambridge, UK (2005). Resnik, A. A., Singh, P. K., Foley, W. K., : An Analysis of the Effect of CO 2 Injection on the Recovery of In-Situ Methane from Bituminous Coal: An Experimental Simulation, Soc. Pet. Eng. J (Oct 1984) Rice, D. D. AAPG Studies in Geology: Compositions and Origins of Coalbed Gas. (1993) 38,

87 Rohling, J. H., Shen, J., Wang, C., Zhou, J., Gu, C. E. : Determination of Binary Diffusion Coefficients of Gases Using Photothermal Deflection Technique, Appl. Phys. B (2007) 87, Seto, C. J : Analytical theory for two-phase, multicomponent flow in porous media with adsorption, Ph.D. Dissertation. Stanford University, Online at Smith, C. : Coal-Bed-Methane: Trends, Expectations and Realities, IHS Energy Inc. (2003), presentation available online at Smith, D. H., Sams, W. N., Bromhal, G., Jikich, S., Ertekin, T. : Simulating Carbon Dioxide Sequestration/ECBM Production in Coal Seams: Effects of Permeability Anisotropy and Other Coal Properties paper SPE presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, 5-8 October 2003 Tang, G. Q., Jessen, K., Kovscek, A. R. : Laboratory and Simulation Investigation of Enhanced Coalbed Methane Recovery by Gas Injection, paper SPE presented at the SPE Annual Technical Conference and Exhibition, Dallas, TX, 9-12 October Watkins, R. W. : A Technique for The Laboratory Measurement of Carbon Dioxide Unit Displacement Efficiency in Reservoir Rock paper SPE 7474 presented at the SPE Annual Technical Conference and Exhibition, Houston, TX, 1-3 October 1978 Zhu, J : Multicomponent multiphase flow in porous media with temperature variation or adsorption, Ph.D. Dissertation. Stanford University, Online at 71

88 Appendix A A. Individual Components of Experimental Setup Following is a brief description of the individual components of the setup and their role while conducting the experiments: Gas cylinder: Injection cylinder for performing ECBM. Commercial cylinders (figure A- a) are used to do pure gas injection experiments where as a piston cylinder (figure A-b) is used to make a mixture of gases of desired composition. Mass flow controller: A Brooks Instrument s Mass flow controller 5850E (figure A-c) is used to regulate the injection flow rate of gases. It uses the thermal mass flow sensing technique, so needs to be calibrated for each different injection gas. It comes with a Brook s flow computer 0151E which is used to set the flow limit and for calibration. The particular MFC has a range of 0-50 cc/min at standard conditions. Pressure gauge: This gauge measures the injection pressure. Valve 1: This is a needle valve and it restricts the flow into the coal tube (figure A-d). Coal tube: The coal tube is the key part of the experiment. It contains the finely ground coal (characteristics described in section 3.1) with a porosity of 44% and a permeability of 700 md determined by helium injection (discussed in chapter 5). Experiments are to be done in a vertical tube in order to prevent gravity effects so, a zig-zag design is chosen to give the tube a 45 0 inclination to horizontal (figure A-e). After filling the tube with coal, both the ends of coal tube are fitted with screens with micron size apertures. This is to avoid coal particles to move out of the tube. These screens are glued on the edge of small hollow metal cylindrical pieces which are pressure 72

89 fitted into the inner surface of the coal tube with screen facing inside the tube. These cylindrical pieces are threaded on the inner face so that they can be pulled out in case the coal tube needs to be refilled. Valve 2: This is a needle valve and it controls the flow out of the tube. Back pressure regulator: The production end of coal tube is under pressure control with a back pressure regulator, a KBP series Swagelok s instrument (figure A-f). 2-way valve: A two way valve is fitted after the BPR. One outlet is for the bubble flow meter to measure the flow rate and the other outlet goes to Gas Chromatograph for measuring the composition of the exit gases (figure A-g). The two-way valve and bubble flow mater were later replaced by an inline rotameter (figure A-h). Bubble flow meter: Time is measured for a rising bubble in a calibrated tube of 10 cc to know the flow rate of gases produced. Gas Chromatograph: The Agilent 6890 gas chromatograph (figure A-1) uses 2 capillary columns to separate the gases involved in the ECBM study. First column is called plot Q column fitted on a ten port valve inside the GC and second column is a molecular sieve column fitted on a six port valve (figure A-2). The temperatures required for detection by a TCD detector are set by an oven. helium or Hydrogen can both be used as carrier gas in the GC. The operating conditions for the GC are discussed in chapter 5. The gases coming out of the GC are finally vented in a methane vent chamber. 73

90 Figure A-1: Gas Chromatograph Figure A-2: Schematic of the valve and column configuration inside the GC The overall setup is shown in figure A-3. 74

91 Figure A-3: Overall setup for single phase experiments For two phase experiments, there are a few minor changes in the setup as discussed below: Water pump: To saturate the tube with water, a high pressure water pump is used to inject water at a constant rate. Back pressure of the coal tube is controlled which affects the injection pressure of water in the tube. The injection is done from a calibrated glass tube filled with water as shown in the figure so that material balance can be done for water (figure A-j). Water trap: A water trap is set after the BPR, before the mixture is passed into the bubble flow meter and then in the GC. It s a glass tube sealed at the top with a rubber stopper with two holes in it. One hole lets in the mixture of gases and liquid coming out of the coal tube. Water settles down in this glass tube and gas comes out through the other hole to the flow meter and then to the GC. The tube is kept inside an ice pack which helps in condensing all the water (figure A-i). 75

92 76 Figure A: The different pieces of the experimental setup