Geologic Storage of CO2 Principal Investigators: Professors Anthony Kovscek and Franklin Orr, Dept. of Energy Resource Engineering and Professors Jerry Harris and Mark Zoback, Dept. of Geophysics

Executive Summary Research has been carried out in four distinct areas related to geologic storage of CO2: geophysical monitoring strategies of sequestration sites (Professor Harris), the feasibility of CO2 sequestration in coal (Professor Kovscek), the utilization of CO2 for extinguishing coal bed fires (Professor Orr) and the feasibility of sequestering CO2 in depleted shale gas reservoirs (Professor Zoback). In the area of geophysical monitoring, Professor Harris and his research team have developed and tested monitoring strategies for continuous, slow-time monitoring of CO2 storage, i.e., “True4-D.” The methods rely on the generation of subsurface images using continuously acquired sparse datasets. Several acquisition scenarios were simulated and evaluated. Some limited tests with traditionally acquired field data were completed. They introduced the design concepts of sparse data acquisition, dynamic imaging, data evolution, and image integration as one complete example demonstrating the implementation of True4-D subsurface monitoring. Sparse data acquisition aims to keep the operational expense of True4-D comparable to traditional time-lapse surveys. Our data processing methods incorporate several possible approaches that can be categorized as either dynamic imaging or data evolution. In dynamic imaging they use patch-based adaptive data acquisition, where small 3-D surveys (or patches) are adaptively deployed according to predictions from reservoir simulation and other information learned from prior subsurface images. The patched data are time-stamped, sorted and stacked, then fed into an iterative algorithm such as an ensemble Kalman filter (EnKF) for inversion or imaging. In data evolution they complete the sparsely sampled field dataset by reconstructing the missing data using a multi-dimensional estimation algorithm, then process the completed data using traditional imaging methods. The resulting subsurface images are dense in slow time but may have lower 3-D spatial resolution. Complementary to the True4-D imaging problem, they developed a low frequency laboratory measurement for the acoustical properties of rock and coal samples. This method, called Differential Acoustical Resonance Spectroscopy, was used to estimate the compressibility and attenuation of small geological samples in the frequency range of 1000 Hz under simulated in situ pressure conditions. Professor Zoback’s research group has principally been addressing the question of the feasibility of sequestering CO2 in coal beds and depleted organic-rich shale formations. Laboratory studies of coal samples from the Powder River Basin, Wyoming, reveal that the mechanical and flow properties of these samples change dramatically in the presence of carbon dioxide. Notably, they observe that CO2 adsorption causes the static bulk modulus to decrease by a factor of two, while simultaneously causing the dynamic bulk modulus to increase by several percent. Permeability decreases by approximately an

order of magnitude in the presence of CO2, which is consistent with observations of adsorption-related swelling of the coal matrix. CO2 also appears to change the constitutive behavior of coal; helium saturated coal samples exhibit elastic behavior, while CO2 saturated samples exhibit viscous, anelastic behavior, as evidenced by creep strain observations. Because natural gas production from organic-rich shales represents a major energy resource of strategic importance, both in the U.S. and internationally. To exploit this resource over the next several decades, tens of thousands of wells need to be drilled in the U.S. alone. To investigate CO2 sequestration in shale utilizing the tens of thousands of wells yet-to-be-drilled, a series of laboratory experiments have been undertaken to investigate the strength, friction, viscoplasticity, permeability and gas adsorption properties of several organic-rich shale formations as well as synthetic clay/sand mixtures. They find that the physical properties of the shales depend strongly on clay content. Samples with relatively high amounts of clay have been found to have a lower elastic stiffness, lower compressive strength and frictional strength and exhibit more viscoplastic creep than samples with less clay. In the presence of CO2, samples of the Barnett shale with moderate clay content exhibit more creep and has slightly lower strength. A synthetic mixture of kaolinite (the principal clay in the Haynesville shale) and quartz sand shows both swelling and preferential adsorption of CO2 with respect to methane and helium. Other experiments on It is not known yet whether the creep will have deleterious affect on permeability, thus limiting the potential for CO2 sequestration in organic-rich shales. Professor’s Kovscek’s group has been developing a quantitative understanding of gas sorption on coal to predict gas transport, carbon dioxide retention, and the potential for enhanced coalbed methane recovery. Due to the special features of coalbed reservoirs and the nature of gas retention, there are unique issues that need to be taken into account when designing field operations and conducting numerical simulations of gas production and CO2 injection in coalbed methane reservoirs. One issue of particular interest is the permeability evolution of the reservoirs as gas is produced or injected. They investigated the magnitude of permeability change caused by gas sorption, and developed an algorithm to simulate numerically gas sorption and sorption-induced permeability change. The amount of gas sorption and the subsequent volumetric and permeability change of coal samples as a function of pore pressure and injection gas composition were measured in the laboratory. A constant net effective stress (difference between the confining pressure and pore pressure) was maintained during experiments. Therefore, the role of effective stress on permeability was eliminated. Several gases, including pure CO2, pure N2, and binary mixtures of CO2 and N2 of various compositions were used. Experimental results showed that the greater the pressure the greater the amount of adsorption for all gases tested. At the same pressure, the amount of adsorption was greater for CO2 than N2. For the binary mixtures, the greater the fraction of CO2 in the injection gas, the greater the amount of total adsorption. Volumetric strain followed the same trend as the amount of adsorption with pressure and injection gas composition. Permeability however decreased with the increase of pressure and the percentage of CO2 in the injection gas. A key finding of this research is that permeability reduction is mitigated when relatively minor amounts of N2 are included in the injection gas.

Following on from measurements of adsorption, Professor Kovscek’s group have modeled coupled multicomponent (ternary) gas diffusion and adsorption in coal, focusing on CO2, N2-CH4 counter diffusion and simultaneous adsorption associated with CO2 sequestration enhanced coal bed methane (CO2-ECBM) recovery. The extended Langmuir (ELM) and Ideal Adsorbate Solution (IAS) models are used to model the adsorption phenomenon of ternary gas mixtures using pure component isotherms. Previously they showed that the ELM is inadequate to describe the behavior of convectively dominated ternary CH4/CO2/N2 displacements. The comparative study suggests that the multicomponent sorption equilibria described using IAS and ELM are quite different. IAS prediction however is strongly dependent upon the choice of the form for pure gas isotherms. The results also show a significant effect of composition on component diffusivities. Thus, concentration dependent diffusivities need to be taken into account in modeling the coalbed methane recovery, particularly for a multicomponent domain. Model results show that multicomponent mass transfer is comparatively fast, relative to field-scale recovery times, for expected centimeter-sized cleat spacings.

Professor Orr’s group has been carrying out extensive field measurements at the site of a naturally occurring, uncontrolled coalbed fire located southwest of Durango, Colorado. Data collected included subsurface temperatures, borehole logs and cuttings, surface locations of fissures associated with the fire, compositions of gases being emitted from fissures above the combustion zone, and magnetometer surveys. An analysis of the geomechanics of the coal fire indicated that sagging and collapse of overburden rocks after combustion removes coal lead to stress distributions that open existing fractures in the rocks above the coalbed. The resulting fissures provide outlets for hot combustion product gases and inlets for air required to support combustion. A small-scale pilot test of inert gas injection was performed. It showed that CO2 could be injected into the fractured zone created by subsidence of overburden rocks and that the injected CO2 was drawn into the combustion zone by density-driven flow through chimney-like fissures, the same mechanism that draws air required to support combustion into the region where the coal is burning. Pilot test results suggest that inert gas injection could be used to extinguish the fire if sufficient inert gas is available.

 

Geological Storage of Carbon Dioxide Investigation of the Feasibility of CO2 Sequestration

in Coal and Organic-Rich Shale Formations Principal Investigators Mark D. Zoback, Professor of Geophysics Investigators Paul Hagin, Research Associate; Laura Chiaramonte, John P. Vermylen, Hiroki Sone, Graduate Research Assistants; Ashley Enderlin, Laboratory Engineer Executive Summary Laboratory studies of coal samples from the Powder River Basin, Wyoming, reveal that the mechanical and flow properties of these samples change dramatically in the presence of carbon dioxide. Notably, we observe that CO2 adsorption causes the static bulk modulus to decrease by a factor of two, while simultaneously causing the dynamic bulk modulus to increase by several percent. Permeability decreases by approximately an order of magnitude in the presence of CO2, which is consistent with observations of adsorption-related swelling of the coal matrix. CO2 also appears to change the constitutive behavior of coal; helium saturated coal samples exhibit elastic behavior, while CO2 saturated samples exhibit viscous, anelastic behavior, as evidenced by creep strain observations. Because natural gas production from organic-rich shales represents a major energy resource of strategic importance, both in the U.S. and internationally. To exploit this resource over the next several decades, tens of thousands of wells need to be drilled in the U.S. alone. To investigate CO2 sequestration in shale utilizing the tens of thousands of wells yet-to-be-drilled, a series of laboratory experiments have been undertaken to investigate the strength, friction, viscoplasticity, permeability and gas adsorption properties of several organic-rich shale formations as well as synthetic clay/sand mixtures. We find that the physical properties of the shales depend strongly on clay content. Samples with relatively high amounts of clay have been found to have a lower elastic stiffness, lower compressive strength and frictional strength and exhibit more viscoplastic creep than samples with less clay. In the presence of CO2, samples of the Barnett shale with moderate clay content exhibit more creep and has slightly lower strength. A synthetic mixture of kaolinite (the principal clay in the Haynesville shale) and quartz sand shows both swelling and preferential adsorption of CO2 with respect to methane and helium. Other experiments on It is not known yet whether the creep will have deleterious affect on permeability, thus limiting the potential for CO2 sequestration in organic-rich shales.

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Introduction Current estimates of unconventional natural gas resources in the U.S. (and the world) are now so large that significantly increased use of domestic natural gas resources needs to be an essential component of U.S. energy policy. Several recent developments have dramatically changed the energy/climate change landscape and make natural gas a cheap, abundant and clean fuel to lead the transition away from fossil fuels while achieving significant reduction in greenhouse gas emissions and minimizing other pollutants. Multiple independent assessments put U.S. domestic gas resources at over 2000 trillion cubic feet (TCF). It would take less than 1 percent of these resources each year to provide the equivalent amount of electricity in the U.S. as coal. A little over a billion tons of coal is burned in the U.S. each year to provide about 85 percent of the electricity we use. Burning coal for electricity may be cheap and easy, but it accounts for over 40 percent of all CO2 emissions in the U.S. Using gas to generate electricity produces about half the CO2 as coal and a tiny fraction of the sulfur oxides, particulates and formaldehyde (and none of the mercury) that comes from burning coal. Substituting natural gas for coal also eliminates the many environmental problems associated with disposal of both coal mine wastes and 130 million tons of fly ash each year (in the U.S. alone) as well as the health impacts (and health care costs) related to mining and burning coal. These same benefits will apply elsewhere in the world. Organic-rich shale gas deposits are extensive in Canada and much of Asia (including China), South America, Europe, Russia, Africa and Australia. Each of these regions should be able to exploit their own domestic shale gas resources at large scale. Offsetting coal-fired electrical generation with gas would meet the ~20 percent reductions in emissions by 2020 mentioned in the climate/energy legislation now being considered by Congress. This is a realistic goal as it can utilize the existing excess capacity for electricity generation from gas-fired plants. Alternatively, if we continue to use coal at current rates, meeting these emission reductions would require large-scale implementation of CCS at hundreds of coal burning plants. At the rates and volumes of CO2 storage required, the great majority of geologic formations in the central and eastern U.S. will not be suitable because of low permeability, which makes it essentially impossible to inject CO2 at high rates, and the limited amount one could increase pressure in these formations without potentially inducing earthquakes. In addition, large-scale implementation of CCS from coal burning plants comes at high capital costs and significant reductions in plant efficiency due the energy required to separate the CO2 from flue gas, which is mostly harmless nitrogen. Thus, even when geologically-suitable sites for CCS are found, it may not be feasible to implement CO2 separation at a large fraction of the aged coal burning plants now operating in the U.S. It is important to emphasize that these critically-important resources must be developed in an environmentally responsible manner - minimizing water use, limiting the foot print of wells, surface facilities and pipe-lines and assuring that hydraulic fractures

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propagation, critical to the successful development of the low permeability shale, does not threaten aquifers. One important aspect of this is to consider geologic sequestration of CO2 generated by natural gas-fueled power plants. Tens of thousands of wells will need to be drilled to develop shale gas resources in the U.S. alone. The research carried out with support from GCEP was to investigate the feasibility of CO2 sequestration in shale utilizing the tens of thousands of wells yet-to-be-drilled. While the feasibility of large-scale geologic sequestration of CO2 is being investigated in saline aquifers, depleted oil and gas reservoirs and unmineable coal seams at sites around the world, there is a pressing need to identify as many sites for geologic sequestration of CO2 as possible. Coal bed methane (CBM) production from unmineable coal seams is another unconventional gas resource of increasing importance. Methane is generated during the coal maturation process and as a result of microbial action and resides in the coal matrix as an immobile, adsorbed phase. During CBM production, the pressure inside a coal seam is reduced and methane desorbs from the coal matrix, at which point it exists as a free gas and can flow through the cleat (natural fracture) system to the producing wells. According to the U.S. Energy Information Agency (EIA), coal bed methane production currently accounts for 10% of the domestic natural gas supply, and is anticipated to increase significantly over the next several decades as conventional gas supplies continue to decline. Coal exhibits the interesting property of selectively adsorbing certain gases. In particular, many coals have been observed to preferentially adsorb carbon dioxide over methane (Radovic, Menon et al. 1997), making coal an attractive candidate for geological sequestration of CO2, since adsorbed gases are essentially immobile (Reeves 2001; Metz, Davidson et al. 2005). In addition, because the adsorption of carbon dioxide forces desorption of methane, it is possible that CO2 can be used to enhance coal bed methane (ECBM) production (Reeves, Taillefert et al. 2003). While several small-scale field studies have been performed (or are currently underway) in various coal seams around the world, the feasibility of ECBM or geological sequestration of CO2 for a given site is still largely dependent on predictions from numerical modeling tools such as reservoir simulators that have been modified for CBM (Sawyer et al., 1990; Law et al., 2004). These numerical models require values for numerous input parameters, many of which can be derived from laboratory data. Furthermore, predictions from reservoir simulators can only be as accurate and realistic as the underlying theoretical and mathematical models allow. Laboratory studies are needed to develop and verify theoretical models of the complex mechanical and chemical behavior of coal. For example, the adsorption of gases onto the surfaces of the coal matrix has been observed to cause volumetric swelling of the coal, while desorption of gases causes volumetric shrinkage (Harpalani and Schraufnagel 1990). This swelling and shrinkage of the matrix changes the width of the cleats and natural fractures in the coal, which in turn causes changes in cleat permeability (Harpalani and Chen 1997) (Levine 1996; Palmer and Mansoori 1996). Because adsorption, and therefore swelling, increases with pressure, permeability is expected to decrease as a function of pressure. However, in

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the absence of swelling, permeability will increase as a function of pressure. These opposing effects need to be better understood if accurate models of permeability change are to be developed for coal. The Power River Basin, which extends from eastern Wyoming into southeastern Montana, is the largest and fastest growing CBM producer in the world, with approximately 17,000 wells currently producing 30 billion cubic feet of gas per month. The primary production coal seams fall within the Wyodak-Anderson zone of the Fort Union Formation, at depths ranging from 500 to 1500 feet. For this study, we obtained four-inch diameter core samples from the Roland and Smith coal zones, from a depth range of 1300-1400 feet. The samples have an initial porosity of approximately 10%, an initial permeability of 1 millidarcy, and ash content that varies from 10-20%. Our research focus for this study has been to better understand the effects of adsorption on the mechanical and flow properties of sub-bituminous coals. We conducted laboratory experiments on one-inch diameter core samples of coal, under hydrostatic and triaxial loading conditions, as a function of effective stress, using both helium and carbon dioxide as saturating gases. We present measurements of elastic stiffness, permeability, swelling strain, and creep strain, for both intact and powdered coal samples. Laboratory Studies on Shale and Clay To our knowledge there are no plans or activities related to large-scale CO2 injection in depleted shale formations although a pilot project is being planned by the Kentucky Geological. If our research demonstrates that it is feasible to consider sequestration of CO2 in these formations after depletion, it has potential for widespread application. The potential for CO2 sequestration in these formations is attractive for several reasons. They are widely distributed (unlike depleted oil and gas reservoirs), there will be an infrastructure of wells, pipelines, etc. available (unlike saline aquifers) and the pore pressure in the shale formations will be depleted prior to CO2 injection thereby reducing the potential for induced seismicity which is potentially another problem in many saline aquifers. Finally, because CO2 is preferentially adsorbed to the organics and clays in shale reservoirs with respect to methane, there is also the potential for enhanced gas recovery from the organic-rich shale formations if CO2 is injected into them; however, we are not proposing to address this topic in this proposal. A series of laboratory experiments have been undertaken to investigate the strength, friction, viscoplasticity, permeability and gas adsorption properties of several organic-rich shale formations as well as synthetic clay/sand mixtures. Samples used in the experiments come from two different gas shale reservoirs: the Barnett shale and the Haynesville shale. Samples for Barnett shale come from various depths of about 2600 m and we categorize them into 2 groups according to their visual appearance as “light” and “dark” colored groups which are thought to reflect their carbonate and clay content. Haynesville samples come from depths of about 3500, and the mineralogical contents are known from XRD analyses of adjacent samples (Table 1). Although visual appearances of Haynesville samples do not vary significantly as in Barnett samples, we call samples

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with more carbonate content as the “light” group and the other as “dark” group to match the description of the Barnett samples. Samples were kept under room humidity condition prior to the test and experiments were performed under dry and drained condition. Due to the dry condition of the samples, we were able to eliminate poro-elastic effects so our data represents the mechanical behavior of the dry framework. All samples were shaped to 25.4 mm (1 inch) diameter. For all Haynesville samples, sample lengths were 50.4 mm (2 inch) and the axes of the cylindrical samples were perpendicular to the bedding plane. Lengths of Barnett samples varied between 38-56 mm (1.5-2.2 inch) except for one short sample (28 mm, 1.1 inch) whose rock strength data was neglected from the analyses. Barnett samples included those cored parallel and perpendicular to the bedding plane. Table 1. Mineral contents of the sample groups and summary of main experimental data. Composition of Barnett samples are rough estimates based on geophysical logging data.

A typical experiment was performed in 3 stages, hydrostatic, triaxial, and failure and friction, as shown in Figure 1. In the hydrostatic stage, samples were subject to 3 steps of isotropic pressures, after which the pressure was held constant for 3 hours to observe any possible hydrostatic creep deformation. After each 3 hour holds, the pressure was decreased and increased over several minutes before proceeding to the next pressure step, in order to measure the elastic bulk modulus of the sample.

Sample Group

Qtz/Felds [%]

Carbonate [%]

Clay [%]

Others [%]

Pc Triax [MPa]

Creep Stress 1st/2nd step

[MPa]

Frictional Coefficient

UCS [MPa]

30 - 0.772 30 46.5 / 92.0 0.641 30 46.5 / 92.1 0.608 20 47.3 / 95.2 0.750

Barnett Dark 60 10 25 5

30 - 0.741

130

30 - 0.822 Barnett Light 35 55 5 5 20 44.7 / 89.7 0.975 220

60 - 0.308 60 29.4 / 58.4 0.288 Haynesville

Dark 45 13 39 3 30 32.1 / 61.0 0.391

90

60 - 0.484 30 37.1 / 77.1 0.571 Haynesville

Light 28 48 22 2 20 34.4 / 74.6 0.663

160

Figure 1. The confining pressure and axial differential loading history

during a typical experiment with shale samples.

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In the triaxial stage, the axial differential load was increased in two steps while holding confining pressure constant at 20, 30, or 60 MPa. Differential load was increased in 2 steps, after which the load was held constant again to observe creep deformation and un-/re-loaded to measure the Young’s modulus and Poisson’s ratio. The size of the differential loads was chosen to reach about 50% of the rock strength after 2 load steps. Finally in the failure and friction stage, the sample was taken to failure while the differential load was servo-controlled to produce constant axial strain rates of about 10-5 s-1. After rock failure was observed, the sample was allowed to slide along the failure plane until a steady frictional strength was observed. After the experiment, the angle of the failure plane was measured relative to the sample axis to obtain the shear and normal stresses resolved on the failure plane. The experimental condition for each sample is summarized in Table 1.

Elastic Properties Figure 2 displays the measured Young’s modulus and Poisson’s ratio of the samples tested during the first triaxial load step. In both Barnett and Haynesville samples, the light groups were observed to be stiffer than the dark groups, which may be caused by the abundant cement contents in the light samples. Also Barnett samples are generally stiffer than Haynesville samples. Poisson’s ratio may tend to increase with increasing Young’s modulus but the trend is not clear. The accuracy of these measurements is confirmed by comparing the bulk modulus calculated by using Young’s modulus and Poisson’s ratio and the bulk modulus obtained from the hydrostatic stage. The differences between the two estimates were distributed within 2.5 GPa standard deviation.

0.15

0.17

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0 20 40 60Young's Modulus [GPa]

Poi

sson

Rat

io

80

Barnett DarkBarnett LightHaynesville DarkHaynesville Light

Figure 2. Young’s Modulus and Poisson’s ratio data obtained from the first

triaxial load step.

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Ductile Properties

Ductility of the sample was studied by observing the creep strain during constant differential load. Samples first show instantaneous shortening in response to a step of differential load, and then show creep strain over time. Figure 3 shows the time-dependent creep strain portion of 4 samples during the first of two triaxial load steps. Creep strain is generally observed to be greater for the dark sample groups and also for Haynesville samples. Comparison of creep strain between the first and second differential load steps does not show a consistent trend (Table 1). Barnett dark and Haynesville light samples crept about twice as much in the second load step compared to the first load step. However others including Haynesville dark sample crept almost the same amount in the first and second load step. In terms of confining pressure dependency, creep tests conducted on same sample groups under different confining pressure (Table 1) did not show clear difference in creep behavior.

Figure 3. Creep during the first load step plotted against time.

Figure 4 shows how much creep (left axis of each figure) occurs on the different samples as a function of Young’s modulus and clay content. Note in the right side of Figure 4, that as the clay content increases, the creep strain increases markedly. Similarly, as Young’s modulus increases the amount of creep strain decreases markedly.

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0

0.0001

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0 10 20 30 40 50 60 70Young's Modulus [GPa]

Cre

ep S

train

in 1

st T

riaxi

al L

oad

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Frictional Coefficient

Bn-D Creep Bn-L Creep Hv-D Creep Hv-L CreepBn-D Friction Bn-L Friction Hv-D Friction Hv-L Friction

0

0.0001

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0 10 20 30 40 50

Clay Content [%]

Cre

ep S

train

in 1

st T

riaxi

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oad

0.0

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1.2Frictional C

oefficient

Bn-D Creep Bn-L Creep Hv-D Creep Hv-L CreepBn-D Friction Bn-L Friction Hv-D Friction Hv-L Friction

Figure 4. Creep strain after the first triaxial load and frictional coefficient plotted

against Young’s modulus (left figure) and clay content (right figure). Strength and Friction The peak axial stress observed in the failure stage of the experiment represents the strength of the samples and the frictional coefficient was calculated by the ratio of the shear and normal stress resolved on the failure plane after the fault was formed. Strengths and friction data generally followed the same trend as the elastic modulus where the strength of both the Barnett and Haynesville samples decrease markedly as the clay contents increases (Table 1). Friction data is also plotted against Young’s modulus and clay content in Figure 4. There is a clear positive correlation between the coefficient of friction and the Young’s modulus and an inverse correlation with clay content. Figure 5 shows that in the presence of CO2 the shale becomes more viscoplastic. Note that with each of the two axial loading steps, more creep strain occurs with CO2 in the pores of the shale than with nitrogen. The presence of CO2 also slightly lowers the strength of the shale. We do not yet understand why this occurs or whether it will have a deleterious affect on permeability or other properties of the shale related to its suitability as a formation for CO2 storage.

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Figure 5 – Creep tests on samples of Barnett shale show that the amount of

creep is enhanced in the presence of CO2. As part of our experiments on synthetic samples, Figure 6 shows time-dependent creep of illite under hydrostatic loading with He, CH4 and CO2 after an increase in confining pressure (pore pressure is held constant). Note that the amount of creep compaction increases in the presence of adsorbing gases. Illite is the principal clay in both the Barnett and Haynesville shales.

Figure 6 – Creep compaction of illite under hydrostatic compression (14 MPa confining

pressure, 2 MPa pore pressure) with He, CH4 and CO2. The swelling effect of adsorbing gases is illustrated in Fig. 7. In this case, a sample of kaolinite subjected to hydrostatic compression is monitored as pore pressure is increased but effective stress is kept constant. The compression of the sample with He in the pores reflects the mechanical effect resulting from the fact that volumetric strain is not strictly a function of effective stress, but the pore pressure term must be modified by the Biot coefficient (Nur and Byerlee 1971). The expansion of the sample in the presence of helium and CO2 is the result of gas adsorption and swelling.

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Figure 7 – Hydrostatic compression of kaolinite under constant effective stress

but varying pore pressure.The sample compacts when He is in the pores but swells in the presence of CH4 and CO2.

Discussion of Shale Experiments

Our laboratory results reflect the variety of mechanical and deformational properties gas shale reservoir rocks potentially exhibit within a reservoir, as well as between different reservoirs. Thus, it is essential to identify key parameters that correlate with and controls the deformational characteristics of these rocks. Laboratory data suggests that Young’s modulus and clay content are good proxies to evaluate the relative differences in friction and ductility between gas shale rocks. There are various parameters that could control the strengths, friction and ductility of a rock, such as porosity, texture, cementation, mineralogy, etc. Comparison with the mineral contents shown in Table 1 gives us some insight. The similarity of properties observed between Barnett dark and Haynesville light samples suggests that clay content may be one of the controlling factors. It is seen that Barnett dark and Haynesville light samples have similar clay contents while quartz and carbonate content differs significantly. Together with the fact that the clay-rich Haynesville dark samples exhibit low-strength/high-ductility and clay-poor Barnett light samples exhibit high-strength/low-ductility, these results suggest that clay content is the strongest control on various deformational properties amongst other parameters. Figure 4 shows that creep strain and frictional coefficient correlates well with the clay content. The idea is also supported by the fact that clay minerals have anomalously low frictional coefficients and mixing of clays reduces the friction of geological materials (Paterson and Wong 2005). Quantitative characterization of the ductile behavior of gas shale reservoir rocks is important for the successful exploitation of the resource. Ductility not only influences the proneness of reservoir rocks to hydraulic fracturing, but also affects the long-term reservoir response during depletion. Over geologic time scales, ductile deformation could also alter the state of stress as commonly observed around salt domes. Past studies of creep behavior of reservoir materials have suggested various formulations for the constitutive law describing time dependent creep deformation (de Waal and Smits 1988; Hagin and Zoback 2007). Amongst which, a power law function of pressure and/or time is known to explain creep of geological materials well. However, our data so far suggests that creep strain is linearly proportional to the logarithm of time, which

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tentatively suggests a logarithmic formulation to describe creep deformation. The pressure dependence of creep strain is so far unclear and needs to be understood in order to constrain the constitutive relation of these rocks. Tests on synthetic clays indicate that the adsorption of CH4 and CO2 has a marked effect on the viscoplastic properties. Laboratory Studies on Coal

As mentioned above, recent experimental efforts have focused on better understanding the relationship between coal swelling/shrinkage and permeability change. Robertson and Christiansen conducted a series of laboratory experiments on coal samples form the Powder River Basin, and found that an empirically derived variable modifier was needed to relate unconfined swelling strain to permeability reductions using the Palmer-Mansoori and Shi-Durucan models (Robertson and Christiansen 2005). This result is interesting because most off-the-shelf reservoir simulators use either the Palmer-Mansoori or Shi-Durucan equations to model shrinkage and swelling. (Fujioka 2008) conducted laboratory experiments on samples of the Bibai coal from the Ishikari Basin, which focused on testing the repeatability of physical properties measurements after flooding a CO2 saturated sample with N2. Interestingly, while shrinkage and swelling strains were observed to be reversible and repeatable, permeability and ultrasonic P-wave velocity were observed to permanently change during the initial CO2 saturation phase. In addition, some fundamental research into how adsorption of CO2 changes the micro and meso pore structure of coal is being carried out (Mastalerz, Rupp et al. 2008). Notably, the authors find that CO2 adsorption decreases the mean pore size of vitrains, but does not effect the pore size distribution of other components of coal.

We obtained 4-inch diameter core samples of sub-bituminous coal from the Roland and Smith coal zones of the Fort Union Formation in the Powder River Basin, Wyoming. The depth to these zones is approximately 1300-1400 feet. Note that these samples are from the same well and depth range as those reported on by (Tang, Lin et al. 2005) in previous GCEP reports. These samples were stored at room conditions, and so it was assumed that the initial methane gas was completely desorbed prior to testing. Due to the numerous cleats and micofractures, obtaining one-inch diameter core plugs for testing was difficult, and some samples were molded from powdered coal. For both the intact and powdered coal samples, sample preparation procedures followed those initiated by (Tang, Lin et al. 2005), in an effort to make comparison of the two data sets possible. For both the intact and powdered samples, cylindrical core plugs were prepared, with a nominal size of one-inch diameter and two-inch length. For reference, the initial porosity of the intact samples was approximately 10%, while that of the molded samples was approximately 30%. The samples contain 10-20% ash content, which serves to reduce the initial bulk density (~1.5 g/cc for the intact samples). Prior to testing, all samples were vacuum-dried until constant mass was achieved, to remove residual moisture and gas.

In an effort to establish a baseline set of measurements, we tried to isolate the effects of stress, pore pressure, temperature, moisture, and gas mixture by varying only one component of the system at a time. For all of the data shown below, measurements were carried out at room temperature, only single phase Helium or CO2 was used as a pore fluid, and moisture and humidity were minimized. However, both pore pressure and

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effective stress were varied during experiments. Measuring permeability as a function of both pore pressure and effective stress is particularly important, as permeability can vary due to swelling/shrinkage (a function of pore pressure) and due to mechanical opening/closure of pathways (a function of effective stress).

Adsorption Isotherms For general reference and internal verification of the isotherms reported by (Tang, Lin et al. 2005), we measured adsorption isotherms for both intact and powdered coal samples. Total adsorption isotherms (at 22°C) were determined for pure CO2 using the volumetric method. Our results are shown in Figure 8. While our isotherms fall slightly below those measured in the lab of Prof. Kovscek’s lab, given the difference in apparatus setups and innate heterogeneity of coal, we believe that a maximum of 15% error between the data sets provides a satisfactory match.

Figure 8: Total adsorption isotherm for powdered and intact coal samples from the Powder River Basin, Wyoming. Experiments performed at a temperature of

22 C. Blue curves show data from this study (“Zoback” in the legend). Black curves are shown for comparison are adapted after

Tang et al 2005 (“Kovscek” in the legend).

Static and Dynamic Elastic Parameters of Coal We measured the elastic stiffness of intact samples of PRB coal using two different methods. Static elastic parameters can be determined from a stress-strain curve. In general, the slope of the tangent of the stress-strain curve at a particular value of strain gives the elastic stiffness at that point. For example, bulk modulus can be calculated by

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plotting hydrostatic stress against volumetric strain. On the other hand, assuming that the sample is an isotropic, homogeneous medium, dynamic elastic parameters can be derived from measurements of ultrasonic velocities. At a particular value of stress or strain, the dynamic bulk modulus is given by:

⎟⎠⎞

⎜⎝⎛ −= 22

34

sp VVK ρ

where K is the bulk modulus, ρ is bulk density, Vp is the P-wave velocity, and Vs is the S-wave velocity. Note that for an isotropic, homogeneous elastic material, the static and dynamic measurements will produce identical values of bulk modulus. For these tests, a series of loading cycles were performed, in which the confining pressure was increased to a target pressure at a rate of 6 MPa/hour, held constant for a period of 10 hours, and then decreased back to the initial pressure value. The pressure holds were used to test whether or not creep strain would occur; please see the section on creep strain below. Pore pressure was held constant during these tests. The samples were first saturated with Helium, and a series of loading cycles was performed. The samples were then unloaded to the initial conditions, and saturated with CO2. The same series of loading cycles was then repeated. Stress and strain data were collected every 10 seconds. P and S wave velocities were captured every 60 seconds. The results from these measurements are shown in Figure 8. There are several important details to note in this Figure. First, note that for the Helium-saturated case, the dynamic and static values of bulk modulus are nearly identical, indicating that the coal sample is elastic, which is the expected behavior. Interestingly, when the same sample is saturated with CO2, the static bulk modulus decreases by approximately a factor of two, while the dynamic modulus increases slightly. This divergence in behavior suggests that the CO2 is bearing some of the externally applied load, and is stiffening micropores while lubricating larger grain and maceral boundaries. In order to verify the observed increase in dynamic bulk modulus with CO2 saturation, we conducted a series of cyclic-loading experiments as a function of pore pressure. Because the stiffness of CO2 increases with pressure, we expected the observed dynamic bulk modulus to increase with pore pressure. The results of these tests are shown in Figure 9, and as anticipated, dynamic bulk modulus increases with increasing pore pressure. While the increase is not large, an approximately 20% change in bulk modulus with a factor of four increase in pore pressure, it is observable.

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Figure 9: Static and dynamic bulk modulus plotted as a function of effective

pressure for Helium and CO2 saturated PRB coal samples. The pore pressure was kept constant at 1 MPa. Note that while the static bulk modulus

decreases by a factor of two after being saturated with CO2, the dynamic bulk modulus actually increases slightly.

Permeability of Intact and Powdered PRB Coal Samples

Klinkenberg-corrected measurements of Darcy-flow permeability are plotted as a

function of effective stress in Figure 10. Please note that unlike most gas permeability measurements on coal, for these tests the pore pressure was held constant at 1 MPa, while the effective stress was increased. We implemented this experimental procedure because we are interested in understanding the effects of both adsorption and stress on permeability.

There are several things to note in Figure 10. For the reference data set collected using Helium, the observed decrease in permeability with increasing effective stress can be attributed to the mechanical closing of cleats and other pathways. Saturating the samples with CO2 causes a decrease in permeability, regardless of effective stress, and can be thought of as a downward shift along the y-axis in this plotting space. Finally, the differences between the powdered and intact samples are interesting. Relative to the intact sample, the powdered sample has a higher initial permeability, a larger change in permeability with increasing effective stress, and a smaller decrease in permeability following CO2 saturation. All of these observations are consistent with the fact that powdered sample has more porosity (30% vs. 10%) and is more compressible (by a factor of 2-3) than the intact sample.

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Figure 10. Gas permeability plotted as a function of effective hydrostatic stress for both powdered and intact PRB coal samples.

Measurements of Confined Swelling Strain The decrease in permeability following CO2 saturation suggests that the coal matrix is swelling in response to adsorption. Because we have been measuring permeability under hydrostatic loading conditions, we elected to measure volumetric swelling strain under the same boundary conditions, in an effort to make relating the two quantities easier. These swelling measurements are shown as a function of time in Figure 11, and as a function of pore pressure in Figure 12. In both figures, the effective hydrostatic stress is held constant at 1 MPa. The swelling behavior as a function of time is interesting because the swelling strain can be seen to increase linearly at first, followed by a much more gradual asymptotic approach to the equilibrium swelling for a given pore pressure. These observations can be attributed to convective behavior while the CO2 is saturating the macro-pore space and cleats, followed by diffusive behavior as the CO2 slowly invades the matrix. As expected, swelling strain increases with adsorption, which in turn increases with pore pressure. While we do not currently have enough data to attempt any quantitative modeling of the adsorption and swelling, we plan to continue making swelling measurements in the future.

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Figure 11: Volumetric swelling strain plotted as a function of time for powdered and intact PRB coal samples. Negative strain indicates swelling. The samples are

initially saturated with Helium. At approximately 3 hours, the samples are flooded with CO2 at constant pore pressure and effective hydrostatic stress.

Figure 12: Volumetric swelling strain plotted as a function of pore pressure for intact PRB coal samples, at a constant effective hydrostatic stress of 1 MPa.

Observations of Creep Strain in Coal

During the cyclic-loading tests we conducted, we observed an interesting change in deformation behavior when the samples were saturated with CO2. Specifically, even when the effective hydrostatic stress was held constant, the samples continue to deform. This time-dependent behavior is typical of materials that have a viscous component of deformation (Figure 13).

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Figure 13: Volumetric creep strain plotted as a function of time for powdered and intact PRB coal samples, at a constant effective

hydrostatic stress of 5 MPa. Notice that the intact, Helium saturated sample behaves elastically: there is no significant time-dependent

strain. On the other hand, the intact, CO2 saturated sample continues to deform as a function of time. The powdered samples show more

complex behavior, but the CO2-saturated sample still exhibits significantly more creep strain than the Helium-saturated sample.

Discussion of Shale Experiments

Our laboratory studies on coal samples from the Powder River Basin, Wyoming, reveal that the mechanical and flow properties of these samples change dramatically in the presence of carbon dioxide and permeability decreases by approximately an order of magnitude in the presence of CO2 which is consistent with observations of adsorption-related swelling of the coal matrix. CO2 also appears to change the constitutive behavior of coal; helium saturated coal samples exhibit elastic behavior, while CO2 saturated samples exhibit viscous, anelastic behavior, as evidenced by creep strain observations.The next obvious step in this research is to combine the types of laboratory studies carried out here with pilot injection tests. Opportunities for such an experiment are now being carried out.

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Published Papers Bohnhoff, M., M. Zoback, et al. (2010). "Seismic detection of CO2 leakage along

monitoring wellbores." International Journal of Greenhouse Gas Control. Chiaramonte, L., M. Zoback, et al. (2008). "Seal integrity and feasibility of CO 2

sequestration in the Teapot Dome EOR pilot: Geomechanical site characterization." Environmental Geology 54(8): 1667-1675.

Hagin, P. and M.D. Zoback (2009) Laboratory studies of the Adsorption, flow, static and dynamic moduli of low-rank coal samples from the Powder River Basin, Wyoming, Stanford Rock and Borehole Geophysics Consortium Annual Meeting.

Sone, H. and M. D. Zoback (2010). Strength, creep and frictional properties of gas shale reservoir rocks 44th US Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, in press.

References Cited in Text de Waal, J. A. and R. M. M. Smits (1988). "Prediction of reservoir compaction and

surface subsidence: Field application of a new model." SPE Formation Evaluation(June): 347-356.

Fujioka, M. (2008). Field experiment of CO2-ECBM in Ishikari Basin of Japan. Coal-Seq VI, Houston, Texas.

Hagin, P. and M. D. Zoback (2007). "A dual power law model for prediction and monitoring of long-term compaction in unconsolidated reservoir sands, submitted." Geophysics 72(5): E165-E173.

Harpalani, S. and G. Chen (1997). "Influence of gas production induced volumetric strain on permeability of coal." Geotechnical and Geological Engineering 15(4): 303-325.

Harpalani, S. and R. Schraufnagel (1990). "Shrinkage of coal matrix with release of gas and its impact on permeability of coal." Fuel 69(5): 551-556.

Levine, J. (1996). "Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs." Geological Society London Special Publications 109(1): 197.

Mastalerz, M., J. A. Rupp, et al. (2008). Evaluating the effects and mechnaisms of CO2 sorption in Illinois Basin Coals. Coal-Seq VI, Houston, Texas.

Metz, B., O. Davidson, et al. (2005). IPCC Special Report on Carbon Dioxide Capture and Storage: Prepared by Working Group III of the Intergovernmental Panel on Climate Change, Cambridge, Cambridge University Press.

Nur, A. and J. D. Byerlee (1971). "An exact effective sress law for elastic deformation of rock with fluids." J. Geophys. Res.: 6414-6419.

Palmer, I. and J. Mansoori (1996). "How Permeability Depends on Stress and Pore Pressure in coalbeds: A New Model. SPE 36737."

Paterson, M. S. and T.-f. Wong (2005). Experimental rock deformation - The brittle field. Berlin, Springer.

Radovic, L., V. Menon, et al. (1997). "On the porous structure of coals: Evidence for an interconnected but constricted micropore system and implications for coalbed methane recovery." Adsorption 3(3): 221-232.

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Reeves, S. (2001). Geological Sequestration of CO2 in Deep, Unmineable Coalbeds: An Integrated Research and Commerical-Scale Field Demonstration Project.

Reeves, S., A. Taillefert, et al. (2003). Allison Unit CO (2)-ECBM Pilot: A Reservoir Modeling Study, NASA Center for AeroSpace Information, 7121 Standard Dr, Hanover, Maryland, 21076-1320, USA.

Robertson, E. and R. L. Christiansen (2005). Modeling permeability in coal using sorption-induced strain data, Paper SPE 97068. 2005 SPE Annual Technical Conference and Exhibition, October 9-12, 2005, Dallas, Texas.

Tang, G. Q., W. Lin, et al. (2005). A laboratory investigation of CO2 injection for enhanced methane recovery for coalbeds. Coal-Seq V, Houston, Texas.

Contact Information Mark Zoback: zoback@stanford.edu, 650-725-9295

Characterization of a Coalbed Fire Near Durango, Colorado: Pilot CO2 Injection Test Summary

Investigators Taku S. Ide, Ph.D. student, Energy Resources Engineering; Franklin M. Orr, Jr., Professor, Energy Resources Engineering; David Pollard, Professor, Geological and Environmental Sciences; Reginald Mitchell, Professor, Mechanical Engineering; Samuel Krevor, Postdoctoral Fellow, Energy Resources Engineering; Bill Flint, Southern Ute Indian Tribe Department of Energy; Kyle Siesser, Southern Ute Indian Tribe Department of Energy. Abstract

This report describes results from the final six months of research on the physical mechanisms that control the behavior of uncontrolled fires in subsurface coal beds. For a detailed discussion of background and previous work on this project, please see the 2009 progress report (Harris et al., pp. 117-1441). New results include sensitive magnetometer surveys that revealed the locations of zones where the coal is currently burning, zones that have burned previously, and zones that have not been affected by the fire. Based on previous modeling and field measurements, a pilot test of CO2 injection was designed. Subsequent to the completion date of the project (December 31, 2009), the pilot test was conducted. Preliminary results of that test are also described.

Introduction The objective of this research effort has been to develop a detailed understanding of

the geomechanical and flow mechanisms that make it possible for coalbed fires to continue to burn for decades or more. That understanding is the basis for the design of an inert gas injection scheme aimed at extinguishing the fire.

The project has investigated an existing fire located in southwest Colorado that was discovered in 1998 (though it is likely that it started well before 1998) and has continued to burn since then. Previous investigations have included drilling of boreholes in which thermocouples for temperature measurements were installed, surface topography, detailed characterization of fissures (types, orientations, apertures, temperatures and lengths), well logs, driller’s logs, subsurface temperature, gas composition, subsurface images using seismic and ground penetrating radar, and regions of snowmelt over the coalbed fire. In addition, numerical simulations of the geomechanical response of the overburden rocks to the conversion of solid coal to combustion product gases and flow simulations have been conducted. A detailed report is available that describes the background of the project, the field site location and geology, and the results of all the previous measurements and simulations (Harris et al., 117-1441).

Very useful new evidence was obtained from two surveys conducted with a sensitive magnetometer, which showed the current location of the combustion zone in addition to unburned regions and those that had burned previously. Results of those surveys are reported here.

The combination of field characterization data and simulations was sufficient to build a conceptual picture of the sequence of events that sustains a coalbed fire, and that picture was used in the design of a pilot test of inert gas injection at the field site. That pilot test was carried out in April, 2010, and preliminary results of the test are also reported here.

Results Over the past three and a half years, one of the four known coal fires on the Southern

Ute Tribal Land has been studied in detail. This fire, known as North Coal Fire, is located along the western rim of the Hogback monocline, just south of the Iron Springs Gulch and Soda Springs Canyon junction. In previous years, efforts were concentrated on characterizing the fire, which includes identifying possible air inlets, delineating the extent of the fire zone, and developing conceptual pictures of the North Coal Fire. Based on our current understanding of the North Coal Fire, a pilot CO2 injection test at the fire site was designed. This pilot test tested whether inert gas injection could be used to extinguish the fire.

There are currently two active regions over the North Coal Fire—one to the North, called the Crestal Extension Fire, and one to the South. We focused on the Crestal Extension Fire for the CO2 injection pilot test. Figure 1 is a contour map of the North Coal Fire area, with the Crestal Extension Fire circumscribed by the red box. Fissures that have formed over the coal fire are also shown. The Fruitland Formation—which contains the lower coal that is burning—outcrops between the two green lines extending from the SW towards the NE.

Figure 2 illustrates the conceptual picture assembled from geomechanical simulations of the stresses created as the overburden rock sags as the solid coal beneath is removed by combustion. Two potential sources of combustion air exist. These fires most likely start near the outcrop, and in the early stages, air is drawn in from the outcrop. As the fire continues to burn, however, the weight of the rock above the coal seam causes the roof to sag and eventually collapse. That collapse causes cracks (fissures) to form where the rock layers are already fractured. Fissures that form near the advancing combustion front provide a pathway for hot combustion product gases to escape. As the combustion front advances past these fissures, air flows in subsequently through one or more of the fissures in the previously burned zone. Rock cuttings, well logs, drillers’ logs, and surface observations suggest that the Crestal Extension Fire is now drawing air from cool fissures in the area. Compacted ash layers and a lack of big void regions on the outcrop side make it less likely that the air is being delivered now to the combustion zone from that direction. In contrast, subsurface voids and fractures encountered during drilling and steep temperature gradients are observed in the subsurface between the fissures. These observations suggest that volumes of gases sufficient to support combustion could flow into and out of the subsurface through fissures.

Figure 1: A contour map of the region over the North Coal Fire (NCF) created using a pack-mounted global positioning system receiver. The scale on the right side shows surface elevation in meters. Fissures over the coal fire are shown (red = thermal elevation, blue = ambient temperature). Borehole (solid squares) and thermocouple (solid triangles) locations are also shown. The red box encompasses the region over the NCF where the fire is most active. The Fruitland Formation Outcrop is located between the two green lines. The thick black line represents service roads. Color bar in m.

Figure 2: Conceptual picture of a coal fire with subsidence. Fresh air and hot exhaust gases enter and leave the subsurface through high permeability fissures that connect the coal seam and the surface.

Magnetometer measurements were used to determine where the fire is currently

burning. A magnetic anomaly map is shown in Figure 3. The magnetic anomalies differentiate between hot burning zones, cooled ash zones, and regions that are unaffected by the fire. When the sandstone above the coal is laid down, the orientation of the magnetization of minerals in the sandstone is random. If it is then heated above the Curie temperature for those minerals, there is no magnetic signature. When the rock cools again below the Curie temperature, magnetic dipoles in the minerals align with the Earth’s magnetic field. Also shown in Figure 3 is the region of snowmelt shortly after a snowfall. The magnetometer measurements are consistent with all of the temperature data from thermocouples, drillers’ logs, observations of cuttings, the locations of hot and cool fissures, and the snowmelt data. Thus, we conclude that magnetic anomaly measurements are a very useful way to determine the location of the combustion zone.

The pilot test was designed to determine if it is possible to flood the combustion zone by injection of an inert gas (CO2). The injection wells were located in an area suitable for drilling and casing the boreholes. Figure 4 shows the fissure distribution over the Crestal Extension Fire. In this figure, the red fissures are venting hot combustion gases, and the blue fissures are at ambient temperatures. Regions around the blue fissures in the subsurface have measured gas compositions close to that of air, and thus air is likely being drawn into the subsurface from the blue fissures.

Figure 3: Magnetometer and snowmelt data in the Crestal Extension Area of the North Coal Fire. Blue indicates a previously burned region, red denotes the current combustion zone, and yellow to green, unburned coal. The snowmelt location (one day after a snowfall) is indicated by a white dotted line. Locations of injection and observation wells are shown. IW-1 and IW-2 were used for CO2 injection. OW-1, OW-2, and OW-3 were observation wells, as was the labeled fissure location. Fissures emitting hot gases are indicated by red lines; those with ambient temperatures are in blue.

Five wells were drilled for the pilot test. Their locations are shown in Figures 3 and 4. In this area, the top of the coal is at a depth of about 12 m, but in these boreholes, nearly all of the coal was missing. Instead a fractured zone was encountered with some ash returns during drilling, an observation that is consistent with the subsidence of the overburden after the coal was consumed. A borehole camera was deployed in IW-2 to investigate the flow setting. Numerous fractures with apertures of order 1 cm, were observed.

Heated air (at 126 C), with a slightly elevated CO2 concentration (3.9%), was observed flowing from borehole IW-2, and the borehole camera indicated that the flow was fracture dominated. CO2 concentrations in other boreholes nearby are shown in Figure 4. Similar CO2 concentrations were observed in other boreholes located in the previously burned region (according to the magnetometer survey and from cuttings obtained during drilling). Those gas samples also contained N2, O2, and small amounts of CO. In contrast, samples taken near the fissures emitting hot gases showed CO2 concentrations near 20% and no O2. These observations are consistent with the conceptual picture of air being drawn in through cool fissures and flowing through and being heated by rocks in the fractured zone where the coal had burned previously, to the combustion zone near the fissures emitting hot gases, where the O2 is consumed.

Wells IW-1 and IW-2 (see Figures 3 and 4) were used for injection in different tests. Wells OW-1, OW-2, and OW-3 were used to monitor gas compositions, temperatures, and flow rates. Hot gas flow rates were estimated from video measurements for the large fissures closest to the injection wells. CO2 was injected for periods of a few hours at several flow rates. A total of 20 tons of CO2 was injected during the three-day test. Isotope measurements were performed with a cavity laser ringdown instrument (Picarro, Inc.). Methods were devised to track the injected CO2 using this instrument.

Figure 5 reports values of δ13C measured prior to CO2 injection. The average values measure prior to injection suggest that the CO2 being emitted from the hot fissures is a

Figure 4: CO2 concentrations at boreholes and fissures (in red) prior to CO2 injection. Gases with CO2 concentrations of 1-5% also contained about 80% N2 and the remainder was O2 and small amounts of CO. Samples with CO2 concentrations near 20% contained N2 and CO but no O2.

Figure 5: δ13C values for gases sampled at boreholes and fissures (in magenta) prior to CO2 injection.

mixture that results from combustion of coal, combustion of CH4, and some of the native CO2. The contribution of CO2 from air is too small relative to other CO2 sources to have any meaningful impact on the isotpope readings at the North Coal Fire. The observed values are quite different from the isotope signature of the injected CO2, which allows use of that CO2 as a tracer even when CO2 is present in the combustion product gases

Cold liquid CO2 was vaporized at the site and injected for a few hours at rates of 37-45 metric tons of CO2/day. The CO2 flowed easily into the fractured zones, with only slightly elevated pressures at the bottom of the injection wells. No evidence of increased flow rate was observed in the observation wells or fissures. That observation is consistent with the idea that injected CO2 replaced air being drawn toward the combustion zone through fractures by the pressure gradient created by the density-driven flow of hot gases upward through the fissures emitting combustion products.

Breakthrough of injected CO2 was observed in the nearby observation wells and at the fissure at the crest. Times required for CO2 response ranged from 9 minutes for the nearest observation well to approximately one hour for the fissure that was about 35 m from IW-1. Figures 6 and 7 show examples of the data obtained.

Figure 6 demonstrates that injected CO2 was detected in the combustion product gases. Note that the fraction of CO2 is lower than that in samples taken from the gases sampled from borehole 1 that are reported in Figure 4 (21.2%). Due to temperature limits for the isotope instrument, samples were taken from the fissure near the surface, where some mixing with ambient air was inevitable. Even so, the rise in CO2 fraction in that gas clearly indicated breakthrough.

Figure 7 shows that the CO2 that contributed to the rise in CO2 fraction came from the injected CO2. The δ13C value increased from the pre-injection value of about -17‰ to about -9.5‰ at the lower injection rate, and then increased again to about -8‰ when the rate was increased. The sampled gas was clearly still a mixture of some injected CO2 and some CO2 that resulted from combustion. These results demonstrate that the CO2 was injected into the fractured zone where the coal had burned reached the area where combustion is occurring now.

Reductions in temperature at the fissure were not observed, despite the fact that the injected CO2 was quite cold (-33 C at the highest injection rate). That observation is an indication that combustion continued with remaining air in the gases flowing toward the combustion zone and that large quantities of heat are stored in the rocks upstream of and in the neighborhood of the combustion zone. These preliminary results from the pilot suggest that CO2 can be introduced into the combustion zone. It will be important, however, to remove enough of the heat from that zone so that the density-driven flow of air will not restart when injection ceases.

Figure 6: Injection rates (blue) and CO2 fractions (%) (magenta) calculated from measured δ13C values for gases sampled at one crest fissure located about 35 m from the injection well. Breakthrough of injected CO2 was detected by the rise in CO2 fraction about one hour after injection began. The CO2 fraction began to decline again about an hour and a half after injection ceased.

Figure 7: Injection rates (blue) and δ13C values (magenta) for gases sampled at one crest fissure located about 35 m from the injection well.

Conclusions Additional field observations at a subsurface coalbed fire and a pilot test of CO2

injection at the site lead to the following conclusions:

1. Well logs and one borehole video observation (for Injection Well 2) confirmed that previous magnetometer measurements accurately determined where the coal had burned previously.

2. Borehole video indicated that the primary flow of air that is supporting the coal combustion is taking place through fractures.

3. Baseline gas composition measurements prior to injection showed that the gas in the subsurface at the observation well locations was air (nitrogen and oxygen) with 1.5 to 5% CO2. Prior to injection, hot gases being emitted from fissures contained essentially no oxygen and about 22% CO2.

4. An increase in CO2 concentration was observed in nearby wells soon after injection began. Timescales for an increase in CO2 concentration depended on the injection rate, and ranged from 9 minutes to an hour or more, depending on the injection rate and location of the observation. Measured δ13C values indicated clearly that the injected CO2 was being detected.

5. No increase in flow rate was detected from observation wells or from the fissures emitting hot gases. Injection pressures in the wells were quite small, even at high injection rates, an indication that CO2 entered the fractured zones easily. These results suggests that the chimney effect of the coal fire determines the flow rate through the system and that injected CO2 must be drawn by that flow toward the hot zone just as air to support combustion is drawn to the fire when CO2 is not being injected.

6. Temperature responses in surrounding wells were small or nonexistent, despite the fact that the injected CO2 was quite cold. This result is consistent with the observation that the amount of heat stored in the rocks in the fractured zone and above is quite large compared to the heat capacity of the injected CO2.

7. After injection of about 10 tons of CO2 in three hours injection at the highest rate (about 45 metric tons CO2/day), the CO2 concentration at the crest fissures had doubled. The δ13C measurements confirmed conclusively that this was injected CO2. This result indicates that even with a relatively small amount of total CO2 injection, a significant change in CO2 concentration near the combustion zone was achieved.

8. The composition and δ13C measurements demonstrate that CO2 can be injected into flow dominating fractures and that the CO2 injected at appropriate depths reaches the fissures where hot gases are being emitted. This result indicates that if enough CO2 can be supplied to the fracture system that is transporting air to the combustion zone, it will replace the air that is supporting combustion now.

These results set the stage for a larger-scale test of the use on inert gas to control coalbed fires. If sufficient CO2 or other inert gas is available, it should be possible to control subsurface fires, which are significant sources of CO2 and pollutant emissions worldwide. It will also be important in any attempt to extinguish a coalbed fire to manage the heat retained in the overburden rocks in a way that prevents a restart of the density-driven flow that sustains combustion.

Acknowledgment The Southern Ute Indian Tribe granted access to the site and provided financial and

considerable technical support for the field portions of this project, which would not have been possible without those contributions. The Global Climate and Energy Project at Stanford provided support for the portion of the research done by Taku Ide and Franklin Orr.

Publications

1. Orr, F.M., Jr.: “Carbon Capture and Storage: Are We Ready?” Energy & Environmental Science,

2009, DOI: 10.1039/B822107N. 2. Orr, F.M., Jr.: “Onshore Geologic Storage of CO2” Science 325 (2009) 1656-1658, DOI:

10.1126/science.1175677. 3. Ide, T.S., Pollard, D., and Orr, F.M., Jr.: “Fissure formation and subsurface subsidence in a

coalbed fire,” Int. J. Rock Mech. 47 (2010) 81-93, doi:10.1016/j.ijrmms.2009.05.007.

References 1. Harris, J., Kovscek, A., Orr, F.M., Jr., and Zoback, M.D., “Geological Storage of Carbon

Dioxide,” http://gcep.stanford.edu/pdfs/-IUwoO0omIeF6HDYZPqYeg/2.5.3_Harris_Web_Public_2009.pdf), pp. 117-144.

Contacts Franklin M. Orr, Jr.: fmorr@stanford.edu Taku S. Ide: idetaku@stanford.edu

Geologic Storage of Carbon Dioxide in Coal Beds Investigators Anthony R. Kovscek, Associate Professor of Energy Resources Engineering; Abhishek Dutta, Wenjuan Lin, Graduate Research Assistants, Energy Resources Engineering Summary

This report describes results from the final period of research on gas transport through coal and the role of gas composition on coal bed permeability. For a detailed discussion of background and previous work on this project, please see the 2008 and 2009 progress reports (Harris et al. (2008; 2009)). New results include predictions of coupled multicomponent mixture diffusion and adsorption through coal pores as well as measurements of permeability evolution of coal as it is exposed to various pure gas and gas mixtures. Key findings of this research are that permeability reduction during CO2 flow is mitigated when relatively minor amounts of N2 are included in the injection gas and that multicomponent mass transfer is predicted to be comparatively fast, relative to field-scale recovery times, for expected centimeter-sized cleat spacings.

Introduction Storage of CO2 in coal seams is a potentially attractive carbon sequestration

technology because it enhances methane (natural gas) production from coalbeds as well as has the potential to be carbon neutral and perhaps a carbon sink (Wong et al., 2000; Harris et al., 2008). In some cases, this can be cost effective as the additional CH4 recovery from coal can either partially or completely offset the operational costs incurred. Accordingly, a quantitative understanding of gas sorption on coal is important to predict gas transport, carbon dioxide retention, and for enhanced coalbed methane recovery. Due to the special features of coalbed reservoirs and the nature of gas retention, there are unique issues that need to be taken into account when designing field operations and conducting numerical simulations of gas production and CO2 injection in coalbed methane reservoirs.

Figure 1. Schematic of CH4 flow dynamics in coal seams. CH4 desorbs from the internal coal surface, diffuses through the bulk matrix, and flows into and through the cleats. The pathway for CO2 and/or N2 is reversed.

The pore structure of coal is highly heterogeneous and varies with coal type and rank (Laxminarayana and Crosdale, 1990). Coalbeds are often characterized by, at least, two distinctive porosity systems, as shown in Fig. 1: a uniformly distributed network of natural fractures and porous blocks between the cleats (King et al., 1986). The natural fractures (also known as cleats) are subdivided into the face and butt cleat. The face cleat is continuous throughout the reservoir whereas the butt cleat is discontinuous and terminates at intersections with the face cleat. The cleat spacing is uniform and ranges from the order of millimeters to centimeters (King et al., 1986).

The heterogeneous pore structure of coal offers pore sizes varying from a few Angstroms to over a micrometer in size. According to the International Union of Pure and Applied Chemistry (IUPAC) classification (1994), pores are classified as macropores (> 50 nm), mesopores (between 2 and 50 nm) and micropores (< 2 nm). Coalbed gas is retained in coals via adsorption in micropores and as free gas in voids, cleats and fractures. Gas adsorption upon the internal surface of the coal is considered, by far, the most important mechanism of gas retention and accounts for approximately 95-98% of the gas in coal seams (Clarkson and Bustin, 1999; Shi and Durucan, 2008). A significant portion of the pore volume is located in micropores (Sharkey and McCartney, 1981) and

Gas Transport in Coal It is generally assumed that the flow of gas (and water) through the cleats is laminar

and obeys Darcy’s law. On the other hand, gas transport through the porous coal matrix is controlled by diffusion (Shi and Durucan, 2008). Three mechanisms have been identified for diffusion of an adsorbing gas in the matrix. They are molecular/bulk diffusion (molecule-molecule collisions dominate), Knudsen diffusion (molecule-wall collisions dominate) and surface diffusion (transport through physically adsorbed layer) (Saulsberry et al. 1996; Shi and Durucan, 2008). Gas diffusion in coals is significantly influenced by coal rank and lithotype, microstructure and secondary mineralization (Gamson et al., 1993; Gamson et al., 1996; Crosdale et al., 1998). As a result, the net effective diffusivity often includes contributions from more than one mechanism.

Molecular/bulk diffusion is significant for large pore sizes and high system pressures in which gas molecule-molecule collisions dominate over gas molecule-wall collisions. In this mode of transport, different species move relative to each other. We formulated a model of multicomponent molecular diffusion through macropores within coal matrix coupled with adsorption. The basis is a Fickian-type diffusivity with pure component adsorption described by the Langmuir equation and multicomponent adsorption computed with the extended Langmuir (ELM) and ideal adsorbed solution (IAS) theory. Dutta (2009) describes the numerical formulation, solution method, model input, and validation exercises. Here, we focus on results.

Figure 2 illustrates typical results for gas component concentration profiles as a function of distance in a one-dimensional matrix of length 2 cm. Constant gas composition is maintained at one boundary and the other boundary is no flux. The initial conditions are a pore saturated with methane in the pore volume and adsorbed to coal surfaces. One of the interesting observations from the concentration profile of CH4 in Fig. 2(c) is the presence of very small concentration gradient in the vicinity of the exit (x=0).

Because the molecular diffusion is driven by concentration gradient, these low CH4 concentrations near the boundary create potential mass transfer resistance, thus hindering the production of CH4. These results do indicate, however, that over roughly 1000 s diffusion and replacement of CH4 with CO2 on coal surfaces are effective at releasing CH4 from the coal given the order cm cleat spacing simulated.

(a)

(b)

(c)

Figure 2. Concentration profiles versus distance; (a) carbon dioxide, (b) nitrogen, and (c) methane. Domain is 2.0 cm and adsorption is described by the extended Langmuir equation.

We also considered the scale up of such diffusion results for use in a dual-porosity

simulator of coalbed methane as a naturally fractured reservoir (NFR). Although cleats and fractures are the main flow paths with considerably greater permeability, the matrix blocks have a much higher storage capacity for CH4 gas (Beckner, 1990). As a result, flow between the matrix block and fracture is fundamental to the productivity of CH4 gas from coal seams.

In the dual-porosity model matrix-fracture interaction governing mass transfer between matrices and fractures is modeled through a “transfer function” (Barenblatt et al., 1960; Warren and Root, 1963) incorporating a “shape factor” (σ). For a NFR, this interaction is defined as

m m

m m f mf

p kc (p p )t

∂ σφ = −

∂ μ (1)

where φ is porosity, c is compressibility, p is pressure, k is permeability, μ is viscosity, and the subscripts f and m refer to matrix and fracture, respectively.

In the above equation, it was assumed that pseudo-steady state exists in the matrix and that the flow in the matrix obeys Darcy’s law. For the case of coalbed reservoirs, the above equation needs to be modified. This is because diffusion is the mode of mass transfer inside the coal matrix. The shape factor, σ, reflects the geometry of the matrix elements and is time independent for pseudo-steady state conditions. The classical pseudo-steady state approach for describing matrix-fracture transfer leads to constant shape factors. But many authors have reported that this is not true during the early transient times and results in discrepancies among experimental and simulation results. Rangel-German and Kovscek (2006) performed water imbibition experiments in a fractured porous medium and found that the shape factor is time dependent when the fractures do not fill rapidly with water. Sarma and Aziz (2006) also reported that a constant value of shape factor cannot be used to get a good match at all times.

With respect to CBM models, the standard industry practice is to assume a constant shape factor. The conventional CBM simulators define a sorption/diffusion time that involves a constant effective diffusivity and a constant shape factor, both of which are not physically correct. In a multicomponent gas mixture, it is not accurate to assume a constant diffusivity (such as Deff) and there can be significant variation of the Fickian diffusivity versus time. In our derivation of shape factor, we do not invoke the pseudo-steady state assumption and thereby, attempt to capture the transient matrix-fracture interactions. The coupled PDE’s that describe the transport phenomena of mass transport in matrices are non linear and do not have any analytical solutions. As a result, in the results to follow, we do not find an analytical expression for shape factor. Our idea is to be able to compute numerically the shape factor which can then be coupled with the fracture/cleat Darcy flow equations. The following methodology is used to compute the shape factor.

Solve the matrix transport equations to obtain the gas composition Cn+1.

Compute the volume averaged mass accumulation, Θ, term for the matrix block.

The volume average gas phase and adsorbate composition are then approximated by numerical integration across the domain.

In a dual-porosity medium, all mass flow is from the matrix to fracture or vice versa. Therefore, the rate of matrix-fracture transfer is related to the rate of mass accumulation in the matrix as follows

avq ∂Θ= −

t∂ (2)

The shape factor is then calculated from the following matrix-fracture mass transfer relation as a function of time:

( )av D Ct

∂Θ= φσ

∂ f avC− (3)

where Cf is the gas composition in the fracture.

For the case of multicomponent gas mixtures, it is inappropriate to assume a single (effective) diffusivity for the gas component. The inlet boundary condition for the matrix block serves as the fracture composition (Cf). Here, it is assumed that these values remain constant in the fracture and thus we do not solve the fracture flow equations simultaneously.

Figures 3 to 6 illustrate results obtained. During the early transient times, the shape factor is a function of the geometry of the system, in our case being the length of matrix block. At late times when pseudo-steady state commences, the product of shape factor and square of length (dimensionless) appears to stabilize and converge for varying matrix lengths, see Fig 3. For this sensitivity study, the input Fickian diffusivity was varied. Based on the shape factor formulation presented in Eq. 3, it is inversely proportional to the Fickian diffusivity, see Fog. 4. Also from the figure, one can observe that varying the diffusivity impacts the shape factor only in the early transient times. The shape factor for the pure diffusion case however is not a function of initial and boundary conditions (Sarma and Aziz, 2006).

Thus, for the above sensitivity study one can see that shape factor value is significantly greater during early transient times and that it is only a function of diffusivity and characteristic length (length of matrix block). A deeper investigation into the early transient behavior of shape factor reveals that the log-log plot of σL2

with time results in straight lines with a -1/2 log slope, see Fig. 4.

Next we investigate the matrix-fracture interactions for a single gas component diffusing into a matrix from the fracture and undergoing adsorption as the same time. In case of adsorption, the gas molecules inside the matrix block can now exist both as a free gas and as an adsorbate phase. This suggests that the rate of accumulation of an adsorbing gas species is higher than that for the pure diffusion case. Figure 5 compares the shape factor for the pure diffusion case against the adsorption-diffusion case. From the figure, one can see that when adsorption occurs, the shape factor value is greater and there is a prolonged time-dependent

period (gradual slope) before attaining pseudo-steady state. Also, comparing the shape factor for gases with varying adsorption capacities (by varying the Langmuir parameters), we observe that the gas with a strong adsorption tendency induces greater matrix-fracture mass transport than a weakly adsorbing gas species, see Fig. 6. As in the previous pure diffusion case, at late times, the product of shape factor and square of length (dimensionless) appears to stabilize and converge for varying matrix lengths and Fickian diffusivities. This means that under pseudo-steady state conditions, the shape factor can still be assumed to be a function of geometry of the matrix block, however, neglect of the early transient portion implies that transport is significantly under estimated. Also, the log-log plot of σL2

with time during the early transient phase again results in straight lines with a -1/2 log slope.

Figure 3. Semi-log plot showing the impact of length of matrix block on shape factor (σ) with time.

Figure 4. Log-log plot showing the impact of Fickian diffusivity on σL2 (dimensionless) with time. In the early transient phase, the shape factors show linear behavior with a log slope of -1/2 on the log-log plot;

L=10mm.

Figure 5. Semi-log plot comparing σL2 (dimensionless) for the pure diffusion case against the adsorption-diffusion case; L=20mm, D=0.1 mm2/s.

Figure 6. Semi-log plot comparing σL2 (dimensionless) for gases with varying adsorption tendencies; L=20mm, D=0.1 mm2/s.

Multicomponent Gas Sorption and Swelling

To investigate the interplay of gas sorption, volumetric swelling, coal permeability, and the nature of the adsorbed phase, experiments were conducted on a coal core at varying pore pressures, hence, different total gas adsorption. The core is a composite type and was made from coal plugs drilled from intact coal samples. The samples are from the Wyodak-Anderson coal zone of the Montana portion of the Powder River Basin. They were collected at the mine face. Upon being received, the samples were washed using distilled water, and afterwards kept in large containers filled with deaerated, distilled water to avoid further oxidization.

A thin-walled diamond core bit (inner diameter = 1 inch) was used for coring. Water was used as a cooling agent while drilling. Core recovery was generally poor due to the fragile nature of the coal. The length of individual coal plugs varied from less than 1 inch

to about 3 inches. Several pieces of such coal plugs were assembled together to make a core of about one foot long. Before assembly, the end faces of the coal plugs were sanded to ensure that they were flush when fitted together. Gas sorption, sorption-induced volumetric and permeability changes measurements were conducted using feed gases 15%CO2/85%N2 and 50%CO2/50%N2. The binary mixture of 15%CO2/85%N2 was used because it was close to flue gas composition. The entire experimental apparatus is shown in Fig. 7. Piston accumulators at either end of the core allowed for injection and production of gas at either constant volumetric flow rate or constant pressure conditions. High pressure syringe pumps injected or received water from the piston accumulators thereby controlling flow rate or pressure. Pressure transducers enabled the measurement of pressure.

A complete description of the apparatus and coal, as well as all experimental results, are available in the thesis of Lin (2010). Experiments were conducted to measure sorption and the consequent volumetric change of the core when injecting different gases at different pressures. The amount of adsorption increased with the increase of pressure, and decreased with the decrease of pressure. No obvious adsorption/desorption hysteresis was observed. At the same pore pressure, the amount of adsorption for CO2 was greater than that of N2. The more CO2 in the injection gas, the greater the total amount of adsorption. Selectivity coefficients of CO2 to N2 were greater than one, but still of the order of one. The selectivity factors obtained in this study were smaller than those obtained by Hall et al. (1994)for supercritical CO2/N2 adsorption on their wet ground coal samples. The selectivity coefficients we obtained and those by Hall et al. (1994) all decreased as pressure increased.

Figure 7. Schematic of experimental apparatus for simultaneous measurement of adsorption, core volume change and core permeability.

Figure 8 shows volumetric strain with the injection of different gases at escalating pressures. The total volumetric strain due to momentary effective pressure decrease and adsorption are plotted together with the volumetric strains caused by adsorption only. The latter are only slightly smaller. Compared with the results of Hagin and Zoback (2010), our volumetric strain values were slightly higher. The volumetric strain with the injection of CO2 obtained by Hagin and Zoback (2010) was less than 1% at a pore pressure of 1 MPa (about 145 psi) and effective pressure of 5 MPa (about 725 psi). The volumetric strain with the injection of CO2 at 1 MPa was about 1.5% under an effective pressure of 400 psi for our system.

Figure 8. Volumetric strain at escalating pressures. Open symbols represent the total volumetric strain, and closed symbols represent volumetric strain due to adsorption only.

Figure 9 plots the permeability over initial permeability of the core after adsorption of different feed gases versus pore pressure. The values of permeability at zero pressure for each gas composition are the helium permeability of the core prior to the injection of the gas.

Figure 9. Permeability reduction of the core with injection of different gases.

Based on the experimental permeability data, the following observations are made:

1. Under constant net effective stress, during flow of CO2, N2, or the binary mixture of them, the permeability of the core decreases with escalating pore pressure.

2. The more CO2 in the feed gas, the more the permeability reduction.

3. Permeability of the core rebounds when decreasing the pore pressure under constant net effective stress. It does not, however, recover to the permeability value prior to adsorption.

4. Under constant effective stress, helium permeability of the core increased slightly with the increase of pore pressure. This means that Klinkenberg effect is negligible for the core we used in our experiments.

5. Density of the core increased (as measured using X-ray densitometry) which might be an indication that the core went through irreversible physical damage (crushing) in the process of the experiments.

Conclusion Enhanced coalbed methane recovery to recover additional natural gas resources

(CH4) with simultaneous greenhouse gas storage by injection of CO2 or by injection of CO2 and N2 is inherently multiphysics and multiscale. Consequently, it is a difficult process to model. Conventional numerical simulators have limited predictive capabilities for the design and development of ECBM/sequestration field projects because they neglect physical mechanisms such as non-constant time dependent transfer of CO2 from the cleat system to the matrix. Likewise, CO2 dependent swelling of the coal matrix is not well parameterized for inclusion in large-scale correlations.

Our matrix-scale modeling effort is targeted towards capturing the physics of ternary gas adsorption-diffusion dynamics. The idea is to understand the impact of intermolecular interactions and mass transfer limitations on CO2 storage predictions. A fully implicit solution method has been developed to model the ternary adsorption-diffusion transport problem. The Fickian diffusivities in our case are computed rigorously from MS diffusivities and composition. From the numerical examples, we observed that these Fickian diffusivities sometimes vary significantly with time and consequently have an important bearing on gas adsorption-diffusion dynamics. The counter diffusion between CO2/N2 and CH4 results in the depletion of CH4 in the matrix pores. As a result, very small concentration gradients for CH4 develop in the vicinity of the CH4 gas exit. Since the molecular diffusion is driven by concentration gradient, these low CH4 concentrations near the boundary may lead to mass transfer resistance, thus curtailing the production of CH4.

We then investigated the matrix-fracture transfer function dictating mass transport from matrix to fracture or vice versa. The conventional CBM simulators define a sorption/diffusion time that involves a constant effective diffusivity and a constant shape factor, both of which are not physically true. We developed an algorithm to compute numerically the shape factors for both pure diffusion and for adsorption-diffusion cases. In the derivation of shape factor, we do not invoke the pseudo-steady state assumption and thereby capture the transient matrix-fracture interactions.

To our knowledge, the experiments summarized above are the first attempt to measure simultaneously the amount of adsorption, the composition of the adsorbed phase, and the consequent volumetric and permeability change of coal. Coal permeability and volumetric strain are sensitive to gas composition. Greater pressure and concentration of CO2 in the injection gas lead to generally lesser coalbed permeability. Coalbed permeability and swelling may be controlled through adjustment of injection gas by addition of small amounts of nitrogen (5 to 15 % by mole).

Publications 1. Chaturvedi, T, J.M. Schembre, and A. R. Kovscek, “ Spontaneous Imbibition and Wettability

Characteristics of Powder River Basin Coal,”. International Journal of Coal Geology 77(1-2), 34-42 (2009). doi:10.1016/j.coal.2008.08.002

2. Dutta, A., “Multicomponent Gas Diffusion and Adsorption in Coals for Enhanced Methane Recovery” MS Thesis Energy Resources Engineering Stanford University (2009). online: http://pangea.stanford.edu/ERE/db/pereports/record_detail.php?filename=Dutta09.pdf

3. Lin, W. “Gas Sorption and the Consequent Volumetric and Permeability Change of Coal” PhD Thesis Energy Resources Engineering Stanford University (2010). online: http://pangea.stanford.edu/ERE/db/pereports/record_detail.php?filename=Lin10.pdf

References

1. Barenblatt, G.E., Zheltov, I.P., and Kochina, I.N.: “Basic Concepts in the Theory of Homogeneous Liquids in Fissured Rocks”, Journal of Applied Mathematical Mechanics 24: 1286-1303 (1960).

2. Beckner, B.L.: “Improved Modeling of Imbibition Matrix/Fracture Fluid Transfer in Double Porosity Simulators. PhD dissertation. Stanford, California, Stanford U (1990).

3. Clarkson, C.R. and Bustin, R.M.: “The Effect of Pore Structure and Gas Pressure upon the Transport Properties of Coal: a Laboratory and Modeling Study. 2. Adsorption rate modeling”, Fuel 78: 1345-1362 (1999).

4. Crosdale, P.J., Beamish, B.B., and Valix, M.: “Coalbed Methane Sorption related to Coal composition”, Intl J of Coal Geology 35, 147-158 (1998).

5. Dutta, A., “Multicomponent Gas Diffusion and Adsorption in Coals for Enhanced Methane Recovery” MS Thesis Energy Resources Engineering Stanford University (2009). online: http://pangea.stanford.edu/ERE/db/pereports/record_detail.php?filename=Dutta09.pdf

6. Gamson, P.D., Beamish, B.B., and Johnson D.P.: “Coal Microstructure and Micropermeability and Their Effects on Natural Gas Recovery”, Fuel 72, 87-99 (1993).

7. Gamson, P.D., Beamish, B.B., and Johnson, D.P.: “Coal Microstructure and Secondary Mineralization: Their Effect on Methane Recovery”, Geological Society of London; 165-179 (1996).

8. Hagin P. and Zoback M.D. 2010. Laboratory Studies of the Compressibility and Permeability of Low-rank Coal Samples from the Powder River Basin, Wyoming, USA. Submitted to the Journal of Coal Geology.

9. Hall F.E., Zhou C.H., Gasem K., Robinson Jr. R.L., and Yee D. 1994. Adsorption of Pure Methane, Nitrogeon, and Carbon Dioxide and Their Binary Mixtures on Wet Fruitland Coal. Paper SPE 29194 presented at Eastern Regional Conference and Exhibition held at Charlston, WV, U.S.A. on November 8-10.

10. Harris, J, Kovscek, A.R., Orr, F.M., and Zoback, M.D.: “Geologic Storage of Carbon Dioxide” 2007-08 Technical Report of the Global Climate and Energy Project, Stanford University http://gcep.stanford.edu/research/technical_report/20012.html.

11. Harris, J., Kovscek, A., Orr, F.M., Jr., and Zoback, M.D., “Geological Storage of Carbon Dioxide,” http://gcep.stanford.edu/pdfs/-IUwoO0omIeF6HDYZPqYeg/2.5.3_Harris_Web_Public_2009.pdf), pp. 117-144.

12. Laxminarayana, C., and Crosdale, P.J.: Role of coal type and rank on methane sorption characteristics of Bowen Basin, Australia, Intl J of Coal Geology 40, 309-325 (1990).

13. Lin, W. “Gas Sorption and the Consequent Volumetric and Permeability Change of Coal” PhD Thesis Energy Resources Engineering Stanford University (2010). online: http://pangea.stanford.edu/ERE/db/pereports/record_detail.php?filename=Lin10.pdf

14. Rangel-German, E.R., and Kovscek, A.R.: “Time-dependent matrix-fracture shape factors for partially and completely immersed fractures”, Journal of Petroleum Science and Engineering, 54, 149-163 (2006).

15. Sarma, P. and Aziz, K. “New transfer functions for simulation of naturally fractured reservoirs with dual-porosity models” SPEJ 11(3) 328-340 (2006).

16. Saulsberry, J.L., Schafer, P.S., and Schraufnagel, R.A.: “A Guide to Coalbed Methane Reservoir Engineering”, Gas Research Institute, Chicago, USA (1996).

17. Sharkey, A.G., Jr. and McCartney, J.T.: “Chemistry of Cal Utilization”, Second Supplementary Volume, Elliott, M.A. Ed. John Willey & Sons Inc., 159-283 (1981).

18. Shi, J.Q., and Durucan, S.: “A bidisperse pore diffusion model for methane displacement desorption in coal by CO2 injection”, Fuel, Vol 82, 1219-1229 (2003).

19. Warren, J.E., and Root, P.J.: “The Behavior of Naturally Fractured Reservoirs. SPE J. 3, 235-255 (1963).

20. Wong, S., Gunter, W.D., and Mavor, M.J.: “Economics of CO2 Sequestration in Coalbed Methane Reservoirs”, SPE 59785, presented at the 2000 SPE/CERI Gas Technology Symposium held in Calgary, Alberta Canada, (2000).

21. Contacts A. R. Kovscek.: kovscek@stanford.edu A. Dutta: abbie.om@gmail.com W. Lin: wenjuanl@stanford.edu

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Subsurface Monitoring of CO2 Storage in Coal Beds

Investigators

Jerry M. Harris, Professor and Youli Quan, Research Associate, Geophysics Department Eduardo T. F. Santos and Bouko Vogelaar Post Doctorate Scholars, Geophysics Department Chuntang Xu, Jolene Robin-McCaskill, Adeyemi Arogunmati, Tope Akinbehinje, Graduate Research Assistants, Geophysics Department

Executive Summary

We have developed and tested monitoring strategies for continuous “slow-time” monitoring of CO2 storage, i.e., “True4-D.” The methods rely on the generation of subsurface images from continuously acquired sparse datasets. Several acquisition scenarios were simulated and evaluated. Some limited tests were completed on traditionally acquired field datasets. True4-D introduced sparse data acquisition, dynamic imaging, data evolution, and image integration as approaches for continuous subsurface monitoring. Sparse data acquisition aims to keep the operational expense of True4-D comparable to traditional time-lapse surveys. Sparse datasets are adaptively acquired, either in small 3-D surveys, either densely sampled with low coverage or coarsely sampled with high coverage, according to predictions from reservoir simulation and other information learned from prior subsurface images. Our data processing methods incorporate several possible approaches that can be categorized as either dynamic imaging or data evolution. In dynamic imaging, the time-stamped data are sorted and stacked, then fed into an iterative imaging algorithm. The ensemble Kalman filter (EnKF) uses small 3-D seismic surveys (or patches). The patched-based data are sorted into CDP order, stacked and then fed into EnKF for dynamic imaging. The EnKF processes each stacked trace and updates the prior subsurface image by integrating the newly available image. We accumulate a large number of images that are dense in slow-time but may have low spatial resolution. We then further process those low- resolution images to synthesize super resolution images by incorporating well logs or other independently acquired data. Another approach to dynamic imaging is to unwrap an iterative inversion algorithm to accept time-stamped incremental data. The algorithm we developed, called Dynamic Simultaneous Iterative Reconstruction Technique, or DynaSIRT, retains slow-time memory on the inversion state and updates the model as new data are introduced to the algorithm. The second approach to handling sparse slow-time data is at the data level. The concept is to pre-process temporally dense but spatially sparse data sets for use in traditional imaging algorithms. In data evolution we complete the sparsely sampled field dataset by reconstructing the missing data using a multi-dimensional estimation algorithm, then process the completed dataset with traditional migration or inversion methods. The subsurface images resulting from the use of these methods are dense in slow-time but may have lower 3-D spatial resolution. In Section 3 we describe methods for data integration and in Sections 4-6 we summarize the work on dynamic imaging methods.

  ‐2‐ 

 

Complementary to the True4-D imaging research, we developed a low frequency laboratory measurement for the acoustical properties of rock and coal samples. This method, called Differential Acoustical Resonance Spectroscopy, was used to estimate the compressibility and attenuation of small geological samples in the frequency range of 1000 Hz under simulated in situ pressure conditions. The goal of this work was to develop a laboratory measurement capable of measuring changes associated with CO2 injected in coals under realistic field conditions of pressure and acoustic frequency. Results from this work on coal samples and other rocks are given in Section 7. Some research work not included in this final report, such as survey configuration for monitoring (2007) and electromagnetic methods for monitoring (2008, 2009) can be found in our annual reports.

  ‐3‐ 

 

Table of Contents

1. Introduction

2. True4-D Seismic Subsurface Monitoring

2.1 An integrated simulation 2.2 Data acquisition 2.3 Dynamic imaging 2.4 Image integration

3. An Approach to Quasi-continuous Time-lapse Seismic Monitoring using Data

Evolution of Sparse Data Recording

3.1 Introduction 3.2 Theory 3.3 Time-lapse field monitoring example 3.4 Time-lapse synthetic monitoring example

4. Ensemble Kalman Filters for Dynamic Imaging

4.1 Introduction 4.2 Model 4.3 Implementation 4.4 An example of time-lapse seismic monitoring 4.5 Conclusions

5. DynaSIRT: A Robust Dynamic Imaging Method for Continuous Slow-time

Monitoring

5.1 Dynamic Imaging 5.2 Row-action solvers 5.3 DynaSIRT 5.4 Numerical simulation 5.5 Conclusions

6. Imaging with Feature-enhanced Adaptive Meshes and Temporal Regularization

6.1 Introduction

6.2 Trigonal meshes

6.3 Temporal data integration

6.4 Diffraction tomography

  ‐4‐ 

 

7. DARS Measurements on Acoustic Properties of Coal and other Porous Rocks

7.1 Measurement of compressibility and attenuation 7.2 Measurement of permeability 7.3 Comparison with Biot-Gassmann equation 7.4 Effects of gas, water, and oil saturation 7.5 DARS II construction

Publications References

Contacts

  ‐5‐ 

 

1. Introduction Geologic CO2 sequestration proposes to store CO2 in an appropriate geological setting, and is a possible solution for reducing greenhouse gas into the atmosphere. Deep coal beds are believed to provide a geological setting, as well as depleted oil/gas reservoirs and deep saline aquifers. For safety and operational reasons, we believe it will be necessary to monitor the containment of the CO2 in the subsurface. This report summarizes our research work on subsurface monitoring of geologic CO2 storage.

In this project we focus on seismic monitoring of the CO2 storage in coal beds. Seismic methods have been extensively used for the characterization and fault evaluation of coal beds. Some of the seismic field work in coal seams can be found in Shuck & Benson (1996), Buchanan et al. (1983), Dunne & Beresfordz (1998), Gochioco (1998), Henson & Sexton (1991), Krey et al. (1982), Ramos & Davis (1997), and Akintunde et al. (2004). Those coal surveys included 3-D high resolution seismic, vertical seismic profiling, crosswell seismic profiling, and sonic logging. Coals have low densities and low seismic wave velocities. Typical in situ P-wave velocities are in a range of 2–3 km/s. Coal beds usually have large seismic contrast against surrounding rocks, and as a result strong guided waves may exist in a coal seam. Coal beds of interest for storage tend to be relatively shallow, with depths less than about 2000m. Coals typically have high attenuation (or low Q-values); the in situ measurement of Q-value given in Buchanan et al. (1983) is about 45. Coal beds may also have strong anisotropy (Buchanan et al. 1983) due to aligned fractures and micro layering. Lab measurements on coal samples show as much as 40% P-wave anisotropy (Wang, 2002). Richardson and Lawton (2002) conducted a simulation study on time-lapse imaging in coal. Akintunde et al. (2004) observed the P-wave velocity changes in range of 5-7% due to methane production and changes in pore pressure from crosswell seismic surveys in coal. McCrank and Lawton (2009) recently reported a mini pilot field study on CO2 injection in coal. They found a P-wave impedance drop of 10% due to CO2 injection in coal, which is much larger than the change of 4% predicted by the Gassmann equation.

Seismic imaging has played an important role in numerous subsurface monitoring projects, especially in petroleum reservoir monitoring (e.g., Lumley 2001, Rickett and Lumley, 2001). When we apply seismic monitoring to CO2 sequestration, we have to consider special requirements, such as cost, long term, and the capability for leak detection. To meet these special requirements, we have developed in this project a novel technique called True4-D monitoring. In this report, we introduce the concept of True4-D monitoring and give a full example simulation of the concept. Special data acquisition and data processing methods have to be used for True4-D. In Section 3 we discuss data integration required for sparse data acquisition. In Sections 4-6 we review dynamic imaging algorithms. In order to have a better understanding on the seismic properties of coal, we also carried out laboratory measurements on coal samples using Differential Acoustic Resonance Spectroscopy (DARS). We report the DARS work in Section 7.

2. True4-D Seismic Subsurface Monitoring Traditional time-lapse seismic subsurface monitoring uses multiple 3-D seismic snapshots to capture temporal changes of the reservoir. The snapshots are repeatedly acquired at time intervals of several months to years. In our approach, reservoir time or “slow-time” is considered to be the independent fourth dimension. We propose to sample slow-time quasi continuously, thus the name True4-D. We need to sample slow-time often enough to detect changes in the subsurface reservoir. The traditional approach suffers from serious temporal aliasing. More importantly, while sensitive to reservoir changes due to CO2 it may take months or years to detect potentially dangerous leaks in a storage site. Figure 2.1 illustrates the traditional snapshot approach of time-lapse imaging. It can be seen that we would have difficulty to identify a small leak (circled) from a single snap shot, especially in the present of noise. However, if we have quasi-continuous data in the temporal axis as shown in Figure 2.2, the leak or other temporal changes can be easily identified with the help of the adequately sampled slow-time axis.

Leak?

Figure 2.1: Traditional monitoring uses a coarse temporal sampling interval. These images are 2-D seismic profiles corresponding to two discrete reservoir times. It is difficult to identify a leak (circled) from these two images.

Leak!

Figure 2.2: Monitoring with a short (quasi-continuous) temporal sampling interval. When we have a large number of time-lapse images, we can better separate signal from noise, in this case a minor leak, from spatially noisy image.   ‐6‐ 

 

Figure 2.3: Quasi-continuous monitoring can detect a leak earlier as indicated at time t3.

As shown in Figure 2.3, we expect quasi-continuous or True4-D monitoring to detect a potentially dangerous leak sooner. In this report we describe a series of synthetic tests to investigate the feasibility of True4-D. The approach can overcome the temporal aliasing problem and help interpret subtle temporal changes. However, the cost of True4-D monitoring will be prohibitively high if we just simply reduce the time interval between traditional 3-D surveys and repeatedly collect complete datasets. We assume the running costs of True4-D should be comparable to the traditional approaches, though spread over time and with some higher startup expense for embedded instrumentation. To accomplish this, we trade spatial resolution for temporal resolution, use embedded data acquisition systems, sparse data evolution, dynamic imaging, and image integration algorithms to implement True4-D monitoring.

In Subsection 2.1, we give a comprehensive synthetic study of True4-D seismic monitoring to demonstrate and investigate its potential and challenges. Then three important issues, sparse data acquisition, dynamic imaging and image integration will be discussed in Subsections 2.2, 2.3, and 2.4. 2.1 An integrated simulation

This integrated monitoring simulation includes flow simulation, rock physics, survey design, seismic modeling, and seismic imaging. Figure 2.4 shows the workflow. We construct a 3-D model of a coal storage reservoir, run a flow simulator to simulate CO2 injection and storage, and

  ‐7‐ 

 

use simulated seismic depth imaging to study the various data acquisition and processing strategies that have the potential to make True4-D practical.

Seismic imaging Seismic modeling Rock physics Flow simulation Model building  Figure 2.4: Workflow of the seismic monitoring simulation

2.1.1 Flow simulation of CO2 storage in a coal bed

An illustrative geological model for a 3-D coal bed was built with GOCAD based on the work of Ross (2007). The model, consisting of three layers (coal, shale and sand), is shown in Figure 2.5. The model is imported into the GEM flow simulator (www.cmgroup.com) for the simulation for CO2 injection and storage. The simulated flow models are output in time steps of weeks and months for 8 years.

Figure 2.5: The coal bed model used in this simulated monitoring study. The area of the model is about 1000 x 900 x 50 (m3), and the thickness is about 500 m. From top to bottom, the three layers are sand, shale, and coal. Here, the overlying shale serves as reservoir seal. We place a low permeability channel in this shale layer to simulate leakage into the overburden.

Initially the model is water saturated. We assume injection begins on January 1, 2008. As CO2 is injected into the coaldbed, a volume becomes gas saturated. Figure 2.6 shows the gas saturation in the coal layer at four different times. The shale layer above the coal normally maintains a seal that keeps the injected CO2 within the coal. To mimic a possible leakage, we place a high permeability channel in the shale. Figure 2.7 shows the gas saturation at two times as leaking through the seal begins and spreads in the top sand layer.

  ‐8‐ 

 

(a) 2008-1-16 (b) 2008-2-1

(c) 2008-3-1 (d) 2008-12-1

Figure 2.6: Gas saturation changes within the coal bed. The objective of subsurface monitoring is to track the gas front and detect possible leakage into the overburden.

(a) (b)

Figure 2.7: CO2 leaking occurs through a high permeability channel and spreading in the sand layer above: (a) 9-1-1009. CO2 leak begins; (b) 10-1-2010. Leak spreads in overburden sand.

2.1.2 Simulated seismic depth imaging

The time-lapse flow models (including porosity, permeability, water saturation, gas/CO2 saturation and pore pressure) are imported into simulated seismic depth imaging software SeisRox (www.norsar.com) for the monitoring study, which does the last three pieces of work shown in Figure 2.4. Simulated seismic depth imaging convolves the reflectivity model with illumination vectors. This method of simulating depth migration is preferred over 1-D wavelet convolution because it includes the effects of acquisition geometry, 3-D illumination, ray paths, anisotropy and lateral resolution in complex models (Lecomte & Kaschwich, 2008). With SeisRox we can convert flow snapshots into seismic velocity snapshots and compute simulated 3-D depth images without the intensive shot simulation and migration steps. Figure 2.8 shows the initial velocity model, converted from the initial flow model. Figure 2.8 shows the velocity changes about one year later on 10-1-2009. The traditional approach is to calculate 3-D seismic data using the finite difference method, and then perform depth imaging. It may take days to get

  ‐9‐ 

 

forward modeling and migration imaging done for a single 3-D model. Now we have more than

one hundred time-lapse models, and it is impossible to do this in the conventional way. The simulated seismic depth imaging, however, is very fast. It takes a few hours to compute hundreds of 3-D depth images. In order to compute the seismic images, 1-D overburden layers are added on the top of the reservoir. Next we will use simulated depth imaging to demonstrate the concepts of True4-D monitoring and study the strategies for True4-D monitoring.

(b) (a)

Figure 2.8: Velocity models converted from flow models. The velocity change shown in (b)

2.1.3 The case of full 3-D surveys

s a potential candidate for CO2 storage, a detailed site

is the difference between the initial model (a) and the model approximately one year later.

When a site is first selected acharacterization must be done. The first baseline characterization should include a full coverage 3-D survey with state-of-the-art-technology. Figure 2.9 shows the traditional data acquisition geometry, with the model and imaging target used in our simulation. Figure 2.10 is the depth image differences between given times and the initial time.

Figure 2.9: A full 3-D data acquisition geometry. Green dots are the mid-points

Source & Receiver Arrays at Surface

corresponding to the sources (red dots). Blue dots indicate receiver locations. Gray dots are detector arrays. Three planes in the model show slices through the depth images at the target area.

  ‐10‐ 

 

(a) 1-11-2008 (b) 1-26-2008

LeakLeak

(c) 9-1-2008 (d) 1-1-2010

Figure 2.10: Depth image differences at four different times. The subsurface image at a given time is subtracted from the image corresponding to the baseline model. The leak starts around 9-1-2008.

(a) Z-T plot at location 1 (b) Z-T plot at location 2

(c) Z-T plot at location 3

Figure 2.11: 2-D visualization of continuous monitoring data. The resulting plot shows depth vs. slow-time display at a specified surface location.

  ‐11‐ 

 

Quasi-continuous monitoring creates a huge volume of data, e.g., Data (X, Y, Z, T), where T is slow-time.. We can visualize subsets of the True4-D dataset in many different ways. A particularly revealing 2-D image is to select a (X, Y) surface location and display the (Z, T) plane as shown in Figure 2.11. There are two distinguished features in Figures 2.11a and 2.11b. The upper one is the leakage of CO2 in the sand layer and lower one is CO2 storage in the coal. Since two images come from different (X, Y) locations, we can see CO2 reaches the locations at different times. The two events at location 1 begin at almost the same time. This is because location 1 is very close to the leaking channel. Location 3 is far away from the leaking channel, and only one event appears. The example in Figure 2.11 illustrates how a small change in subsurface conditions has a very good chance of being detected with the help of adequate slow-time sampling.

2.1.4 The case of sparse 3-D surveys

The acquisition of a full 3-D seismic survey is very expensive and takes a long period of time. It is impractical to do True4-D monitoring with regular full surveys. We now present another extreme case of 3-D acquisition geometry as shown in Figure 2.12, which consists of a source array and a receiver array. This simple cross array geometry generates a true 3-D image albeit at single fold (Harris et al. 2006; Walton 1972). However, it may not produce adequate signal-to-noise because of its low fold and poor coverage. We here use simulated depth imaging as an idealized seismic migration to see how it works. Figure 2.13 is the depth image difference obtained from cross array geometry. Clearly, the migration artifacts are severe, though the effects of CO2 injection can also be seen.

Figure 2.12: Cross array acquisition geometry that has a source array (gray dots) and receiver array (blue dots). The green dots show the mid-points for the given source (red square).

  ‐12‐ 

 

(a) 1-11-2008 (b) 1-26-2008

Figure 2.13: Depth difference images (relative to baseline). It can be seen that the imaging artifacts are dominant.

2.2 Data acquisition

We have discussed two extreme cases (full survey and the sparse cross-array survey) in previous subsection. The cost and quality are the main problems for continuous monitoring. It seems that we need to choose a proper trade-off between them. The migration-based imaging approach usually requires dense data acquisition geometry that is quite difficult if we want to carry out continuous monitoring. This motivates us to use pre-stack data directly.

We propose to embed sources and receivers (Figure 2.14a) near the surface and continuously collect the data, say every week. Then the recorded trace can be display in a plot of seismic time (fast) and reservoir time (slow). To test this idea, we use the finite difference method and the time-lapse velocity models to compute the seismic data. The computed seismic traces are displayed in Figure 2.14b. The attribute is amplitude difference. The horizontal axis shows the reservoir time when the data is collected. The traveltime and amplitude of the seismic reflection change slightly as CO2 injection continues.

Time lapse (Day)

Trav

el T

ime

(Sec

.)

50 100 150 200

0

0.05

0.1

0.15

0.2

0.25

0.3

Receiver Source

Amplitude & travel time changes

(a) Data acquisition (b) Seismic time vs. reservoir time

Figure 2.14: Embedded sources and receivers for continuous operation (left) and the corresponding time image reflect the subsurface changes (right).

  ‐13‐ 

 

Another possible sparse data acquisition is patch-based surface survey. Seismic traces within a patch can be sorted and stacked to improve the signal-to-noise. The resulting seismic traces can be used for dynamic inversion with ensemble Kalman filter (EnKF) that will be fully discussed in Section 4. Figure 2.15 illustrates an adaptive monitoring strategy where small 3-D survey patches are adaptively moved around according to the results of reservoir simulation and observations from previous monitoring interpretation. If we want to use sparse data to do migration or tomography that need complete data coverage, we have to do data integration as discussed in Section 3. Small survey patches

Figure 2.15: 3-D survey patches can be adaptively moved in order to target certain areas of interest. Localized patches provide seismic traces for EnKF inversion.

2.3 Dynamic imaging Although we can see the changes in the raw seismic data as demonstrated in Figure 2.14b, it will be very helpful if we can perform seismic inversion and transform the amplitude vs. seismic-time data into acoustic impedance or other elastic properties of subsurface vs. depth. True4-D seismic monitoring is such a typical dynamic process. The dynamic inversion approaches introduced by Quan & Harris (2008) and Jin et al. (2008) are especially suitable for streaming or our continuous data flow.

Dynamic imaging uses slow-time data that consist of a sampled series of time-lapse datasets ( ). Here superscript i is the index of subsurface changes or slow time. Dynamic imaging integrates temporal information in the data by introducing temporal regularization or recursive inversion of the data and obtain a series of dynamic images ( ) such as

)(id

)(im

][ )1()()1()( −− −+= iiii ddKmm .

Development of dynamic imaging algorithms is one of the key tasks for True4-D monitoring. We have introduced Kalman filter (Section 4), DynaSIRT (Section 5) and adaptive meshes and temporal regularization (Section 6) for dynamic imaging. For the Kalman filter method, the factor K in the equation above is called Kalman gain. In dynamic imaging, K is the back-projection operator.

  ‐14‐ 

 

2.4 Image integration

In principle, sparse data acquisition and patch-based seismic imaging produce a large number of low-resolution images (i is slow-time index). If we combine these images, we may create a higher resolution result or a super resolution image (see Figure 2.16). Super resolution means the actual resolution is higher than each individual image would be expected to yield.

)(ily

Low resolution time-lapse images

……

y1(i)

y2(i)

y3(i)

Y4(i) ……

……High resolution images

X(i-1)

X(i)

……

Figure 2.16: Construction of a super resolution image from low resolution images.

Mathematically, we can define this problem as

)()()()( iiii nXDY += , (2.1)

or

  ‐15‐ 

 

.

)()(

)(4

)(3

)(2

)(1

)(4

)(3

)(2

)(1

ii

i

i

i

i

i

i

i

i

nX

d

d

d

d

y

y

y

y

+

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

Here X(i) are the super resolution images to be synthesized from multiple images Y(i), D(i) are decimation and translation matrices, and n(i) are noise matrices. (To simplify the presentation, four low resolution images are used as an example.) We need to construct matrices D(i) and then to solve the system determinately or stochastically. For example, using the Kalman filter we can solve the system and obtain the synthesized high resolution image X at time i as

1)()()1()()()1()( ][ −−− += iTiiiTiii RDCDDCK , (2.2)

][ )1()()()1()( −− −+= iiiii YYKXX , (2.3) )1()()()( ][ −−= iiii CDKIC , (2.4)

where K is the Kalman gain, C is model (high resolution image X) covariance matrix, and R is data (low resolution image Y) covariance matrix. Next we give a simple synthetic example to test using the Kalman filter approach to image integration. A 2-D coal bed model similar to the 3-D model in Figure 2.5 is used for this test. We run the flow simulator GEM and obtain 175 slow-time flow models over a period of 10 years. These flow models are converted into Vp models. In Figures 2.17-2.20, we show four of these 175 models. The original images are shown in Figure 2.17. We randomly extract 8 traces from each image as the low-resolution sparse samples as (Figure 2.18). The Kalman filter algorithm is then used to construct high-resolution images from those low-resolution samples. Figure 2.19 is the reconstructed high-resolution result after the image integration. For better visualization, we show the velocity changes in Figure 2.20. As the first test, we use the model at T=1 as initial model X(1), and use a diagonal initial model covariance matrix and a diagonal data covariance matrix . According to Equations 2.2 and 2.3, a smaller comparing with means that newly observed data has less error, and gives larger contribution to the newly estimated image. Let us use a 1x1 matrix D=1 to clarify this argument. For this case, Equations 2.2-2.4 become

2)1(XσIC = 2

YσIR =2Yσ

2Xσ

22

2

YX

XKσσ

σ+

= , (2.5)

)(22

2)1(

22

2)1()(

22

2)1()( ˆ]ˆ[ i

YX

Xi

YX

Yii

YX

Xii XXXXXXσσ

σσσ

σσσ

σ+

++

=−+

+= −−− , (2.6)

  ‐16‐ 

 

)1(22

2)( −

+= i

YX

Yi CCσσ

σ. (2.7)

Here, is the estimated model only based on the observed data at Time i. If

, then , which means less contribution from the previous model to the newly updated model. Similarly, if the data at this time have larger error, i.e., , then

, which means less contributions from current data to the updated model.

DYX ii /ˆ )()( =0 )(iX →

)1( −→ iX

2 →Yσ

)(iX

)(ˆ iX∞→2

Yσ

Figure 2.17: Four original full models.

Figure 2.18: At each reservoir time, 8 traces are randomly extracted as low resolution images.

Figure 2.19: Reconstructed high-resolution images with the Kalman filter.

Figure 2.20: Velocity changes in the reconstructed images.

  ‐17‐ 

 

  ‐18‐ 

 

3. An Approach to Quasi-continuous Time-lapse Seismic Monitoring using Data Evolution of Sparse Data Recording

In data evolution, we take advantage of small changes in the seismic property of the geological reservoir that are expected to occur in small time intervals. The goal of this approach is to obtain high temporal at the expense of spatial resolution in the reconstructed, slow-time geophysical images using comparable resources available with conventional approaches. This is accomplished by acquiring spatially sparse data at small time intervals. In this case, a spatially sparse dataset refers to that dataset which is a small fraction (as little as 5%) of what would be acquired to reconstruct a high spatial resolution tomographic image of the subsurface. The high spatial resolution obtained by the proposed approach occurs because unrecorded data are predicted from future and past data. With high temporal and accompanying higher spatial resolution, early detection of important reservoir changes is more likely to occur.

3.1 Introduction

Geophysical imaging has played a large part in subsurface monitoring projects, especially in petroleum reservoir monitoring projects (e.g., Harris et al., 1995; Rickett and Lumley, 2001). This is primarily due to the kind of seismic changes that occur in the reservoir rock properties (Wynn, 2003). In addition, seismic data analysis is a well developed and understood subject (Yilmaz, 1987; Yilmaz, 2001). Seismic signals are able to penetrate deep into the earth and can be used in virtually any geologic setting (Wynn, 2003). The use of seismic tomography in time-lapse monitoring takes advantage of the changes in a seismic property of the reservoir rock during the time interval under consideration. For example, a reservoir velocity model can be quantitatively reconstructed from either seismic reflection or transmission traveltimes using tomography.

Consider a time-lapse seismic monitoring study designed to last for several decades as might be the case in whole-life monitoring of a petroleum reservoir or for a CO2 storage site. The conventional approach is to acquire a large amount of seismic data such that a high spatial resolution image of the subsurface can be obtained each time a dataset is acquired. The time intervals between successive data acquisition campaigns are often so large that there are large changes in the successive seismic data acquired. The time intervals are usually of the order of years (e.g., Mathisen et al., 1995; Landrø et al., 1999; Arts et al., 2004). Such a strategy works very well for some time-lapse projects but for other applications such as monitoring CO2 storage, the late identification of a reservoir leak by a year could have dire consequences. In other words, some time-lapse monitoring strategies are more effective when the changes in successive time-lapse datasets are small. In such cases, temporal resolution is as important as spatial resolution, and sometimes, more important.

If resources are to be kept comparable, two scenarios are possible – acquiring data such that the monitoring provides either high spatial resolution and low temporal resolution images, or low spatial resolution and high temporal resolution. In the second scenario, low spatial resolution results because a small amount of data is acquired each time, and high temporal resolution results because data are acquired more frequently. The traditional approach to inverting sparse data is to reduce the number of model parameters solved. Because only a fraction of the data that will

normally be used to get a high resolution image is used, the resulting seismic image has a lower spatial resolution. We propose to estimate unrecorded data (Harris et al.; 2007; 2008), and then reconstruct geophysical models without reducing the number of model parameters solved, thereby maintaining the high spatial resolution.

Although the idea posed here is somewhat similar to the recently developed concept of compressive sampling (Candès and Romberg, 2007) in the sense that sparse data are acquired and used in estimating unrecorded data, we deal here with datasets that are even sparser than what would be acquired as compressive sampling. Also, we take advantage of the large portion of the data space available in the dense baseline data.

3.2 Theory

Let the dense time-lapse data be composed of a recorded sparse part and an unrecorded part. i.e.

ddd d S)-(ISdd += (3.1)

usd ddd += (3.2)

where S is the data sampling operator that selects which data are recorded from the “dense” dataset , and and are “sparse” and “unrecorded” datasets respectively. From (3.1) and (3.2), we see that

dd sd ud

, ds Sdd = du d S)-(Id = (3.3)

In this notation, each vector d contains all previously measured and some future measured data. Our goal is to find an estimate d for the unrecorded dataset from the measured data du

%s . The

fitting goal for estimating finding d is u%

(3.4) 0Ad ≈d

subject to the constraint

us dSd ~= (3.5)

where in (3.4) the operator A is the model constraint or estimation operator. Substitution of (3.2) into (3.4) gives

(3.6) Ad Ad 0s u+ ≈%

The estimated unrecorded data, d is then obtained using (3.6), and minimizing the objective function

u%

2

Φ= Ad +Ad u s% (3.7)

  ‐19‐ 

 

3.3 Time-lapse field monitoring example

The field data example presented here are crosswell data from the McElroy field in West Texas. The datasets were acquired to monitor velocity changes in the reservoir in response to CO2 injection (Harris et al., 1995; Lazaratos and Marion, 1997) between 1993 and 1995. The wells are over 3000ft deep and are separated by approximately 600ft. Figure 3.1 shows common-shot gathers data from the surveys. First arrival seismic traveltimes were picked from the data. The largest traveltime differences occur at the depths corresponding to the location of the reservoir between 2750 and 3150 ft. Using these traveltimes, velocity models were reconstructed using the tomography code, FAST (Zelt and Barton, 1998). Figure 3.2 shows the reconstructed velocity models and the difference between them when the complete dataset in both cases are used. The most obvious difference in the velocity models is the significant drop in the P-wave velocity between 1993 and 1995, resulting from the injection of CO2 into the reservoir. Having a time interval of two years between the baseline image and the monitor image is satisfactory for some monitoring projects. However, if potentially dangerous consequences could occur from an abnormality in the reservoir, it will be necessary to monitor the reservoir with a finer sampling in time. Also, if resources necessary for data acquisition are limited, a more efficient time-lapse monitoring strategy is needed. This, scenario illustrates the need for a quasi-continuous monitoring strategy using sparse data.

Figure 3.1: Common-source gathers from the 1993 and the 1995 surveys at the McElroy field in West Texas. The red lines indicated first arrivals.

  ‐20‐ 

 

Figure 3.2: Reconstructed velocity models from the baseline (1993) and monitor (1995) surveys, and the difference between both models.

Figure 3.3: Reconstructed contrast model from the decimated 1995 field dataset.

To test the efficiency of the approach presented in this paper on field data, we used the complete dataset from the 1993 survey and 1% of the dataset from the 1995 survey to estimate the discarded data from the 1995 dataset. Here, the A operator in equation (3.7) was the first order derivative. The velocity models were then reconstructed from the estimated data. Figure 3.3 shows the resulting contrast model. We obtained a good comparison between the true contrast model and the contrast model from the reconstructed dataset.

3.4 Time-lapse synthetic monitoring example

In order to test this approach of quasi-continuous monitoring, we created a series of 70 two-dimensional P-wave velocity models from the baseline model reconstructed using the 1993 dataset, and a set of simulated fluid flow models converted to velocity models. The conversion was done using a Gassmann fluid substitution model. These models are intended to simulate CO2 injection into the reservoir over a period of 32 months. We included a fracture in the model

  ‐21‐ 

 

which allowed injected CO2 to flow out of the reservoir. Leakage occurred after the injected CO2 reached the fracture zone approximately 10 months after the start of injection. Using the finite differencing eikonal solver scheme given by Hole and Zelt (1995), we calculated dense first arrival seismic traveltimes recorded in crosswell data acquisition geometry for all 70 synthetic velocity models. Gaussian noise with a standard deviation that we consider to be the picking error of the field data was then added to the synthetic dataset. To simulate sparse data, we reduced the data size to 10%, 5%, 2%, and 1% of the original size for a given dataset in time. The reduction was done such that the total data volume in each sampling scenario was constant. From these sparse synthesized datasets, we estimated the dense datasets using the methods described in the previous section, and then reconstructed the corresponding velocity models using traveltime tomography.

In estimating missing data, we used zeroth, first and second order derivative operators as the A operator in equation (3.7). We then used the resulting dataset to reconstruct the synthetic velocity models. We present the results of the reconstructed velocity models by their root mean square (rms) errors with respect to the known synthetic models (Figure 3.4). In this case, we use the rms errors measured in the regions of the model where changes are known to occur. The rms error curves of the estimated datasets show a consistent pattern. This implies that we can maintain an approximately equal level of misfit in our estimated datasets and reconstructed velocity models if we reduce data size and sample the data space more frequently in time. From the plots, we see that the rms error reduces with time, indicating the impact of additional data on data estimation. What is not captured by the rms error plots is that using only 1% data measured every two weeks, the leaked CO2 was detected soon after it occurred. With the conventional strategy such a leak might not be discovered for years.

Figure 3.4: RMS error plots of the reconstructed velocity models using the estimated datasets.

  ‐22‐ 

 

  ‐23‐ 

 

4. Ensemble Kalman Filter for Dynamic Imaging 4.1 Introduction

Subsurface monitoring is a dynamic process. Seismic monitoring data observed at the surface change with time and consist of a series of time-lapse datasets. We want to integrate the temporal information captured by time-lapse datasets into the spatial seismic inversion (or imaging) method and develop the spatio-temporal seismic inversion for the monitoring. The Kalman filter is a classical method for integrating temporal and spatial information. The standard Kalman, however, has problems with a large number of model parameters as we have in seismic inversion. To overcome this problem, Evensen introduced the ensemble Kalman filter (EnKF). A complete introduction to EnKF can be found in Evensen (2007).

EnKF is a Monte Carlo implementation of the Kalman filter. EnFK can be used for linear and non-linear stochastic inversion. It can also integrate different types of data in the inversion. Taking advantage of these features, we combine waveform data and travel time data for seismic inversion. The waveform inversion in our study is non-linear. The use of travel time data significantly improves the estimation of the absolute seismic velocity.

The purpose of inversion is to recover the subsurface seismic properties e.g., acoustic impedance and velocity. For example, Oldenburg et al. (1983) discussed a deterministic approach for impedance inversion; Hass and Dubrule (1994) introduced a stochastic impedance inversion; Cao et al. (1989) presented an inversion method to estimate the background velocity and impedance simultaneously. Francis (2005) and Sancevero et al. (2005) compared deterministic and stochastic impedance inversion using examples. In general, stochastic seismic inversion has higher vertical resolution than deterministic inversion.

We first introduce the EnKF method and then use surface seismic data simulated for CO2 monitoring in coal to demonstrate the monitoring method. The method can also be used for general stationary reservoir characterization.

4.1 Model

Consider the seismic signal d recorded at surface as a function of subsurface model vector m. In this seismic experiment, d is normal incidence reflection data obtained after all necessary signal processing, and m is the 1-D seismic velocity model directly below the receiver. Data d and model m are related through an observation matrix G for the linear case:

d = Gm. (4.1)

A more general observation function g includes non-linear cases:

d = g(m). (4.2)

We want to estimate model m from observed data d by a stochastic inversion procedure implemented with the ensemble Kalman filter.

We follow the derivation in Evensen (2003) and apply the general EnFK theory to our monitoring problem, i.e., joint inversion using both waveform and traveltime data. In our case, m is an n-dimensional model vector composed with discretized 1-D velocity below the receiver; d is an m-dimensional data vector having m1 waveform data points and m2 traveltime data points, where m=m1+m2. A proper scaling factor is needed to normalize the two types of data.

Assume model m has a Gaussian probability distribution with mean m0 and covariance C, and data d also has a Gaussian probability distribution with mean d0 and covariance R. We create a model ensemble

M = [m1, …, mN] (4.3)

that has the mean m0 and the covariance C, and a data ensemble

D = [d1, …, dN] (4.4)

that has the mean d0 and the covariance R. Here, mi and di are ensemble members; N is the ensemble size that should be large enough to provide a good approximation to the probability distribution for the model and the data. The EnKF gives the statistical solution for a linear problem shown in equation (4.1):

, (4.5) )(ˆ GMDKMM −+=

where

(4.6) 1)( −+= RGCGCGK TT

is called the Kalman gain. The EnKF solution for a non-linear version equation (4.2) will be discussed in next section. The matrix M is an ˆ n × N matrix; each column represents a realization from the posterior probability distribution. The average of all columns (or realizations) forms the solution for the model estimation. In a time-lapse inversion problem, new data are coming in continuously, and the model can be continuously updated by repeating the procedure above, equations (4.3)-(4.5), using the estimated model obtained in current step as the initial model for next time step.

4.2 Implementation

We start with an initial model m0 created from prior knowledge, e.g., sonic logs and their interpolations, or just a constant model in the worst case. Then we construct the model ensemble in equation (4.3) as

mi = m0 + ε i ,

where εi is a n-dimensional random vector with Gaussian statistics. Convolution is used as the observation function for waveform data modeling, that is, we calculate reflection coefficients from 1-D velocity and convolve the reflection profile with a wavelet extracted from the normal incidence seismogram and a sonic log. The observation function in this study is not a linear function, and we cannot directly use equation (4.6), because it is difficult to find an observation matrix G for this convolution modeling operation. Instead we have to use a matrix-free implementation (Mandel, 2006) for this inversion.

  ‐24‐ 

 

The model covariance C in equation (4.6) can be approximated by the ensemble covariance as

  ‐25‐ 

 

) , (4.7) 1/( −= NTAAC

where

. 1)(1∑=

−=−=N

iiN

E mMMMA

Then model update equation (4.5) can be performed with

, )]([)(1

1ˆ 1 MDPGAAMM gN

T −−

+= − (4.8)

where

, RGAGAP +−

= T

N)(

11 (4.9)

and the ith column of matrix GA can be obtained from

.gN

gN

jjii ∑

=

−=1

)(1)(][ mmGA (4.10)

For the data ensemble D, we perturb the observed data d and have

di = d + γ i .

Here, γ i is an m-dimensional random vector from Gaussian statistics. The data covariance R required in equation (4.9) can be obtained from the ensemble covariance

R = γγ T / (N − 1).

We next apply the procedure described above to a synthetic example.

4.3 An Example of time-lapse seismic monitoring

This is an integrated simulation study for seismic monitoring of CO2 sequestration in coal beds. The primary goal of this simulation is to create a series of relatively realistic CO2 storage models and the corresponding surface reflection seismic data for monitoring tests.

4.3.1 Time-lapse models

We first build a 2-D reservoir flow model according to the geology and flow parameters of unmineable coal beds in the Powder River Basin. Over a period of 10 years, 175 time-lapse models are generated using the flow simulator GEM. Various cases, e.g., CO2 storage with or without leakage, are simulated. In the coal bed, matrix porosity equals 5%, cleat porosity equals 1-5%, matrix permeability equals 0.5md and cleat permeability equals 100md.

Next, we convert the flow simulation results to time-lapse P-wave velocity models with the help of a rock physics model. Figure 4.1 shows four velocity models at time =0, 3 months, 1 year, and 3 years. It can be seen that the P-wave velocity decreases due to the CO2 saturation. The methods discussed in previous sections are applied to these models to test if we can track the CO2 front using EnKF.

D

epth

(m)

200

400

600

800

  ‐26‐ 

 

Figure 4.1: Four time-lapse P-wave velocity modes created based on CO2 flow simulation in the coal beds. A: time=0; B: time=3 months; C: time=1 year; D: time=3 years.

4.3.2 Seismic data

The finite difference method is used to calculate the realistic seismic data (serves as observed data) for all 4 time-lapse models. Forty (40) shot gathers are calculated for each model. The source peak frequency is 50 Hz. Figure 4.2 gives a few samples of the shot gathers calculated using model D. Pre-stack depth migration is then used to produce the depth image from these seismic data, where one of the resulting depth images is shown in Figure 4.3. The time image shown in Figure 4.4 is constructed from the zero-offset seismic traces. The reflection waveform in the depth images plus the reflection picks from time and depth images are used for joint seismic inversion. Table 4.1 lists the reflectors picked from depth and time images (Figures 4.3 & 4.4) at a distance of 500 m, which provides the travetime data used for the joint inversion.

Distance(m)0 200 400 600 800

2500

3000

3500

4000

4500

5000

v(m/s)

Distance(m)

Dep

th(m

)

0 200 400 600 800

200

400

600

800

A  B 

C  D 

Tim

e (s

ec)

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 4.2: Sample shot gathers calculated using the finite difference seismic simulator.

Distance(m)

Dep

th(m

)

220 380 580 780

100

200

300

400

500

600

700

800

Figure 4.3: Prestack depth image of model D.

Tim

e (s

ec)

Distance (m)100 300 500 700 900

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 4.4: Time image of model D.

  ‐27‐ 

 

Table 4.1: Samples of traveltime picks used for the inversion.

Reflector 1 2 3 4 5 Depth (m) 270 310 550 670 750 Time (sec) 0.1675 0.1918 0.3340 0.4173 0.4595

  ‐28‐ 

 

Figure 4.5: Time-lapse velocity models inverted using EnKF. Models A-D correspond to time=0, 3 months, 1 year, and 3 years, respectively.

4.3.3 Seismic inversion with EnKF

Fast forward modeling tools are essential for EnKF inversion, because we must calculate g(mi), equation (4.10), for each sample of the ensemble that usually has a size of hundreds of models. There are two types of forward modeling involved in the joint inversion. For waveform data, we assume a sonic log is available for source wavelet estimation and use the source wavelet for convolutional modeling. In this study, we simply use the true velocity profile for the wavelet estimation. Constant density is assumed for impedance calculation. The forward modeling in the inversion for traveltime t is a summation down to a given reflector, i.e.,

t = 2 1 / vii∑ ,

where is the 1-D velocity of ith depth pixel. vi

Applying the procedure described in previous section to the synthesized “observed” seismic data, we obtain the inverted velocity models shown in Figure 4.5. In order to see the velocity changes

Dep

th (m

)

200

400

600

800

Distance (m)200 400 600 800

2500

3000

3500

4000

4500

5000

v (m/s)Distance (m)

Dep

th (m

)

200 400 600 800

200

400

600

800

A 

C 

B 

D 

more clearly, the velocity difference between models B-D and base model A are shown in Figure 4.6. A constant initial model is used in this test. It can be seen that the overall absolute velocity structure and the velocity drop due to CO2 injection are sufficiently recovered. Profiles in Figure 4.7 give a closeup comparison between the given model and the inverted model. Figure 4.8 compares the “observed” (or given data) and the data calculated with the inverted velocity. The given data and modeled data are virtually identical, though the given velocity model and the inverted velocity model exhibit some difference, especially the high frequency noise, which may be caused by the amplitude distortion in the depth imaging. True amplitude imaging will be very important for this seismic inversion.

  ‐29‐ 

 

Figure 4.6: Velocity differences between time-lapse models B-D and base model A. Left: given models. Right: Inverted models.

Distance(m)200 300 400 500 600 700 800

-200

-100

0

100

dv(m/s)

Dep

th(m

)

200

400

600

800

Dep

th(m

)

200

400

600

800

Distance(m)

Dep

th(m

)

200 300 400 500 600 700 800

200

400

600

B 

C 

D 

800

2000 3000 4000 5000

100

200

300

400

500

600

700

800

Velocity (m/s)

Dep

th (m

)

TrueInit.Inv.

Figure 4.7: A comparison between true model (solid black line) and inverted model (Dashdot blue line) at distance=500 m. Dotted yellow line is the initial model.

-0.5 0 0.5

100

200

300

400

500

600

700

800

Amplitude

Dep

th (m

)

GivenConv.

Figure 4.8: A comparison between “observed” data (solid line) and modeled data (dotted line). Solid line is sampled from distance=500m from the depth image and the dotted line is calculated from inverted velocity at the same location.

4.4 Conclusions

The ensemble Kalman filter provides a powerful tool for stochastic seismic inversion, especially for dynamic inversion in True4-D seismic monitoring. Integrating traveltime data into the inversion makes the estimation of absolute velocity possible. Waveform data alone in the joint inversion gives the short wavelength (spatial) components of inverted velocity.

  ‐30‐ 

 

  ‐31‐ 

 

5. DynaSIRT: A Robust Dynamic Imaging Method for Time-lapse Monitoring 5.1 Dynamic imaging

Dynamic imaging incorporates the temporal dimension into time-lapse seismic inversion. Instead of considering independent inversions for each time-lapse image, the temporal dynamics of the model are incorporated into inversion method, becoming a true spatio-temporal approach. This section describes a new algorithm for inversion of time-lapse seismic data named DynaSIRT. While conventional methods solve a system of equations independently for each survey for each snapshot in time, DynaSIRT incorporates information of previous surveys to estimate the current model without the reprocessing of previous data. Continuous or quasi-continuous monitoring present some special challenges for geophysical imaging. The amount of processing in case of joint inversion using data from older surveys or cross-equalization (Rickett and Lumley, 2001) can be excessively large and will grow in time. Practical implementation of dynamic imaging methods for seismic imaging must deal with memory and processing constraints. It can be done by incrementally solving the inversion problem and preserving solver state for later updates, keeping the problem tractable.

Regularization (Tikhonov and Arsenin, 1977) is usually applied to improve seismic imaging. Many conventional seismic imaging methods use spatial similarity along axes as additional information to perform inversion, applying spatial regularization (Santos, 2006). Analogously, similarities occur along time axes and can be used as well by means of temporal regularization (Ajo-Franklin et al., 2005). Dynamic imaging goes one step further beyond separated spatial and temporal regularization. It treats the evolution of the imaged area as a dynamic process, an integrated approach that intrinsically includes spatio-temporal dynamics on inversion method. Although medical imaging has successfully applied dynamic imaging methods, geophysics still widely uses static methods adapted for time-lapse imaging. This is due to the larger amount of data to be processed, the long time between geophysical surveys, and the larger number of parameters to be estimated from geophysical inversion methods.

DynaSIRT extends the static snapshot inversion method in order to incorporate temporal dynamic imaging. This method is efficient, processing equation by equation to incrementally update a previous model from new data. This incremental update is further explored for an additional advantage. The current state of the solver is saved for the next survey inversion, thus optimizing processing of sparse time-lapse data. Thus, DynaSIRT provides an efficient method for dynamic imaging, incorporating previous data into inversion without the burden caused by re-processing all the previous data. These features make DynaSIRT well suited for continuous monitoring of CO2 injection.

DynaSIRT reduces computational effort by saving the solver state of last time-lapse inversion, avoiding increasing amounts of data to be processed along time. It can also provide snapshots of updated image during acquisition, due to its incremental way of processing and update.

5.2 Row-action solvers

Row-action solvers compute an inversion problem solution iteratively, processing a linear system row by row, which means the updates are calculated equation by equation. These methods are the starting points for a practical implementation of dynamic imaging. A classic row-action method called ART (Algebraic Reconstruction Technique) computes parameter updates based on the difference between observed and computed data for each row (Peterson et al., 1985). The ART update equation for a linear system d=Gm is given by

( )( 1) ( )

2

kk k i

l l ilij

j

dm m gg

+ Δ= +

∑.

Here, di is the i-th data element; gij is a kernel matrix element, and ml is the parameter element.

Artifacts may occur due to the row nature of ART since updates are computed separately for each row. Artifacts can be reduced by computing an average update from all equation updates. SIRT (Simultaneous Iterative Reconstruction Technique) averages the update using the expression (Stewart, 1992)

( )( 1) ( )

21

1 knk k i

l l ilil i

j

dm m gN g

+

=

Δ= + ∑

j∑.

The iterative nature of these methods, dealing with each equation separately to update the model allows us to save the solver state and restart later from this saved state. This feature was implemented on DynaSIRT, avoiding reprocessing previous surveys data. Other row-action methods or methods that act on subsets of data may be used as well.

5.3 DynaSIRT

The continuous imaging/inversion approach must address three important questions:

(1) How to preserve the influence of older survey equations on current model estimation?

(2) How to balance influence between older and newer surveys equations?

(3) How to avoid reprocessing older surveys equations?

DynaSIRT addresses these questions through the incorporation of three upgrades over original SIRT method:

(1) Apply updates during computation, instead of later averaging and updating;

(2) Apply temporal damping penalty effects for earlier surveys because the model changes with time (aging effects);

(3) Save linear solver state for future surveys, thus avoiding reprocessing of older surveys equations.

  ‐32‐ 

 

The first upgrade was achieved by means of a moving average implementation. It yields a weighted expression that incorporates a single parameter update considering its influence over data when compared with previous surveys illumination Nl:

( ) ( ) ( ).1

11

11 k

l

k

l

lk mN

mN

Nm Δ⎟⎟⎠

⎞⎜⎜⎝

⎛+

+Δ⎟⎟⎠

⎞⎜⎜⎝

⎛+

= −+

The second upgrade was attained by exponential decay of older data over current model estimation. The third upgrade requires storing current model and timestamps for equations and parameters.

The DynaSIRT solver state is kept by four state variables: current estimated solution, number of equations that influence each parameter and timestamp arrays for equations and parameters. The aging factor α controls the decay of older survey equations influence, which is equivalent to the effective model illumination by previous surveys exponentially damped over time, i.e.

( )( 1) ( ) tse tspk kl lN N e α− −+ = ,

where Nl, called effective illumination, is the number of previous equations that updated a certain parameter with index l, α is a temporal damping factor for aging, tse and tsp are the respective timestamps for equations and parameters. Placing the last two expressions into update equation yields the DynaSIRT update equation:

( )( ) ( )

( ) ( )

( )

( ) ( )

( ).

11

1

12

12

11

∑ ∑

∑ ∑

=−−

=

+

−−

−−+

Δ⎥⎦

⎤⎢⎣

⎡+

+Δ

⎥⎦

⎤⎢⎣

⎡+

=

N

i j ij

ki

iltsptsekl

N

i j ij

ki

iltsptsekl

tsptseklk

gdg

eN

gdg

eNeNm

α

α

α

Model illumination Nl is damped, providing an effective number of equations that update each parameter over time, i.e., an effective illumination. Thus, the DynaSIRT update is based on survey acquisition timestamp and last parameter update timestamp, holding a trade-off between older and newer data in order to provide model estimation.

The most important factor controlling dynamic imaging in DynaSIRT is the aging factor (α) that controls how the relative influence of the older data with respect to newer data. It basically controls how the equivalent effective illumination of the model is updated according to how new the information timestamp is and how much illumination the new survey provides. This aging factor is related by analogy to the learning process of a system that incorporates new data but preserves older data to a degree. In seismic imaging, a very high factor would be equivalent to considering only the newest survey and to discard all previous ones (α >> 0), what is not usually wanted for when the current dataset is sparse. On the other hand, a very low aging factor would mean to keep all the older data but to resist against newer data. A very low aging factor would be equivalent to consider mostly the information from previous surveys but to minimize the influence of newer data, what is not usually wanted either (α << 0).

  ‐33‐ 

 

  ‐34‐ 

 

Two particular cases are theoretically interesting. The first one happens when α is infinite, which would be analog to a system without memory. For this particular case, DynaSIRT becomes equivalent to SIRT applied only to the latest survey. Another particular case happens when α is zero, which means that the influence of older surveys is not damped and that all surveys are equally important, what is usually incorrect since the imaged area is usually changing over time.

Since the extremes are not desired, α should be chosen within a limited range. Lower α emphasizes older surveys influence. Higher α emphasizes newer surveys influence. The effects associated to intermediary values of α are somehow analog to control the regularization factor of temporal regularization in a very sophisticated and adaptive way. It means that conventional tools for regularization factor selection can be adapted for this purpose, such as L-curve (Hansen, 1992) or θ-curve (Santos and Bassrei, 2007).

5.4 Numerical simulation

We applied DynaSIRT to a synthetic dataset generated with crosswell tomography surveys computed for 175 time-lapse 30×30 velocity models. The models show an expanding CO2 leakage computed using the reservoir simulator (GEM) and monitored by a permanently emplaced crosswell acquisition system. The background velocity model (Figure 5.1 shows a coal bed between 550m and 650m of depth where the CO2 is injected, causing a negative velocity contrast. All figures show distances in meters and velocities in m/s. Each time-lapse tomographic inversion was performed using diffraction tomography (Devaney, 1984; Harris, 1987; Wu and Toksöz, 1987). The discretization of the original continuous formulation leads to a linear system, which has to be inverted in order to estimate the velocity field (Rocha Filho, 1997; Santos and Bassrei, 2007). DynaSIRT was applied to estimate each time-lapse tomography solution, incrementally updating the estimated velocity field without reprocessing of previous surveys data. The error comparison between a conventional approach using SIRT and the proposed approach using DynaSIRT is shown on Figure 5.2 for the full survey (30 sources × 15 receivers) and on Figure 5.3 for sparse partial survey (6 sources × 15 receivers) along 175 time-lapse images for α=2. Good results were achieved and they show that inversion error is notably reduced when comparing DynaSIRT with SIRT for sparse partial surveys. Even when SIRT provides good results, the DynaSIRT method performs well, making SIRT an upper bound for its error. The true velocity models for six time-lapse images equally spaced in time are shown on Figure 5.4 as absolute velocity contrast relatively to the background velocity field. The respective estimated models computed using DynaSIRT for sparse partial surveys are shown in the same way in Figure 5.5. Although this partial survey has only 20% of the data from the full survey, the DynaSIRT results still show good agreement with true models as expected from error comparison with SIRT.

Figure 5.1: Background velocity field.

Figure 5.2: Error comparison along time for SIRT vs. DynaSIRT (full survey).

Figure 5.3: Error comparison along time for SIRT vs. DynaSIRT (partial survey).

  ‐35‐ 

 

Figure 5.4: True model (CO2 leakage modeling): velocity field contrast modulus. Time-lapse number shown on image top.

Figure 5.5: Time-lapse tomographic inversion using DynaSIRT (partial survey): velocity field contrast modulus. Time-lapse number shown on image top.

5.5 Conclusions

We presented in this section a dynamic imaging method that takes spatio-temporal aspects into account in time-lapse seismic imaging. The method was applied to a synthetic dataset. The current solver state can be saved, thus significantly improving computational efficiency. The next slow-time inversion starts from the last solver state, incorporates effective illumination and time-stamps representing when model parameters were last updated and when data were acquired. DynaSIRT combines simplicity, robustness and efficiency, important features for continuous monitoring. They also simplify the design of acquisition scenarios because the algorithm allow, in principle, incremental data as little as one trace of seismic data.

  ‐36‐ 

 

  ‐37‐ 

 

6. Imaging with Feature-enhanced Adaptive Meshes and Temporal Regularization 6.1 Introduction

The expected subsurface changes are expected to occur in localized regions due to changes in CO2 saturation and pressure. The geology changes little if any. Conventional imaging approaches often estimate many more parameters than needed because these main structural features do not change. This results in image artifacts from computing differences between surveys due to different successive estimations of these static geological structures (Rickett & Lumley, 2001). In order to minimize such undesirable effects, we propose a temporal integration technique combined with a reduction in the number of model parameters to be estimated. Temporal integration is accomplished through joint inversion of incremental new data with data from previous surveys. New data are more strongly related with current subsurface models and therefore should have heavier weights in this joint inversion.

6.2 Trigonal meshes

Reduction in the number of parameters is achieved by feature-enhanced adaptive meshing. One of the advantages of the adaptive triangular mesh (Maybeck, 1979) is the resolution achieved through use of a finer mesh near the front of the injected CO2 plume. Another advantage is the implicit spatial regularization that occurs due to the use of coarser meshes in slow-varying regions. Thus, we use adaptive triangular adaptive meshes, temporal integration and spatial regularization (Tikhonov & Arsenin, 1977) for the time-lapse imaging. Moreover, the triangular mesh is used to reduce the number of model parameters. However, we also want to keep the simple formulation of the tomographic matrix and regularization for conventional regular grids. Thus, we derived a different formulation for the use of triangular meshes that allows mapping between triangle vertexes and a regular grid. This approach can be used as a general framework to solve linear inverse problems for different areas using triangles instead of cells as basic elements, with minimal impact to original problem formulation. The key concept is to describe each cell of a regular grid as a linear combination of control nodes values at triangle vertexes, considering the respective triangle that covers each region of regular grid. Thus, a linear operator T may be explicitly defined to map any regular grid into control nodes of a triangular mesh. This approach also keeps the possibility of using its inverse mapping T-1 to find a regular (or rectangular) grid representation from a triangular representation, which is useful to display the resulting image of tomographic inversion. The algorithm that computes matrix T has the following steps for each triangle of mesh: (1) Identify its three vertexes to compute vertex weights based on relative position of interior cells of the triangle; (2) compute weights for each cell of regular grid within current triangle using barycentric coordinates interpolation; (3) store these weights into a matrix T that maps each cell value as a linear combination of control nodes triangle vertexes. The interpolation using barycentric coordinates is based on the areas of three imaginary triangles formed by lines between triangle vertexes and an interior point (Bottema, 1982). These three areas are used as a measurement of influence of each control node vertex onto a point belonging to a triangular mesh element, resulting in three respective weights for each interior point. Considering v1, v2 and

v3 as the control values at respective positions r1, r2 and r3 corresponding to vertexes of each triangle, the weights for each interior point at position r are given by the following expressions:

( ) ( ) ( )( ) ( ) ,

32321

32321 errrr

errrrr

⋅−×−⋅−×−

=w

( ) ( ) ( )( ) ( ) ,

31312

31312 errrr

errrrr⋅−×−⋅−×−

=w

( ) ( ) ( )( ) ( ) ,

31213

31213 errrr

errrrr

⋅−×−⋅−×−

=w

where e3 is the unitary vector (0,0,1). This leads to the following expression that maps nodes control values from triangular mesh into a regular grid cell value o(r) for each triangle:

)()()( 3

1rrr ii i vwo ∑=

= .

The matrix T performs this mapping for each cell of regular grid using respective triangles that covers its different regions. Thus, nodes control values at triangle vertexes are mapped into a regular grid using the forward mapping expression vo T= and the inverse mapping from regular grid into control nodes values of triangular mesh is given by . This allows a straightforward modification to convert a regular grid method into a triangular mesh method. From a simple regular grid formulation for linear problems

ov 1−= T

op W= , where p is the data vector and o is the model parameter vector, one may use the expression for triangular meshes vp WT= . For linear inverse problems, this expression may be applied to estimate triangular mesh control node values from data vector

pv += )(WT ,

where the superscripted plus symbol means pseudo-inverse (Penrose, R., 1955) computed using SVD. An equivalent regularized system may also be obtained from

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡0p

vTD

Wλ

,

where D is a numerical derivative matrix and λ is a constant (Santos, 2006). After parameter estimation, the resulting triangular mesh control values can be easily displayed as a regular grid using forward mapping of linear operator T, as described earlier. 6.3 Temporal data integration

The second component this scheme is time regularization. Time-lapse imaging conventionally inverses different data sets independently and then analyzes image subtraction to identify changes. This straightforward approach repetitively estimates fixed geology structures as well model changes due to pressure and saturation, ignoring the similarities between successive images that could be useful during inversion. A smarter approach uses a temporal derivative operator to integrate data along time using previous information combined with repeated surveys (Ajo-Franklin et al., 2005). It requires solving an integrated linear system that contains previous survey equations and temporal derivative equations minimization. We adopted a different

  ‐38‐ 

 

approach that integrates previous surveys information but uses a scalar factor to damp the influence of each previous survey into the latest survey information available by forming an augmented system

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−+

−

+−+

−

1ns-k

-1k

1ns-k

-1k

1

1

1

1

nsk

k

k

nsk

k

k

W

WW

p

pp

o

α

α

α

αMM

,

where index k represents the newest survey, ns is the number of available surveys and αk-i is a normalized scalar proportional to the influence of earlier survey k-i into current inversion, being smaller for older surveys. Since relevant information from previous surveys is included in this equivalent system, a new smaller and less expensive survey may be performed to update subsurface image. This procedure can be repeated for newer datasets and keeps relevant information from previous ones, increasing the number of rows by the number of newer survey equations but keeping fixed the number of columns of equivalent linear system, which may not occur when using temporal derivative operator approaches. 6.4 Diffraction tomography

The imaging method with triangular mesh and temporal integration discussed above can be used for relatively general linear geophysical inversion. We now apply it to seismic diffraction tomography (Wu & Toksöz, 1987; Harris, 1987), where the incident field from a source at rs can be represented through the Green's function G(rs | r' ) and the scattered field at receiver rg can be calculated by

''''20 )|()|()(),( rrrrrrrr dGGOkP gsgss ∫−= .

This formula is the space domain forward modeling equivalent to the diffraction tomography formula used above to create the fast filter image simulator. Discretization of the above equation leads to the linear system p = Wo, which has to be inverted in order to recover O(r) (Rocha Filho, 1997). In this work the inversion was done using SVD, but could be done using other linear system solvers.

Next, we simulate a CO2 monitoring experiment to test this time regularization algorithm. As discussed above, we have 221 time-lapse CO2 flooding models. Five of these time-lapse models are presented in Figure 6.1 for the VSP geometry. The figures show only the velocity difference compared with the background medium (~4,000 m/s). There is a negative velocity contrast (2%) caused by CO2 injection. Data are simulated for each model for 28 sources and 28 receivers. Triangular adaptive meshes (column b) are generated based on velocity gradient from a priori information, leading to the inversion results shown in column c. A regular grid would provide good results for this base survey as well, since a reasonable number of sources and receivers are employed.

  ‐39‐ 

 

(a1) True model for baseline survey (#1).

(b1) Adaptive mesh for survey (#1).

(c1) Trigonal inversion for survey (#1).

(a2) True model for update survey (#2).

(b2) Adaptive mesh for survey (#2).

(c2) Trigonal inversion for survey (#2).

(a3) True model for update survey (#3).

(b3) Adaptive mesh for survey (#3).

(c3) Trigonal inversion for survey (#3).

(a4) True model for update survey (#4).

(b4) Adaptive mesh for survey (#4).

(c4) Trigonal inversion for survey (#4).

(a5) True model for update survey (#5).

(b5) Adaptive mesh for survey (#5).

(c5) Trigonal inversion for survey (#5).

Figure 6.1: Monitoring test with adaptive triangular meshes. True models, adaptive meshes and reconstructions are shown in columns a, b and c, respectively. Distances are in meters and velocities in m/s.

As discussed above, a priori information from reservoir flow simulation or from previous surveys may be used to generate adaptive meshes. The adaptive mesh inversion reduces the number of parameters but maintains robustness, since triangles at slow-varying velocity fields regions are coarser but still useful to perform good imaging even with low quality a priori information. Since the previous datasets is integrated into inversion, the successive updates use a

  ‐40‐ 

 

  ‐41‐ 

 

fewer and consequently less expensive datasets. In our example, we use a constant scalar for the immediately previous survey α = 0.3 and adopt respectively α2, α3 and so on when other earlier surveys were available and evenly sampled along time. We apply spatial regularization for order 2 and λ = 0.02 for all inversions. A naive regular grid inversion for such image resolution would require 50 sources and 50 receivers for each time-lapse inversion, which means that it would require three times more data measurements than we used here. This reduction in the number of parameters is reinforced by temporal integration of previous survey to achieve current subsurface image. Thus, problems that are originally underdetermined can be reformulated as overdetermined without the drastic decrease of resolution required for regular grids under similar circumstances.

7. DARS Measurements on Acoustic Properties of Coal and other Porous Rocks An good understanding on the acoustic properties of porous rocks, such as seismic velocity and attenuation, can provide guide lines for our seismic monitoring work. We need to know how much changes of the seismic velocity could be introduced when CO2 is injected into coal, so that we can develop proper strategies for a monitoring project. Coal has some special properties, including absorption and matrix swelling, which can complicate the acoustic properties of CO2 saturation in coal. For example, McCrank and Lawton (2009) noticed that Gassmann equation predicted a much smaller acoustic impedance decrease than their observation in a small field pilot test. An experiment conducted in Zoback lab (GCEP Technical Annual Report, 2008), as shown Figure 7.1, found that CO2 saturation in coal results in a much lower bulk modulus than that caused by helium saturation at a static condition (zero frequency), but a slightly higher bulk modules at a dynamic condition (MHz frequency). The frequency we are interested most is the seismic wave frequency that ranges 10 Hz to10 KHz. This leads to a problem that has frustrated the earth science community for years is the large discrepancy in frequency used in traditional pulse transmission measurements (~1 MHz) and seismic field measurements. Issues of frequency dispersion are often raised but most often go unresolved.

Figure 7.1: Static and dynamic bulk modulus plotted as a function of effective pressure (measurement in Zoback lab).

Traditional laboratory methods of measuring the acoustic properties of say a 1-inch plug fall into three categories: (1) pulsed traveling-waves, where a high frequency pulse (500 kHz - 5 MHz) is transmitted through the sample; (2) vibrating systems, where the natural resonance (~50 kHz) of the sample is excited; and (3) quasi-static stress/strain response. Attenuation is usually a secondary measurement and none of these traditional methods can easily measure small samples at the frequencies used in field seismic experiments. The most popular of these is time-of-flight using pulse transmission in a precision cut sample. Low frequency measurements can be made using resonant bar techniques but these require large samples and are more difficult and

  ‐42‐ 

 

expensive than pulse transmission. Moreover, attenuation estimates are very difficult to make from pulse transmission measurements. Our DARS (Differential Acoustic Resonance Spectroscopy) method is a low frequency (~1000 Hz) measurement that can be applied to acoustically small samples, even unconsolidated samples or samples with irregular shape. The primary target of our DARS measurement is attenuation.

Acoustic Resonance Spectroscopy is a well-established methodology used by NIST (National Institute of Standards and Technology) to measure the velocity and Q of gases. Cavity resonators have been shown to provide a remarkably accurate means of measuring the velocity of sound in gases. The resonant frequency of a cavity depends on the size and shape of the cavity and the velocity of sound in the contained fluid. The frequency at resonance can be measured with an accuracy of one part in a million and the velocity of sound easily determined to accuracy better than 0.05% when the cavity dimensions are well characterized. Measurements with precision of 0.003% have been reported. Moreover, the velocity is easily measured as a function temperature and pressure. The measurement is routinely made at a few kilohertz, e.g., 4 KHz, in the laboratory. This technique is called Acoustic Resonance Spectroscopy or ARS.

Source 

Cavity 

Receiver

Sample

(a) Cross section

(b) Signal path

Figure 7.2: DARS I setup

  ‐43‐ 

 

We are implementing a variation on ARS, that we call Differential Acoustic Resonance Spectroscopy or DARS. DARS is being developed specifically for acoustically small samples of porous material, namely rocks, and appears to be especially well suited for coal samples, e.g., poorly consolidated and possible irregular. The DARS principle of operation is quite simple. First we measure the resonant spectrum of the simple cavity filled with a fluid. Next, we introduce into the cavity a small sample of the test sample and measure the change in the complex resonance frequencies, i.e., frequency and Q. A combination of calibration and numerical modeling is then used to extract an estimate of the modulus and Q of the sample. Accurate measurements can be made with DARS for acoustically small samples because the resonances in laboratory-size cavities occur in the hundreds to thousands of Hertz. Figure 7.2 shows the DARS I setup (the first generation of DARS) used in our lab. Figure 7.3 is an example of the resonance data from DARS I. The data measured using DARS is the resonance frequency (f), the half-power linewidth (W) of the resonance curve, and the amplitude of the resonant curve (A).

1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 12000

0.05

0.1

0.15

0.2

0.25

Frequency (Hz)

Acoustic Resonance Spectrocopy

d31:c15.85Td31:c46.85T

Boise SS

Q= f / W

Empty

ws

As

A

  ‐44‐ 

 

w

f

Ener

gy D

ensi

ty

fsFrequency (Hz)

Figure 7.3: DARS I resonance curves for the empty cavity (blue) and the cavity with a small sample of sandstone (red).

The second generation of DARS is called DARS II, which can be used to determine the sound properties at different effective pressures. In summary, DARS II is capable of measuring the compressive modulus and loss factor of acoustically small samples under the following conditions:

(1) Low frequencies on small samples in the range of 100's to 1000's of Hertz; (2) Narrow band at a specified center frequency, e.g., 1000 Hz; (3) Unconsolidated samples and samples with somewhat irregular shapes; (4) Under varying conditions of effective pressure.

Frequency (Hz)

Posi

tion

AcousticVelocity(1st mode)

Acousticpressure

Figure 7.4: DARS I resonance profile, recorded as the sample (red rectangle in the cavity to the right) moves along the axis of the cavity in the varying pressure and velocity fields, allows for the estimation of several acoustic properties of the sample.

The DARS profile involves moving the sample (relative to the cavity) in a manner illustrated in Figure 7.4. In this way, different combinations of acoustic pressure and velocity can be used to extract different acoustic properties of the sample, namely modulus, density, compressive losses and flow losses.

7.1 Measurement of compressibility and attenuation

The resonant frequency of a cavity can be found using the perturbation formula originally developed by Morse and Ingard (1968):

(7.1) δρραδκα ><−><−=− 22222222 UcBfpAfff ooos

where is the sample-loaded cavity resonant frequency, is the empty cavity resonant frequency,

sf 0fα =Vs Vc is the ratio of the sample volume to the cavity volume, and are the average acoustic pressure and velocity distributions,

>< 2p>< 2cρ 22U δκ = (κ2 −κo ) κo is

the contrast in sample compressibility to the fluid, δρ = (ρ2 − ρo ) ρs is the contrast in sample density to the fluid, and A and B are system constants (e.g., cavity geometry) determined through calibration with known samples. We expanded upon the Morse and Ingard derivation to add two important features to the model: (1) sample attenuation, and (2) a double difference formulation for use with a reference sample. For attenuation, we assume that the compressibility and density parameters are complex

  ‐45‐ 

 

quantities. Complex compressibility captures compressive losses whereas complex density models losses to fluid flow, e.g., acoustic flow or micro-tortuosity in porous samples:

κ r =κnr 1+ i Qn( ) (7.2a)

ρr = ρnr 1+ i qn( ), (7.2b)

where is the “quality factor” related to compressive losses and is the quality factor related to flow losses. The double difference model has the advantage of producing smaller frequency shifts, thus maintaining validity of the perturbation approach for the unknown sample in comparison to the reference sample. (We do not show the double-difference formula here.) The procedure is to first use the frequency shift to estimate the compressibility, and then the linewidth is added to estimate the loss factors Q and q.

nQ nq

Three coal samples (Figure 7.4) were measured with DARS I at room temperature and atmosphere pressure. The largest sample (#1) is a hard semi Anthracite. Samples #2 and #3 are soft sub-bituminous. The smallest sample (#3) is slightly irregular in shape. The DARS data are shown in Figure 7.5. The difference curves (7.5c and 7.5d) clearly show the smooth changes in frequency and linewidth as the samples are moved through the cavity. These responses were simulated with the perturbation model to yield estimates for compressibility and Q. The results of estimated compressibility by DARS I shown in Table 7.1 demonstrate the robust and well-behaved nature of the DARS measurements. These are believed to be the first low frequency measurements of Q on coal samples. The anthracite sample #1 has the highest value of Q. The perturbation model does not capture the complicated behavior observed in the linewidth near the ends of the cavity. This behavior is likely due to fluctuations in the acoustic velocity fields that are not well modeled near the ends of the cavity. Nevertheless, these measurements were made at zero effective pressure and must be updated for in situ conditions using the new DARS II system being built. The DARS II system is discussed in Subsection 7.5.

Figure 7.4: Coal samples measured by DARS.

  ‐46‐ 

 

Figure 7.5: DARS I profile responses for three coal samples. (a) Resonance curves. (b) Resonance frequencies. (c) Difference frequencies (cavity perturbations Df). (d) Difference linewidths (cavity perturbations DW).

Table 7.1: Summary of coal samples measured using DARS I. Permeability was measured for sample #1 but estimated for samples #2 and #3 using the DARS dynamic diffusion theory.

Sample #Comments

Boundary Conditions -

Sealed

Measured Volume (in3)

Measured Porosity (%)

Permeability (mD)

Bulk Modlus (Gpa)

Q

#1 Hard, semi-anthracite

Yes 1.21 1.9 0.05-0.1 2.84 38

#2 Weak sub-bituminous

No 1.15 7.14 218 3.33 30

#3 Weak, sub-bituminous

NO 0.95 13.9 325 3.06 21

DARS Estimates

7.2 Measurement of permeability

Xu (2007) developed a model for dynamic diffusion or micro-flow of the DARS acoustic fields into porous samples. This result enables estimation of a micro permeability and its connection to the traditional acoustic properties. The result also shows how the DARS acoustic fields penetrate

  ‐47‐ 

 

a porous sample. The penetration depth depends on the frequency of the acoustic wave and the permeability of the sample. An example of the pressure distribution (at 1000 Hz) for a permeable sample is shown in Figure 7.6. This result was computed using a finite element model for dynamic diffusion. The permeability was estimated from the dynamic diffusion model developed by Xu (2007). These estimates are also shown in Table 7.1. The anthracite sample #1 has the lowest permeability.

Figure 7.6: DARS diffusion pressure distribution in a cylindrical sample of porous sample estimated using a finite element model Xu (2007)

6.3 Comparison with Bio-Gassmann modulus

The Biot-Gassmann equation can be used to predict the impact of fluid saturation in a porous rock. In order to have a better understanding on the DARS results, let us compare the bulk modulus of the open and sealed samples obtained by the DARS technique with the computed Biot-Gassmann modulus. This latter modulus is calculated from the porosity and the bulk moduli of the grains and the saturating fluid. In addition, the bulk and shear modulus of the matrix are needed. These are calculated from the dry rock density and the dry Vp and Vs in the usual manner. A set of 23 consolidated natural and artificial rocks are investigated. Table 7.2 shows their rock physical properties measured with the conventional methods. All samples are fully saturated with silicone oil that is the same as the cavity fluid. For the purpose of this experiment, the pores of the tested samples are initially open, so that the pore-fluid can communicate with the surrounding fluid. The second batch of DARS measurements is on the same samples, but now with the outer surface carefully sealed by means of an epoxy resin. Table 7.3 gives the estimated bulk modulus by DARS and the predicted bulk modulus by the Boit-Gassmann equation. From the table, we find that the DARS bulk modulus of the sealed samples is generally higher than the DARS bulk modulus of the samples with open pores. Obviously, sealed samples are stiffer than samples with open pores, since fluid flow is restricted. In Figure 7.7, we cross plot

  ‐48‐ 

 

  ‐49‐ 

 

the Biot-Gassmann modulus with the DARS bulk modulus of the open samples. We observe that this DARS bulk modulus is generally lower than the Biot-Gassmann modulus for all samples. As described in previous sub-section, Xu et al. (2006) estimated the flow properties in porous media with a model for dynamic diffusion and related the effective compressibility to permeability, and found that the permeability of the sample greatly influences the DARS-compressibility. To further investigate this claim, we cross plot the Biot-Gassmann modulus with the DARS bulk modulus of the sealed samples as shown in Figure 7.8. We observe a good agreement between the DARS bulk modulus of the sealed samples and the Biot-Gassmann modulus.

Table 7.2: Rock physical properties of the porous materials under study obtained from independent laboratory measurements: dry density, the Klinkenberg corrected permeability, and the porosity. The error is the standard deviation of the measurements.

Sample ID Density [kg/m3]

Permeability [mD]

Porosity [%]

SSA04 2086 ± 1 362 ± 18 20.80 ± 0.01

SSB07 1847 ± 1 2748 ± 6 28.56 ± 0.01

SSC05 2317 ± 2 0.74 ± 0.04 11.75 ± 0.04

SSF02 1930 ± 1 2666 ± 26 26.78 ± 0.01

SSG01 2004 ± 1 1862 ± 12 24.29 ± 0.01

YBE03 2111 ± 5 182 ± 1 18.94 ± 0.02

VIF01 1603 ± 7 11928 ± 137 37.99 ± 0.02

VIC05 1497 ± 10 25557 ± 2783 42.86 ± 0.03

QUE09 2067 ± 7 2214 ± 4 21.89 ± 0.01

B1P13 2132 ± 4 330 ± 3 20.06 ± 0.05

CAS16 2159 ± 2 5.51 ± 0.01 18.66 ± 0.03

B1N20 2119 ± 3 205 ± 1 20.62 ± 0.01

COL23 2357 ± 4 0.77 ± 0.03 11.44 ± 0.03

BEN27 2010 ± 7 1151 ± 4 24.11 ± 0.02

B2P30 2144 ± 2 161 ± 1 19.52 ± 0.01

B2N32 2164 ± 3 92.7 ± 1.7 19.03 ± 0.02

FEL36 2039 ± 4 10.1 ± 0.1 23.02 ± 0.02

NIV44 1847 ± 1 6544 ± 132 30.18 ± 0.02

UNK50 2245 ± 2 0.09 ± 0.00 15.84 ± 0.05

NN356 2195 ± 3 1.50 ± 0.08 16.99 ± 0.04

NN458 2225 ± 1 5.76 ± 0.19 15.75 ± 0.02

GL160 1884 ± 2 17935 ± 1031 34.02 ± 0.01

GL261 1895 ± 3 18324 ± 613 35.57 ± 0.01

  ‐50‐ 

 

Apparently, the bulk modulus measured with DARS depends on whether or not the pore fluid is allowed to communicate with the surrounding fluid. The mechanism responsible for the bulk modulus measured with the DARS set-up is a combination of bulk modulus of the saturated frame and fluid flow. Future work on DARS should concentrate on investigating the theoretical relation between the DARS bulk modulus of open samples and relative fluid flow.

Table 7.3: Bulk moduli of the fully oil-saturated samples. The bulk moduli of the open and sealed samples are determined using the DARS method with a different sample surface condition. Their error reflects the uncertainty in the system. The Biot-Gassmann modulus is calculated from independent laboratory measurements.

Sample ID

Bulk modulus open sample

[GPa]

Bulk modulus sealed sample

[GPa]

Biot-Gassmann modulus [GPa]

SSA04 4.1 ± 0.4 8.7 ± 1.6 9.6 ± 0.5

SSB07 3.0 ± 0.2 14.3 ± 4.0 15.3 ± 0.7

SSC05 10.2 ± 2.2 17.6 ± 5.8 16.5 ± 0.8

SSF02 2.9 ± 0.2 6.9 ± 1.0 7.9 ± 0.4

SSG01 3.3 ± 0.2 10.1 ± 2.1 9.5 ± 0.5

YBE03 5.6 ± 0.7 11.0 ± 2.5 11.1 ± 0.5

VIF01 2.3 ± 0.1 6.0 ± 0.8 5.2 ± 0.2

VIC05 1.9 ± 0.1 3.7 ± 0.3 3.4 ± 0.2

QUE09 3.3 ± 0.2 10.3 ± 2.2 10.1 ± 0.5

B1P13 5.5 ± 0.6 9.8 ± 2.0 12.3 ± 0.6

CAS16 9.3 ± 1.8 9.1 ± 1.8 8.8 ± 0.4

B1N20 4.3 ± 0.4 8.2 ± 1.4 9.9 ± 0.5

COL23 9.1 ± 1.8 13.0 ± 3.4 14.8 ± 0.7

BEN27 3.4 ± 0.2 13.6 ± 3.7 12.7 ± 0.6

B2P30 5.5 ± 0.7 9.7 ± 2.0 12.8 ± 0.6

B2N32 6.2 ± 0.8 11.5 ± 2.7 12.3 ± 0.6

FEL36 6.4 ± 0.9 9.2 ± 1.8 12.1 ± 0.6

NIV44 3.2 ± 0.2 12.1 ± 3.0 7.9 ± 0.4

UNK50 8.5 ± 1.5 14.1 ± 3.9 15.9 ± 0.8

NN356 9.3 ± 1.8 12.9 ± 3.3 13.9 ± 0.7

NN458 13.6 ± 3.7 18.3 ± 6.2 20.0 ± 1.0

GL160 2.5 ± 0.1 5.0 ± 0.5 8.8 ± 0.4

GL261 2.5 ± 0.1 5.6 ± 0.7 10.0 ± 0.5

0

5

10

15

20

25

0 5 10 15 20 25

Biot-Gassmann modulus [GPa]

DA

RS

bul

k m

odul

us o

pen

sam

ple

[GP

a]

Figure 7.7: Cross-plot of the Biot-Gassmann modulus and the bulk modulus of the porous samples with open pores obtained by the DARS method.

0

5

10

15

20

25

0 5 10 15 20 25

Biot-Gassmann modulus [GPa]

DA

RS

bul

k m

odul

us s

eale

d sa

mpl

e [G

Pa]

Figure 7.8: Cross-plot of the Biot-Gassmann modulus and the bulk modulus of the porous samples with open pores obtained by the DARS method   ‐51‐ 

 

  ‐52‐ 

 

7.4 Effects of gas, water and oil saturation

The DARS experiments in previous subsections were merely oil saturation in the porous samples. The silicone oil in the pore space is identical to the surrounding fluid in the cavity. However, a goal of this DARS project is to measure coal samples with CO2 saturation under certain effective pressure. As a step towards to this goal, we measured three samples saturated with gas, water and oil respectively, and assess the capability and accuracy of the DARS I setup to distinguish between different pore fluid contents.

Three samples are made from glued spherical glass beads (0.5 mm diameter) with a specific gravity of 2.46 g/cc. These samples have a cylindrical shape with a length of 27.4 mm and a diameter of 25.2 mm. The outer surface of each sample was carefully sealed using an epoxy resin in two steps. In step one, the bottom and the mantle of each cylinder were sealed. After drying, all three samples were evacuated in a vacuum chamber in which a beaker of mineral water and a beaker of 5 cSt silicone oil were present too. The chamber was depressurized for several hours. When the pressure was below 1 kPa, two of the samples were carefully immersed in either fluid. Then, the chamber was disconnected from the pump and equilibrated to atmospheric pressure. Several depressurize cycles were repeated to allow full saturation. Finally, all three samples were removed from the vacuum chamber and the top surface of all three samples was sealed (step two) to obtain one water-saturated sample, one oil-saturated sample, and one air-saturated sample. Sealing prevents communication of the pore fluid with the surrounding fluid of the container.

We measure the empty and sample-loaded resonance profiles as a function of frequency and position in DARS for each sample. We repeat the measurement for each sample 12 times in several weeks. The frequency sweeps between 860 and 960 Hz with a center frequency of 910 Hz for the empty measurements. The temperature of the oil is continuously measured and varies within 0.1 degree Celsius per measurement.

The average results of the temperature-corrected individual measurements are given in Figures 7.9-7.13. Figure 7.9 shows the characteristic differences in (i) resonance frequency, (ii) linewidth and (iii) peak amplitude between the empty measurements and sample-loaded measurements. These three observations are exemplified in Figures 7.10-7.13. In Figure 7.10, we plot the frequency shift as a function of sample position along the axis of the cylindrical cavity. Two points are here of interest: (i) the different fluids in the sample cause a different shift in resonance frequency. Although the differences are small, the air-saturated sample has the largest shift (i.e. the lowest compressibility), while the oil-saturated sample shows the smallest shift (i.e. the highest compressibility) at the center position (# 50). One would expect that the air-saturated sample has the highest compressibility. Apparently, saturating with oil and water weakens the samples. (ii) The shift caused by oil- and water-saturation is of the same order at the cavity ends (position # 15 and 84), which confirms that their densities are of the sample order and higher than the density of the air-saturated sample. Figure 7.11 shows the difference in amplitude between the empty and sample-loaded measurements. We see that the oil-saturated sample exhibits the highest amplitude decrease at

position # 50, so the highest loss of energy. This high attenuation of the oil-saturated sample is also clearly seen in Figure 7.12, since the frequency over linewidth equals the quality factor (inverse attenuation). In Figure 7.13, we see that the quality factor of the empty system is 342, while when loaded with the air-, water-, and oil-saturated sample it decreases to 335, 310, and 247, respectively. Apparently, the oil has weakened the sample’s frame, making it more compliable than the air-, and water-saturated samples. To conclude, the DARS apparatus is capable to measure the difference in pore fluid if the dry rock properties are identical. The usefulness of this result is that DARS can be used to predict the properties of the pore fluid content if the dry rock properties are known, to analyze the effect of fluid substitution using Gassmann’s equations, including the effects of, for example, partial saturation with a gas and liquid.

860 870 880 890 900 910 920 930 940 950 9600

10

20

30

40

50

60

70

80

90

100

Am

plitu

de

Frequency [Hz]

air0airwat0watoil0oil

Empty

Air saturated sample

Oil saturated sample

Water saturated sample

Figure 7.9: Average acoustic response due to the presence of samples saturated with a different fluid, located in the center of the tube (position # 50). The unperturbed pressures, denoted by ‘empty’, are on the left.

  ‐53‐ 

 

0 20 40 60 80 100 120-6

-4

-2

0

2

4

6

Position #

Freq

uenc

y sh

ift (D

iffer

ence

in re

s fre

q) [H

z]

airwatoil

Empty

Figure 7.10: Average difference in resonance frequency due to the presence of samples saturated with a different fluid. The unperturbed pressures, denoted by ‘empty’, are from position 98 to 110.

0 20 40 60 80 100 120-25

-20

-15

-10

-5

0

5

10

Position #

Am

plitu

de s

hift

(Diff

eren

ce in

pea

k am

pl) [

-]

airwatoil

Empty

Figure 7.11: Average difference in peak amplitude due to the presence of samples saturated with a different fluid. The unperturbed pressures, denoted by ‘empty’, are from position 98 to 110.   ‐54‐ 

 

0 20 40 60 80 100 120-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Position #

Line

wid

th s

hift

(Diff

eren

ce in

hal

fwid

th) [

Hz]

airwatoil

Empty

Figure 7.12: Average difference in line width due to the presence of samples saturated with a different fluid. The unperturbed pressures, denoted by ‘empty’, are from position 98 to 110.

0 20 40 60 80 100 120240

260

280

300

320

340

360

Position #

Qua

lity

fact

or [-

]

airwatoil

Empty

Figure 7.13: Difference in quality factor of the system due to the presence of samples saturated with a different fluid. The unperturbed pressures, denoted by ‘empty’, are from position 98 to 110.

  ‐55‐ 

 

7.5 DARS II construction

The first generation of DARS, called DARS I, measures the acoustic compressibility and attenuation at atmosphere pressure and conditions of full saturation. DARS II is designed to have independent control on pore pressure and saturation and confining pressure. The design for DARS II is to take the DARS I setup and place it into a pressure vessel. A sketch of the design and a picture of the DARS II system are shown in Figure 7.14. DARS II has a high pressure pump connected to the pressure vessel. Inside the pressure vessel is an aluminum cavity which has 18 inch length, 1.5 inch diameter and 0.5 inch wall thickness. A piezoelectric disc source located at the bottom of the pressure vessel and a hydrophone receiver located at the top of the cavity for signal generation and detection, respectively.

(a) Sketch of the system

(b) Pressure vessel and high pressure pump

Figure 7.14: DARS II design and construction

  ‐56‐ 

 

The system Q for DARS II is about 240 at atmosphere pressure. This is reduced from DARS I, whose Q is about 300. The drop in Q from DARS I to DARS II was not expected. The drop in Q is due to changes in both resonance frequency and linewidth, that is

WfQ = .

We measured 5 different cavities. The estimated empty Q-values for each of them are shown in Table 7.4 and Figure 7.15.

Table 7.4: DARS I Q-values with various cavities

Length (in) Inner diameter (in) Outer diameter (in) Thickness (in) Q

18 2.505 3 0.25 348

14.7 2.596 3.348 0.375 285

18 1.99 3 0.5 297

18 2.96 3.975 0.5 288

18 1.4935 3.014 0.75 252

Q vs. Cavity Wall Thickness

245

265

285

305

325

345

0.25 0.375 0.5 0.5 0.75

Wall Thickness (in)

Q

Figure 7.15: Values of Q using different cavity wall thickness

  ‐57‐ 

 

DARS II was tested to measure the empty cavity up to 500 PSI at 50 PSI intervals. The resonance frequency of DARS II is 961 Hz. The resonant frequency of DARS I is 1083 Hz so DARS II has reduced the empty cavity resonant frequency by 120 Hz due to a longer cavity.

Figure 7.16 is a plot of the resonance frequency vs. pressure. There are two measurements are shown: the black curve (on the right panel in the figure) was taken in the afternoon and the red curve was the first measurement taken the following day. Notice the resonance frequencies do not change very much. However the measurements on the right are closer. The linewidths are shown against confining pressure in Figure 7.17. When looking at the linewidths the variation is larger than with the resonance frequencies. However, it is expected for the Q to rise as the pressure increases. Therefore, since the resonance frequencies did not change very much the linewidths must decrease. This is more evident with the black curve. The amplitude shown in Figure 7.18 also follows the trend of increasing with an increase in pressure. This is expected since the Q increased the amplitude should increase also. As expected the Q-value shown in Figure 7.19 increases with pressure when looking at the black curve. It is believed to get repeatable results that the system needs time to reach equilibrium prior to measurements. This system wait time needs to be determined and incorporated into the measurement procedure.

Figure 7.16: Frequencies measured at times with different confining pressures.

  ‐58‐ 

 

Figure 7.17: Linewidths measured with different confining pressures

Figure 7.18: Amplitudes measured with different confining pressures

  ‐59‐ 

 

Figure 7.19: Q-values vs. confining pressures

Two accomplishments in DARS II development have been made. One is determining the best source and receiver configuration for the DARS II pressure conditions. The second is placing pressure on the DARS II system and taking measurements with the empty system. All the confining pressure components work as they should. However, the pore pressure portion of DARS II needs to be added. The pore pressure system will mimic the confining pressure system as shown above in Figure 7.14. The core holder has been designed and an acrylic version has been made. Construction of the pore pressure system should be completed in months. Measurement procedure details also need to be determined.

Conclusions Our research and simulation showed that True4-D is an achievable new technique for subsurface monitoring. True4-D monitoring does not mean simply to run more time-lapse surveys. Special methods, including sparse data acquisition, dynamic imaging and image integration developed in this project, could make the operation cost of True4-D comparable to the traditional time-lapse monitoring. True4-D offers a continuous slow-time axis. With this axis we can detect a dangerous leak early, and may also detect small reservoir changes that cannot be seen by traditional snapshot monitoring approaches.

  ‐60‐ 

 

  ‐61‐ 

 

Publications

1. Arogunmati, A. and J. M. Harris, 2009, An approach for quasi-continuous time-lapse seismic monitoring with sparse data: SEG Expanded Abstracts.

2. Santos, E. T. F. and J. M. Harris, 2009, DynaSIRT: A robust dynamic imaging method applied to CO2 Injection Monitoring: SEG Expanded Abstracts.

3. Vogelaar, B., D. Smeulders, J.M. Harris, 2009, Experimental evidence of the relation between the Biot-Gassmann modulus and the bulk modulus measured by DARS of oil-saturated rocks: SEG Expanded Abstracts.

4. Santos, E. T. T., J. M. Harris, A. Bassret, J.C. Costa, 2009, Trigonal Messes in diffraction tomography with optimum regularization: An Application for carbon sequestration monitoring: Journal of Seismic Exploration, 18, 135-156.

5. Quan, Y. and J. M. Harris, 2008, Stochastic Seismic Inversion using both Waveform and Traveltime Data and Its Application to Time-lapse Monitoring: SEG Expanded Abstracts.

6. Xu, Chuntang, J. M. Harris, and Youli Quan, 2006, Estimating flow properties of porous media with a model for dynamic diffusion, SEG Expanded Abstract, 2006.

7. Harris, J. M., Zoback, M. D., Kovscek, A. R., Orr, F. M. Jr, 2007-2008, Geologic Storage of CO2, GCEP Annual Technical Reports.

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Arts, R., Eiken, O., Chadwick , A., Zweigel, P., van der Meer, L., Zinszner, B., 2004, Monitoring of CO2 injected at Sleipner using time-lapse seismic data: Energy, 29, 1383–1392.

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Candès, E., and Romberg, J., 2007, Sparsity and incoherence in compressive sampling: Inverse Problems 23, 969–985

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Cao, D., W.B. Bevdoun, S.C. Singn and A. Tarantola, A simultaneous inversion for background velocity and impedance maps: Geophysics, 55, 458–469.

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Harris, J. M., Zoback, M. D., Kovscek, A. R., Orr, F. M. Jr, 2008, Geologic Storage of CO2, in Global Climate and Energy Project Annual Technical Report.

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Landrø, M., Solheim, O. A., Hilde, E., Ekren, B. O., Strønen, L. K., 1999, The Gullfaks 4D seismic study: Petroleum Geoscience, 5, 213-226.

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Contacts

Jerry M. Harris: jerry.harris@stanford.edu Youli Quan: quany@stanford.edu Eduardo Santos: eduardo.telmo@terra.com.br Bouko vogelaar: vogelaar@stanford.edu Chuntang Xu: cxu7@mexico-city.oilfield.slb.com Jolene Robin-McCaskill: jmrobin@stanford.edu Adeyemi Arogunmati: aadeyemi@stanford.edu Tope Akinbehinje: (Graduated from Stanford. Current email is not available.)