The flux of CO2 along a leaking wellbore requires a model of fluid properties and of transport along the leakage pathway. This model should accurately represent the geometry of any discrete leakage pathway, because this geometry strongly affects the coupling between geochemical reactions and geomechanical response. Validating a transport model in advance of large-scale sequestration is difficult because instances of CO2 plumes reaching abandoned wells are presently rare. However, natural gas leakage events along wellbores can provide insights into conductive pathways analogous to those anticipated for CO2 sequestration. We apply a simple transport model to field measurements of sustained casing pressure (SCP) vs. time. We treat as unknowns the effective permeability of the leakage path and the depth at which leakage into the wellbore is occurring. These parameters are useful for forecasting likely leakage rates in sequestration sites located near oil and gas fields and for choosing candidate sites based on past exploration history. For several cases of SCP, conductive pathways (e.g. open fracture, gas channel, micro annulus) must exist to explain the large inferred values of effective permeability. Extended to more SCP wells, this approach can provide a probabilistic distribution of leakage rates given regional and well parameters. For CO2 sequestration purposes this provides a tool to assess the risk of carbon dioxide escape along leaky wells, which is necessary for site selection, permitting, and properly crediting sequestration operations. Introduction The success of any geologic CO2 sequestration operation depends on our ability to ensure that injected CO2 is properly credited and that assets overlying the storage reservoir remain uncontaminated. To achieve both goals we need to verify that CO2 does not leak out of the target formation at a rate large enough to adversely affect other compartments of economic or environmental value. A physics-based model for leakage will be a valuable tool for assessing risks associated with a prospective storage project and for analyzing field observations. The most probable pathways for leakage are faults and wells. Wells provide a relatively direct path to shallower subsurface formations and to the surface, but their geometry and their sealing capability are highly variable. The petroleum industry has extensive experience with leaky wells. In some of these wells, the leakage path involves a cement/steel interface (typically a micro annulus) and/or a conduit within the cement (gas channel or micro fractures). The leakage path terminates at a sealed wellhead, whence the evolution of sustained pressure in the casing annulus. In contrast, the leakage path of primary concern in CO2 sequestration continues outside the casing. The similarity between gas leakage and CO2 migration is in the leakage pathway. Conduits within cement should behave in essentially the same way in both cases. The cement/steel interface relevant to gas well leakage differs in some important ways from the cement/earth interface relevant to CO2 migration. Nevertheless the effective permeabilities of the two types of interface should be of similar magnitude. Thus by studying the nature of leakage pathways in oil and gas wells, we can estimate the range of leakage rates likely to occur in a CO2 sequestration operation. Well Geometry. Construction of each well is a unique event both in terms of planning and implementation. However, all wells share some common features and must perform certain functions. A typical well completion has several strings of casing cemented in place over some interval (Fig. 1). The key functions of a cemented annulus are to provide support for the weight of the casing, protect the steel casing from corrosive fluids, and isolate geologic zones with respect to fluid migration (Nelson and Guillot, 2006). Loss of zonal isolation can lead to contamination of overlying aquifers or loss of hydrocarbon resources. Gas migration into shallow formations or accumulation to significant pressure under a wellhead could create a health and safety hazard.

Summary Large-scale geological storage of carbon dioxide (CO2) is likely to bring CO2 plumes into contact with a large number of existing wellbores. The flux of CO2 along a leaking wellbore requires a model of fluid properties and of transport along the leakage pathway. Knowing the range of effective permeability of faulty cement is essential for estimating the risk of CO2 leakage. The central premise of this paper is that the leakage pathway in wells that exhibit sustained casing pressure (SCP) is analogous to the rate-limiting part of the leakage pathway in any wellbore that CO2 might encounter. Thus, field observations of SCP can be used to estimate transport properties of a CO2-leakage pathway. Uncertainty in the estimate can be reduced by accounting for constraints from well-construction geometry and from physical considerations. We then describe a simple CO2-leakage model. The model accounts for variation in CO2 properties along the leakage path and allows the path to terminate in an unconfined (constant-pressure) exit. The latter assumption provides a worst-case leakage flux. By use of pathway permeabilities consistent with observations in SCP wells, we obtain a range of CO2 fluxes for the cases of buoyancy-driven (post-injection) and pressure-driven (during injection) leakage. Assuming the frequency distribution is representative of SCP wells, we observe that in leakage pathways corresponding to the slow but nonnegligible buildup of casing pressure (several psi/D), the effective permeability of the leakage path is in the range of microdarcies to hundreds of microdarcies, and the corresponding CO2 fluxes are comparable with naturally occurring background fluxes observed at the ground surface. In pathways corresponding to intermediate and fast buildup rate of casing pressure (tens to hundreds of psi/D), the effective permeability is in the range of tenths to tens of millidarcies, and the CO2 fluxes are comparable with surface flux measurements at the Illinois basin and at the natural seep at Crystal Geyser (Utah). In pathways corresponding to very fast buildup rate (thousands of psi/D), the effective permeability is from tens to hundreds of millidarcies and the CO2 fluxes are up to three orders of magnitude higher than those measured at Crystal Geyser.

Large-scale geological storage of CO2 is likely to bring CO2 plumes into contact with a large number of existing wellbores. The flux of CO2 along a leaking wellbore requires a model of fluid properties and of transport along the leakage pathway. The leakage pathway in wells that exhibit sustained casing pressure (SCP) is analogous to the rate-limiting part of the pathway in existing wellbores along which CO2 may leak. Thus field observations of SCP can be used to estimate transport properties of a CO2 leakage pathway. We develop a more robust optimization algorithm to get the best data fit in the SCP model. Constraints from well construction geometry and from physical considerations reduce the range of estimated permeability. We then describe a simple CO2 leakage model. The model accounts for variation in CO2 properties along the leakage path and allows the path to terminate in an unconfined (constant pressure) exit. The latter assumption provides a worst-case leakage flux. Using pathway permeabilities consistent with observations in SCP wells, we obtain a range of CO2 fluxes for various boundary conditions. In leakage pathways corresponding to the slow but nonnegligible buildup of casing pressure, the CO2 fluxes are comparable to naturally occurring background fluxes observed at ground surface. In pathways corresponding to rapid buildup of casing pressure, the fluxes are comparable to measurements at Crystal Geyser (Utah), a natural CO2 seep. Uncertainty in pathway permeability has a first-order effect on uncertainty of CO2 flux. Uncertainty in the length of the pathway has a comparatively minor effect. Increasing the CO2 at the base of the pathway does not dramatically increase the CO2 flux above the purely buoyancy-driven value.

Large-scale geological storage of CO2 is likely to bring CO2 plumes into contact with a large number of existing wellbores. Estimating the flux of CO2 along a leaking wellbore requires a model of fluid properties and of transport along the leakage pathway. Wells that exhibit sustained casing pressure (SCP) in an intermediate annulus have a leakage path along a cement/steel interface, or within the cement in the annulus. The former path is analogous to a leakage path along a cement/earth interface outside the casing. The latter path can occur in cement outside the casing. Thus the likely magnitude of the permeability of leakage paths outside the well can be estimated from the permeability of these analog paths. A sustained casing pressure (SCP) model yields information about effective permeability of the pathway. By choosing reasonable ranges for other well construction parameters, we apply the SCP model to obtain a range of effective permeabilities for a well based on a measured casing pressure build up history. We illustrate the approach with several field examples. For a relatively slow pressure build up (several psi/day), the permeability of the leakage path is in the range of microdarcy to hundreds of microdarcy. Fast pressure build up (thousands psi/day) indicates permeabilities in the range of tens of millidarcy to hundreds of millidarcy. To account for the uncertainty in wellbore construction parameters, we calculate the distribution of effective permeability of a leaky well using Monte-Carlo simulation. The resulting permeability shows an approximately log-normal distribution skewed toward the maximum possible value. The expected value and a confidence interval are obtained for each well, which represents the most probable permeability of the well for a given pressure build up. For the wells studied here the expected values range from 10 microdarcy to 100 millidarcy. The expected leakage path permeability correlates reasonably well with pressure build up rate. This is to be expected from Darcy’s law, and thus a strong correlation between leakage path permeability and other characteristics of the wells in this sample does not exist. Obtaining the statistics of the expected leakage path permeability will thus require more observations of SCP wells. The effective permeability of a leaky well is essential in calculating the CO2 leakage flux. Under the assumption that a leaky well encountered by a CO2 plume has a leakage pathway with the similar properties to an SCP well, we calculate the CO2 flux for the best, worst and most probable scenarios for the example wells. In the most probable scenario of CO2 flux, we calculate the expected CO2 leakage rate. Slow leakage yields a 0.1 kg/y CO2 rate while fast leakage could have a rate of 1000 kg/y.

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