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Abstract
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.

Introduction
In the past decade, geological storage of CO2 has been widely regarded as an important mitigation option to avoid emitting CO2 into the atmosphere (IPCC, 2005). The main environmental concern in geological storage of CO2 is leakage of the injected CO2, as well as possible leakage or large-scale displacement of the resident brine (Celia et al., 2010). Escaped CO2 could contaminate shallow overlying aquifers used for municipal water supply, hydrocarbon reservoirs or mineral resources.

One of the most likely paths for buoyant fluid to migrate into overlying formations or reach the surface is through wellbores. Wellbores that no longer provide proper zonal isolation establish a potential migration pathway for a buoyant CO2-rich phase to escape from the intended storage formation (Huerta et al., 2008). Risk assessment of the hazard of CO2 leakage along wellbores will require the estimation of CO2 leakage rate. To predict the flux of CO2 along a leaky wellbore, a model of fluid properties and of transport along the leakage pathway would be necessary. Leakage rates large enough to be a concern is most likely to occur along an interface in the steel/cement/earth system that may include defects such as fracture, microannulus or channel (Crow et al., 2010), while small leakage rates through the cement matrix are likely to be at the range of naturally occurring background fluxes, because the permeability of intact cement is of order a few microdarcies.