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Abstract
After injection of CO2 into the subsurface formation, various storage mechanisms help immobilize CO2 in the porous medium. Injection strategies that promote the buoyant movement of CO2 after injection can increase immobilization by the mechanisms of dissolution and residual phase trapping. In a heterogeneous storage formation where capillary entry pressure of the rock is correlated with other petrophysical properties, numerous local capillary barriers exist and can trap rising CO2 below them. In this work, we study the effect of these barriers on CO2 leakage from the storage formation. We first introduce a no-risk-of-leakage scenario for storage, which sets an upper bound on the amount of CO2 that can be stored without contacting the overlying seal. Accounting for capillary heterogeneity reduces this upper bound. In practice operators are likely to seek to store more CO2 than the no-risk-of-leakage bound in any given reservoir. Thus we also examine the form of the gas cap established by the rising CO2 plume, and we simulate leakage from this gas cap through the top seal. Our leakage scenario is simulated in different cases with homogeneous and heterogeneous capillary pressure field, and CO2  trapping is quantified based on the results of the leakage. Capillary heterogeneity is introduced via Leverett scaling group. A new parameter called security index is also defined to quantify the risk of leakage. Finally, the statistics of the local capillary barriers are used to find a probability distribution of leakage amounts from the storage formation.

We conclude that ignoring heterogeneity gives the worst case estimate of the risk. Local capillary trapping reduces potential leakage through failed seal, but a range of CO2 leakage amounts can occur depending on heterogeneity and location of leak. The thickness of the sealing layer and the presence of an active open aquifer connected to the leak do not change the leakage volume of CO2

Introduction .
A probabilistic approach based on statistics of local capillary barriers can be used to analyze the risk associated with leakage.  Carbon sequestration is a developing technology that can contribute significantly to reduce greenhouse gas emissions. Storage of CO2 in deep subsurface aquifers or depleted oil and gas reservoirs has recently drawn considerable interest. Three modes of secure storage are widely known for sequestration of CO2 in geological formations: dissolution, residual, and mineral trapping. Local capillary trapping is another mode which occurs during buoyancy-driven flow through rocks with fine-scale heterogeneity (Saadatpoor et al., 2010). The key to the behavior is that the rising CO2 plume cannot enter any region unless the capillary pressure at the leading edge of the plume exceeds the entry pressure for that region. Therefore, in a heterogeneous storage formation, where capillary entry pressure of the rocks is correlated for example with other petrophysical properties such as porosity and permeability, local capillary barriers exist. When the range of entry pressures is comparable to capillary pressure due to CO2 column height, rising CO2 moves through highly ramified flow paths that avoid these local capillary entry pressure barriers. Some CO2 is trapped below these barriers as well.

If large volume of CO2 is injected into the lower portion of an aquifer and allowed to rise, some above-residual saturations of CO2 will accumulate below the top seal. As it expands to form a “gas cap”, this accumulation broadens the ramified structure established earlier by the rising CO2. The average CO2 saturation in the gas cap is slightly smaller than that in an accumulation in a homogeneous formation beneath a structural trap, because some regions of large entry pressure are not invaded by CO2. Leakage from a homogeneous structure will continue until the entire accumulation is reduced to residual saturation. The question addressed here is how much of the CO2 that has risen into a heterogeneous structure would leak out, if the top seal were to lose its integrity.