[1] This work extends an existing analytical solution for pressure buildup because of CO 2 injection in brine aquifers by incorporating effects associated with partial miscibility. These include evaporation of water into the CO 2 rich phase and dissolution of CO 2 into brine and salt precipitation. The resulting equations are closed-form, including the locations of the associated leading and trailing shock fronts. Derivation of the analytical solution involves making a number of simplifying assumptions including: vertical pressure equilibrium, negligible capillary pressure, and constant fluid properties. The analytical solution is compared to results from TOUGH2 and found to accurately approximate the extent of the dry-out zone around the well, the resulting permeability enhancement due to residual brine evaporation, the volumetric saturation of precipitated salt, and the vertically averaged pressure distribution in both space and time for the four scenarios studied. While brine evaporation is found to have a considerable effect on pressure, the effect of CO 2 dissolution is found to be small. The resulting equations remain simple to evaluate in spreadsheet software and represent a significant improvement on current methods for estimating pressure-limited CO 2 storage capacity.

CO 2 injected into porous formations is accommodated by reduction in the volume of the formation fluid and enlargement of the pore space, through compression of the formation fluids and rock material, respectively. A critical issue is how the resulting pressure buildup will affect the mechanical integrity of the host formation and caprock. Building on an existing approximate solution for formations of infinite radial extent, this article presents an explicit approximate solution for estimating pressure buildup due to injection of CO 2 into closed brine aquifers of finite radial extent. The analysis is also applicable for injection into a formation containing multiple wells, in which each well acts as if it were in a quasi-circular closed region. The approximate solution is validated by comparison with vertically averaged results obtained using TOUGH2 with ECO2N (where many of the simplifying assumptions are relaxed), and is shown to be very accurate over wide ranges of the relevant parameter space. The resulting equations for the pressure distribution are explicit, and can be easily implemented within spreadsheet software for estimating CO 2 injection capacity. 123 384 S. A. Mathias et al. List of symbols A Formation plan area [L 2 ] b Forchheimer parameter [L −1 ] b r Relative Forchheimer parameter [-] c o Compressibility of CO 2 [M −1 LT 2 ] c r Compressibility of geological formation [M −1 LT 2 ] c w Compressibility of brine [M −1 LT 2 ] h CO 2 brine interface elevation [L] h D = h/H Dimensionless interface elevation [-] H Formation thickness [L] k Permeability [L 2 ] k r Relative permeability [-] M 0 Mass injection rate [MT −1 ] p Fluid pressure [ML −1 T −2 ] p D = 2π Hρ o k r kp/M 0 μ o Dimensionless pressure [-] q o CO 2 flux [LT −1 ] q oD = 2π Hr w ρ o q o /M 0 Dimensionless CO 2 flux [-] q w Brine flux [LT −1 ] q wD = 2π Hr w ρ o q w /M 0 Dimensionless brine flux [-] r Radial distance [L] r c Radial extent of reservoir [L] r cD = r c /r w Dimensionless radial extent of reservoir [-] r D = r/r w Dimensionless radius [-] r w Well radius [L] S r Residual brine saturation [-] t Time [T] t cD = αr 2 cD /2.246γ Dimensionless time at which the pressure disturbance meets the reservoir boundary [-] t D = M 0 t/2π(1 − S r )φ Hr 2 w ρ o Dimensionless time [-] α = M 0 μ o (c r + c w )/2π(1 − S r )Hρ o k r k Dimensionless compressibility [-] β = M 0 k r kb r b/2π Hr w μ o Dimensionless Forchheimer parameter [-] γ = μ o /k r μ w Viscosity ratio [-] = (1 − S r )(c o − c w )/(c r + c w ) Normalized fluid compressibility difference [-] μ o Viscosity of CO 2 [ML −1 T −1 ] μ w Viscosity of brine [ML −1 T −1 ] ρ o Density of CO 2 [ML −3 ] ρ w Density of brine [ML −3 ] σ = b r ρ o /ρ w Density ratio [-] φ Porosity [-]

Citation for published item:w thi sD FeF nd qluy sD tFqF nd qonz¡ lez w rt¡ %nez de wiguel D qFtF nd fry ntD FvF nd ilsonD hF @PHIQA 9yn the import n e of rel tive perme ility d t for estim ting gyP inje tivity in rine quifersF9D sntern tion l journ l of greenhouse g s ontrolFD IP F ppF PHHEPIPF Further information on publisher's website:httpXGGdxFdoiForgGIHFIHITGjFijgg FPHIPFHWFHIU Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in International Journal of Greenhouse Gas Control. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in International Journal of Greenhouse Gas Control, 12, 2013, 10.1016/j.ijggc.2012.09.017. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.

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