Comments on “Abrupt-Interface Solution for Carbon dioxide Injection into Porous Media” by M. Dentz and D. Tartakovsky

Lu, Chuan; Lee, Jun Young; Han, Weon Shik; McPherson, Brain J.; Lichtner, Peter C.

doi:10.1007/s11242-009-9362-9

Cited by 18 publications

(23 citation statements)

References 6 publications

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“…3b it is seen that for times > 0.1 years, there is a significant difference between the vertically averaged CO 2 saturation from 2D Miscible and that of 1D Miscible. This is due to the effect of gravity segregation (Lu et al 2009;Yamamoto and Doughty 2011). Figure 3d compares pressures estimated by 1D Miscible and 2D Miscible.…”

Section: Comparison With Tough2 Eco2nmentioning

confidence: 96%

Pressure Buildup During CO2 Injection into a Closed Brine Aquifer

et al. 2011

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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 [-]

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Section: Comparison With Tough2 Eco2nmentioning

confidence: 96%

Pressure Buildup During CO2 Injection into a Closed Brine Aquifer

et al. 2011

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“…In a recent publication, Lu et al (2009) compared fully resolved numerical simulations to simple analytical solutions based on the vertical-equilibrium and sharp-interface assumptions. The examples were based on injection of supercritical CO 2 from a single vertical well into a hypothetical formation that was considered to be homogeneous, isotropic, and horizontal with no leakage along the top or bottom boundaries, which leads to a radially symmetric solution.…”

Section: Introductionmentioning

confidence: 99%

“…Several p cap -s functions representative of the range found in the literature are selected, and used to study a generic injection scenario of an industrial-scale CO 2 capture and sequestration (CCS) operation. We also use the parameters and associated k r -s and p cap -s functions applied by Lu et al (2009). Direct comparisons are made between results from the commercial simulator ECLIPSE and results from a relatively simple vertical-equilibrium, sharpinterface model named ELSA Dobossy et al, 2011;Nordbotten et al, 2009) and the more general verticalequilibrium model called VESA (Gasda, 2008;Gasda et al, 2009Gasda et al, , 2010Gasda et al, , 2011Janzen, 2010).…”

Section: Introductionmentioning

confidence: 99%

Applicability of vertical-equilibrium and sharp-interface assumptions in CO2 sequestration modeling

Court

Bandilla

Celia

et al. 2012

International Journal of Greenhouse Gas Control

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“…The shape of the solution by Nordbotten et al (2005) depends on the viscosity of both CO 2 and brine, while the one derived by Dentz and Tartakovsky (2009a) depends on both the density and viscosity differences between the two phases. The validity of these sharp interface solutions has been discussed in, e.g., Dentz and Tartakovsky (2009a); Lu et al (2009);Dentz and Tartakovsky (2009b).…”

Section: Introductionmentioning

confidence: 99%

Effects of CO2 Compressibility on CO2 Storage in Deep Saline Aquifers

et al. 2010

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The injection of supercritical CO 2 in deep saline aquifers leads to the formation of a CO 2 plume that tends to float above the formation brine. As pressure builds up, CO 2 properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO 2 compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO 2 -rich phase and the formation brine. We introduce a correction to account for CO 2 compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO 2 compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.

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Comments on “Abrupt-Interface Solution for Carbon dioxide Injection into Porous Media” by M. Dentz and D. Tartakovsky

Cited by 18 publications

References 6 publications

Pressure Buildup During CO2 Injection into a Closed Brine Aquifer

Pressure Buildup During CO2 Injection into a Closed Brine Aquifer

Applicability of vertical-equilibrium and sharp-interface assumptions in CO2 sequestration modeling

Effects of CO2 Compressibility on CO2 Storage in Deep Saline Aquifers

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