Transport in Porous Media

, 79:265 | Cite as

Approximate Solutions for Pressure Buildup During CO2 Injection in Brine Aquifers

  • Simon A. Mathias
  • Paul E. Hardisty
  • Mark R. Trudell
  • Robert W. Zimmerman


If geo-sequestration of CO 2 is to be employed as a key emissions reduction method in the global effort to mitigate against climate change, simple yet robust screening of the risks of disposal in brine aquifers will be needed. There has been significant development of simple analytical and semi-analytical techniques to support screening analysis and performance assessment for potential carbon sequestration sites. These techniques have generally been used to estimate the size of CO 2 plumes for the purpose of leakage rate estimation. A common assumption is that both the fluids and the geological formation are incompressible. Consequently, calculation of pressure distribution requires the specification of an arbitrary radius of influence. In this article, a new similarity solution is derived using the method of matched asymptotic expansions. A large time approximation of this solution is then extended to account for inertial effects using the Forchheimer equation. By allowing for slight compressibility in the fluids and formation, the solutions improve on previous work by not requiring the specification of an arbitrary radius of influence. The validity of both solutions is explored by comparison with equivalent finite difference solutions, revealing that the new method can provide robust and mathematically rigorous solutions for screening level analysis, where numerical simulations may not be justified or cost effective.


CO2 injection Forchheimer’s equation Matched asymptotic expansions Pressure buildup 



Forchheimer parameter [L−1].


Compressibility of CO2 [M−1LT2].


Compressibility of geological formation [M−1LT2].


Compressibility of brine [M−1LT2].


Gravitational acceleration [LT−2].


CO2 brine interface elevation [L].

hD = h/H

Dimensionless interface elevation [–].


Formation thickness [L].


Permeability [L2].


Mass injection rate [MT−1].


Fluid pressure [ML−1T−2].

pD = 2πHρokp/M0μo

Dimensionless pressure [–].


CO2 flux [LT−1].

qoD = 2πHrwρoqo/M0

Dimensionless CO2 flux [–].


Brine flux [LT−1].

qwD = 2πHrwρoqw/M0

Dimensionless brine flux [–].


Radial distance [L].

rD = r/rw

Dimensionless radius [–].


Well radius [L].

S = SsH

Storativity [–].

\({S_{\rm s}=\rho_{\rm w}g\phi(c_{\rm w}+c_{\rm r})}\)

Specific storage [L−1].


Time [T].

\({t_{\rm D}=M_0t/2\pi\phi Hr_{\rm w}^2\rho_{\rm o}}\)

Dimensionless time [–].

T = ρwgkHw

Transmissivity [L2T−1].

α = M0μo(cr + cw)/2πHρok

Dimensionless compressibility [–].

β = M0kb/2πHrw μo

Dimensionless Forchheimer parameter [–].

γ = μo/μw

Viscosity ratio [–].

\({\epsilon=(c_{\rm o}-c_{\rm w})/(c_{\rm r}+c_{\rm w})}\)

Normalized fluid compressibility difference [–].

κ≈ 0.5772

Euler-Mascheroni constant [–].


Viscosity of CO2 [ML−1T−1].


Viscosity of brine [ML−1T−1].


Density of CO2 [ML−3].


Density of brine [ML−3].

σ = ρo/ρw

Density ratio [–].


Porosity [–].


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Simon A. Mathias
    • 1
  • Paul E. Hardisty
    • 1
    • 2
  • Mark R. Trudell
    • 3
  • Robert W. Zimmerman
    • 4
  1. 1.Department of Civil and Environmental EngineeringImperial College LondonLondonUK
  2. 2.WorleyParsonsPerthAustralia
  3. 3.WorleyParsonsLong BeachUSA
  4. 4.Department of Earth Science and EngineeringImperial College LondonLondonUK

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