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Transport in Porous Media

, Volume 89, Issue 3, pp 383–397 | Cite as

Pressure Buildup During CO2 Injection into a Closed Brine Aquifer

  • Simon A. MathiasEmail author
  • Gerardo J. González Martínez de Miguel
  • Kate E. Thatcher
  • Robert W. Zimmerman
Article

Abstract

CO2 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 CO2 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 CO2 injection capacity.

Keywords

CO2 injection Forchheimer’s equation Closed formation Pressure buildup 

List of symbols

A

Formation plan area [L2]

b

Forchheimer parameter [L−1]

br

Relative Forchheimer parameter [-]

co

Compressibility of CO2 [M−1 LT2]

cr

Compressibility of geological formation [M−1 LT2]

cw

Compressibility of brine [M−1 LT2]

h

CO2 brine interface elevation [L]

hD = h/H

Dimensionless interface elevation [-]

H

Formation thickness [L]

k

Permeability [L2]

kr

Relative permeability [-]

M0

Mass injection rate [MT−1]

p

Fluid pressure [ML−1 T−2]

pD = 2π Hρokrkp/M0μo

Dimensionless pressure [-]

qo

CO2 flux [LT−1]

qoD = 2π Hrwρoqo/M0

Dimensionless CO2 flux [-]

qw

Brine flux [LT−1]

qwD = 2π Hrwρoqw/M0

Dimensionless brine flux [-]

r

Radial distance [L]

rc

Radial extent of reservoir [L]

rcD = rc/rw

Dimensionless radial extent of reservoir [-]

rD = r/rw

Dimensionless radius [-]

rw

Well radius [L]

Sr

Residual brine saturation [-]

t

Time [T]

\({t_{c{D}}= \alpha r_{c{D}}^2 / 2.246\gamma}\)

Dimensionless time at which the pressure disturbance meets the reservoir boundary [-]

\({t_{D}=M_0t/2\pi(1-S_{r})\phi Hr_{w}^2\rho_{o}}\)

Dimensionless time [-]

α = M0μo(cr + cw)/2π(1 − Sr) okrk

Dimensionless compressibility [-]

β = M0krkbrb/2π Hrwμo

Dimensionless Forchheimer parameter [-]

γ = μo/krμw

Viscosity ratio [-]

\({\epsilon=(1-S_{r})(c_{o}-c_{w})/(c_{r}+c_{w})}\)

Normalized fluid compressibility difference [-]

μo

Viscosity of CO2 [ML−1 T−1]

μw

Viscosity of brine [ML−1 T−1]

ρo

Density of CO2 [ML−3]

ρw

Density of brine [ML−3]

σ = brρo/ρw

Density ratio [-]

\({\phi}\)

Porosity [-]

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Simon A. Mathias
    • 1
    Email author
  • Gerardo J. González Martínez de Miguel
    • 1
    • 2
  • Kate E. Thatcher
    • 1
  • Robert W. Zimmerman
    • 3
  1. 1.Department of Earth SciencesDurham UniversityDurhamUK
  2. 2.ERC Equipoise LimitedLondonUK
  3. 3.Department of Earth Science and EngineeringImperial College LondonLondonUK

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