Transport in Porous Media

, Volume 76, Issue 2, pp 219–246 | Cite as

An Equation-of-State Compositional In-Situ Combustion Model: A Study of Phase Behavior Sensitivity

  • Morten R. Kristensen
  • Margot G. Gerritsen
  • Per G. Thomsen
  • Michael L. Michelsen
  • Erling H. Stenby
Article

Abstract

In order to facilitate the study of reactive-compositional porous media processes we develop a virtual kinetic cell (single-cell model) as well as a virtual combustion tube (one-dimensional model). Both models are fully compositional based on an equation of state. We employ the models to study phase behavior sensitivity for in situ combustion, a thermal oil recovery process. For the one-dimensional model we first study the sensitivity to numerical discretization errors and provide grid density guidelines for proper resolution of in situ combustion behavior. A critical condition for success of in situ combustion processes is the formation and sustained propagation of a high-temperature combustion front. Using the models developed, we study the impact of phase behavior on ignition/extinction dynamics as a function of the operating conditions. We show that when operating close to ignition/extinction branches, a change of phase behavior model will shift the system from a state of ignition to a state of extinction or vice versa. For both the rigorous equation of state based and a simplified, but commonly used, K-value-based phase behavior description we identify areas of operating conditions which lead to ignition. For a particular oil we show that the simplified approach overestimates the required air injection rate for sustained front propagation by 17% compared to the equation of state-based approach.

Keywords

Reactive transport processes Compositional processes Phase behavior Equation of state Multi-scale methods Enhanced oil recovery In situ combustion 

Nomenclature

Symbol

Description    SI units

Ci

Overall molar concentration of component i    mole/m3

D

Reservoir depth    m

\({{E_{a}^{\gamma}}}\)

Activation energy for reaction γ    J/mole

\({{f_i^j}}\)

Fugacity of component i in phase j    Pa

g

Gravitational acceleration    m/s2

hj

Molar enthalpy of phase j    J/mole

k

Absolute permeability (tensor)    m2

kc

Effective thermal conductivity (tensor)    J/m s K

\({{k_c^j}}\)

Thermal conductivity of phase j    J/m s K

\({{{\bf k}_{c}^{r}}}\)

Thermal conductivity of rock (tensor)    J/m s K

\({{k_r^j}}\)

Relative permeability of phase j    –

Ki

Equilibrium K-value for component i    –

Kγ

Rate constant for reaction γ    –

Mi

Molecular weight of component i    kg/mole

P

Pressure    Pa

\({{{\bf q}_{i}^{m}}}\)

Molar flux of component i    mole/m2 s

qh,adv

Heat flux due to advection    J/m2 s

qh,cond

Heat flux due to conduction    J/m2 s

\({{Q_i^{m,{\rm {\rm reac/well}}}}}\)

Molar source density due to chemical reactions/wells    mole/m3 s

Qh,reac/well

Heat source density due to chemical reactions/wells    J/m3 s

Rγ

Reaction rate for reaction γ    mole/m3 s

Rg

Universal gas constant    J/mole K

Sj

Volumetric saturation of phase j    –

t

Time    s

T

Temperature    K

Text

Set point for temperature controller    K

ua

Heat transfer coefficient (controller gain)    J/s K

uj

Flow velocity og phase j    m/s

Uj

Molar internal energy of phase j    J/mole

Ur

Volumetric internal energy of rock    J/m3

Vj

Volume of phase j    m3

Vp

Void pore volume    m3

\({{x_i^j}}\)

Mole fraction of component i in phase j    –

zi

Overall mole fraction of component i    –

Zj

Compressibility of phase j    –

αγ

Frequency factor for reaction γ    –

μj

Viscosity of phase j    Pa s

ξj

Molar density of phase j    mole/m3

ρj

Mass density of phase j    kg/m3

\({{\phi_f}}\)

Fluid porosity    –

\({{\phi_v}}\)

Void porosity    –

\({{\varphi_i^j}}\)

Fugacity coefficient for component i in phase j    –

ωi

Accentric factor for component i    –

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Morten R. Kristensen
    • 1
  • Margot G. Gerritsen
    • 2
  • Per G. Thomsen
    • 3
  • Michael L. Michelsen
    • 1
  • Erling H. Stenby
    • 1
  1. 1.Department of Chemical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  3. 3.Informatics and Mathematical ModellingTechnical University of DenmarkKgs. LyngbyDenmark

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