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

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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.

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Abbreviations

Symbol:

Description    SI units

C i :

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

h j :

Molar enthalpy of phase j    J/mole

k :

Absolute permeability (tensor)    m2

k c :

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    –

K i :

Equilibrium K-value for component i    –

K γ :

Rate constant for reaction γ    –

M i :

Molecular weight of component i    kg/mole

P :

Pressure    Pa

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

Molar flux of component i    mole/m2 s

q h,adv :

Heat flux due to advection    J/m2 s

q h,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

Q h,reac/well :

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

R γ :

Reaction rate for reaction γ    mole/m3 s

R g :

Universal gas constant    J/mole K

S j :

Volumetric saturation of phase j    –

t :

Time    s

T :

Temperature    K

T ext :

Set point for temperature controller    K

u a :

Heat transfer coefficient (controller gain)    J/s K

u j :

Flow velocity og phase j    m/s

U j :

Molar internal energy of phase j    J/mole

U r :

Volumetric internal energy of rock    J/m3

V j :

Volume of phase j    m3

V p :

Void pore volume    m3

\({{x_i^j}}\) :

Mole fraction of component i in phase j    –

z i :

Overall mole fraction of component i    –

Z j :

Compressibility of phase j    –

α γ :

Frequency factor for reaction γ    –

μ j :

Viscosity of phase j    Pa s

ξj :

Molar density of phase j    mole/m3

ρ j :

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    –

ω i :

Accentric factor for component i    –

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Correspondence to Morten R. Kristensen.

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Kristensen, M.R., Gerritsen, M.G., Thomsen, P.G. et al. An Equation-of-State Compositional In-Situ Combustion Model: A Study of Phase Behavior Sensitivity. Transp Porous Med 76, 219–246 (2009). https://doi.org/10.1007/s11242-008-9244-6

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Keywords

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