Transport in Porous Media

, Volume 105, Issue 1, pp 191–209 | Cite as

Diffusive Effects on Recovery of Light Oil by Medium Temperature Oxidation

  • Negar Khoshnevis Gargar
  • Alexei A. Mailybaev
  • Dan Marchesin
  • Hans Bruining


Volatile oil recovery by means of air injection is studied as a method to improve recovery from low permeable reservoirs. We consider the case in which the oil is directly combusted into small products, for which we use the term medium temperature oil combustion. The two-phase model considers evaporation, condensation and reaction with oxygen. In the absence of thermal, molecular and capillary diffusion, the relevant transport equations can be solved analytically. The solution consists of three waves, i.e., a thermal wave, a medium temperature oxidation (MTO) wave and a saturation wave separated by constant state regions. A striking feature is that evaporation occurs upstream of the combustion reaction in the MTO wave. The purpose of this paper is to show the effect of diffusion mechanisms on the MTO process. We used a finite element package (COMSOL) to obtain a numerical solution; the package uses fifth-order Lagrangian base functions, combined with a central difference scheme. This makes it possible to model situations at realistic diffusion coefficients. The qualitative behavior of the numerical solution is similar to the analytical solution. Molecular diffusion lowers the temperature of the MTO wave, but creates a small peak near the vaporization region. The effect of thermal diffusion smoothes the thermal wave and widens the MTO region. Capillary diffusion increases the temperature in the upstream part of the MTO region and decreases the efficiency of oil recovery. At increasing capillary diffusion the recovery by gas displacement gradually becomes higher, leaving less oil to be recovered by combustion. Consequently, the analytical solution with no diffusion and numerical solutions at a high capillary diffusion coefficient become different. Therefore high numerical diffusion, significant in numerical simulations especially in coarse gridded simulations, may conceal the importance of combustion in recovering oil.


Air Injection Medium temperature oxidation Diffusive effects Light oil recovery In-situ combustion 

List of Symbols


MTO reaction pre-exponential factor (1/s)

\(c_\mathrm{l}, c_\mathrm{g}\)

Heat capacity of liquid and gas (J/mol K)


Heat capacity of porous matrix (J/\(\hbox {m}^{3}\) K)


Gas-diffusion coefficient (\(\hbox {m}^2\)/s)


Fractional flow function for liquid phase


Leverett \(J\)-function


Rock permeability (\(\hbox {m}^2\))

\(k_\mathrm{l}, k_\mathrm{g}\)

Liquid and gas phase permeabilities (\(\hbox {m}^2\))


MTO Reaction order with respect to oxygen


Gas pressure (Pa)


Liquid pressure (Pa)


MTO reaction enthalpy per mole of oxygen at reservoir temperature (J/mol)


Liquid fuel vaporization heat at reservoir temperature (J/mol)


Ideal gas constant (J/(mol K)

\(s_\mathrm{l}, s_\mathrm{g}\)

Saturations of liquid and gas phases


Time (s)


Temperature (K)


Boiling temperature of liquid at elevated pressure (K)


Reservoir temperature (K)


MTO activation temperature (K)

\(u_\mathrm{l}, u_\mathrm{g}, u\)

Liquid, gas and total Darcy velocities (m/s)


Darcy velocity of component \(j = h,o,r\) in gas phase (m/s)


Injection Darcy velocity of gas (m/s)

\(W_\mathrm{v}, W_\mathrm{r}\)

Vaporization rate, and MTO reaction rate (mol/\(\hbox {m}^{3}\) s)


Spatial coordinate (m)

\(Y_\mathrm{h}, Y_\mathrm{o}, Y_\mathrm{r}\)

Gas molar fractions: hydrocarbons, oxygen, remaining components (mol/mol)


Oxygen fraction in injected gas

\(\varphi \)


\(\kappa _\mathrm{l}\)

Phase transfer parameter

\(\lambda \)

Thermal conductivity of porous medium (W/m K)

\(\mu _\mathrm{l}, \mu _\mathrm{g}\)

Viscosity of liquid and gas (Pa s)

\(\nu _\mathrm{l}, \nu _\mathrm{g}\)

Stoichiometric coefficients in the MTO reaction

\(\rho _\mathrm{l}, \rho _\mathrm{g}\)

Molar densities of liquid and gas (\(\hbox {mol/m}^{3}\))

\(\sigma \)

Liquid oil surface tension (N/m)

\(\theta \)

Liquid oil/rock contact angle



This research was carried out within the context of the ISAPP Knowledge Centre. ISAPP (Integrated Systems Approach to Petroleum Production) is a joint project of the Netherlands Organization of Applied Scientific Research TNO, Shell International Exploration and Production, and Delft University of Technology. The paper was also supported by Grants of PRH32(ANP 731948/2010, PETROBRAS 6000.0061847.10.4), FAPERJ(E-26/102.965/2011, E-26/111.416/2010, E-26/110.658/ 2012, E-26/110.237/2012, E-26/111.369/2012) and CNPq (301564/2009-4,472923/2010-2, 477907/2011-3, 305519/2012-3, 402299/2012-4, 470635/2012-6) and Capes/Nuffic 024/2011. The authors thank TU Delft and IMPA for providing the opportunity for this work.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Negar Khoshnevis Gargar
    • 1
  • Alexei A. Mailybaev
    • 2
  • Dan Marchesin
    • 2
  • Hans Bruining
    • 1
  1. 1.Civil Engineering and GeosciencesDelft University of TechnologyDelftThe Netherlands
  2. 2.Instituto Nacional de Matemática Pura e Aplicada (IMPA)Rio de JaneiroBrazil

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