Transport in Porous Media

, Volume 102, Issue 2, pp 227–259 | Cite as

Simulations of Microbial-Enhanced Oil Recovery: Adsorption and Filtration

  • S. M. NielsenEmail author
  • I. Nesterov
  • A. A. Shapiro


In the context of microbial-enhanced oil recovery (MEOR) with injection of surfactant-producing bacteria into the reservoir, different types of bacteria attachment and growth scenarios are studied using a 1D simulator. The irreversible bacteria attachment due to filtration similar to the deep bed filtration (DBF) is examined along with the commonly used reversible equilibrium adsorption (REA). The characteristics of the two models are highlighted. The options for bacteria growth are the uniform growth in both phases and growth of attached bacteria only. It is found that uniform growth scenario applied to filtration model provides formation of two oil banks during recovery. This feature is not reproduced by application of REA model or DBF with growth in attached phase. This makes it possible to select a right model based on the qualitative analysis of the experimental data. A criterion is introduced to study the process efficiency: the dimensionless time at which average recovery between pure water injection and maximum surfactant effect is reached. This characteristic recovery period (CRP) was studied as a function of the different MEOR parameters such as bacterial activity, filtration coefficients, and substrate injection concentrations. For both growth scenarios, there is a zone of optimal activity at which the CRP is minimal. Dependence of the CRP on substrate concentration for uniform growth scenario has also an optimal zone. Therefore, growth rate and the substrate concentration should be above a certain threshold value and still not be too high to obtain the minimum CRP. On the other hand, no such zone was found if the bacteria could grow only in the attached phase. Dependencies on both the injected concentration and filtration coefficient are monotonous in this case.


Microbial-enhanced oil recovery Modeling Surfactant Deep bed filtration Equilibrium adsorption Bacteria 

List of Symbols



Exponent in Corey relative permeabilities


Constant in Thullner’s expression


Exponent in Corey relative permeabilities


Fractional flow function for phase j


Overall component flux

\({\mathcal {F}}\)

Check function for multivariable Newton procedure in appendix

\(g(\sigma _\mathrm{ow})\)

Interpolation function




Partitioning coefficient for surfactant


Half saturation constant in Monod expression (kg/m\(^{3}\))


Phase relative permeability


Endpoint relative permeability for oil at swi


Endpoint relative permeability for water at (\(1-{s}_\mathrm{or})\)


Length of the reservoir (m)

\({\mathcal {M}}_\mathrm{b}\)

Mass of bacteria adsorbed per unit area \((\hbox {kg}/\hbox {m}^{2})\)


Exponent in interpolation function


Number of phases


Threshold porosity constant for Thullner’s expression


Source term \((\hbox {m}^{3}/\hbox {day})\)


Volumetric injection velocity \((\hbox {m}^{3}/\hbox {day})\)


Bacterial reaction rate \((\hbox {day}^{-1})\)


Overall reaction rate \((\hbox {day}^{-1})\)


Sum of water and attached bacteria saturations \((\hbox {m}^{3}/\hbox {m}^{3})\)


Saturation of phase \(j\) \((\hbox {m}^{3}/\hbox {m}^{3})\)


Residual oil saturation \((\hbox {m}^{3}/\hbox {m}^{3})\)


Initial water saturation \((\hbox {m}^{3}/\hbox {m}^{3})\)


Specific surface (\(\hbox {m}^{2}/\hbox {m}^{3}\) total volume)

\({\mathcal {S}}\)

Efficient-specific surface (\(\hbox {m}^{2}/\hbox {m}^{3}\) PV)


Time (day)


Dimensionless velocity


Linear velocity (m/day)


Injection velocity (m/day)


Volume fraction (\(\hbox {m}^{3}/\hbox {m}^{3}\) PV)


Porous volume of one block (\(\hbox {m}^{3}\) PV)


Constant in the Langmuir type expression for partitioning of bacteria (m)


Constant in the Langmuir type expression for partitioning of bacteria (m\(^3\)/kg)


Horizontal axis in sample reservoir (m)


Horizontal axis in sample reservoir (m)


Yield of bacteria on substrate (kg/kg)


Yield of surfactant/metabolite on substrate (kg/kg)

Greek Symbol

\(\alpha \)

Constant describing the time for injection of one pore volume

\(\beta \)

Constant in permeability modification model for DBF

\({\bar{\eta }}\)

Characteristic recovery

\(\lambda '\)

Filtration coefficient \((\hbox {m}^{-1})\)

\(\lambda \)

Dimensionless filtration coefficient

\(\mu _{j}\)

Phase viscosity (cP)

\(\mu _\mathrm{gen}\)

General bacterial activity \((\hbox {day}^{-1})\)

\(\mu _\mathrm{max}\)

Maximum growth rate in Monod expression \((\hbox {day}^{-1})\)

\(\omega _{ij}\)

Concentration of component \(i\) in phase \(j\) (\(\hbox {kg}/\hbox {m}^{3}\) phase)

\(\varOmega _{i}\)

Overall concentration of component \(i\) (\(\hbox {kg}/\hbox {m}^{3}\) PV)

\(\varphi _{0}\)

Initial porosity

\(\rho _{i}\)

Component density \((\hbox {kg}/\hbox {m}^{3})\)

\(\sigma \)

Phase saturation for attached bacteria \((\hbox {m}^{3}/\hbox {m}^{3})\)

\(\sigma _\mathrm{ow}\)

Interfacial tension between oil and water (mN/m)

\(\tau \)

Dimensionless time (PVI)

\({\bar{\tau }}\)

Characteristic recovery period

\(\xi \)

Dimensionless length

Subscripts and Superscripts


Estimated/predicted value


Index indicating injection


Index for component


Index for phase


Spatial index for discretization in appendix


Index for bacteria


Index for surfactant (metabolite)


Time index for discretization in appendix


Index for oil


Index for substrate


Index indicating at surfactant flooding


Index for water



Characteristic recovery period


Deep bed filtration


Enhanced oil recovery


Interfacial tension


Microbial-enhanced oil recovery


Original oil in place


Pore volumes injected


Reversible equilibrium adsorption


Water flooding



We acknowledge The Danish National Advanced Technology Foundation, Maersk Oil and DONG E&P for financial support. As a part of the BioRec project, we also would like to acknowledge all project partners for relevant scientific input: DTU, Maersk Oil, DONG E&P, Novozymes, Danish Technological Institute and Roskilde University.


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Center for Energy Resources Engineering - CERE, Department of Chemical and Biochemical EngineeringTechnical University of DenmarkLyngbyDenmark

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