Mathematical model for microbial enhanced oil recovery …iea-eor.ptrc.ca/2009/papers/F1PR.pdf · · 2009-09-21Green, D. W. and G. P. Willhite (1998). Enhanced oil recovery, Vol

Mathematical model for microbial enhanced oil recoverywith surfactant distributed between phases

Sidsel Marie [email protected]

Alexander ShapiroMichael Michelsen

Erling Stenby

IVC-SEP, DTU Chemical Engineering

IEA EOR 2009

Outline

1 Introduction

2 The reactive transport model

3 Simulation results

4 Conclusion

Sidsel Marie Nielsen (IVC-SEP) Microbial enhanced oil recovery September 2009 2 / 20

Introduction

Introduction

Tertiary oil recovery method

Application of injected or indigeneous microorganisms

Addresses the same effects as chemical EOR

Typical MEOR effects

Reduction of oil/water interfacial tension and alteration of wettability(surfactant)

Fluid diversion

Viscosity reduction due to gas production or degradation ofhydrocarbons (minor effect)


Introduction

Introduction

Tertiary oil recovery method

Application of injected or indigeneous microorganisms

Addresses the same effects as chemical EOR

Typical MEOR effects

Reduction of oil/water interfacial tension and alteration of wettability(surfactant)

Fluid diversion

Viscosity reduction due to gas production or degradation ofhydrocarbons (minor effect)


Introduction

Surfactant effect

In situ production ofsurfactants

Interfacial tension reduction

From 30 mN/m to 10−2

mN/m

Additional contribution frombacterial surface

Relative permeability changes 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sw

krw

kro


The reactive transport model

The 1D model

Oil Metabolite

MetaboliteWater

Substrate BacteriaBacteria

Substrate MetaboliteBacteria

Phases

Water

Oil

Components

Water

Oil

Bacteria

Substrate

Metabolite



The 1D model

Flow equations

∂

∂t

(φ

np∑j=1

ωijρj sj

)+

∂

∂x

v np∑j=1

ωijρjfj

= φ qi, i = 1..nc

where ωij are mass fractions.

Phases

Water

Oil

Components

Water

Oil

Bacteria

Substrate

Metabolite



Assumptions

Flow equations

∂

∂t

(φ

np∑j=1

ωijρj sj

)+

∂

∂x

v np∑j=1

ωijρjfj

= φ qi, i = 1..nc

where ωij are mass fractions.

1D two-phase model

Application of Darcy’s law

Capillary pressure neglected

Dispersion term neglected

No volume change on mixing

No adsorption to pore walls

Monod kinetics for bacterial growth



Reaction rates µ

Growth rate with onelimiting substrate

µ = µmaxCs

Ks+Cs

Reaction rate

qb = sw Ysb Cb µ

qm = sw Ysm Cb µ

qs = −qm − qb0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cs

µ

K=0.5K=0.05



Implementation of surfactant effect

Correlation between surfactant concentration and IFT

Approaches to relativepermeability modifications

1 Capillary number related toresidual oil saturation

2 Interpolation of parameters inCorey relative permeabilitycorrelations

3 Coats’ interpolation methodbetween relative permeabilitycurves 10

−610

−410

−210

−6

10−4

10−2

100

IFT

[mN

/m]

Cm



Capillary number related to residual oil saturation

Capillary number

Nca = v µwσ

Correlation between capillary number and residual oil sor

10−8

10−6

10−4

10−2

100

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Nca

sor/sorw

Green, D. W. and G. P. Willhite (1998). Enhanced oil recovery, Vol. 6. SPE Textbook Series.


Simulation results

Flooding results

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

s

Surfactant floodWater floodMEORsor surfactant flood

sor MEOR

The capillary numbermethod

Injection volume fractions

Bacteria 1 · 10−5

Substrate 0.5 · 10−5

Formation of an oil bank

Oil bank front travels fasterthan water flood front


Simulation results

Flooding results

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

s


sor MEOR

The capillary numbermethod

Injection volume fractions

Bacteria 1 · 10−5

Substrate 0.5 · 10−5


Oil bank front travels fasterthan water flood front


Simulation results

Recovery factor

Qualitatively, the oil recovery is enhanced

Incremental recovery up to 40–45%

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

s


sor MEOR

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

τ

Rec

over

y

Surfactant floodingMEORWater flooding


Simulation results

Comparison of the interpolation methodsfor modification of relative permeabilities

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

τ [PVI]

Reco

very

CoreyCapillary numberCoats


τ = 0.15 PVI


Simulation results

Coats’ interpolation model

Interpolation function

f(σ) =(

σσbase

) 1n

Relative permeability curves

s∗or = f(σ)sor

s∗wc = f(σ)swc0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sw

krw

kro

krw = f(σ)krw(base) + [1 − f(σ)]krw(misc)

kro = f(σ)kro(base) + [1 − f(σ)]kro(misc)


Simulation results

Interpolation of Corey parameters

Interpolation function

f(σ) =(

σσbase

) 1n

Parameters

s∗or = sor · f(σ)s∗wc = swc · f(σ)

α∗w = αw · f(σ) + (1 − f(σ))α∗o = αo · f(σ) + (1 − f(σ))

k∗rwor = krwor · f(σ) + (1 − f(σ))k∗rowc = krowc · f(σ) + (1 − f(σ))

Relative permeabilities

krw = k∗rwor

(sw−s∗wi

1−s∗or−s∗wi

)α∗wkro = k∗rowc

(1−sw−s∗or1−s∗or−s∗wi

)α∗o

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sw

krw

kro


Simulation results

Comparison of the interpolation methodsfor modification of relative permeabilities

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

τ [PVI]

Reco

very



τ = 0.15 PVI


Simulation results

Partitioning of surfactant

Surfactant is removed from water phase

Partitioning determines residual oil

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

s

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

τ [PVI]

Reco

very

Ki = 10 3

Ki = 10 0

Ki = 10 −2

Ki = 10 3

Ki = 10 0

Ki = 10 −1

Ki = 10 −2

τ = 0.15 PVI


Simulation results

Growth rate

Maximum growth rate µmax is investigated

The ability to maintain a certain growth rate is important

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ξ

s

µ = 0.2 d −1

µ = 2.0 d −1

µ = 0.02 d −1

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

τ [PVI]

Reco

very

µ = 0.2 d −1

µ = 2.0 d −1

µ = 0.02 d −1

τ = 0.15 PVI


Simulation results

Injection concentrations

Injection concentrations have a significant influence on oil recovery

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

τ [PVI]

Reco

very

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

τ [PVI]

Reco

very

DoubleRegularHalf

DoubleRegularHalfQuarter

Coats’ methodCapillary number method

Bacterial volumetric fraction 1 · 10−5 (regular)

Substrate volumetric fraction 0.5 · 10−5 (regular)


Conclusion


Recovery determined by surfactant-induced residual oil

Important MEOR considerations

Partitioning of surfactant

Growth rate

Injection concentration of substrate and bacteria

Sensitivity to method for interpolation of the relativepermeabilities


Documents

Mathematical model for microbial enhanced oil recovery …iea-eor.ptrc.ca/2009/papers/F1PR.pdf · · 2009-09-21Green, D. W. and G. P. Willhite (1998). Enhanced oil recovery, Vol