The distillation The distillation mechanism in steam mechanism in steam displacement of oildisplacement of oil

Dan Marchesin and Hans Bruining, Dan Marchesin and Hans Bruining,

ECMOR X

Sept 4-7, 2006

An example of all the An example of all the pathological problems with pathological problems with conservation lawsconservation laws• Elliptic regions (Not discussed here)Elliptic regions (Not discussed here)

• Non-Lax shocks (*) and uniquenessNon-Lax shocks (*) and uniqueness

• Small diffusion is dominating Small diffusion is dominating efficiency of processefficiency of process

Amsterdam: ECMOR X: Sept. 4-7, 2006: 20 slides

*E. Isaacson. D. Marchesin, and B. Plohr , Transitional waves for *E. Isaacson. D. Marchesin, and B. Plohr , Transitional waves for conservation laws, SIAM J. Math. Anal. 21, 831-866 (1990)conservation laws, SIAM J. Math. Anal. 21, 831-866 (1990)

Steam injectionSteam injection

Steam

condensation front gl

Liquid zone l

Steam zone g

H

L

Injection well

Production well

y

x

z

W

g

Steam injection is commercially Steam injection is commercially applied to recover viscous oilsapplied to recover viscous oils

Amsterdam: ECMOR X: Sept. 4-7, 2006: 19 slides

Volatile oil enhanced steam Volatile oil enhanced steam drive drive

• Proposed by Dietz Proposed by Dietz (1979)(1979)

Steam+Vol-oil Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

Amsterdam: ECMOR X: Sept. 4-7, 2006: 18 slides

ES-SAGD ES-SAGD ((Ian GatesIan Gates))

waterdead oilVol. oilSteam+

vol. oil

Steam zone cold zoneLiq.

Vol. oil initialoil

Vol. oil vaporZero oleic phase

Co-inject some Co-inject some volatile oil with volatile oil with steamsteam

Courtesy: Claes Palmgren

Amsterdam: ECMOR X: Sept. 4-7, 2006: 17 slides

Laboratory tests showing the Laboratory tests showing the effect of coinjected volatile oileffect of coinjected volatile oil

Steam+Vol-oil Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

ContentsContents• Reasons why modeling of this process Reasons why modeling of this process

is complex is complex • Formulation including capillary and Formulation including capillary and

diffusion effectsdiffusion effects• Dodecane, cyclo butane and heptane: Dodecane, cyclo butane and heptane:

Bifurcations depending on boiling Bifurcations depending on boiling pointspoints

• Importance of diffusion processesImportance of diffusion processes• Peak wave and effect on recoveryPeak wave and effect on recovery

Amsterdam: ECMOR X: Sept. 4-7, 2006: 15 slides

MOC models complicated due to saddle MOC models complicated due to saddle to saddle connection in shocks (not a to saddle connection in shocks (not a Lax shock)Lax shock)

• Shock velocityShock velocity

• SSww(-)(-)

• SSgg(-)(-)

• SSww(+)(+)

• Darcy velocity (+)Darcy velocity (+)

• Water balanceWater balance

• Oil balanceOil balance

• Energy balanceEnergy balance

• Welge shock conditionWelge shock condition

• Missing equation?Missing equation?

Steam Sw,Sg,So=0,vov =0 initialSw,So,vov =0

Bruining, J., Duijn, C.J. van, "Uniqueness Conditions in a Bruining, J., Duijn, C.J. van, "Uniqueness Conditions in a Hyperbolic Model for Oil Recovery by Steamdrive“, Hyperbolic Model for Oil Recovery by Steamdrive“, Computational Geosciences" No 4, pp 65-98 (2000), “Computational Geosciences" No 4, pp 65-98 (2000), “Traveling Traveling waves in a finite condensation rate model for steam injection”, waves in a finite condensation rate model for steam injection”, ibid. 2006ibid. 2006

Simulation gives unrealistic Simulation gives unrealistic results due to numerical results due to numerical dispersion dispersion

Steam+Vol-oil Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

Steam Sw,Sg,So=0,vov =0

Volatile oil bank

initial

Initial composition

Sw,So,vov >0

Amsterdam: ECMOR X: Sept. 4-7, 2006: 13 slides

Motivation of combined Motivation of combined analytical and numerical analytical and numerical approachapproach• Simulators overemphasize diffusion/ capillary Simulators overemphasize diffusion/ capillary

diffusion; are the solutions realistic?diffusion; are the solutions realistic?• Are we allowed to disregard diffusion all together?Are we allowed to disregard diffusion all together?• Does the form of the diffusion e.g. saturation Does the form of the diffusion e.g. saturation

dependence affect the global solution even if it is dependence affect the global solution even if it is small?small?

• Existence and uniqueness? We are using empirical Existence and uniqueness? We are using empirical relations to describe the convection flowrelations to describe the convection flow

• Possible bifurcations analysis i.e. solutions change Possible bifurcations analysis i.e. solutions change behavior if parameters cross critical values (*).behavior if parameters cross critical values (*).

• Discovery of new recovery mechanismsDiscovery of new recovery mechanisms* Bruining, J. and Marchesin, D. , Nitrogen and steam injection * Bruining, J. and Marchesin, D. , Nitrogen and steam injection in a porous medium with water, TIPM in a porous medium with water, TIPM (March 2006), 62 (3), 251-(March 2006), 62 (3), 251-281 281

Amsterdam: ECMOR X: Sept. 4-7, 2006: 12 slides

ModelModel• Injection steam and volatile oil vapor in core Injection steam and volatile oil vapor in core

SSww=S=Swcwc, S, Soo=1-S=1-Swcwc

• No dissolution of water in the oleic phase. No dissolution of water in the oleic phase. • Volatile oil vapor mixes in all proportions with Volatile oil vapor mixes in all proportions with

steam. Liquid volatile oil mixes with “dead” oil. steam. Liquid volatile oil mixes with “dead” oil. Dead oil only occurs in the oleic phase. Dead oil only occurs in the oleic phase.

• Viscosities depend on T and the composition vViscosities depend on T and the composition vovov . . • No volume effects on mixingNo volume effects on mixing• Capillary forces and diffusional effects Capillary forces and diffusional effects

incorporatedincorporated• Local thermodynamic equilibrium -> f = c – p + 2Local thermodynamic equilibrium -> f = c – p + 2

Steam+Vol-oil Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

Four conservation laws: water, Four conservation laws: water, dead oil, dead oil, volatile oilvolatile oil, energy, energy

ovov(T) volatile oil concentration in oleic phase(T) volatile oil concentration in oleic phase

gvgv(T) volatile oil concentration in gaseous phase (T) volatile oil concentration in gaseous phase

• uuovov(T) Darcy velocity volatile oil in oleic phase(T) Darcy velocity volatile oil in oleic phase

• uugvgv(T) Darcy velocity volatile oil in gaseous phase (T) Darcy velocity volatile oil in gaseous phase

( ) 0ov o gv g ov ov gv gvS S u ut x

gvgv gv gv g g gu u S D

x

+ cap. dif. termg gu uf

Formulations of interestFormulations of interest• Analytical solution; without capillary and diffusion Analytical solution; without capillary and diffusion

-> hyperbolic problem (solution discussed here); -> hyperbolic problem (solution discussed here); details in paper submitted to Phys. Rev. Edetails in paper submitted to Phys. Rev. E

• Numerical solution; with capillary and diffusion Numerical solution; with capillary and diffusion (see Figs. 1, 2, 3.); details in paper submitted to (see Figs. 1, 2, 3.); details in paper submitted to Phys. Rev. EPhys. Rev. E

• Traveling wave solution in steam Traveling wave solution in steam condensation zone (formulation presented in condensation zone (formulation presented in paper) paper)

( )x t

* Bruining, J. and Marchesin, D. , Maximal Oil Recovery by * Bruining, J. and Marchesin, D. , Maximal Oil Recovery by simultaneous condensation of alkane and steam, Submitted to simultaneous condensation of alkane and steam, Submitted to Phys Rev EPhys Rev E

Amsterdam: ECMOR X: Sept. 4-7, 2006: 9 slides

Dodecane coinjected (num. Dodecane coinjected (num. sol.)sol.)

Steam+Vol-oil Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

Cyclo-butane coinjected (num. Cyclo-butane coinjected (num. sol.)sol.)

Steam+Vol-oil Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

Comparison numerical (left) and analytical Comparison numerical (left) and analytical solution; Medium boiling (heptane) volatile solution; Medium boiling (heptane) volatile oiloil

Saturations 0 S 1., vov: fraction of volatile oil in the oleic phase.

Steam+Vol-oil

Sw,Sg,So=0,vov >0

Volatile oil bank

initial

Initial composition

Sw,So,vov = 0

Numerical (left) and analytical solution, Numerical (left) and analytical solution, Medium boiling volatile oil initially presentMedium boiling volatile oil initially present

Saturations 0 S 1., vov: fraction of volatile oil in the oleic phase.

Amsterdam: ECMOR X: Sept. 4-7, 2006: 5 slides

Medium volatile oil slug injection problem.

Rescaled temperature 0 T 1., vov is fraction of volatile oil in the oleic phase.

Amsterdam: ECMOR X: Sept. 4-7, 2006: 4 slides

Blow up of previous plotBlow up of previous plot

Structure of the transition zone consisting of a 3- and a 2-phase part. Rescaled temperature 0 T 1. Volatile oil peak indicated by vov between hot steam zone and cold liquid zone.

Amsterdam: ECMOR X: Sept. 4-7, 2006: 3 slides

Stability of diffusion bankStability of diffusion bank

First 7 time intervals: volatile oil is coinjected with the steam. Second 7 time intervals: pure steam injection. volatile oil peak is essentially preserved ensuring high recovery of oil

Amsterdam: ECMOR X: Sept. 4-7, 2006: 2 slides

ConclusionsConclusions• During steam injection with co-injection of volatile During steam injection with co-injection of volatile

oil a volatile oil peak is formed between the oil a volatile oil peak is formed between the steam zone and the liquid zone steam zone and the liquid zone

• The volatile oil peak is a component of a traveling The volatile oil peak is a component of a traveling wave solution; this is a new type of wave wave solution; this is a new type of wave

• After turning to pure steam injection the volatile After turning to pure steam injection the volatile oil peak remains more or less unchanged oil peak remains more or less unchanged

• A steady volatile oil peak is capable of reducing A steady volatile oil peak is capable of reducing the residual oil during steam drive and hence the residual oil during steam drive and hence enhances the oil recovery enhances the oil recovery

• These conclusions must still be rigorously These conclusions must still be rigorously validated by solving the traveling wave problemvalidated by solving the traveling wave problem

Amsterdam: ECMOR X: Sept. 4-7, 2006: last slide

ConclusionsConclusions• Finite volume methods can give Finite volume methods can give

erroneous results when describing non-erroneous results when describing non-Lax shocksLax shocks

• Only medium range boiling volatile oils Only medium range boiling volatile oils added to the steam help to improve the added to the steam help to improve the oil recovery; low range boiling oils form oil recovery; low range boiling oils form a 3-ph zone beyond the SCF. High range a 3-ph zone beyond the SCF. High range boiling oils stay behind. boiling oils stay behind.

• Molecular diffusion plays an important Molecular diffusion plays an important role in determining the efficiency of role in determining the efficiency of volatile oil enhanced steam drive volatile oil enhanced steam drive recovery. recovery.

• (un) stable nodal points (un) stable nodal points