1. The distillation mechanism in steam displacement of oil Dan Marchesin and Hans Bruining, ECMOR X Sept 4-7, 2006

2. An example of all the pathological problems with conservation laws Elliptic regions (Not discussed here) Elliptic regions (Not discussed here) Non-Lax shocks (*) and uniqueness Non-Lax shocks (*) and uniqueness Small diffusion is dominating efficiency of process Small diffusion is dominating efficiency of process Amsterdam: ECMOR X: Sept. 4-7, 2006: 20 slides *E. Isaacson. D. Marchesin, and B. Plohr, Transitional waves for conservation laws, SIAM J. Math. Anal. 21, 831-866 (1990)

3. Steam injection Steam injection is commercially applied to recover viscous oils Amsterdam: ECMOR X: Sept. 4-7, 2006: 19 slides

4. Volatile oil enhanced steam drive Proposed by Dietz (1979) Proposed by Dietz (1979) Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0 Amsterdam: ECMOR X: Sept. 4-7, 2006: 18 slides

5. ES-SAGD ( Ian Gates ) water dead oil Vol. oil Steam+ vol. oil Steam zone cold zone Liq. Vol. oil initial oil Vol. oil vapor Zero oleic phase Co-inject some volatile oil with steam Courtesy: Claes Palmgren Amsterdam: ECMOR X: Sept. 4-7, 2006: 17 slides

6. Laboratory tests showing the effect of coinjected volatile oil Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0

7. Contents Reasons why modeling of this process is complex Reasons why modeling of this process is complex Formulation including capillary and diffusion effects Formulation including capillary and diffusion effects Dodecane, cyclo butane and heptane: Bifurcations depending on boiling points Dodecane, cyclo butane and heptane: Bifurcations depending on boiling points Importance of diffusion processes Importance of diffusion processes Peak wave and effect on recovery Peak wave and effect on recovery Amsterdam: ECMOR X: Sept. 4-7, 2006: 15 slides

8. MOC models complicated due to saddle to saddle connection in shocks (not a Lax shock) Shock velocity Shock velocity S w (-) S w (-) S g (-) S g (-) S w (+) S w (+) Darcy velocity (+) Darcy velocity (+) Water balance Water balance Oil balance Oil balance Energy balance Energy balance Welge shock condition Welge shock condition Missing equation? Missing equation? Steam S w,S g,S o =0,v ov =0initialS w,S o,v ov =0 Bruining, J., Duijn, C.J. van, "Uniqueness Conditions in a Hyperbolic Model for Oil Recovery by Steamdrive“, Computational Geosciences" No 4, pp 65-98 (2000), “Traveling waves in a finite condensation rate model for steam injection”, ibid. 2006

9. Simulation gives unrealistic results due to numerical dispersion Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0 Steam S w,S g,S o =0,v ov =0 Volatile oil bank initial Initial composition S w,S o,v ov >0 Amsterdam: ECMOR X: Sept. 4-7, 2006: 13 slides

10. Motivation of combined analytical and numerical approach Simulators overemphasize diffusion/ capillary diffusion; are the solutions realistic? Simulators overemphasize diffusion/ capillary 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 dependence affect the global solution even if it is small? Does the form of the diffusion e.g. saturation dependence affect the global solution even if it is small? Existence and uniqueness? We are using empirical relations to describe the convection flow Existence and uniqueness? We are using empirical relations to describe the convection flow Possible bifurcations analysis i.e. solutions change behavior if parameters cross critical values (*). Possible bifurcations analysis i.e. solutions change behavior if parameters cross critical values (*). Discovery of new recovery mechanisms Discovery of new recovery mechanisms * Bruining, J. and Marchesin, D., Nitrogen and steam injection in a porous medium with water, TIPM (March 2006), 62 (3), 251-281 Amsterdam: ECMOR X: Sept. 4-7, 2006: 12 slides

11. Model Injection steam and volatile oil vapor in core S w =S wc, S o =1-S wc Injection steam and volatile oil vapor in core S w =S wc, S o =1-S wc No dissolution of water in the oleic phase. No dissolution of water in the oleic phase. Volatile oil vapor mixes in all proportions with steam. Liquid volatile oil mixes with “dead” oil. Dead oil only occurs in the oleic phase. Volatile oil vapor mixes in all proportions with steam. Liquid volatile oil mixes with “dead” oil. Dead oil only occurs in the oleic phase. Viscosities depend on T and the composition v ov. Viscosities depend on T and the composition v ov. No volume effects on mixing No volume effects on mixing Capillary forces and diffusional effects incorporated Capillary forces and diffusional effects incorporated Local thermodynamic equilibrium -> f = c – p + 2 Local thermodynamic equilibrium -> f = c – p + 2 Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0

12. Four conservation laws: water, dead oil, volatile oil, energy  ov (T) volatile oil concentration in oleic phase  ov (T) volatile oil concentration in oleic phase  gv (T) volatile oil concentration in gaseous phase  gv (T) volatile oil concentration in gaseous phase u ov (T) Darcy velocity volatile oil in oleic phase u ov (T) Darcy velocity volatile oil in oleic phase u gv (T) Darcy velocity volatile oil in gaseous phase u gv (T) Darcy velocity volatile oil in gaseous phase

13. Formulations of interest Analytical solution; without capillary and diffusion -> hyperbolic problem (solution discussed here); details in paper submitted to Phys. Rev. E Analytical solution; without capillary and diffusion -> hyperbolic problem (solution discussed here); details in paper submitted to Phys. Rev. E Numerical solution; with capillary and diffusion (see Figs. 1, 2, 3.); details in paper submitted to Phys. Rev. E Numerical solution; with capillary and diffusion (see Figs. 1, 2, 3.); details in paper submitted to Phys. Rev. E Traveling wave solution in steam condensation zone (formulation presented in paper) Traveling wave solution in steam condensation zone (formulation presented in paper) * Bruining, J. and Marchesin, D., Maximal Oil Recovery by simultaneous condensation of alkane and steam, Submitted to Phys Rev E Amsterdam: ECMOR X: Sept. 4-7, 2006: 9 slides

14. Dodecane coinjected (num. sol.) Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0

15. Cyclo-butane coinjected (num. sol.) Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0

16. Comparison numerical (left) and analytical solution; Medium boiling (heptane) volatile oil Saturations 0  S   1., v ov : fraction of volatile oil in the oleic phase. Steam+ Vol-oil S w,S g,S o =0,v ov >0 Volatile oil bank initial Initial composition S w,S o,v ov = 0

17. Numerical (left) and analytical solution, Medium boiling volatile oil initially present Saturations 0  S   1., v ov : fraction of volatile oil in the oleic phase. Amsterdam: ECMOR X: Sept. 4-7, 2006: 5 slides

18. Medium volatile oil slug injection problem. Rescaled temperature 0  T  1., v ov is fraction of volatile oil in the oleic phase. Amsterdam: ECMOR X: Sept. 4-7, 2006: 4 slides

19. Blow 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 v ov between hot steam zone and cold liquid zone. Amsterdam: ECMOR X: Sept. 4-7, 2006: 3 slides

20. Stability 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

21. Conclusions During steam injection with co-injection of volatile oil a volatile oil peak is formed between the steam zone and the liquid zone During steam injection with co-injection of volatile oil a volatile oil peak is formed between the steam zone and the liquid zone The volatile oil peak is a component of a traveling wave solution; this is a new type of wave The volatile oil peak is a component of a traveling wave solution; this is a new type of wave After turning to pure steam injection the volatile oil peak remains more or less unchanged After turning to pure steam injection the volatile oil peak remains more or less unchanged A steady volatile oil peak is capable of reducing the residual oil during steam drive and hence enhances the oil recovery A steady volatile oil peak is capable of reducing the residual oil during steam drive and hence enhances the oil recovery These conclusions must still be rigorously validated by solving the traveling wave problem These conclusions must still be rigorously validated by solving the traveling wave problem Amsterdam: ECMOR X: Sept. 4-7, 2006: last slide

22. Conclusions Finite volume methods can give erroneous results when describing non-Lax shocks Finite volume methods can give erroneous results when describing non-Lax shocks Only medium range boiling volatile oils added to the steam help to improve the oil recovery; low range boiling oils form a 3- ph zone beyond the SCF. High range boiling oils stay behind. Only medium range boiling volatile oils added to the steam help to improve the oil recovery; low range boiling oils form a 3- ph zone beyond the SCF. High range boiling oils stay behind. Molecular diffusion plays an important role in determining the efficiency of volatile oil enhanced steam drive recovery. Molecular diffusion plays an important role in determining the efficiency of volatile oil enhanced steam drive recovery. (un) stable nodal points (un) stable nodal points