Estimation of Flow Functions During Drainage Using Genetic Algorithm
- Xuefei Sun (U. of Houston) | Kishore K. Mohanty (U. of Houston)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2005
- Document Type
- Journal Paper
- 449 - 457
- 2005. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 4.3.1 Hydrates, 4.3.4 Scale, 5.5.1 Simulator Development, 1.6.9 Coring, Fishing, 5.5.2 Core Analysis, 5.5.8 History Matching, 5.3.2 Multiphase Flow, 5.6.2 Core Analysis, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment
- 1 in the last 30 days
- 507 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
Unsteady-state relative permeability experiments followed by automatichistory matching have been used in the past for estimating relativepermeability and capillary pressure simultaneously. The performance of theautomatic history matching largely depends on the simulator, the functionalform of the flow functions, and the optimization tool. The Newton method iscommonly used as the optimization tool for the automatic history matching; wehave used a genetic algorithm (GA) as the optimization tool in this work. Oneof the advantages of GA is that it requires only function evaluations for thesolution searching and not Jacobian or gradient calculations as required by theNewton method. The Corey model and piece-wise spline interpolation were used torepresent the relative permeability. A new coding method in GA was developedfor piece-wise spline interpolation. In-situ saturation data were collectedduring an unsteady-state primary drainage experiment by CT scanning. Simulationand experimental data were used to test the performance of the algorithm. Testresults showed a good match between the simulation data and experimental datafor low-injection-rate primary drainage. At higher rates, GA did not convergeto the global optimum.
Relative permeability and capillary pressure are two important functions fordescribing multiphase flow through porous media. They depend on saturation,saturation history, wettability, porous medium microstructure, capillarynumber, and Bond number, in general. Pore network models are being developed toestimate these functions, but most researchers rely on experimentalmeasurements of these functions.
Capillary pressure and relative permeability have been measured separatelyin previous works. Capillary pressure can be measured by the porous-platemethod, the centrifuge method, or by mercury porosimetry. Relative permeabilitycan be measured by steady-state or unsteady-state coreflooding experiments. Thedrawback of determining capillary pressure and relative permeability separatelyis that the capillary pressure measured in this manner gives a static capillarypressure curve, while it is the dynamic capillary pressure that influences theflow. As pointed out by Bentsen and Manai and then in Bentsen, the capillarypressure in a dynamic system may be different from that in a static case,because the dynamic capillary pressure is affected by many factors includingflow rate, possible variations of the wetting property, and microheterogeneity.Therefore, simultaneously estimating the capillary pressure and the relativepermeability for a given flow system is preferable. In the present work, we useunsteady-state experiments followed by the history-matching method to estimaterelative permeability and capillary pressure.
History-matching techniques have been developed to estimate relativepermeability and capillary pressure simultaneously. Functional forms with a setof parameters are presumed for relative permeability of each phase andcapillary pressure. A series of forward simulations is run with the parameterstaking a certain set of values. The parameters are automatically tuned by anoptimization tool to match the simulation data (generally the pressure drop andthe production) with the experimental data.
|File Size||491 KB||Number of Pages||9|
1. Bentsen, R.G. and Manai, A.A.: "Measurement of Cocurrent andCountercurrent Relative Permeability Curves Using the Steady-State Method,"AOSTRA J. Res. (1991) 7, 169.
2. Honarpour, M. and Mahmood, S.M.: "Relative-Permeability Measurements:An Ovewiew," JPT (August 1988) 963.
3. Siddiqui, S., Hicks, P.J., and Ertekin, T.: "Two-Phase RelativePermeability Models in Reservoir Engineering Calculations," Energy Sources(1999) 21, 145.
4. Kerig, P.D. and Watson, A.T.: "Relative-Permeability Estimation FromDisplacement Experiments: An Error Analysis," SPERE (March 1986) 175;Trans., AIME, 281.
5. Kerig, P.D. and Watson, A.T.: "A New Algorithm for EstimatingRelative Permeabilities From Displacement Experiments," SPERE (February1987) 103; Trans., AIME, 283.
6. Schembre, J.M. and Kovscek, A.R.: "Direct Measurement of DynamicRelative Permeability From CT Monitored Spontaneous ImbibitionExperiments," paper SPE 71484 presented at the 2001 SPE Annual TechnicalConference and Exhibition, New Orleans, 30 September-3 October.
7. Goodfield, M., Goodyear, S.G., and Townsley, P.H.: "New Coreflood Interpretation Methodfor Relative Permeabilities Based on Direct Processing of In-Situ SaturationData," paper SPE 71490 presented at the 2001 SPE Annual TechnicalConference and Exhibition, New Orleans, 30 September-3 October.
8. Watson, A.T. et al.: "Estimation of Porous MediaFlow Functions," Meas. Sci. Technol. (1998) 9, 898.
9. Ucan, S., Civan, F., and Evans, R.D.: "Uniqueness and SimultaneousPredictability of Relative Permeability and Capillary Pressure by Discrete andContinuous Means," JCPT (1997) 36, No. 4, 52.
10. Bentsen, R.G.: "Influence ofhydrodynamic forces and interfacial momentum transfer on the flow of twoimmiscible phases," J. Petr. Sci. Engng. (1998) 19, 177.
11. Chardaire-Rivière, C. et al.: "Multiscale Representation forSimultaneous Estimation of Relative Permeabilities and Capillary Pressure,"paper SPE 20501 presented at the 1990 SPE Annual Technical Conference andExhibition, New Orleans, 23-26 September.
12. Forrest, S.: "Genetic Algorithm: Principles of Natural Selection Appliedto Computation," Science (1993) 261, 872.
13. Fogel, D.B.: "An Introduction to Simulated Evolutionary Optimization,"IEEE Trans. on Neural Networks (1994) 5, No. 1, 3.
14. Reed, P and Minsker, B.: "Designing a Competent SimpleGenetic Algorithm for Search and Optimization ," Water Resources Research(2000) 36, No. 12, 3757.
15. Harik, G.R. et al.: "The Gambler's Ruin Problem, Genetic Algorithm, andthe Sizing of Populations," Proc. of the 1997 IEEE Conference on EvolutionaryComputation, IEEE Press, Piscataway, New Jersey (1997) 7-12.
16. Kazarlis, S.A. et al.: "Microgenetic Algorithm as GeneralizedHill-Climbing Operators for GA Optimization," IEEE Trans. on EvolutionaryComputation (2001) 5, No. 3, 204.
17. Jansen, T and Wegener, I.: "Evolutionary Algorithms—How to Cope WithPlateaus of Constant Fitness and When to Reject Strings of the Same Fitness,"IEEE Trans. on Evolutionary Computation (2001) 5, No. 6, 589.
18. Leung, Y. and Wang, Y.: "An Orthogonal Genetic Algorithm withQuantization for Global Numerical Optimization," IEEE Trans. on EvolutionaryComputation (2001) 5, No. 1, 41.
19. Sun, X.: "Implicit Simulation of Transport in Porous Media with PhaseChanges," PhD dissertation, U. of Houston (2005).