Evolving simple-to-use method to determine water-oil relative permeability in petroleum reservoirs

Abstract

In the current research, a new approach constructed based on artificial intelligence concept is introduced to determine water/oil relative permeability at various conditions. To attain an effective tool, various artificial intelligence approaches such as artificial neural network (ANN), hybrid of genetic algorithm and particle swarm optimization (HGAPSO) are examined. Intrinsic potential of feed-forward artificial neural network (ANN) optimized by different optimization algorithms are composed to estimate water/oil relative permeability. The optimization methods such as genetic algorithm, particle swarm optimization and hybrid approach of them are implemented to obtain optimal connection weights involved in the developed smart technique. The constructed intelligent models are evaluated by utilizing extensive experimental data reported in open literature. Results obtained from the proposed intelligent tools were compared with the corresponding experimental relative permeability data. The average absolute deviation between the model predictions and the relevant experimental data was found to be less than 0.1% for hybrid genetic algorithm and particle swarm optimization technique. It is expected that implication of HGAPSO-ANN in relative permeability of water/oil estimation leads to more reliable water/oil relative permeability predictions, resulting in design of more comprehensive simulation and further plans for reservoir production and management.

Keywords

Crude oil / Water / Optimization / Relative permeability / Neural network / Porous media

References

[1] W.G. Anderson, Wettability literature survey part 5: the effects of wettability on relative permeability, SPE J. Pet. Technol. 39 (11) (1987) 1453-1468.

[2] L.F. Koederitz, M.N.M. Ibrahim, Developing a proficient relative permeability resource from historical data™ in: Canadian International Petroleum Conference, Petroleum Society of Canada, Calgary, Alberta, 2002.

[3] J.T. Hawkins, Comparison of three methods of relative permeability measurement, Log Analyst 30 (5) (1989).

[4] G.L. Hassler,U.S. Patent 2,345,935, 1944.

[5] M. Honarpour, F. Koederitz, A. Herbert, Relative Permeability of Petroleum Reservoirs, CRC Press, 1986.

[6] M.N.M. Ibrahim, L.F. Koederitz, Two-phase relative permeability prediction using a linear regression model, in: SPE Eastern Regional Meeting, Society of Petroleum Engineers Inc., Morgantown, West Virginia, 2000.

[7] T. Geffen, Experimental investigation of factors affecting laboratory relative permeability measurements, J. Pet. Technol. 3 (4) (1951) 99-110.

[8] B. Caudle, R. Slobod, E. Brownscombe, Further developments in the laboratory determination of relative permeability, J. Pet. Technol. 3 (5) (1951) 145-150.

[9] J. Richardson, Laboratory determination of relative permeability, J. Pet. Technol. 4 (8) (1952) 187-196.

[10] V. Josendal, B. Sandiford, J. Wilson, Improved multiphase flow studies employing radioactive tracers, J. Pet. Technol. 4 (3) (1952) 65-76.

[11] A.G. Loomis, D.C. Crowell, Relative Permeability Studies: Gas-oil and Water-oil Systems, San Francisco Petroleum Research Lab, Bureau of Mines, San Francisco, Calif. (USA), 1961.

[12] W. Leas, J. Jenks, C. Russell, Relative permeability to gas, J. Pet. Technol. 2 (3) (1950) 65-72.

[13] J.I. Gates, W.T. Lietz, Relative permeabilities of California cores by the capillary-pressure method, Drill. Prod. Pract. (1 January, 1950).

[14] E.R. Brownscombe, R.L. Slobod, B.H. Caudle, Laboratory determination of relative permeability, Oil Gas J. 48 (1950) 98.

[15] E. Johnson, D. Bossler, V.O. Naumann, Calculation of relative permeability from displacement experiments, Trans. AIME 216 (1959) 370-372.

[16] W.R. Purcell, Capillary pressures-their measurement using mercury and the calculation of permeability therefrom, J. Pet. Technol. 1 (2) (1949) 39-48.

[17] I. Fatt, H. Dykstra, Relative permeability studies, J. Pet. Technol. 3 (9) (1951) 249-256.

[18] R. Slobod, A. Chambers, W. Prehn Jr., Use of centrifuge for determining connate water, residual oil, and capillary pressure curves of small core samples, J. Pet. Technol. 3 (4) (1951) 127-134.

[19] E. Van Spronsen, Three-phase Relative Permeability Measurements Using the Centrifuge Method, K/Shell Explor en Prod Lab, Neth, 1982.

[20] D. O'Meara, Multiphase Relative Permeability Measurements Using an Automated Centrifuge, Shell Development Co, 1983.

[21] A.T. Corey, The interrelation between gas and oil relative permeabilities, Prod. Mon. 19 (1) (1954) 38-41.

[22] P. Sigmund, F. McCaffery, An improved unsteady-state procedure for determining the relative-permeability characteristics of heterogeneous porous media, Old SPE J. 19 (1) (1979) 15-28.

[23] M. Honarpour, L. Koederitz, A. Harvey, Empirical equations for estimating two-phase relative permeability in consolidated rock, J. Pet. Technol. 34 (12) (1982) 2905-2908.

[24] G. Chierici, Novel relations for drainage and imbibition relative permeabilities, Old SPE J. 24 (3) (1984) 275-276.

[25] W.E. Galloway, T. Ewing, C. Garrett, N. Tyler, D. Bebout, Atlas of Major Texas Oil Reservoirs, 1983, p. 106.

[26] C. Clayton, M.F. Cohen, M. Anis, T. Cooley, M. Honarpour, J. Wallace, M. Chambers, A. Fadase, F. Pebdani, E. Odior, Ubit field rejuvenation: a case history of reservoir management of a giant oil field, offshore Nigeria,in: SPE Annual Technical Conference and Exhibition, 1998.

[27] G. Pope, W. Wu, G. Narayanaswamy, M. Delshad, M. Sharma, P. Wang,Modeling relative permeability effects in gas-condensate reservoirs, in:SPE Annual Technical Conference and Exhibition, 1998.

[28] M. Sumnu-Dindoruk, J. Jones,Determination of gas-condensate relative permeabilities from field production data, in:SPE Annual Technical Conference and Exhibition, 1998.

[29] J. Edwards, M. Honarpour, R. Hazlett, M. Cohen, A. Membere, v Pebdani, C. Clayton, R. Al-Hussainy,Validation of gravity-dominated relative permeability and residual oil saturation in a giant oil reservoir, in:SPE Annual Technical Conference and Exhibition, 1998.

[30] G. Virnovsky, K. Vatne, S. Skjæveland A. LOHN,Implementation of multirate technique to measure relative permeabilities accounting for capillary effects, in:SPE Annual Technical Conference, 1998, pp. 904-911.

[31] N. Bech, D. Olsen, C.M. Nielsen, Determination of oil/water saturation functions of chalk core plugs from two-phase flow experiments, SPE Reserv. Eval. Eng. 3 (2000) 50-59.

[32] C. Chu, A.E. Tremble, Numerical simulation of steam displacement field performance applications, J. Pet. Technol. 27 (1975) 765-776.

[33] F.N. Schneider, W.W. Owens, Relative permeability studies of Gas-Water flow following solvent injection in carbonate rocks, Soc. Pet. Eng. J. 16 (1976) 23-30.

[34] E.E. Gomaa, J.H. Duerksen, P.T. Woo, Designing a steamflood pilot in the thick monarch sand of the midway-sunset field, J. Pet. Technol. 29 (1977) 1559-1568.

[35] A.W. Talash,Experimental and calculated relative permeability data for systems containing tension additives, in:SPE Improved Oil Recovery Symposium, 1976.

[36] P.T. Bail, S.S. Marsden,Saturation distribution in a linear system during oil displacement, in:Fall Meeting of the Petroleum Branch of AIME, 1956.

[37] B. Abernathy, Waterflood prediction methods compared to pilot performance in carbonate reservoirs, J. Pet. Technol. 16 (1964) 276-282.

[38] H.R. Johnson, D.W. Boley, Waterflooding possibilities of the Clinton Sand, Logan Oilfield, Hocking County, Ohio, Prod. Mon. 27 (1963) 22-26.

[39] C.R. Sandberg, L.S. Gournay, R.F. Sippel, The effect of fluid-flow rate and viscosity on laboratory determinations of oil-water relative permeabilities, Trans. AIME 213 (1958) 36-43.

[40] G. Hetherington Jr.,Relative Permeabilities and Capillary Pressure in the Burgan and Wara Sands.

[41] O. Baptist, E.J. White, C.S. Land, Laboratory predictions of water sensitivity compared with field observations of well damage-Patrick Draw, Wyoming, in:SPE Rocky Mountain Regional Meeting, 1964.

[42] W.W. Slack, R. Ehrlich,Immiscible displacement of oil by simultaneous injection of water and nitrogen, in:SPE/DOE Enhanced Oil Recovery Symposium, 1981.

[43] I. Fatt, The effect of overburden pressure on relative permeability, J. Pet. Technol. 5 (1953) 15-16.

[44] R.D. Thomas, D.C. Ward, Effect of overburden pressure and water saturation on gas permeability of tight sandstone cores, J. Pet. Technol. 24 (1972) 120-124.

[45] F.E. Merliss, J.D. Doane, M.J. Rzasa,Influence of rock and fluid properties on immiscible fluid-flow behavior in porous Media, in:Fall Meeting of the Petroleum Branch of AIME, 1955.

[46] W.A. Ver Wiebe, Oil Fields in the United States, McGraw-Hill book company, inc, 1930.

[47] F.F. Craig, The Reservoir Engineering Aspects of Waterflooding, Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers, Richardson, TX, 1993.

[48] L.F. Koederitz, A.H. Harvey, M. Honarpour, Introduction to Petroleum Reservoir Analysis, Gulf Publishing Company, 1989.

[49] J.L. Shelton, The effects of water injection on miscible flooding methods using hydrocarbons and carbon dioxide, Old SPE J. 15 (1975) 217-226.

[50] R.E. Jenkins, Characteristics of the Delaware formation, J. Pet. Technol. (1961) 1230-1236.

[51] C. Tielong, Z. Yong, P. Kezong, P. Wanfeng,Experimental studies and field trials of relative permeability modifier for water control of gas wells in low permeability reservoir, in:GTS: Gas Technology Symposium, 1996, pp. 385-392.

[52] J.K. Ali, P.J. McGauley, C.J. Wilson,The effects of high-velocity flow and PVT changes near the wellbore on condensate well performance, in:SPE Annual Technical Conference and Exhibition, 1997.

[53] P.E. Oren, S. Bakke, O.J. Arntzen, Extending predictive capabilities to network models, SPE J. 3 (1998) 324-336.

[54] W. Boom, K. Wit, J.P.W. Zeelenberg, H.C. Weeda, J.G. Maas,On the use of model experiments for assessing improved gas-condensate mobility under near-wellbore flow conditions, in:SPE Annual Technical Conference and Exhibition, 1996.

[55] J.S. Archer, S.W. Wong, Use of a reservoir simulator to interpret laboratory waterflood data, Old SPE J. 13 (1973) 343-347.

[56] R. Raghavan, W.C. Chu, J. Jones,Practical considerations in the analysis of gas-condensate well tests, in:SPE Annual Technical Conference and Exhibition, 1995.

[57] M.N.M. Ibrahim, Two-phase Relative Permeability Prediction Using a Linear Regression Model, 1999.

[58] A. Bain, Mind and Body: the Theories of Their Relation, D. Appleton and Company, New York, 1873.

[59] W. James, The Principles of Psychology, H. Holt and Company, New York, 1890.

[60] M.T. Hagan, H.B. Demuth, M. Beal, Neural Network Design, PWS Publishing Company, Boston, 1966.

[61] H.R. Vallés, A Neural Networks Method to Predict Activity Coefficients for Binary Systems Based on Molecular Functional Group Contribution,Master thesis, University of Puerto Rico, 2006.

[62] K. Hornick, M. Stinchcombe, H. White, Multilayer feed forward networks are universal approximators, Neural Netw. 2 (1989) 359-366.

[63] M.A. Ahmadi, Neural network based unified particle swarm optimization for prediction of asphaltene precipitation, Fluid Phase Equilib. 314 (2012) 46-51.

[64] S. Zendehboudi, M.A. Ahmadi, O. Mohammadzadeh, A. Bahadori, I. Chatzis, Thermodynamic investigation of asphaltene precipitation during primary oil production: laboratory and smart technique, Ind. Eng. Chem. Res. 52 (2013) 6009-6031.

[65] J.H. Holland, Adaptation in Natural and Artificial Systems, second ed., MIT Press, Cambridge, MA, 1975, p. 183.

[66] H.P. Schwefel, Evolution and Optimum Seeking, second ed., John Wiley & Sons Inc., New York, 1995, p. 456.

[67] M.A. Ahmadi, M. Ebadi, Robust intelligent tool for estimation dew point pressure in retrograded condensate gas reservoirs: application of particle swarm optimization, in: Journal of Petroleum Science and Engineering, 2014, http://dx.doi.org/10.1016/j.petrol.2014.05.023.

[68] M.A. Ahmadi, M. Masoumi, R. Kharrat, A.H. Mohammadi, Gas analysis by in situ combustion in heavy oil recovery process: experimental and modeling studies, J. Chem. Eng. Technol. 37 (3) (2014) 1-11.

[69] Y. Shi, R.C. Eberhart,A modified particle swarm optimizer, in:Proceedings of IEEE International Conference on Evolutionary Computation, 1988, pp. 69-73.

[70] M.A. Ahmadi, S.R. Shadizadeh, New approach for prediction of asphaltene precipitation due to natural depletion by using evolutionary algorithm concept, J. Fuel 102 (December 2012) 716-723.

[71] S. Zendehboudi, M.A. Ahmadi, L. James, I. Chatzis, Prediction of condensateto-gas ratio for retrograde Gas condensate reservoirs using artificial neural network with particle swarm optimization, Energy Fuels 26 (2012) 3432-3447.

[72] C.F. Juang, A hybrid of genetic algorithm and particle swarm optimization for recurrent network design, IEEE Trans. Syst. Man Cybern. Part B Cybern. 34 (2) (2004) 997-1006.

[73] M.A. Ahmadi, M. Golshadi, Neural network based swarm concept for prediction asphaltene precipitation due natural depletion, J. Pet. Sci. Eng. 98-99 (November 2012) 40-49.

[74] M.A. Ahmadi, S. Zendehboudi, A. Lohi, A. Elkamel, I. Chatzis, Application of hybrid genetic algorithm with particle swarm optimization and neural network for reservoir permeability prediction, Geophys. Prospect. 61 (2013) 582-598.

[75] M.A. Ahmadi, M. Ebadi, A. Shokrollahi, S.M.J. Majidi, Evolving artificial neural network and imperialist competitive algorithm for prediction oil flow rate of the reservoir, Appl. Soft Comput. 13 (2013) 1085-1098.

[76] M.A. Ahmadi, Prediction of minimum miscible pressure by using neural network based hybrid genetic algorithm and particle swarm optimization, J. Pet. Sci. Eng. (2012). http://dx.doi.org/10.1016/j.petrol.2012.08.015.

[77] D.C. Montgomery, G.C. Runger, Applied Statistics and Probability for Engineers, Student Solutions Manual, John Wiley and Sons, New York, 2006.

[78] D.C. Montgomery, Introduction to Statistical Quality Control, John Wiley and Sons, New York, 2008.