An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test
Keywords:
quivalent single-phase flow, equivalent viscosity, two-phase flow, numerical well test, PEBI gridAbstract
In this work an equivalent single-phase flow model is proposed based on the oil-water two-phase flow equation with saturation-dependent parameters such as equivalent viscosity and equivalent formation volume factor. The equivalent viscosity is calculated from the oil-water relative permeability curves and oil-water viscosity. The equivalent formation volume factor is obtained by the fractional flow of the water phase. In the equivalent single-phase flow model, the equivalent viscosity and phase saturation are interdependent when the relative permeability curves are known. Four numerical experiments based on PEBI grids show that equivalent single-phase flow has a good agreement with the oil-water two-phase flow, which shows that the equivalent single-phase flow model can be used to interpret oil-water two-phase pressure data measured in the wellbore during the buildup period. Because numerical solution of single-phase flow model is several times faster than that of the two-phase flow model, whether the new model interprets the pressure data directly or offers good initial values for the true oil-water two-phase pressure data interpretation, it will obviously improve the efficiency of the interpretation of oil-water pressure data and decrease the burden of engineers.
Cited as: Zha, W., Li, D., Lu, Z., Jia, B. An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test. Advances in Geo-Energy Research, 2018, 2(2): 218-227, doi: 10.26804/ager.2018.02.09
ReferencesAlcalde, O.R., Teufel, L.W. Diagnosis of formation damage by rock deformation/compaction through numerical Well-Test simulations. Paper SPE 98053 Present at International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 15-17 February, 2006.
Ayan, C., Lee, W.J. The effects of multiphase flow on the interpretation of buildup tests. Paper SPE 15537 Presented at the 61st Annual Technical Conference and Exhibition held in New Orleans, LA, 5-8 October, 1986.
Cai, J.C., Hu, X., Xiao, B., et al. Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation. Int. J. Heat Mass Transf. 2017, 105(10): 623-637.
Chu, W.C., Reynolds, A.C., Raghavan, R. Pressure transient analysis of two-phase flow problems. SPE Form. Eval. 1986, 1(2):151-164.
Earlougher, R.C., Miller, F.G., Mueller, T.D. Pressure buildup behavior in a two-well gas-oil system. Soc. Petrol. Eng. J. 1967, 7(2): 195-204.
Fetkovich, M.J., Vienot, M.E. Rate normalization of buildup pressure by using afterflow data. J. Pet. Technol. 1984, 36(12): 1813-1824.
Li, D.L., Xu, C.Y., Wang, J.Y.L., et al. Effect of Knudsen diffusion and Langmuir adsorption on pressure transient response in shale gas reservoir. J. Pet. Sci. Eng. 2014, 124(10): 146-154.
Li, D.L., Zha, W.S., Liu, S.F., et al. Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient. J. Pet. Sci. Eng. 2016a, 147(5): 308-316.
Nnadi, M., Onyekonwu, M. Numerical welltest analysis. Paper SPE 88876 Presented at the 28th Annual SPE international technical conference and exhibition in Abuja, Nigertia, 2-4 August, 2004.
Palagi, C.L., Aziz, K. Use of voronoi grid in reservoir simulation. Paper SPE 22889 Presented at the 1991 SPE Annual Technical Conference and Exhibition, Dallas, 6-9 October, 1991.
Perrine, R.L. Analysis of pressure buildup curves. Drill. Prod. Prac. 1956, 482-509.
Pinzon, C.L., Chen, H.Y., Teufel, L.W. New mexicotech numerical well test analysis of stress-sensitive reservoirs. Paper SPE 71034 Prepared at the SPE Rocky Mountain Petroleum Technology Conference held in Keystone, Colorado, 21-23 May, 2001.
Raghavan, R. Well test analysis: wells producing by solution gas drive wells. Soc. Petrol. Eng. J. 1976, 16(4): 196-208.
Raghavan, R. Well test analysis for multiphase flow. Paper SPE 14098 Presented at the SPE 1986 International Meeting on Petroleum Engineering held in Beijing, China, 17-20 March, 1986.
Raghavan, R. A note on the theoretical foundations for multiphase pressure analysis for flow in porous media. J. Pet. Sci. Eng. 2009, 68(1): 81-88.
Thompson, L.G., Reynolds, A.C. Well testing for radially heterogeneous reservoirs under single and multiphase flow conditions. SPE Form. Eval. 1997, 12(1): 57-64.
Yue, X.A., Wei, H.G. Low pressure gas percolation charac-teristic in ultra-low pemeability porous media. Transp. Porous Media 2010, 85(1): 333-345.
Zhang, T., Li, Z., Adenutsi, C.D., et al. A new model for calculating permeability of natural fractures in dual-porosity reservoir. Adv. Geo-Energy Res. 2017, 1(2): 86-92.
Zhao, Y., Shan, B.C., Zhang, L.H., et al. Seepage flow behaviors of multi-stage fractured horizontal wells in arbitrary shaped shale gas reservoirs. J. Geophys. Eng. 2016, 13(5): 1-10