Unified relative permeability model and waterflooding type curves under different levels of water cut

Abstract Understanding the relative permeability of multiphase flow in porous media is crucial for the efficient development of waterflooding reservoirs. The semi-log linear relationship between oil-water relative permeability ratio (kro/krw) and water saturation (Sw) has been commonly used to derive waterflooding type curve—an empirical and practical tool for the forecast of production performance. However, recent experiments suggest that owing to the highly dispersed oil in water phase, the kro/krw vs Sw correlation deviates from a straight line in a semi-log plot at high water-cut stage (>90%). Considering the linear model of ln(kro/krw) vs Sw fails to describe the multiphase flow behavior for average water saturation greater than ~65%, we present a unified mathematical model to account for different water saturations and develop two type curves to predict the waterflooding performance. Data from previous literatures, numerical simulations, and actual oilfields are employed to examine the capability of the proposed method. In comparison with traditional Type-A and -B curves, in which the correlation of ln(kro/krw) vs Sw is linear, the proposed model provides remarkably accurate results. Although the nonlinear relationship occurs only at high water saturations, neglecting this feature of the relative permeability curve can cause a significant error in the prediction. This work provides a comprehensive model of ln(kro/krw) vs Sw and new Type-A and -B curves for reservoirs at high water-cut stage, which are beneficial for accurate performance forecasts for the entire duration of waterfloods.

[1]  Zhengming Yang.  A New Diagnostic Analysis Method for Waterflood Performance , 2009 .

[2]  C. S. Kabir,et al.  Simple tools for forecasting waterflood performance , 2014 .

[3]  Gang Lei,et al.  Effect of the drawdown pressure on the relative permeability in tight gas: A theoretical and experimental study , 2015 .

[4]  Jiexiang Wang,et al.  Research and Application of a New Type of Water Flooding Characteristic Curve in Oilfield Development , 2016 .

[5]  R. H. Brooks,et al.  Properties of Porous Media Affecting Fluid Flow , 1966 .

[6]  Sen Wang,et al.  A new approach to thief zone identification based on interference test , 2010 .

[7]  M. Ghazanfari,et al.  Relative permeability and capillary pressure curves for low salinity water flooding in sandstone rocks , 2015 .

[8]  Feng Xu,et al.  New Expression of Oil/Water Relative Permeability Ratio vs. Water Saturation and its Application in Water Flooding Curve , 2014 .

[9]  Kamy Sepehrnoori,et al.  CO2 injection for enhanced oil recovery in Bakken tight oil reservoirs , 2015 .

[10]  F. Civan,et al.  Convenient formulae for determination of relative permeability from unsteady-state fluid displacements in core plugs , 2002 .

[11]  Ren Yu-lin,et al.  A New Generalized Water Drive Curve , 2006 .

[12]  D. A. Barry,et al.  Approximation for the exponential integral (Theis well function) , 2000 .

[13]  S. E. Buckley,et al.  Mechanism of Fluid Displacement in Sands , 1942 .

[14]  G. I. Barenblatt,et al.  The Mathematical Model of Nonequilibrium Effects in Water-Oil Displacement , 2003 .

[15]  Anthony R. Kovscek,et al.  Nonequilibrium Effects and Multiphase Flow in Porous Media , 2013, Transport in Porous Media.

[16]  C. Tsakiroglou,et al.  The effect of micro-heterogeneity and capillary number on capillary pressure and relative permeability curves of soils , 2008 .

[17]  A. Skauge,et al.  Foam Performance in Low Permeability Laminated Sandstones , 2014 .

[18]  Applying Method of Characteristics to Study Utilization of Nanoparticles to Reduce Fines Migration in Deepwater Reservoirs , 2015 .

[19]  Saman A. Aryana,et al.  A Bayesian model selection analysis of equilibrium and nonequilibrium models for multiphase flow in porous media , 2017 .

[20]  Iraj Ershaghi,et al.  A Prediction Technique for Immiscible Processes Using Field Performance Data (includes associated papers 13392, 13793, 15146 and 19506 ) , 1984 .

[21]  W. R. Purcell,et al.  Capillary Pressures - Their Measurement Using Mercury and the Calculation of Permeability Therefrom , 1949 .

[22]  R. B. Boozarjomehry,et al.  Joint estimation of absolute and relative permeabilities using ensemble-based Kalman filter , 2015 .

[23]  H. J. Welge,et al.  A Simplified Method for Computing Oil Recovery by Gas or Water Drive , 1952 .

[24]  Changbing Tian,et al.  New understanding on water-oil displacement efficiency in a high water-cut stage , 2012 .

[25]  Xiaodong Han,et al.  A dynamic pore-scale network model for two-phase imbibition , 2015 .

[26]  I. Ershaghi,et al.  A Method for Extrapolation of Cut vs Recovery Curves , 1978 .

[27]  Mark A. Knackstedt,et al.  The effect of displacement rate on imbibition relative permeability and residual saturation , 2006 .

[28]  A. Al-Abri,et al.  Mobility ratio, relative permeability and sweep efficiency of supercritical CO2 and methane injection to enhance natural gas and condensate recovery: Coreflooding experimentation , 2012 .

[29]  P. Sivasankar,et al.  Numerical modelling of enhanced oil recovery by microbial flooding under non-isothermal conditions , 2014 .

[30]  Fengpeng Lai,et al.  Derivation of water flooding characteristic curve for high water-cut oilfields , 2013 .

[31]  William G. Gray,et al.  Thermodynamic basis of capillary pressure in porous media , 1993 .

[32]  Faruk Civan,et al.  Relative Permeability From Unsteady-State Displacements With Capillary Pressure Included , 1989 .

[33]  M. F. Hawkins,et al.  Applied Petroleum Reservoir Engineering , 1991 .

[34]  Michael A. Celia,et al.  Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow , 2002 .

[35]  U. Karabakal,et al.  Determination of Wettability and Its Effect on Waterflood Performance in Limestone Medium , 2004 .

[36]  Peng Xu,et al.  Development prediction and the theoretical analysis in the ultra-high water cut stage for water-flooding sandstone reservoirs , 2016, Journal of Petroleum Exploration and Production Technology.

[37]  Yin Zhang,et al.  CO 2 storage potential and trapping mechanisms in the H-59 block of Jilin oilfield China , 2016 .

[38]  V. V. Bondar,et al.  Analysis and Interpretation of Water-Oil-Ratio Performance , 2002 .

[39]  Christine W. Chan,et al.  Effect of Temperature on Two-Phase Relative Permeabilities of Heavy Oil, Water, Carbon Dioxide, and Methane Determined by Displacement Technique , 2013 .

[40]  Jian Hou,et al.  A New Water Displacement Curve for the High Water-cut Stage , 2013 .

[41]  H. Tchelepi,et al.  Experimental Study of CO2 Injection Into Saline Formations , 2009 .

[42]  S. Bryant,et al.  Maximizing Local Capillary Trapping During CO2 Injection , 2014 .

[43]  Turgay Ertekin,et al.  An Artificial Neural Network Based Relative Permeability Predictor , 2003 .

[44]  E. H. Timmerman.  Predict performance of water floods graphically , 1971 .