Miscible displacements with concentration-dependent diffusion and velocity-induced dispersion in porous media

Abstract Diffusion and dispersion play significant roles in miscible displacements. In the present study, the frontal instabilities in miscible displacements incorporating both concentration-dependent diffusion coefficient (CDDC) and velocity-induced dispersion (VID) are investigated in homogeneous porous media through nonlinear numerical simulation. Special characteristics have been presented and analyzed for such CDDC-VID case by examining the frontal instabilities. In particular, the VID has more important influence on stabilizing displacements than CDDC. While with CDDC considered, the displacements are more unstable compared with the ConstD-VID case with constant diffusion coefficient (ConstD) and velocity-induced dispersion (VID). Parametric analysis is conducted to study the effects of longitudinal dispersion strength, transverse dispersion, mobility ratio, and Peclet number for the CDDC-VID case. They all affect the development of frontal instabilities, while their roles are different with those of ConstD-VID case. Furthermore, the relative importance of these parameters is analyzed. It is found that the same parameter plays different roles in affecting breakthrough time and sweep efficiency. The correlated equations are obtained to predict breakthrough time and sweep efficiency which agree quite well with the simulated values. It is therefore capable of predicting breakthrough time and sweep efficiency with high accuracy for the CDDC-VID cases in miscible displacements.

[1]  S. Das Diffusion and Dispersion in the Simulation of Vapex Process , 2005 .

[2]  R. J. Blackwell,et al.  Factors Influencing the Efficiency of Miscible Displacement , 1959 .

[3]  Swapan Das,et al.  Diffusion coefficients of propane and butane in peace river bitumen , 1996 .

[4]  J. Bear Dynamics of Fluids in Porous Media , 1975 .

[5]  Abbas Firoozabadi,et al.  Effect of mixing from Fickian diffusion and natural convection in binary non-equilibrium fluid phases , 2010 .

[6]  Eckart Meiburg,et al.  Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium , 2000, Journal of Fluid Mechanics.

[7]  A. Muggeridge,et al.  Gas–oil non-equilibrium in multicontact miscible displacements within homogeneous porous media , 2009 .

[8]  J. Azaiez,et al.  Fully implicit finite difference pseudo‐spectral method for simulating high mobility‐ratio miscible displacements , 2005 .

[9]  S. Hejazi,et al.  Estimation of concentration‐dependent diffusion coefficients of gases in heavy oils/bitumen using experimental pressure‐decay data , 2016 .

[10]  A. Kantzas,et al.  Monitoring bitumen-solvent interactions with low-field nuclear magnetic resonance and X-ray computer-assisted tomography , 2005 .

[11]  T. Maxworthy The nonlinear growth of a gravitationally unstable interface in a Hele-Shaw cell , 1987, Journal of Fluid Mechanics.

[12]  Yannis C. Yortsos,et al.  Dispersion driven instability in miscible displacement in porous media , 1988 .

[13]  Omar Chaalal,et al.  Numerical and experimental modeling of viscous fingering during liquid-liquid miscible displacement , 2000 .

[14]  T. Maxworthy,et al.  Miscible displacements in capillary tubes. Part 1. Experiments , 1996, Journal of Fluid Mechanics.

[15]  J. Azaiez,et al.  Stability of miscible displacements of shear thinning fluids in a Hele-Shaw cell , 2002 .

[16]  A. W. Woods,et al.  Dispersion, scale, and time dependence of mixing zones under gravitationally stable and unstable displacements in porous media , 2005 .

[17]  J. Azaiez,et al.  Inertial effects in cyclic time‐dependent displacement flows in homogeneous porous media , 2015 .

[18]  Zhaoli Guo,et al.  Localized lattice Boltzmann equation model for simulating miscible viscous displacement in porous media , 2016 .

[19]  Prabir Daripa,et al.  Stabilizing effect of diffusion in enhanced oil recovery and three-layer Hele-Shaw flows with viscosity gradient , 2007 .

[20]  E. J. Peters,et al.  Scaling miscible fluid displacements in porous media , 1998 .

[21]  J. Azaiez,et al.  Viscous Fingering Instability in Porous Media: Effect of Anisotropic Velocity-Dependent Dispersion Tensor , 2008 .

[22]  Eckart Meiburg,et al.  High-Accuracy Implicit Finite-Difference Simulations of Homogeneous and Heterogeneous Miscible-Porous-Medium Flows , 2000 .

[23]  J. Azaiez,et al.  Inertial effects of miscible viscous fingering in a Hele-Shaw cell , 2015 .

[24]  J. Azaiez,et al.  Heat and mass transfer in melting porous media: Stable miscible displacements , 2015 .

[25]  Fanhua Zeng,et al.  Investigation of Concentration-Dependent Diffusion on Frontal Instabilities and Mass Transfer in Homogeneous Porous Media† , 2018 .

[26]  Effect of Transverse Diffusion on Fingering In Miscible-Phase Displacement , 1963 .

[27]  J. Azaiez,et al.  Miscible Displacements in Porous Media with Time-Dependent Injection Velocities , 2014, Transport in Porous Media.

[28]  R. Johns,et al.  Scale-Dependent Mixing for Adverse Mobility Ratio Flows in Heterogeneous Porous Media , 2016, Transport in Porous Media.

[29]  G. Homsy,et al.  Stability of miscible displacements in porous media: Rectilinear flow , 1986 .

[30]  H. J. Morel-Seytoux,et al.  Multiphase Fluid Flow Through Porous Media , 1976 .

[31]  Eckart Meiburg,et al.  Density-driven instabilities in capillary tubes: Influence of a variable diffusion coefficient , 2006 .

[32]  A. Kantzas,et al.  Investigation of Diffusion Coefficients of Heavy Oil and Hydrocarbon Solvent Systems in Porous Media , 2008 .

[33]  E. Meiburg,et al.  Variable density and viscosity, miscible displacements in capillary tubes , 2008 .

[34]  F. J. Fayers,et al.  Detailed validation of an empirical model for viscous fingering with gravity effects , 1988 .

[35]  J. Azaiez,et al.  Cyclic time-dependent reactive flow displacements in porous media , 2014 .

[36]  A. Hamouda,et al.  The effect of light gas on miscible CO2 flooding to enhance oil recovery from sandstone and chalk reservoirs , 2013 .

[37]  Simant R. Upreti,et al.  Diffusivity of CO2, CH4, C2H6 and N2 in athabasca bitumen , 2002 .

[38]  Franklin M. Orr,et al.  Diffusion of CO2 at Reservoir Conditions: Models and Measurements , 1988 .

[39]  T. Norton,et al.  Viscous Fingering in Size Exclusion Chromatography: Insights from Numerical Simulation , 1996 .

[40]  Hamdi A. Tchelepi,et al.  Numerical simulation of immiscible two-phase flow in porous media , 2006 .

[41]  E. Meiburg,et al.  Miscible displacements in capillary tubes. Part 2. Numerical simulations , 1996, Journal of Fluid Mechanics.

[42]  T. Okazawa,et al.  Impact of Concentration-Dependence of Diffusion Coefficient on VAPEX Drainage Rates , 2009 .

[43]  S. Hill,et al.  Channeling in packed columns , 1952 .

[44]  Mukul M. Sharma,et al.  Experimental study of the growth of mixing zone in miscible viscous fingering , 2015 .

[45]  William B. Zimmerman,et al.  Nonlinear viscous fingering in miscible displacement with anisotropic dispersion , 1991 .

[46]  R. L. Slobod,et al.  X-Ray Shadowgraph Studies of Areal Sweepout Efficiencies , 1952 .

[47]  F. Civan,et al.  Rapid simultaneous evaluation of four parameters of single-component gases in nonvolatile liquids from a single data set , 2009 .

[48]  Ching-Yao Chen,et al.  Controlling radial fingering patterns in miscible confined flows. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  K. Sepehrnoori,et al.  A 3D compositional miscible gas flooding simulator with dispersion using Element-based Finite-Volume method , 2013 .

[50]  M. Mishra,et al.  Nonlinear simulations of miscible viscous fingering with gradient stresses in porous media , 2015 .

[51]  Eckart Meiburg,et al.  Linear stability of radial displacements in porous media: Influence of velocity-induced dispersion and concentration-dependent diffusion , 2004 .

[52]  Simant R. Upreti,et al.  Experimental measurement of gas diffusivity in bitumen: Results for carbon dioxide , 2000 .

[53]  George M. Homsy,et al.  Viscous fingering in periodically heterogeneous porous media. II. Numerical simulations , 1997 .

[54]  George M. Homsy,et al.  Simulation of nonlinear viscous fingering in miscible displacement , 1988 .

[55]  N. Rashidnia,et al.  Measurement of the mass diffusivity of miscible liquids as a function of concentration using a common path shearing interferometer , 2004 .

[56]  Fanhua Zeng,et al.  Nonlinear simulation of miscible displacements with concentration-dependent diffusion coefficient in homogeneous porous media , 2017 .

[57]  J. Bacri,et al.  Miscible viscous fingering : experiments versus continuum approach , 1992 .