多相非牛顿流体驱替过程的格子Boltzmann模拟

摘要/Abstract

摘要： 将非牛顿流体模型引入多相格子Boltzmann方法（LBM），研究多相非牛顿流体的驱替过程.首先以牛顿流体驱替过程作对照，比较非牛顿流体的驱替特性.然后基于简单结构模型，分析不同界面张力下，非牛顿流体的驱替能力和驱替过程中被驱替相的形态变化规律，揭示界面张力的影响机理.结果表明：界面张力在驱替过程中起阻碍作用，其它参数相同情况下，界面张力越低，流体的驱替能力越强.最后，结合四参数随机生长（QSGS）结构生成方法，模拟不同压差、不同界面张力以及不同润湿性条件下多孔复杂结构内的非牛顿多相驱替过程，分析这些参数对过程的影响.

关键词: 多相流, 非牛顿流体, 流体驱替, 界面捕捉, 格子Boltzmann方法

Abstract: Non-Newtonian fluid model is introduced into multiphase LBM to investigate non-Newtonian fluid displacement in porous media. To begin with,process of a Newtonian fluid displaced by pseudo-plastic fluid and Newtonian fluid in a simple pore with a small obstacle is studied. It shows that fluid displaced by pseudo-plastic fluid is faster than that by Newtonian fluid. Besides,interface tension effects on displacement process is investigated in detail. It indicates that interface tension plays a resistant role during displacement process. Lower interface tension enhances displacement. By using quartet structure generation set (QSGS) algorithm,we perform a series of modeling of displacement in porous media systems. Impacts of interface tension,wettability and pressure difference on final production are discussed.

Key words: multiphase flow, non-Newtonian fluids, fluid displacement, interface capture, lattice Boltzmann method

中图分类号:

TE357

谢驰宇, 张建影, 王沫然. 多相非牛顿流体驱替过程的格子Boltzmann模拟[J]. 计算物理, 2016, 33(2): 147-155.

XIE Chiyu, ZHANG Jianying, WANG Moran. Lattice Boltzmann Modeling of Non-Newtonian Multiphase Fluid Displacement[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(2): 147-155.

参考文献

[1] FUERSTMAN M,GARSTECKI P,WHITESIDES G M. Coding/decoding and reversibility of droplet trains in microfluidic networks[J]. Science,2007, 315(5813):828-832.
[2] PRAKASH M,GERSHENFELD N. Microfluidic bubble logic[J]. Science,2007, 315(5813):832-835.
[3] THEBERGE A,COURTOIS F,SCHAERLI Y,et al. Microdroplets in microfluidics:An evolving platform for discoveries in chemistry and biology[J]. Angewandte Chemie International Edition,2010, 49(34):5846-5868.
[4] KELLY B,BARET J,TALY V,GRIFFITHS A. Miniaturizing chemistry and biology in microdroplets[J]. Chemical Communications,2007,(18):1773-1788.
[5] ZHENG B,ROACH L,ISMAGILOV R. Screening of protein crystallization conditions on a microfluidic chip using nanolitersize droplets[J]. Journal of the American Chemical Society,2003, 125(37):11170-11171.
[6] SONG H,TICE J,ISMAGILOV R. A microfluidic system for controlling reaction networks in time[J]. Angewandte Chemie, 2003, 115(7):792-796.
[7] CYGAN Z,CABRAL J,BEERS K,AMIS E. Microfluidic platform for the generation of organic-phase microreactors[J]. Langmuir,2005, 21(8):3629-3634.
[8] BRILL J. Multiphase flow in wells[J]. Journal of Petroleum Technology,1987, 39(1):15-21.
[9] LENORMAND R,TOUBOUL E,ZARCONE C. Numerical models and experiments on immiscible displacements in porous media[J]. Journal of Fluid Mechanics. 1988, 189(4):165-187.
[10] THORMAS S. Enhanced oil recovery-an overview[J]. Oil & Gas Science and Technology-Rev IFP,2008, 63(1):9-19.
[11] HAJIBEYGI H,JENNY P. Multiscale finite-volume method for parabolic problems arising from compressible multiphase flow in porous media[J]. Journal of Computational Physics,2009, 228(14):5129-5147.
[12] NORDBOTTEN J. Adaptive variational multiscale methods for multiphase flow in porous media[J]. Multiscale Modeling & Simulation,2009,7(3):1455-1473.
[13] NATVIG J,LIE K. Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements[J]. Journal of Computational Physics,2008, 227(24):10108-10124.
[14] JENNY P,LEE S,TCHELEPI H. Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media[J]. Journal of Computational Physics,2006, 217(2):627-641.
[15] JENNY P,LEE S,TCHELEPI H. Adaptive multiscale finite-volume method for multiphase flow and transport in porous media[J]. Multiscale Modeling & Simulation,2005,3(1):50-64.
[16] LUNATI I,JENNY P. Multiscale finite-volume method for compressible multiphase flow in porous media[J]. Journal of Computational Physics,2006, 216(2):616-636.
[17] JUANES R. A variational multiscale finite element method for multiphase flow in porous media[J]. Finite Elements in Analysis and Design,2005, 41(7):763-777.
[18] PESZEYNSKA M,WHEELER M,YOTOV I. Mortar upscaling for multiphase flow in porous media[J]. Computational Geosciences,2002,6(1):73-100.
[19] KIM J,DEO M. Finite element,discrete-fracture model for multiphase flow in porous media[J]. AIChE Journal,2000,46(6):1120-1130.
[20] BLUNT M. Flow in porous media-pore-network models and multiphase flow[J]. Current Opinion in Colloid & Interface Science,2001,6(3):197-207.
[21] CHEN S,DOOLEN G. Lattice Boltzmann method for fluid flows[J]. Annual Review of Fluid Mechanics,1998, 30(1):329-364.
[22] AIDUN C,CLAUSEN J. Lattice-Boltzmann method for complex flows[J]. Annual Review of Fluid Mechanics,2010, 42(1):439-472.
[23] WANG M,KANG Q. Electrokinetic transport in microchannels with random roughness[J]. Analytical Chemistry,2009,81(8):2953-2961.
[24] WANG M. Structure effects on electro-osmosis in microporous media[J]. Journal of Heat Transfer,2012, 134(5):051020.
[25] GUNSTENSEN A,ROTHMAN D,ZALESKI S,ZANETTI G. Lattice Boltzmann model of immiscible fluids[J]. Physical Review A,1991, 43(8):4320-4327.
[26] GUNSTENSEN A,ROTHMAN D. Lattice-Boltzmann studies of immiscible two-phase flow through porous media[J]. J Geophys Res,1993, 98(B4):6431-6441.
[27] SHAN X,CHEN H. Lattice Boltzmann model for simulating flows with multiple phases and components[J]. Physical Review E,1993, 47(3):1815-1819.
[28] SWIFT M,OSBORN W,YEOMANS J. Lattice Boltzmann simulation of nonideal fluids[J]. Physical Review Letters,1995, 75(5):830-833.
[29] HE X,CHEN S,DOOLEN G. A novel thermal model for the lattice Boltzmann method in incompressible limit[J]. Journal Computational Physics,1998, 146(1):282-300.
[30] HE X,CHEN S,ZHANG R. A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh-Taylor instability[J]. Journal of Computational Physics,1999, 152(2):642-663.
[31] INAMURO T,OGATA T,TAJIMA S,KONISHI N. A lattice Boltzmann method for incompressible two-phase flows with large density differences[J]. Journal Computational Physics,2004, 198(2):628-644.
[32] ZHENG H W,SHU C,CHEW Y T. A lattice Boltzmann model for multiphase flows with large density ratio[J]. Journal of Computational Physics,2006, 218(1):353-371.
[33] HUANG J J,SHU C,CHEW Y T. Mobility-dependent bifurcations in capillarity-driven two-phase fluid systems by using a lattice Boltzmann phase-field model[J]. International Journal for Numerical Methods in Fluids,2009, 60(2):203-225.
[34] ARTOLI A. Mesoscopic computational haemodynamics[D]. Amsterdam,Netherlands:University van Amsterdam,2003.
[35] CHEN S,HE X,BERTOLA V,WANG M. Electrokinetic flow of non-Newtonian fluid in porous media[J]. Journal of Colloid and Interface Science. 2014, 436:186-193.
[36] ZOU Q,HE X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model[J]. Physics of Fluids, 1997,9(6):1591-1598.
[37] WANG M,WANG J,PAN N,CHEN S. Mesoscopic predictions of the effective thermal conductivity for microscale random porous media[J]. Physical Review E,2007, 75(3):036702.