三维孔隙网络模型渗流机理算法及软件研制
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摘要
本文以多孔介质作为研究对象,通过将多孔介质视为相互连通的通道和节点组成的三维网络结构,研究如何建立储层岩石孔隙空间的准静态网络模型,用逾渗理论描述微观渗流机制,模拟驱替过程;结合网络模型的研究,编制相应的软件,应用于流体渗流过程,求取宏观参数(相渗曲线和毛管压力曲线)。实验方法求取这些参数是非常昂贵,且耗费时间。应用网络模型模拟节省了大量的钱物及时间成本。
描述孔隙网络空间的参数主要有:网络的维数、孔喉半径、孔喉长度、配位数、孔喉比、形状因子、孔喉分布规律以及其它性质参数。主要的分布函数有:正态分布、对数分布、伽玛分布、截断正态分布和截断威布尔分布。结合前人的研究成果,分析各个参数的分布规律(分布函数适应性)。
研究了两大类网络模型(准静态网络模型和动态网络模型)的特征及其适用范围。本论文研究了准静态模型中的油水两相的渗流机理。研究不同驱替方式下的流体驱替模式(活塞式、卡断式、孔隙填充式),根据驱替过程中的油水接触情况得到的入口毛管压力公式表达式,计算相渗曲线和毛管压力曲线。
应用网络模型分析微观参数对水驱开发效果的影响,主要思路是建立油水两相孔隙网络模型,分析不同微观参数对相渗曲线和采收率曲线的影响。研究结果表明,随着孔喉比的降低、配位数和形状因子的增大,两相共流区变大,残余油饱和度减小,在相同注入倍数下驱油效率增加;孔喉半径较大的模型,水驱最终采收率较好,孔道半径越长,水驱油效果越好。
This research focuses on porous medium. A porous medium is modeled with a similar structure in three dimensions, the porous medium may be represented as a network of narrow chambers ( called throats ) that intersect at larger void spaces (called pores ). Using percolation theory to describe micro-flow mechanism, we have developed quasi-static models to simulate single-phase flow ,two-phase primary drainage and secondary imbibition in disordered networks. In particular. These models calculate capillary pressures, relative permeabilities, saturation paths, flow regimes, and spatial clusters of the different fluids in the network.
Microscope parameters of pore networks, i.e., volumes, areas, lengths, inscribed circle radii and shape factors is very important for constructing the quasi-static models. We analysis the distribution of these parameters, goodness of fit to a theoretical probability distribution, the probability distribution functions: normal, lognormal, gamma, and weibull.
There are two basic models of multiphase flow in pore networks: dynamic and quasi-static. In dynamic models, capillary, gravity, and viscous forces in the fluids are accounted for simultaneously,. In quasi-static models, capillary forces dominate, gravity modifies the magnitude of capillary pressure, and the microscopic fluid distributions are frozen at each level of the capillary pressure. In this study we adopt the quasi-static approach and ignore the effects of viscous forces. The pore-level displacement mechanisms: piston-type, snap-off, cooperative pore-body filling are considered with arbitrary receding and advancing contact angles. We describe the physics of two-phase flow in a single pore, i.e., the capillary entry pressure in piston-type displacement, snap-off and cooperative pore-body filling.
Using pore network modeling, we analysis the effects of microscope parameters on water drive reservoir. Results show coordinate number and shape factor increasing, residual oil saturation decreasing. Water displacement recovery of model with large inscribed circle radii is improved.
描述孔隙网络空间的参数主要有:网络的维数、孔喉半径、孔喉长度、配位数、孔喉比、形状因子、孔喉分布规律以及其它性质参数。主要的分布函数有:正态分布、对数分布、伽玛分布、截断正态分布和截断威布尔分布。结合前人的研究成果,分析各个参数的分布规律(分布函数适应性)。
研究了两大类网络模型(准静态网络模型和动态网络模型)的特征及其适用范围。本论文研究了准静态模型中的油水两相的渗流机理。研究不同驱替方式下的流体驱替模式(活塞式、卡断式、孔隙填充式),根据驱替过程中的油水接触情况得到的入口毛管压力公式表达式,计算相渗曲线和毛管压力曲线。
应用网络模型分析微观参数对水驱开发效果的影响,主要思路是建立油水两相孔隙网络模型,分析不同微观参数对相渗曲线和采收率曲线的影响。研究结果表明,随着孔喉比的降低、配位数和形状因子的增大,两相共流区变大,残余油饱和度减小,在相同注入倍数下驱油效率增加;孔喉半径较大的模型,水驱最终采收率较好,孔道半径越长,水驱油效果越好。
This research focuses on porous medium. A porous medium is modeled with a similar structure in three dimensions, the porous medium may be represented as a network of narrow chambers ( called throats ) that intersect at larger void spaces (called pores ). Using percolation theory to describe micro-flow mechanism, we have developed quasi-static models to simulate single-phase flow ,two-phase primary drainage and secondary imbibition in disordered networks. In particular. These models calculate capillary pressures, relative permeabilities, saturation paths, flow regimes, and spatial clusters of the different fluids in the network.
Microscope parameters of pore networks, i.e., volumes, areas, lengths, inscribed circle radii and shape factors is very important for constructing the quasi-static models. We analysis the distribution of these parameters, goodness of fit to a theoretical probability distribution, the probability distribution functions: normal, lognormal, gamma, and weibull.
There are two basic models of multiphase flow in pore networks: dynamic and quasi-static. In dynamic models, capillary, gravity, and viscous forces in the fluids are accounted for simultaneously,. In quasi-static models, capillary forces dominate, gravity modifies the magnitude of capillary pressure, and the microscopic fluid distributions are frozen at each level of the capillary pressure. In this study we adopt the quasi-static approach and ignore the effects of viscous forces. The pore-level displacement mechanisms: piston-type, snap-off, cooperative pore-body filling are considered with arbitrary receding and advancing contact angles. We describe the physics of two-phase flow in a single pore, i.e., the capillary entry pressure in piston-type displacement, snap-off and cooperative pore-body filling.
Using pore network modeling, we analysis the effects of microscope parameters on water drive reservoir. Results show coordinate number and shape factor increasing, residual oil saturation decreasing. Water displacement recovery of model with large inscribed circle radii is improved.
引文
[1]. Blunt M J, King M J. Simulation and theory of two-phase flow in porous media. Physical Review A, 1992, 46(12):7680~7699
[2]. Bryant, S. P., King, R., and Mellor, D. W. Network model evaluation of permeability and spatial correlation in a real random sphere packing. Transport in Porous Media, 1993,11: 53–70.
[3]. Valvatne P., Blunt M.., Predictive Pore-Scale Network Modeling. SPE,84550,2003:1-12.
[4]. Bo Qiliang,Zhong Taixian,Liu Qingjie. Pore scale net-work modeling of relative Permeability in chemical flooding. SPE International Improved oi1 Recovery Conference,SPE84906 2003,1-6.
[5]. Mason, G., and N. R. Morrow, Capillary Behavior of a Perfectly Wetting Liquid in Irregular Triangular Tubes. Journal of Colloid and Interface Science, 1991, 141:262-274.
[6]. Lenormand, R., C. Zarcone, and A. Sarr, Mechanisms of the Displacement of One Fluid by Another in a Network of Capillary Ducts. Journal of Fluid Mechanics, 1983,135:337-353.
[7]. Brian Berkowitz, Robert P Ewing. Percolation theory and network modeling applications in soil physics, Surveys in Geophysics, 1998, 19(1): 2372
[8]. Oak M J. Three-phase relative permeability of water-wet berea. In: Proceedings of the SPE/DOE Seventh Symposium on Enhanced Oil Recovery, SPE20183, Tulsa, 1990.109~120
[9]. Blunt M J, Jackson M D, Piri M, et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Advances in Water Resources, 2002, 25: 1069~1089.
[10]. Oren P E, Bakke S, Arntzen O J. Extending predictive capabilities to network models. In: Proceedings of the SPE Annual Technical Conference and Exhibition,SPE38880 Tulsa, 1997. 369~381
[11]. Blunt M J, King P. Relative permeabilities from two- and three-dimensional pore-scale network modeling. Transport in Porous Media,1991,6: 407~433
[12]. Dias M M, Payatakes A C. Network models for two-phase flow in porous media Part 1: Immiscible micro displacement of non-wetting fluids. J Fluid Mechanics, 1986, 164:305~336
[13]. Lenormand Roland, Zarcone Cesar. Role of roughness and edges during imbibition in square capillaries. In: Proceedings of the 59th SPE Annual Technical Conference and Exhibition, SPE13264, Houston, 1984. 1~17
[14]. Tsakiroglou C D, Payatakes A C. Pore-wall goughness as a fractal surface and theoretical simulation of mercury intrusion/retraction in porous media. Journal of Colloid and interface Science, 1993, 159: 287~301
[15]. Adler P M, Jacquin C G, Thovert J F. The formation factor of reconstructed porous media. Water Resources Research, 1992, 28: 1571~1576
[16]. Bryant S, Blunt M J, Prediction of relative permeability in simple porous media. Phys Rev A, 1992, 46: 2004~2011
[17]. Bakke S, Oren P E. 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J, 1997, 2: 136~149
[18]. Oren P E, Bakke S. Process based reconstruction of sandstones and prediction of transport properties. Transport in Porous Media, 2002, 46: 311~343
[19]. Jackson M D, Valvatne P H, Blunt M J. Prediction of wettability variation and its impact on waterflooding using pore to-reservoir-scale simulation. In: Proceedings of the SPE Annual Technical Conference and Exhibition, SPE77543 Texas. 2002. 111
[20]. Blunt M J. Physically-based network modeling of multiphase flow in intermediate-wet porous media. Journal of Petroleum Science and Engineering, 1998, 20: 117~125
[21]. Hughes R G, Blunt M J. Pore scale modeling of rate effects in imbibition. Transport in Porous Media, 2000, 40: 295~322
[22]. Wilkinson D, Willemsen J F. Invasion percolation: a new form of percolation theory. J Phys A, 1983, 16: 3365~3375
[23]. Wong P Z, Koplik J, Tomanic J. Conductivity and permeability of rocks. Physical Review B, 1984, 30(11): 6606~6614
[24]. 王金勋,刘庆杰,杨普华. 应用Bethe网络研究孔隙结构对两相相对渗透率的影响. 重庆大学学报(自然科学版),2000, 23; 130~132
[25]. 王金勋,吴晓东,杨普华等. 孔隙网络模型法计算气液体系吸吮过程相对渗透率. 天然气工业,2003, 23(2): 8~11
[26]. 王金勋,吴晓东,潘新伟. 孔隙网络模型法计算水相滞留对气体渗流的影响. 石油勘探与开发,2003, 5: 113~115
[27]. 胡雪涛,李允. 随机网络模拟研究微观剩余油分布. 石油学报,2000, 21(4): 46~51
[28]. 张玮. 计算机孔隙网络模型及其在注水油藏储层保护中的应用:[硕士论文]. 西安:西安石油学院石油工程系2000. 31~45
[29]. 李贤兵, 刘莉, 朱斌. 低张力体系油水相渗特征的研究. 石油勘探与开发,2004, 31(增刊):44-51
[30]. 任晓娟,刘宁,曲志浩,等. 改变低渗透砂岩亲水性油I气层润湿性对其相渗透率的影响. 石油勘探与开发,2005, 32(3) : 123-124.
[2]. Bryant, S. P., King, R., and Mellor, D. W. Network model evaluation of permeability and spatial correlation in a real random sphere packing. Transport in Porous Media, 1993,11: 53–70.
[3]. Valvatne P., Blunt M.., Predictive Pore-Scale Network Modeling. SPE,84550,2003:1-12.
[4]. Bo Qiliang,Zhong Taixian,Liu Qingjie. Pore scale net-work modeling of relative Permeability in chemical flooding. SPE International Improved oi1 Recovery Conference,SPE84906 2003,1-6.
[5]. Mason, G., and N. R. Morrow, Capillary Behavior of a Perfectly Wetting Liquid in Irregular Triangular Tubes. Journal of Colloid and Interface Science, 1991, 141:262-274.
[6]. Lenormand, R., C. Zarcone, and A. Sarr, Mechanisms of the Displacement of One Fluid by Another in a Network of Capillary Ducts. Journal of Fluid Mechanics, 1983,135:337-353.
[7]. Brian Berkowitz, Robert P Ewing. Percolation theory and network modeling applications in soil physics, Surveys in Geophysics, 1998, 19(1): 2372
[8]. Oak M J. Three-phase relative permeability of water-wet berea. In: Proceedings of the SPE/DOE Seventh Symposium on Enhanced Oil Recovery, SPE20183, Tulsa, 1990.109~120
[9]. Blunt M J, Jackson M D, Piri M, et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Advances in Water Resources, 2002, 25: 1069~1089.
[10]. Oren P E, Bakke S, Arntzen O J. Extending predictive capabilities to network models. In: Proceedings of the SPE Annual Technical Conference and Exhibition,SPE38880 Tulsa, 1997. 369~381
[11]. Blunt M J, King P. Relative permeabilities from two- and three-dimensional pore-scale network modeling. Transport in Porous Media,1991,6: 407~433
[12]. Dias M M, Payatakes A C. Network models for two-phase flow in porous media Part 1: Immiscible micro displacement of non-wetting fluids. J Fluid Mechanics, 1986, 164:305~336
[13]. Lenormand Roland, Zarcone Cesar. Role of roughness and edges during imbibition in square capillaries. In: Proceedings of the 59th SPE Annual Technical Conference and Exhibition, SPE13264, Houston, 1984. 1~17
[14]. Tsakiroglou C D, Payatakes A C. Pore-wall goughness as a fractal surface and theoretical simulation of mercury intrusion/retraction in porous media. Journal of Colloid and interface Science, 1993, 159: 287~301
[15]. Adler P M, Jacquin C G, Thovert J F. The formation factor of reconstructed porous media. Water Resources Research, 1992, 28: 1571~1576
[16]. Bryant S, Blunt M J, Prediction of relative permeability in simple porous media. Phys Rev A, 1992, 46: 2004~2011
[17]. Bakke S, Oren P E. 3-D pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J, 1997, 2: 136~149
[18]. Oren P E, Bakke S. Process based reconstruction of sandstones and prediction of transport properties. Transport in Porous Media, 2002, 46: 311~343
[19]. Jackson M D, Valvatne P H, Blunt M J. Prediction of wettability variation and its impact on waterflooding using pore to-reservoir-scale simulation. In: Proceedings of the SPE Annual Technical Conference and Exhibition, SPE77543 Texas. 2002. 111
[20]. Blunt M J. Physically-based network modeling of multiphase flow in intermediate-wet porous media. Journal of Petroleum Science and Engineering, 1998, 20: 117~125
[21]. Hughes R G, Blunt M J. Pore scale modeling of rate effects in imbibition. Transport in Porous Media, 2000, 40: 295~322
[22]. Wilkinson D, Willemsen J F. Invasion percolation: a new form of percolation theory. J Phys A, 1983, 16: 3365~3375
[23]. Wong P Z, Koplik J, Tomanic J. Conductivity and permeability of rocks. Physical Review B, 1984, 30(11): 6606~6614
[24]. 王金勋,刘庆杰,杨普华. 应用Bethe网络研究孔隙结构对两相相对渗透率的影响. 重庆大学学报(自然科学版),2000, 23; 130~132
[25]. 王金勋,吴晓东,杨普华等. 孔隙网络模型法计算气液体系吸吮过程相对渗透率. 天然气工业,2003, 23(2): 8~11
[26]. 王金勋,吴晓东,潘新伟. 孔隙网络模型法计算水相滞留对气体渗流的影响. 石油勘探与开发,2003, 5: 113~115
[27]. 胡雪涛,李允. 随机网络模拟研究微观剩余油分布. 石油学报,2000, 21(4): 46~51
[28]. 张玮. 计算机孔隙网络模型及其在注水油藏储层保护中的应用:[硕士论文]. 西安:西安石油学院石油工程系2000. 31~45
[29]. 李贤兵, 刘莉, 朱斌. 低张力体系油水相渗特征的研究. 石油勘探与开发,2004, 31(增刊):44-51
[30]. 任晓娟,刘宁,曲志浩,等. 改变低渗透砂岩亲水性油I气层润湿性对其相渗透率的影响. 石油勘探与开发,2005, 32(3) : 123-124.