储层孔隙分布及流体渗流特征的分形描述与应用
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摘要
油藏原始状态的多样性、动态过程的多变性及其问题的不确定性,使得油藏动态系统是一个远离平衡态的非线性复杂系统。基于简单的线性渗流规律已不能满足描述油藏动态系统非线性规律的需要,必须利用新理论、新方法建立新的模型。本文在充分调研国内外油藏动态系统研究新理论、新方法的基础上,针对储层孔隙空间结构的非均质性及其多相流体渗流特征,综合利用分形数学、室内实验和计算机模拟方法进行了系统研究。
根据分形幂律关系,利用岩心进汞-退汞毛细管压力曲线,研究了不同渗透率储层的孔隙结构非均质特征与分形维数的对应关系,对比分析了低渗透岩心孔隙分形特征与中、高渗透岩心的差异,结果表明低渗透岩心孔隙结构具有多重分形分布特征。
通过分析多孔介质中流体运移动力学特征,指出粘性指进对形成剩余油的重要作用。利用赫尔-肖元胞实验装置和颗粒充填模型开展的粘性指进可视化实验,分析了驱替相与被驱替相的界面非稳定性和介质非均质性,尤其是注入端和采出端附近的非线性渗流对诱发粘性指进的重要作用。研究表明,初期指进形态对后续轴向指进形态和剩余油分布具有重要影响,粘性指进生长过程是驱替相粒子表面(界面)成核和分形生长的结果,指进图形具有自相似结构特征。根据能量的转化分析给出了分形体形态增长的模式。
根据粒子扩散运动的随机性以及驱替过程中粘性指进前缘演化动力学方程与DLA(有限扩散凝聚)模型动力学方程的一致性,利用DLA模拟分析了粘性指进前缘的分形生长规律并对储层剩余油挖潜提出了建议。初始优势生长方向决定了整个分形生长图形的轴向形貌特征;界面张力影响粒子横向扩散几率,决定整个分形生长图形的横向形貌特征。
在分析润湿性对储层渗流规律和剩余油分布影响的基础上,根据分形理论推导了包含排替和渗吸过程的广义毛细管压力曲线模型和相对渗透率曲线新模型。通过实验对比分析表明,广义毛细管压力曲线分形模型提高了曲线拟合效果,尤其适应于Brooks-Corey模型不能描述的毛细管压力曲线;根据毛细管压力曲线拟合参数预测了相对渗透率曲线,其流体的相变、相间传质的变化幅度与非线性渗流作用度相关:非线性作用度强,相应相变和相间传质变化的幅度就大。
分形方法的应用结果表明,粘土矿物颗粒堵塞岩心后,孔隙分布发生较大变化,大孔隙数目减少,微孔隙比例增加,表现为岩心分形维数值增大,岩心非均质性增强,从而使束缚水饱和度和残余油饱和度增加,两相相对渗透率区间变窄,迫使油井过早废弃;储层中粘性指进前缘接近油井附近时,由于该区域介质的非均质分布以及较强的非线性渗流特征,油井动态时间序列分形模型参数将发生变化,据此可以诊断油井生产动态的改变。
The dynamic reservoir is a non-linear complex system far away from equilibrium for its versatile original state, variable dynamic process and uncertain problems. The simple linear percolation law couldn’t satisfy the description of the nonlinear law in the dynamic reservoir and new theories, methods should be used to build new models for prediction. In this paper, aiming at the heterogeneous pore structure and the inside multiphase flow characteristics, A comprehensive method including fractal mathematics, laboratory studies and computer simulations was used for research on the bases of the extensive investigation about the new theories and new methods related to dynamic reservoir system home and abroad.
According to the fractal power law relationship, based on the intrusion-extrusion mercury capillary pressure curves, the correlation was analyzed between the heterogeneous pore structure and the fractal dimension for reservoirs with different permeability. The characteristic fractal curve of the low permeability rock samples was also compared to that of the moderate and high permeability rock samples. The results show the low permeability reservoir pore structure has a multi-fractal feature.
The analysis of the fluid movement kinetics within porous medium indicates the important effect of the viscous fingering on the formation of the residual oil. With the experimental sets as Hele-Shaw cell and the particle packed model of injection-production well pattern, several visual experiments were performed to analyze such factors that greatly cause viscous fingering as the heterogeneous media and the unstable interface between the displacing phase and the displaced phase, particularly the non-linear percolation near the injection and the production points. The results show that the initial viscous fingering pattern has great influence on the subsequent axial fingering shape and the remaining oil distribution. The viscous fingering is the consequence of the surface/interface nucleus formation of the displacing phase particles and their fractal growth. The viscous fingering pattern is of self-similarity. The growth pattern models of fractal bodies were presented according to the analysis of energy transformation.
According to the randomicity of the moving particles and the consistent formulations between the front viscous finger evolution and the Diffusion-Limited-Aggregate model, the fractal growth laws was analyzed for the viscous fingering evolution based on the DLA modeling. Also some suggestions were given for the remaining oil stimulation. The initially prominent growth direction determines the axial pattern of the overall fractal cluster. And the interfacial tension has effect on the transverse diffusion probability of particles and then determines the transverse pattern of the overall fractal cluster.
After analysis of the effects of wettability on the formation fluid flow laws and the retaining oil distribution, the generalized capillary pressure model including the displacement and the imbibition processes and the new relative permeability model were derived by the fractal method. In comparison with experimental results, the generalized capillary pressure enhanced the curve fitting effect and was particularly fit for describing the capillary pressure curves that couldn’t be described by Brooks-Corey model. The prediction method for relative permeability curves based on the fitted parameters from capillary pressure curves is especially suitable for acquiring the relative permeability curves of the fluid system including phase transition or interphase mass transfer. The variation range of the fluid phase transition and the mass transfer between phases correlates to the degree of reaction of the non-linear percolation: the stronger degree of the non-linear reaction, the wider variation range of the fluid phase transition and the mass transfer between phases.
The application of the fractal method showed that the plugging of the clay particles might make the pore distribution change a lot, reduce the number of the big pores and increase the fractal dimension of the rock. It will increase the rock heterogeneity to enhance the irreducible water saturation and residual oil saturation, to narrow the permeability area of the two phases, and then to make the oil well wasted earlier. While the front viscous finger approaches near the oil-wells through reservoir, because of the formation heterogeneity and the great non-linear percolation within this area, the dynamic performance of the oil wells could be diagnosed from special parameters of the fractal model of the time series of oil wells.
根据分形幂律关系,利用岩心进汞-退汞毛细管压力曲线,研究了不同渗透率储层的孔隙结构非均质特征与分形维数的对应关系,对比分析了低渗透岩心孔隙分形特征与中、高渗透岩心的差异,结果表明低渗透岩心孔隙结构具有多重分形分布特征。
通过分析多孔介质中流体运移动力学特征,指出粘性指进对形成剩余油的重要作用。利用赫尔-肖元胞实验装置和颗粒充填模型开展的粘性指进可视化实验,分析了驱替相与被驱替相的界面非稳定性和介质非均质性,尤其是注入端和采出端附近的非线性渗流对诱发粘性指进的重要作用。研究表明,初期指进形态对后续轴向指进形态和剩余油分布具有重要影响,粘性指进生长过程是驱替相粒子表面(界面)成核和分形生长的结果,指进图形具有自相似结构特征。根据能量的转化分析给出了分形体形态增长的模式。
根据粒子扩散运动的随机性以及驱替过程中粘性指进前缘演化动力学方程与DLA(有限扩散凝聚)模型动力学方程的一致性,利用DLA模拟分析了粘性指进前缘的分形生长规律并对储层剩余油挖潜提出了建议。初始优势生长方向决定了整个分形生长图形的轴向形貌特征;界面张力影响粒子横向扩散几率,决定整个分形生长图形的横向形貌特征。
在分析润湿性对储层渗流规律和剩余油分布影响的基础上,根据分形理论推导了包含排替和渗吸过程的广义毛细管压力曲线模型和相对渗透率曲线新模型。通过实验对比分析表明,广义毛细管压力曲线分形模型提高了曲线拟合效果,尤其适应于Brooks-Corey模型不能描述的毛细管压力曲线;根据毛细管压力曲线拟合参数预测了相对渗透率曲线,其流体的相变、相间传质的变化幅度与非线性渗流作用度相关:非线性作用度强,相应相变和相间传质变化的幅度就大。
分形方法的应用结果表明,粘土矿物颗粒堵塞岩心后,孔隙分布发生较大变化,大孔隙数目减少,微孔隙比例增加,表现为岩心分形维数值增大,岩心非均质性增强,从而使束缚水饱和度和残余油饱和度增加,两相相对渗透率区间变窄,迫使油井过早废弃;储层中粘性指进前缘接近油井附近时,由于该区域介质的非均质分布以及较强的非线性渗流特征,油井动态时间序列分形模型参数将发生变化,据此可以诊断油井生产动态的改变。
The dynamic reservoir is a non-linear complex system far away from equilibrium for its versatile original state, variable dynamic process and uncertain problems. The simple linear percolation law couldn’t satisfy the description of the nonlinear law in the dynamic reservoir and new theories, methods should be used to build new models for prediction. In this paper, aiming at the heterogeneous pore structure and the inside multiphase flow characteristics, A comprehensive method including fractal mathematics, laboratory studies and computer simulations was used for research on the bases of the extensive investigation about the new theories and new methods related to dynamic reservoir system home and abroad.
According to the fractal power law relationship, based on the intrusion-extrusion mercury capillary pressure curves, the correlation was analyzed between the heterogeneous pore structure and the fractal dimension for reservoirs with different permeability. The characteristic fractal curve of the low permeability rock samples was also compared to that of the moderate and high permeability rock samples. The results show the low permeability reservoir pore structure has a multi-fractal feature.
The analysis of the fluid movement kinetics within porous medium indicates the important effect of the viscous fingering on the formation of the residual oil. With the experimental sets as Hele-Shaw cell and the particle packed model of injection-production well pattern, several visual experiments were performed to analyze such factors that greatly cause viscous fingering as the heterogeneous media and the unstable interface between the displacing phase and the displaced phase, particularly the non-linear percolation near the injection and the production points. The results show that the initial viscous fingering pattern has great influence on the subsequent axial fingering shape and the remaining oil distribution. The viscous fingering is the consequence of the surface/interface nucleus formation of the displacing phase particles and their fractal growth. The viscous fingering pattern is of self-similarity. The growth pattern models of fractal bodies were presented according to the analysis of energy transformation.
According to the randomicity of the moving particles and the consistent formulations between the front viscous finger evolution and the Diffusion-Limited-Aggregate model, the fractal growth laws was analyzed for the viscous fingering evolution based on the DLA modeling. Also some suggestions were given for the remaining oil stimulation. The initially prominent growth direction determines the axial pattern of the overall fractal cluster. And the interfacial tension has effect on the transverse diffusion probability of particles and then determines the transverse pattern of the overall fractal cluster.
After analysis of the effects of wettability on the formation fluid flow laws and the retaining oil distribution, the generalized capillary pressure model including the displacement and the imbibition processes and the new relative permeability model were derived by the fractal method. In comparison with experimental results, the generalized capillary pressure enhanced the curve fitting effect and was particularly fit for describing the capillary pressure curves that couldn’t be described by Brooks-Corey model. The prediction method for relative permeability curves based on the fitted parameters from capillary pressure curves is especially suitable for acquiring the relative permeability curves of the fluid system including phase transition or interphase mass transfer. The variation range of the fluid phase transition and the mass transfer between phases correlates to the degree of reaction of the non-linear percolation: the stronger degree of the non-linear reaction, the wider variation range of the fluid phase transition and the mass transfer between phases.
The application of the fractal method showed that the plugging of the clay particles might make the pore distribution change a lot, reduce the number of the big pores and increase the fractal dimension of the rock. It will increase the rock heterogeneity to enhance the irreducible water saturation and residual oil saturation, to narrow the permeability area of the two phases, and then to make the oil well wasted earlier. While the front viscous finger approaches near the oil-wells through reservoir, because of the formation heterogeneity and the great non-linear percolation within this area, the dynamic performance of the oil wells could be diagnosed from special parameters of the fractal model of the time series of oil wells.
引文
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