油藏动态系统演化过程的描述与表征
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摘要
油藏深埋地下,注水、注化学剂驱替开发的油藏系统是一个远离平衡态的、开放的复杂动态系统,其动态演化过程具有多层次规律性。随机理论中的马尔可夫过程具有较高的准确性和较强的适应性,适用于对具有随机性的复杂油藏动态系统状态进行描述。
在油藏动态系统中,储层孔隙通道具有复杂性和随机性。注入流体驱替原油过程中,注入溶液与地层中流体存在浓度差,使溶质颗粒在孔隙中的运动是分子扩散和对流弥散共同作用的结果。实验表明,弥散性随颗粒平均直径的增加而增加。对流弥散现象具有随机统计特征。注剂经过弥散区域的某段时间内,粒子在孔隙中位移的状态跃迁是具有无后效性的马尔可夫过程,其转移概率用查普曼—柯尔莫哥洛夫方程来描述,经过推导,得到其微分形式,并简化为福克—普朗克扩散方程。在此基础上,建立砂粒充填圆管模型,通过随机建模,推导出考虑吸附颗粒效应的对流弥散方程,并用数值分析方法对无限大油藏、半无限大油藏、有限长岩芯悬浮液浓度进行研究,深入分析了无因次弥散率对弥散现象的影响。
油藏系统与外界不断地进行物质交换,造成油藏动态系统更加复杂化。传统的建模方法不能准确描述复杂动态系统从微观到宏观的状态跃迁演化过程,需要以创新的思维构建反映其变动过程的模型。针对油藏开发过程中注入能力下降的客观事实,利用描述考虑悬浮颗粒吸附效应的对流弥散数学模型和描述外部泥饼结构形成的数学模型对注入能力下降进行了分析,颗粒越大,孔隙越小,地层损害越大。以原油产量增量变动为标准,应用马尔可夫链对原油产量进行了预测,为油田生产决策提供依据。
动态系统与外界物质、能量交换传递中存在抉择规律。动态系统的复杂性及目标的多样性等使抉择主体在如何做出选择时常面临冲突的环境,认清所处的环境和冲突类型有助于决策者更好地做出决定。传统的经济抉择期望效用理论无法解释动态系统中的一些现象,而行为经济学预期理论中S形曲线可以解释决策者面临损失时比面临收益时对价值变化更为敏感的现象。油藏动态系统的决策同样是复杂系统的决择问题,遵循同样的抉择规律。
The reservoir is a system buried deep under the ground. The one flooded by water or chemical agents is an open, complex and dynamic reservoir system far away from equilibrium. Its dynamic evolutionary process embodies the multi-level regularity. As a famous random theory, the Markov process is very good in exactitude and flexible in adaptation, which is applicable to the description of the dynamic reservoir system with randomicity and complexity.
In the dynamic reservoir system, the distribution of pores and channels is random and complex. When the fluid is injected to displace the crude oil, the concentration difference between the injected solution and the in-site fluid makes the movement of particles in solution the common results of both molecular diffusion and convectional dispersion. Experiments show that the dispersivity increases with the average diameter of particles in solution. In the period of flooded agent flowing through the dispersion area, the transition between states of particles’locations is a Markov Process without aftereffect, of which the transition probability can be described by the Chapman-Kolmogroff equation. Based on its differential form, the Fokker-Planck equation is obtained by simplification. Then on the physical model of sand packing with circular tubes, the diffusion-dispersion equation is deduced considering the effect of particles adsorption. Also, the concentration distributions of the suspending liquid are solved by the method of Numerical analysis for different cases such as in the finite reservoir, the semi-infinite reservoir and the core with limited length. And the effect of the dimensionless dispersivity on the extent of the diffusion-dispersion is analyzed detailedly.
Between the reservoir system and the external environment the constant material exchange makes the dynamic reservoir system more complex. Since the traditional modeling method can’t describe the evolutionary processes of transition between states from micro to macro in the complex dynamic system, a creative idea is required to guide the construction of a new modeling in accordance with the changes.
It is objective that injection decline in the process of reservoir development. In this paper a combined model is used to predict the extent of injectivity decline including both diffusion-dispersion model with particle adsorption and the outer mud cake formation model. The results show that the bigger the particles and the smaller the porosity, the larger the formation damage. In order to provide reference for production decision the paper takes the increment change of crude oil production as a foundation and predicts the crude oil production by using Markov Chain.
There is disciplinarian in the transfer of substance and energy between a dynamic system and its external environment. The complexity of the dynamic system and multiformity of the objectives make the main body that makes choices face the conflicting circumstances frequently. So it is helpful for decision makers to make better decisions if they get a clear understanding of the environment and conflicting types. The traditional Expected Utility Theory for economic choice cannot explain some phenomena in the dynamic system. The Sigmoid curve in the Expectation Theory of Behavioral Economics can explain the phenomena that decision-makers are more sensitive in face of loss than of benefit. The decision for the dynamic reservoir system is the same problem as any other complex system, and follows the same choosing law.
在油藏动态系统中,储层孔隙通道具有复杂性和随机性。注入流体驱替原油过程中,注入溶液与地层中流体存在浓度差,使溶质颗粒在孔隙中的运动是分子扩散和对流弥散共同作用的结果。实验表明,弥散性随颗粒平均直径的增加而增加。对流弥散现象具有随机统计特征。注剂经过弥散区域的某段时间内,粒子在孔隙中位移的状态跃迁是具有无后效性的马尔可夫过程,其转移概率用查普曼—柯尔莫哥洛夫方程来描述,经过推导,得到其微分形式,并简化为福克—普朗克扩散方程。在此基础上,建立砂粒充填圆管模型,通过随机建模,推导出考虑吸附颗粒效应的对流弥散方程,并用数值分析方法对无限大油藏、半无限大油藏、有限长岩芯悬浮液浓度进行研究,深入分析了无因次弥散率对弥散现象的影响。
油藏系统与外界不断地进行物质交换,造成油藏动态系统更加复杂化。传统的建模方法不能准确描述复杂动态系统从微观到宏观的状态跃迁演化过程,需要以创新的思维构建反映其变动过程的模型。针对油藏开发过程中注入能力下降的客观事实,利用描述考虑悬浮颗粒吸附效应的对流弥散数学模型和描述外部泥饼结构形成的数学模型对注入能力下降进行了分析,颗粒越大,孔隙越小,地层损害越大。以原油产量增量变动为标准,应用马尔可夫链对原油产量进行了预测,为油田生产决策提供依据。
动态系统与外界物质、能量交换传递中存在抉择规律。动态系统的复杂性及目标的多样性等使抉择主体在如何做出选择时常面临冲突的环境,认清所处的环境和冲突类型有助于决策者更好地做出决定。传统的经济抉择期望效用理论无法解释动态系统中的一些现象,而行为经济学预期理论中S形曲线可以解释决策者面临损失时比面临收益时对价值变化更为敏感的现象。油藏动态系统的决策同样是复杂系统的决择问题,遵循同样的抉择规律。
The reservoir is a system buried deep under the ground. The one flooded by water or chemical agents is an open, complex and dynamic reservoir system far away from equilibrium. Its dynamic evolutionary process embodies the multi-level regularity. As a famous random theory, the Markov process is very good in exactitude and flexible in adaptation, which is applicable to the description of the dynamic reservoir system with randomicity and complexity.
In the dynamic reservoir system, the distribution of pores and channels is random and complex. When the fluid is injected to displace the crude oil, the concentration difference between the injected solution and the in-site fluid makes the movement of particles in solution the common results of both molecular diffusion and convectional dispersion. Experiments show that the dispersivity increases with the average diameter of particles in solution. In the period of flooded agent flowing through the dispersion area, the transition between states of particles’locations is a Markov Process without aftereffect, of which the transition probability can be described by the Chapman-Kolmogroff equation. Based on its differential form, the Fokker-Planck equation is obtained by simplification. Then on the physical model of sand packing with circular tubes, the diffusion-dispersion equation is deduced considering the effect of particles adsorption. Also, the concentration distributions of the suspending liquid are solved by the method of Numerical analysis for different cases such as in the finite reservoir, the semi-infinite reservoir and the core with limited length. And the effect of the dimensionless dispersivity on the extent of the diffusion-dispersion is analyzed detailedly.
Between the reservoir system and the external environment the constant material exchange makes the dynamic reservoir system more complex. Since the traditional modeling method can’t describe the evolutionary processes of transition between states from micro to macro in the complex dynamic system, a creative idea is required to guide the construction of a new modeling in accordance with the changes.
It is objective that injection decline in the process of reservoir development. In this paper a combined model is used to predict the extent of injectivity decline including both diffusion-dispersion model with particle adsorption and the outer mud cake formation model. The results show that the bigger the particles and the smaller the porosity, the larger the formation damage. In order to provide reference for production decision the paper takes the increment change of crude oil production as a foundation and predicts the crude oil production by using Markov Chain.
There is disciplinarian in the transfer of substance and energy between a dynamic system and its external environment. The complexity of the dynamic system and multiformity of the objectives make the main body that makes choices face the conflicting circumstances frequently. So it is helpful for decision makers to make better decisions if they get a clear understanding of the environment and conflicting types. The traditional Expected Utility Theory for economic choice cannot explain some phenomena in the dynamic system. The Sigmoid curve in the Expectation Theory of Behavioral Economics can explain the phenomena that decision-makers are more sensitive in face of loss than of benefit. The decision for the dynamic reservoir system is the same problem as any other complex system, and follows the same choosing law.
引文
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