MCMC方法在多孔介质流体预测中的应用
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摘要
孔隙度和渗透率作为油气储层的重要参数,对石油产量的预测有至关重要的作用。在多孔介质流体流动过程中,孔隙度和渗透率的概率密度分布函数结构复杂,难以用经典分布予以描述,该文介绍了应用马尔可夫链蒙特卡罗方法(Markov chain Monte Carlo method)对孔隙度和渗透率进行贝叶斯估计,然后在其后验概率分布中采样,得到部分已知流量数据并计算流量的似然分布,最终得到生产曲线并用该方法成功预测了生产曲线的走势。同时在文章的最后,基于现存方法中存在的问题,提出了相关的改进方向。
Permeability and porosity, which significantly describing of subsurface properties, are essential factors for the predicting gas production. But given the fact that in porous media flow process, the probability density functions for permeability and porosity are usually too complex for direct sampling, using classical statistical ways to describe the process is troublesome. This article introduced a relative Markov chain Monte Carlo method to solve this kind of problems. In this article, we demonstrated the process consisting Bayes estimation of permeability and porosity, sampling from their posterior distribution, finding the likelihood of the flows and prediction for the production given limited training data. Also, at the end of this article also listed the problems existing in current methods and provided several potential ways for improving.
Permeability and porosity, which significantly describing of subsurface properties, are essential factors for the predicting gas production. But given the fact that in porous media flow process, the probability density functions for permeability and porosity are usually too complex for direct sampling, using classical statistical ways to describe the process is troublesome. This article introduced a relative Markov chain Monte Carlo method to solve this kind of problems. In this article, we demonstrated the process consisting Bayes estimation of permeability and porosity, sampling from their posterior distribution, finding the likelihood of the flows and prediction for the production given limited training data. Also, at the end of this article also listed the problems existing in current methods and provided several potential ways for improving.
引文
[1]Classical Text in Translation:A.A.Markov,An Example of Statistical Investigation of the Text Eugene Onegin Concerning the Connec-tion of Samples in Chains,trans.David Link.Science in Context 19.4(2006):591-600.
[2]陈平,徐若曦.Metropolis-Hasting自适应算法及其应用[J].系统工程理论与实践,2008(1):100-108.
[3]Rosenthal,Jeffrey(March 2004)."W.K.Hastings,Statistician and Developer of the Metropolis-Hastings Algorithm".Retrieved 2009-06-02.
[4]V.Ginting,Multiple Markov Chains Monte Carlo Approach for Flow Forecasting in Porous[J].Procedia Computer Science,2012(9):707-716.
[5]邵维志,解经宇,等.低孔隙度低渗透率岩石孔隙度与渗透率关系研究[J].测井技术,2013(4):149-153.
[6]李留仁,袁士义.分形多孔介质渗透率与孔隙度理论关系模型[J].西安石油大学学报:自然科学版,2010(5):49-51.
[7]卢斌,华仁海.基于MCMC方法的中国期货市场流动性研究[J].管理科学学报,2004(9):98-106.
[8]张广智,王丹阳.利用MCMC方法估算地震参数[J].石油地球物理勘探,2011,46(4):605-609.
[9]杨海东,肖宜.突发性水污染事件溯源方法[J].水科学进展,2014,25(1):122-129.
[10]石文辉,别朝红.大型电力系统可靠性评估中的马尔可夫链蒙特卡洛方法[J].中国电机工程学报,2008,28(4):9-15.
[2]陈平,徐若曦.Metropolis-Hasting自适应算法及其应用[J].系统工程理论与实践,2008(1):100-108.
[3]Rosenthal,Jeffrey(March 2004)."W.K.Hastings,Statistician and Developer of the Metropolis-Hastings Algorithm".Retrieved 2009-06-02.
[4]V.Ginting,Multiple Markov Chains Monte Carlo Approach for Flow Forecasting in Porous[J].Procedia Computer Science,2012(9):707-716.
[5]邵维志,解经宇,等.低孔隙度低渗透率岩石孔隙度与渗透率关系研究[J].测井技术,2013(4):149-153.
[6]李留仁,袁士义.分形多孔介质渗透率与孔隙度理论关系模型[J].西安石油大学学报:自然科学版,2010(5):49-51.
[7]卢斌,华仁海.基于MCMC方法的中国期货市场流动性研究[J].管理科学学报,2004(9):98-106.
[8]张广智,王丹阳.利用MCMC方法估算地震参数[J].石油地球物理勘探,2011,46(4):605-609.
[9]杨海东,肖宜.突发性水污染事件溯源方法[J].水科学进展,2014,25(1):122-129.
[10]石文辉,别朝红.大型电力系统可靠性评估中的马尔可夫链蒙特卡洛方法[J].中国电机工程学报,2008,28(4):9-15.
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