Abstract: The Markov chain model is gradually applied to get 2D or 3D lithofacies images of reservoir in the domain of stochastic reservoir modeling in recent years. It is necessary to extend 1D Markov chain model into 2D or 3D model and give the effective solutions for estimating the transition probability matrix and initializing border status. The 1D, 2D and 3D Markov chain models were discussed on the basis of foregoing studies. A way for estimating transition probability matrix from tally matrix by the use of Walther's law was proposed. The methods for initializing border status were investigated, and a simulation algorithm for 2D Markov chain model was outlined. A calculation case indicates that the solution scheme mentioned above is effective.

Key words: reservoir modeling, Markov chain model, lithofacies image, tally matrix, transition probability matrix, Walther's law

摘要： 将Markov链模型应用于储层建模来获取二维或三维的储层岩相展布图像是近年来储层随机建模领域的一个研究热点。在应用该模型时,须将一维的Markov链模型拓展到二维、三维,同时要对侧向转移概率矩阵的估算和顶层初始化这2个关键问题给出有效的解决方案。笔者对二维和三维的空间Markov链模型进行了阐述,提出了依据Walther相序定律从岩相状态之间的转移记数矩阵入手,来估算侧向转移概率矩阵的方法,并对顶层初始化的解决办法进行了探索。在相关原理及技术细节问题得到解决的基础上,提出了应用Markov链模型进行二维储层岩相空间分布随机模拟的具体算法。二维空间Markov链模型的实际算例表明,对相关问题的解决方案是有效的。

关键词: 储层建模, Markov链模型, 岩相图像, 转移记数矩阵, 转移概率矩阵, Walther相序定律