基于三维马尔可夫链模型的岩性随机模拟

Lithologic stochastic simulation based on the three-dimensional Markov chain model

应用马尔可夫链模型进行三维储层随机模拟一直是油气储层随机模拟中的难点,在二维马尔可夫链模型的基础上提出了三维马尔可夫链模型及其计算公式,解决了应用马尔可夫链进行三维储层岩性随机模拟的问题。对于水平方向岩性转移概率矩阵求取困难的问题,提出了从钻井的岩性资料出发,运用瓦尔特相律来推测其他方向岩性转移概率的方法,并推导出了利用垂直方向的转移记数矩阵求取水平方向上转移记数矩阵和转移概率矩阵的公式。在此思路下,对某地区进行岩性模拟,并与序贯指示模拟方法结果进行了对比,证明了这种方法能更准确反映砂体的空间分布特征。

One of difficulties in oil-gas reservoir characterization is to apply the Markov chain model to a three-dimensional（3D） sto- chastic simulation of reservoirs. Here, we presented a novel approach to achieving a 3D Markov chain model and its calculation for- mulae based on the 2D Markov chain model,that can solve the simulation problem mentioned above. As for difficulties to have a li- thologic transition probability matrix in the horizontal direction, the Wahher＇s law was applied to speculating on a lithologic transi- tion probability matrix in other directions according to lithologic data of drilling, and some formulae were deduced to achieve horizon- tal transition tally matrixes and transition probability matrixes by using vertical transition tally matrixes. The model was then applied to simulating on the lithology of a region and the results were compared with those by the sequential indicator simulation. Analyses show that this new approach can image sandbodies~ spatial distribution features more objectively.