In this paper, we present a novel methodology by employing the finite element method (FEM) for creating probability fields of rock types (facies) present in a reservoir. The method is developed for a hydrocarbon reservoir, which, situated thousands of meters underground, has a high uncertainty regarding its geology. However, from the exploration phase, are collected facies observations (hard data) about the rock types present at some sparse locations of the reservoir domain. These observations are projected into a continuous probabilistic space, which is the environment of the FEM. The novelty consists of the fact that the probability field of a facies type is viewed as a deformation field of a plate. For each facies type, the FEM constructs a deformation profile which will be a probability field. The fields generated with the FEM verify the conditions of the probability theory without post-regularization techniques. We test the methodology for a two-dimensional reservoir model with three facies types. We also show the applicability of the new method by introducing the probability fields in the truncated pluri-Gaussian simulation method for simulating facies fields which are the inputs in the assisted history matching of the reservoir.

在本文中，我们通过采用有限元方法（FEM）提出了一种新颖的方法，以创建存在于储层中的岩石类型（相）的概率场。该方法是针对碳氢化合物储层开发的，该碳氢化合物储层位于地下数千米处，其地质条件具有高度不确定性。但是，从勘探阶段开始，收集了有关储层中某些稀疏位置处存在的岩石类型的相观测（硬数据）。这些观察结果被投影到一个连续的概率空间中，这是FEM的环境。新颖性包括以下事实：相类型的概率场被视为板的变形场。对于每种相类型，FEM都会构造一个变形轮廓，这将是一个概率场。FEM生成的字段无需后正则化技术即可验证概率论的条件。我们测试了具有三种相类型的二维油藏模型的方法学。我们还通过在截断的pluri-Gaussian模拟方法中引入概率场来模拟新的方法来显示新方法的适用性，该方法用于模拟相场，这些相场是水库辅助历史匹配中的输入。