The accurate determination of saturation-height functions for modeling multiphase fluid flow in porous media is critical for applications, such as hydrocarbon recovery and subsurface CO/H storage. The challenges associated with water saturation distribution in carbonate reservoirs arise from their inherent heterogeneity and complex pore systems. Addressing such challenges, this study aims to introduce a robust saturation-height function model that considers a non-linear relationship between capillary pressure and saturation, leading to more reliable estimates of fluid saturations. To achieve this, modifications were performed on a saturation height model based on the relationship between porosity, permeability, and pore size distribution (PSD). First of all, the capillary pressure model implemented in the previously introduced PSD-based approach was replaced by a model suitable for heterogeneous reservoirs, fitting the available mercury injection capillary pressure (MICP) data with higher accuracy. Additionally, the derivation of the relations between the optimum pore throat radius and matching parameters of the capillary pressure model was conducted by finding the best correlation among all the available data in the previous approach. For the first time in this study, considering the resemblance in rock properties like capillary pressure and PSD within each rock type, individual correlations among these parameters were established for each reservoir rock type. The predicted saturation height model was cross-checked against the log and core-derived saturation heights, demonstrating a high level of consistency, particularly along the gas-saturated regions. The obtained results were also compared with the conventional saturation height models, including the Leverett J-Function, Johnson's method, and Cuddy's approach. The significance of the modifications was underscored through a comparison of results with those achieved by the previous approach in which the rock typing was ignored. Although the PSD method, which ignored rock types, exhibited high consistency with log data, our modifications yielded far better predictions by improving the coefficient of determination from 0.68 to 0.84.

中文翻译：

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将孔径分布应用到储层岩石类型的饱和度高度函数建模中：以碳酸盐岩气藏为例

准确确定饱和度高度函数以模拟多孔介质中的多相流体流动对于碳氢化合物回收和地下 CO/H 储存等应用至关重要。与碳酸盐岩储层含水饱和度分布相关的挑战源于其固有的非均质性和复杂的孔隙系统。为了解决这些挑战，本研究旨在引入一种稳健的饱和度高度函数模型，该模型考虑毛细管压力和饱和度之间的非线性关系，从而更可靠地估计流体饱和度。为了实现这一目标，根据孔隙度、渗透率和孔径分布 (PSD) 之间的关系对饱和高度模型进行了修改。首先，将之前引入的基于PSD的方法中实施的毛细管压力模型替换为适合非均质油藏的模型，以更高的精度拟合可用的压汞毛细管压力（MICP）数据。此外，通过寻找先前方法中所有可用数据之间的最佳相关性，推导了最佳孔喉半径与毛细管压力模型匹配参数之间的关系。本研究首次考虑到每种岩石类型内毛细管压力和 PSD 等岩石特性的相似性，为每种储层岩石类型建立了这些参数之间的个体相关性。预测的饱和度高度模型与测井和岩心导出的饱和度高度进行了交叉检查，证明了高度的一致性，特别是在气体饱和区域。获得的结果还与传统的饱和高度模型进行了比较，包括 Leverett J-Function、Johnson 方法和 Cuddy 方法。通过将结果与之前忽略岩石定型的方法所获得的结果进行比较，强调了修改的重要性。尽管忽略岩石类型的 PSD 方法与测井数据表现出高度一致性，但我们的修改通过将确定系数从 0.68 提高到 0.84，产生了更好的预测。