Abstract The predictions of two recent and two classical mathematical models are compared with experimentally measured three-phase relative permeabilities. Experimentally determined constitutive relationships in two-phase systems were used as model input parameters to numerically predict relative permeabilities (kr) in three-phase systems. Then the estimated results were compared with experimental three-phase permeabilities measured along decreasing water saturation/decreasing oil saturation/increasing gas saturation (DDI) paths. The results of the individual models to each of the three fluids involved (water, oil, and gas) were analyzed in detail. The simulated results showed that the Total Differential (TD) compatible model overestimates significantly both the global mobilities as well as the relative phase permeabilities in the three-phase system. There was improvement in the prediction with the TD compatible model when experimental data were used to locally impose the global mobility and fractional water and gas fluxes in the ternary diagram. Globally, the best prediction of the measured kr values was obtained with the so-called mechanistic model. However, its numerical implementation requires a preliminary calibration of the relative phase permeabilities in a three-phase system against experimental data along one DDI path to quantify the required six characteristic coefficients. In contrast to the TD compatible model, which by construction does not exhibit any numerical instabilities, elliptic zones in the water-oil (NAPL)-gas ternary diagram were identified in the mechanistic model.

中文翻译：

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利用两相本构关系预测三相相对渗透率

摘要 将两个新近和两个经典数学模型的预测与实验测量的三相相对渗透率进行了比较。两相系统中实验确定的本构关系用作模型输入参数，以数值预测三相系统中的相对渗透率 (kr)。然后将估计结果与沿降低水饱和度/降低油饱和度/增加含气饱和度 (DDI) 路径测量的实验三相渗透率进行比较。详细分析了所涉及的三种流体（水、油和气）中的每一种的各个模型的结果。模拟结果表明，总微分 (TD) 兼容模型显着高估了三相系统中的整体迁移率和相对相渗透率。当使用实验数据在三元图中局部施加全球流动性和部分水和气通量时，TD兼容模型的预测有所改进。在全球范围内，测量 kr 值的最佳预测是通过所谓的机械模型获得的。然而，其数值实现需要根据沿一条 DDI 路径的实验数据对三相系统中的相对相位磁导率进行初步校准，以量化所需的六个特征系数。与 TD 兼容模型相比，该模型在构造上不表现出任何数值不稳定性，