Compositional modeling is essential when simulating any process that involves significant changes in the composition of reservoir fluids. This includes modeling the flow of multicomponent hydrocarbons in pipes, surface facilities, and subsurface rocks. However, the rigorous thermodynamics approach to obtain phase composition is computationally expensive. So, various researchers have considered using machine learning models trained with rigorous phase-equilibrium (flash) calculations to improve computational speed.

Unlike previous publications that apply classical deep learning (DL) models to flash calculations, this work will demonstrate the first attempt to incorporate thermodynamics constraints into the training of these models to ensure that they honor physical laws. To this end, we generated one million different compositions with a space-filling mixture design and performed two-phase flash to obtain the corresponding phase compositions. We performed seven-fold cross-validation to ensure reliable estimates of model accuracy. We compared the physics-constrained and standard DL model results to quantify the ability of our approach to honor physical constraints.

The evaluation of our physics-informed neural network (PINN) model compared to a standard DL model shows that we can incorporate physical constraints without a considerable reduction in model accuracy. Based on the test data, our model evaluation results indicate that both PINN and standard DL models achieve coefficients of determination of 97%. In contrast, the root-mean-square error of the physics-constraint errors in the PINN model is at least two times smaller than in the standard DL model. To further demonstrate that our PINN model outperforms the DL model in terms of honoring physical constraints, we generate phase envelopes using the overall compositions predicted using the PINN and DL models for several fluid mixtures in the test data. These results show the importance of incorporating the thermodynamic constraints into DL models.

在模拟任何涉及油藏流体成分显着变化的过程时，成分建模是必不可少的。这包括模拟管道、地面设施和地下岩石中多组分碳氢化合物的流动。然而，获得相组成的严格热力学方法在计算上是昂贵的。因此，各种研究人员已经考虑使用经过严格相位平衡（闪光）计算训练的机器学习模型来提高计算速度。

与之前将经典深度学习 (DL) 模型应用于闪存计算的出版物不同，这项工作将展示首次尝试将热力学约束纳入这些模型的训练中，以确保它们遵守物理定律。为此，我们使用空间填充混合物设计生成了一百万种不同的成分，并进行了两相闪蒸以获得相应的相成分。我们进行了七重交叉验证，以确保模型准确性的可靠估计。我们比较了物理约束和标准 DL 模型的结果，以量化我们的方法遵守物理约束的能力。

与标准 DL 模型相比，我们的物理信息神经网络 (PINN) 模型的评估表明，我们可以在不显着降低模型精度的情况下合并物理约束。根据测试数据，我们的模型评估结果表明，PINN 和标准 DL 模型均达到了 97% 的决定系数。相比之下，PINN 模型中物理约束误差的均方根误差至少比标准 DL 模型小两倍。为了进一步证明我们的 PINN 模型在遵守物理约束方面优于 DL 模型，我们使用使用 PINN 和 DL 模型对测试数据中的几种流体混合物预测的整体成分生成相位包络。这些结果表明了将热力学约束纳入 DL 模型的重要性。