Accurate prediction of the CO₂ plume migration and pressure is imperative for safe operation and economic management of carbon storage projects. Numerical reservoir simulations of CO₂ flow could be used for this purpose allowing the operators and stakeholders to calculate the site response considering different operational scenarios and uncertainties in geological characterization. However, the computational toll of these high-fidelity simulations has motivated the recent development of data-driven models. Such models are less costly, but may overfit the data and produce predictions inconsistent with the underlying physical laws. Here, we propose a physics-informed deep learning method that uses deep neural networks but also incorporates flow equations to predict a carbon storage site response to CO₂ injection. A 3D synthetic dataset is used to show the effectiveness of this modeling approach. The model approximates the temporal and spatial evolution of pressure and CO₂ saturation and predicts water production rate over time (outputs), given the initial porosity, permeability and injection rate (inputs). First, we establish a baseline using data-driven deep learning models namely, Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM). To build a physics-informed model, the loss term is modified using the constraints defined by a simplified form of the governing partial differential equations (conservation of mass coupled with Darcy's law for a two-phase flow system). Our results indicate that incorporating the domain knowledge significantly improves the accuracy of predictions. The proposed modeling approach can be integrated in CO₂ storage management to accurately predict the critical site response indicators for a range of relevant input parameters, even when limited training data is available.

准确预测CO ₂羽流迁移和压力对于碳储存项目的安全运行和经济管理至关重要。CO ₂储层数值模拟流量可用于此目的，允许运营商和利益相关者考虑不同的运营场景和地质特征的不确定性来计算现场响应。然而，这些高保真模拟的计算成本推动了数据驱动模型的最新发展。此类模型成本较低，但可能会过度拟合数据并产生与基本物理定律不一致的预测。在这里，我们提出了一种基于物理的深度学习方法，该方法使用深度神经网络，但也结合了流动方程来预测碳储存站点对CO ₂注入的响应。一个 3D 合成数据集用于展示这种建模方法的有效性。该模型近似了压力和给定初始孔隙度、渗透率和注入速率（输入），CO ₂饱和度并预测随时间推移的产水速率（输出）。首先，我们使用数据驱动的深度学习模型建立基线，即多层感知器 (MLP) 和长短期记忆 (LSTM)。为了建立一个基于物理的模型，使用由控制偏微分方程的简化形式（质量守恒与达西定律耦合的两相流系统）定义的约束条件来修改损失项。我们的结果表明，结合领域知识显着提高了预测的准确性。建议的建模方法可以集成到CO ₂ 存储管理以准确预测一系列相关输入参数的关键站点响应指标，即使可用的培训数据有限。