Abstract: To enhance the efficacy and safety of CO₂ geological storage, accurate forecasting of CO₂ plume distribution and migration within geological formations has become essential. Deep neural network models have been developed to predict CO₂ plume distributions, with constraints imposed by multiphase flow mechanics. The models utilize automatic differentiation techniques to incorporate partial differential equation (PDE) constraints of multiphase flow into the loss function, ensuring that the model's predictions are consistent with both the observed distribution patterns and the fundamental physical laws governing fluid flow. To validate the model's effectiveness, two Physics-Informed Neural Networks (PINNs) were constructed using a Multi-Layer Perceptron (MLP) and a Long Short-Term Memory (LSTM) deep neural network, respectively. The models were applied to a practical case study involving CO₂ storage in a depleted oil reservoir. Compared to purely data-driven models, the PINNs-based models demonstrated superior predictive accuracy. The findings of this research provide robust technical support for the design and implementation of CO₂ geological storage projects, while also offering a strong theoretical foundation for the practical application of this technology.