The inherent complexity of the fluid flow in subsurface systems brings potential inevitable uncertainty in their characterization. Computationally intensive high-dimensional inversion problems often emerge in solving the fluid flow problems of various scenarios, which required to be probed. To improve the efficiency of solving such problems, surrogate strategies are widely used to quantify the uncertainty of underground multiphase flow models. In this paper, a deep learning surrogate model is developed for predicting the time-dependent dynamic multiphase flow in a two-dimensional (2D) channelized geological system. The surrogate model is combined with a residual U-net and an autoregressive strategy, which considers the output at the previous time step as input and predict the output at the current time step. The residual U-net has a symmetric network structure similar to U-net and contains extra residual units. The rich skip connections in the network can promote information dissemination and achieve better prediction performance with fewer parameters. We demonstrated the performance of the autoregressive residual U-net (AR-Runet) for predicting the migration of solute transport in heterogeneous 2D binary model. The result shows the AR-Runet surrogate model can provide an accurate approximation of saturation and pressure fields at different times. We also have demonstrated that with the autoregressive strategy this network can achieve similar predict results with relatively less training data. The performance of the AR-Runet network is also compared with the autoregressive Dense net (AR-Dense). The findings indicate that the AR-Runet can provide effective measures for developing surrogate model and uncertainty analysis in dynamic multiphase flow predictions of subsurface systems.

地下系统中流体流动的内在复杂性为其表征带来了不可避免的潜在不确定性。在解决各种情况下的流体流动问题时，经常会出现计算密集型高维反演问题，需要对此进行探讨。为了提高解决此类问题的效率，广泛使用替代策略来量化地下多相流模型的不确定性。在本文中，开发了一种深度学习替代模型，用于预测二维（2D）通道化地质系统中随时间变化的动态多相流。替代模型与残差U-net和自回归策略相结合，该策略将前一时间步长的输出视为输入，并预测当前时间步长的输出。残留的U-net具有类似于U-net的对称网络结构，并包含额外的残留单元。网络中丰富的跳过连接可以促进信息传播，并以较少的参数获得更好的预测性能。我们展示了自回归残差U-net（AR-Runet）的性能，用于预测异构2D二进制模型中溶质迁移的迁移。结果表明，AR-Runet替代模型可以在不同时间提供饱和度和压力场的精确近似值。我们还证明，利用自回归策略，该网络可以使用相对较少的训练数据获得相似的预测结果。还将AR-Runet网络的性能与自回归密集网络（AR-Dense）进行了比较。