A new deep-learning-based surrogate model is developed and applied for predicting dynamic temperature, pressure, gas rate, oil rate, and water rate with different boundary conditions in pipeline flow. The surrogate model is based on the multilayer perceptron (MLP), batch normalization and Parametric Rectified Linear Unit techniques. In training, the loss function for data mismatch is considered to optimize the model parameters with means absolute error (MAE). In addition, we also use the dynamic weights, calculated by the input data value, to increase the contribution of smaller inputs and avoid errors caused by large values eating small values in total loss. Finally, the surrogate model is applied to simulate a complex pipeline flow in the eastern part of the South China Sea. We use flow and pressure boundary as the input data in the numerical experiment. A total of 215690 high-fidelity training simulations are performed in the offline stage with commercial software LeadFlow, in which 172552 simulation runs are used for training the surrogate model, which takes about 240 min on an RTX2060 graphics processing unit. Then the trained model is used to provide pipeline flow forecasts under various boundary conduction. As a result, it is consistent with those obtained from the high-fidelity simulations (e.g., the media of relative error for temperature is 0.56%, pressure is 0.79%, the gas rate is 1.02%, and oil rate is 1.85%, and water is 0.80%, respectively). The online computations from our surrogate model, about 0.008 s per run, achieve speedups of over 1,250 relative to the high-fidelity simulations, about 10 s per run. Overall, this model provides reliable and fast predictions of the dynamic flow along the pipeline.

Summary A new deep-learning-based surrogate model is developed and applied for predicting dynamic oil rate and water rate with different well controls. The surrogate model is based on the graph neural networks (GNNs) and long-short-term memory (LSTM) techniques. The GNN models are used to characterize the connections of injector-producer pairs and producer-producer pairs, while an LSTM structure is developed to simulate the evolution of the constructed GNN models over time. In this way, we use geological attributes at wells and well controls with different times as input data. The oil rates and water rates at different times are generated. In this study, the GNN-LSTM surrogate model is applied to a high dimensional oil-gas-water field case with flow driven by 189 wells (i.e., 96 producers and 93 injectors) operating under time-varying control specifications. A total of 500 high-fidelity training simulations are performed in the offline stage, out of which 450 simulations are used for training the GNN-LSTM surrogate model, which takes about 150 minutes on an RTX2060 GPU. The trained model is then used to provide production forecasts under various well control scenarios, which are shown to be consistent with those obtained from the high-fidelity simulations (e.g., around 4.8% and 4.3% average relative errors for water production rates and oil production rates, respectively). The online computations from our GNN-LSTM model take about 0.3 seconds per run, achieving a speedup of over a factor of 1,000 relative to the high-fidelity simulations, which takes about 363 seconds per run. Overall, this model is shown to provide reliable and fast predictions of oil rates and water rates with a large level of perturbations in the well controls. Finally, the proposed GNN-LSTM model, in conjunction with the particle swarm optimization (PSO) technique, is applied to optimize the field oil production by varying the well control schedule of all injectors. Due to the significant speedup and high accuracy of the proposed surrogate model, the improved well-control strategies can be efficiently obtained.

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