Efficient production process and smart management are key to the sustainable development of natural gas wells. At present, shale gas mining in actual production still faces the problem of liquid loading in wellbores causing the gas well production capacity to decrease. In this paper, a “dual-element integration” plunger-foam compound drainage device is designed to improve the productivity and drainage efficiency of gas wells, taking full advantages of both shale gas foam drainage and plunger drainage gas recovery systems. A novel LSTM-WGAN predictive control method based on Long short-term memory networks (LSTM) and Wasserstein generative adversarial networks (WGAN) is proposed. Density-based spatial clustering of applications with noise (DBSCAN) is used to preprocess the data to avoid the impact of abnormal data on model prediction. The generator and the discriminator compete with each other and update the weights of their respective gradient directions, and the predicted values of oil-casing pressure difference and water-gas ratio are continuously optimized to approach the true value. This enables the model to accurately predict the oil-casing pressure difference and water-gas ratio at the next moment. The predicted plunger-foam drainage strategy is implemented through the plunger-foam drainage composite drainage intelligent management system. Compared with LSTM models, the LSTM-WGAN model reduces the root mean square error (RMSE), mean square error (MSE), and mean absolute error (MAE) of the predicted oil-casing pressure difference and water-gas ratio by 2.64%, 5.13%, 11.75% and 8.81%, 8.07%, 6.60%, respectively. The experimental results demonstrate that the prediction model can accurately predict the oil-casing pressure difference and water-gas ratio data, guide the plunger-foam compound drainage system to issue correct instructions to deploy foam and plungers, and the intelligent delivery of plunger-foam is realized.