Laplacian Echo-State Networks for production analysis and forecasting in unconventional reservoirs

Production data analysis for low permeability shale reservoirs is crucial in characterizing flow regimes and reservoir properties, and the forecasting of production is essential for portfolio and reservoir management. However, traditional methods have failed due to incorrect physics or complicated convolution from the well control history. In this research, we provide a physics-assisted analytics workflow using Laplacian Eigenmaps Coupled Echo-State Network (LEESN) to facilitate and accelerate the analysis of noisy historical production data. Pressure-rate deconvolution is an ill-posed, complex time-series problem. When using the traditional Echo-State Network (ESN), the number of training sets is less than the number of neurons. To solve this problem, we apply LEESN to first deconvolve noisy variable-pressure variable-rate histories into smooth constant-pressure rate responses. The physics-based training features and training algorithm provide additional benefits in addition to the analytic approach by honoring transient flow physics. After training, the constant-pressure rate response can be predicted and used for reservoir characterization, and the trained model could be further used for production and EUR forecasting through long-term rate predictions to the economic limit. The proposed workflow was first validated by synthetic cases where the production data were obtained through simulation. The short-term flow rate history was obtained by specifying highly variable controlling pressures. We also added artificial white Gaussian noise to mimic measured signals collected in the field and input this information into LEESN for deconvolution. The constant-pressure rate response was generated after training to determine flow regimes and properties such as permeability using a traditional transient testing specialized plot. All outcomes from the analytics approach were validated by comparison against the input data of the synthetic simulation model. The advantages of the analytics approach were maintained with a moderate variation of noisy pressure-rate signals. For production forecasting, both the trained analytics model and simulator were used to predict for an extended period, and the results indicated good agreement between the response predictions. We performed a further sensitivity analysis on important parameters such as the training scale as well as the capability of Laplacian Eigenmaps handling moderate noise in training data. The comparison between the model predictions and simulation data showed significantly increased accuracy in production estimates. The efficacy was further demonstrated from additional single-phase and multiphase synthetic and field cases. This study shows that the LEESN approach is a powerful alternative to interpret pressure-rate-time information from production data. The discussion and comparison of LEESN with other traditional production analysis and forecast methods are included as well. Deconvolved pressure-rate data greatly enhances traditional rate-transient analysis (RTA) used to characterize reservoir parameters, and the trained model enables engineers to predict future production even with noisy, highly-variable production histories. The robustness of the proposed analytics methodology is strengthened by coupling the training features with transient flow physics and provides a unique approach for production analysis and forecasting for unconventional reservoirs.