Machine learning applied to evaluation of reservoir connectivity

In mature reservoirs, there are hundreds or thousands of producing and injecting wells operating simultaneously, so it is important to understand the impact of injection wells on producers to maintain pressure and control water production. In this work, we propose a workflow with two strategies, reduced-physics and data-driven modeling, to monitoring producer and injector wells based on interwell connectivity. The monitoring the wells allows to increase oil production, reducing water rate, and avoiding possible fracturing or fault reactivations. Both strategies use production history data only. The inputs in both strategies are injection rates, while output are liquid production rates. The first one, the reduced-physics modeling strategy, is based on the capacitance-resistance modeling for producers (CRMP), which calculates the liquid flowrate of the producing well based on the injection rate, productivity index of producers, time constant, and the connectivity between injectors and producers. The parameters of the CRMP model are obtained by minimizing the error between the observed and calculated liquid flowrates. The optimization algorithm that minimizes the error is the Sequential Quadratic Programming (SQP) and the gradient is obtained by finite differences. The second one, the data-driven modeling strategy is based on artificial neural networks (ANNs), which only use input and output data. The parameters of the artificial neural network, weights, and biases, are adjusted during the training process. Three architectures are proposed to match the outputs based on the inputs: single-layer perceptron, deep learning with multiple layers, and convolutional neural networks. The backpropagation algorithm is used to adjust the weights and biases of the architectures during training. In this study, we propose three alternatives for calculating the connectivities based on the trained model. The first one is based on the optimal weights. The second one is based on the average error after training and shuffling the input data, and the last one is based on the gradient importance. Two synthetic models, Two-phases, and Brush Canyon Outcrop, are used to validate the proposed workflow. The results show that the connectivities calculated by the gradient importance approach are closer to the connectivities obtained by the capacitance-resistance model. On the other hand, the connectivities obtained through the optimal weights and average error strategies show differences