Deep Similarity Learning for Well Test Model Identification

Over the years, well test analysis or pressure transient analysis (PTA) methods have progressed from straight lines via type curve analysis to pressure derivatives and deconvolution methods. Today, analysis of the log-log (pressure and its derivative) response is the most used method for PTA. Although these methods are widely available through commercial software, they are not fully automated, and human interaction is needed for their application. Furthermore, PTA is described as an inverse problem, whose solution in general is non-unique, and several models (well, reservoir and boundary) can be found applicable to similar pressure-derivative response. This tends to always bring about confusion in choosing the correct model using the conventional approach. This results in multiple iterations that are time consuming and requires constant human interaction. Our approach automates the process of PTA using a Siamese neural network (SNN) architecture comprised of Convolutional neural network (CNN) and Long Short-Term Memory (LSTM) layers. The SNN model is trained on simulated experimental data created using a design of experiments (DOE) approach involving most common 14 interpretation scenarios across well, reservoir, and boundary model types. Across each model type, parameters such as permeability, horizontal well length, skin factor, and distance to the boundary were sampled to compute 560 different pressure derivative responses. SNN is trained using a self-supervised training strategy where the positive and negative pairs are generated from the training data. We use transformations such as compression and expansion to generate positive pairs and negative pairs for the well test model responses. For a given well test model response, similarity scores are computed against the candidates in each model class, and the best match from each class is identified. These matches are then ranked according to the similarity scores to identify optimal candidates. Experimental analysis indicated that the true model class frequently appeared among the top ranked classes. The model achieves an accuracy of 93% for the top one model recommendations when tested on 70 samples from the 14 interpretation scenarios. Prior information on the top ranked probable well test models, significantly reduces the manual effort involved in the analysis. This machine learning (ML) approach can be integrated with any PTA software or function as a standalone application in the interpreter's system. Current work using SNN with LSTM layers can be used to speed up the process of detecting the pressure derivative response explained by a certain combination of well, reservoir and boundary models and produce models with less user interaction. This methodology will facilitate the interpretation engineer in making the model recognition faster for detailed integration with additional information from sources such as geophysics, geology, petrophysics, drilling, and production logging.