A novel approach to pore pressure modeling based on conventional well logs using convolutional neural network

Accurate prediction of pore pressure (PP) is among the most critical concerns to the design of drilling operation because of the remarkable role of this parameter in preventing particular drilling problems such as wellbore instability, drilling pipe stuck, mud loss, kicks, and even blow outs. Given the limitations of PP measurement through in-hole well tests, a number of analytic and intelligent techniques have been developed to estimate the PP from conventionally available petrophysical logs at offset wells. In this contribution, analytic equations are combined with intelligent algorithms (IAs) in an integrated workflow for estimating the PP. For this purpose, we collected the required data from two wells (herein referred to as Wells A and B) penetrating a carbonate reservoir in two fields in southwestern Iran. The collected data included full-set petrophysical log data at a total of 2850 points as well as 15 measured PPs using the RFT tool. In order to model and validate the results, the data from Well A was used to train the model, with the Well-B data used for validation. Once finished with data collection, a noise attenuation stage was implemented through median filtering. Subsequently, PP estimation was practiced using a couple of popular analytic models, namely modified Eaton's, Bowers', and compressibility models, with the results compared to the measured PPs. Next, a feature selection phase was conducted where depth (Depth), gamma ray log (CGR), density log (RHOB), resistivity log (RT), pore compressibility (Cp), and slowness log (DT) were selected as the most effective parameters for estimating the PP out of the 8 parameters studied at Well A. Feature selection was performed using the second version of nondominated-sorting genetic algorithm (NSGA-II) combined with multilayer perceptron (MLP) neural network (NN). Next, deep learning techniques, simple form of the least square support vector machine (LSSVM) and its hybrid forms with particle swarm optimization (PSO), cuckoo optimization algorithm (COA), and genetic algorithm (GA), and multilayer extreme learning machine (MELM) hybridized with the PSO, COA, and GA were used to estimate the PP based on the data at Well A, with the results then validated using the data at Well B. Results of the training and testing phases showed that, among the 9 models considered in this research, the best results were produced by the CNN model followed by MELM-COA, and LSSVM-COA, corresponding to root-mean-square errors (RMSEs) of 0.1072, 0.1175, and 0.1237 and determination coefficients (R2) of 0.9884, 0.9860, and 0.9844, respectively, indicating the higher accuracy and generalizability of these models compared to other investigated models. Evaluation of these models on the validation data from Well B further remarked the superiority of the CNN model, as per an RMSE and R2 of 0.1066 and 0.9806, respectively. Indeed, the better performance of the CNN model than the other models in both the training and validation phases reflects the high generalizability of this model in the range of the studied data. In general, the good performance of the intelligent models in similar formation along two wells – where the analytic models rather failed to exhibit consistently good performance – proves the superiority of the IAs over conventional analytic models. This methodology is strongly recommended provided more diverse data is available at in larger amounts.