Estimating shear wave velocity in carbonate reservoirs from petrophysical logs using intelligent algorithms

Shear-wave velocity (Vs) is a key petrophysical data for a wide spectrum of applications in the upstream oil industry. In many wells, however, the corresponding log cannot be acquired due to technical and/or cost-related issues. Appreciating the importance of this parameter, its relationship to other petrophysical logs has been extensively studied. For the most part, such studies focus on modes based on either rock physics, analytic equations, or artificial intelligence (AI). Inherent complexity of hydrocarbon reservoirs, especially carbonate ones, has made it difficult to build a comprehensive model of adequately high accuracy for various fields, keeping the research on novel models for such a purpose a still hot topic. This paper presents a high-accuracy high-generalizability model for predicting Vs from logging data. The required logs were acquired along three wells penetrating three carbonate reservoirs in SW Iran. In a preprocessing step, a robust regression technique was applied to identify and omit outliers. Subsequently, the data at two wells were used for training the model, with the data at the third well used for validating the trained model. Feature selection was performed by NSGA-II and five parameters were selected (Vp, Depth, RHOB, NPHI, and RT) as inputs to the model. For the first time, we employed the convolutional neural network (CNN) and multilayer extreme learning machine (MELM) in simple and hybrid forms with a few optimization algorithms, including particle swarm optimization (PSO), cuckoo optimization algorithm (COA), and genetic algorithm (GA) to build different models for predicting Vs from logging data. For the sake of comparison, we further applied the least-squares support-vector machine (LSSVM) in simple and hybrid forms with COA, PSO, and GA as well as a couple of popular analytic methods. Results of the training showed the superiority of the CNN, as measured by RMSE. Nevertheless, the MELM-COA model provided for much shorter learning time although its RMSE was only marginally higher than the CNN. Results of the testing phase showed better generalizability and accuracy of the MELM-COA. The same outcome was confirmed in the validation phase. A comparison between the developed IAs and well-known empirical equations showed the higher performance of the IAs. Accordingly, the methodology proposed in this study is highly recommended for estimating the shear-wave velocity at other wells across similar fields provided the model can b