A rigorous data-driven approach to predict Poisson's ratio of carbonate rocks using a functional network

Linear elastic behavior of rocks is represented by two parameters, Poisson's ratio and Young's modulus. Proper estimation of elastic parameters of reservoir rocks is very important in alleviating the risk associated with oil and gas well drilling. The reasonable estimation of these two parameters also helps optimize well placement, mud-weight window calculations, appropriate completion design, and fracture orientation geometry. All these factors contribute to maximizing hydrocarbon recovery. Improper estimation of elastic parameters may falsely lead towards large investment decisions and unsuitable field development strategies. Poisson's ratio is very sensitive to the way it is estimated from laboratory data. Simultaneously, it plays a critical role in developing a profile of horizontal stresses and therefore its improved estimation is highly desirable. Retrieving cores through the depth of the interest and conducting laboratory experiments on them under simulated reservoir conditions is the most appropriate way to measure these parameters but this approach is very expensive as well as time consuming. Often, most wells have very limited core data (possibly due to economics). On the other hand, log data are always available. Therefore, most often these parameters are estimated from the log data using empirical correlations. Most of the empirical correlations were developed using linear or nonlinear regression techniques which may not be generalized for unseen data. Artificial intelligence (AI) tool once optimized for training can predict elastic parameters more accurately than the nonlinear regression techniques, because AI tools can capture highly complex and nonlinear relationships between the input and the target data. In this study, an improved model to predict static Poisson's ratio is presented. The model uses geophysical well-log data as input and laboratory experimental data as output. Functional network (FN) is used as an AI tool to model Poisson's ratio prediction. The dataset on which the AI model is trained was obtained from different wells in a giant carbonate reservoir that covers a wide range of values. To translate the FN model into a simple mathematical form, neural functions and empirical coefficients were extracted from the trained FN model. This allowed us to develop FN-based equivalent empirical correlation to predict static Poisson's ratio. The use of the proposed equation is very cost-effective in terms of saving the cost of core retrieval and conducting laboratory experiments. The proposed equation can be employed without the use of any AI software. The developed model, with empirical correlations, can serve as a useful tool to assist geomechanical engineers in estimating the profile of static Poisson's ratio in a given reservoir.