**1. Introduction**

Rock characterization is a crucial aspect in the oil and gas industry, with a major impact on the exploration and production processes [1]. It requires a high level of efficiency and accuracy as minor errors in the identification of the rock characteristics incur significant losses in time and

money. On the other hand, improvements in the prediction accuracy of these characteristics result in a significant positive impact in the economic and technical optimization of a range of processes [2,3]. Even though recently developed models for rock characterization meet the basic requirements of the oil and gas industry, the enormous impact of even minor improvements in the prediction accuracy on the optimization process makes further enhancement of prediction worthwhile [4].

Geo-mechanical earth models are one of the tools used to represent the in-situ state of rock [5]. The development of such models depends on the in-situ stresses encountered within a formation, which can be estimated using the values of its elastic parameters, Poisson's ratio, and Young's modulus [6,7]. These parameters are very important in describing the elastic behavior of rock [8]. These parameters are crucial for avoiding many problems and minimizing the risks associated with well drilling operations [5,9–11]. An accurate estimation of these parameters helps to solve wellbore instability issues, identify the safe mud-weight window while drilling, and optimize the fracture geometry and orientation, etc. [12,13]. On the other hand, the inaccurate determination of the elastic parameters of formations may cause critical problems affecting the strategies of field development negatively from both technical and financial points of view [5,14–16].

The most commonly used reliable tool for estimating the mechanical properties of formations is conducting laboratory measurements. This approach requires retrieving core samples representing the area of interest under in-situ conditions to accurately simulate the formation conditions. However, this approach has some drawbacks due to its high cost and time-consuming nature [17,18]. Hence, an alternate approach in which the experimentally-determined elastic parameters are correlated with the available log data, which are normally collected during drilling, is used [5,19] These petrophysical log data comprise bulk density (*RHOB*), porosity logs, and the measurements of the P-wave and S-wave transit times (Δ*tcomp* and Δ*tshear*, respectively) [19–21].

The correlations derived from the well log data can provide a real-time, continuous profile of static Poisson's ratio (*PRstatic*) values. However, the applicability of the developed profile is limited to the section from which the core samples are collected, limiting the feasibility of the application of these correlations due to their accuracy and reliability [5,16]. Alternatively, the profiles of dynamic Poisson's ratio (*PRdynamic*) are estimated using sonic log data, which are calibrated by determining the difference between *PRdynamic* and *PRstatic* of the measured core data using Equation (1). All dynamic Poisson's ratio values can then be adjusted by adding this difference, resulting in a shift in the *PRdynamic* profile towards the actual values of *PRstatic* [11,15,17,21]. However, the accuracy of this technique is limited to the interval which the core samples represent [5,14]. Also, a large scatter in the data is observed, making it difficult to establish a reasonable relationship, especially in heterogeneous reservoirs [11,17].

When core data and direct downhole rock strength measurements are unavailable, *PRstatic* values are estimated using empirical correlations of the petrophysical log data. D'Andrea et al. [22] have found that *PRstatic* values for different rock samples decrease with increasing transit time (Δ*t*). Also, higher *PRstatic* values are associated with rocks containing larger pores, and a new correlation was developed to predict *PRstatic* values using porosity values [23,24]. Kumar [23] introduced an empirical correlation to predict *PRstatic* values using the velocities of the P-wave and S-wave (*VP* and *Vs*, respectively) stated in Equation (2). Kumar et al. [25] have presented a new correlation relating *PRstatic* values to *VP* and *Vs* using a non-linear regression technique, but it is only limited to isotropic rocks. Al-Shayea [26] showed that *PRstatic* values are dependent on the microcracks within a rock and correlated them with confining pressure. Singh and Singh [27] developed a predictive model to estimate *PRstatic* values for different rocks using unified compressive strength (*UCS*) and tensile strength (*T*). Shalabi et al. [28] applied linear regression to correlate *PRstatic* values with rock hardness and *UCS*. Al-Anazi and Gates [29] have presented different correlations using the support vector regression (SVR) technique relating *PRstatic* values for limestone formations with different parameters, such as *VP*, *Vs*, Young's modulus (*Es*), and the rigidity modulus. They also developed a model to predict *PRstatic* values using several input parameters such as rock porosity, *RHOB*, *VP*, *Vs*, overburden stress (σ*v*), and minimum horizontal

stress (σ*h*). Abdulraheem [30] developed new models to predict *PRstatic* values of carbonate rocks from well log data using fuzzy logic and an artificial neural network.

$$PR\_{dynamic} = \frac{{V\_p}^2 - 2{V\_s}^2}{2({V\_p}^2 - {V\_s}^2)}\tag{1}$$

$$PR\_{static} = 1.316 - 1.5313 \,\frac{V\_s}{V\_p} \tag{2}$$

The literature survey indicates that there have been no significant studies performed to estimate *PRstatic* values from well log data for sandstone rocks using empirical formulations. Most of the correlations reported in the literature for predicting *PRstatic* values have been developed using datasets representing carbonate rocks. Thus, in this study a new model to predict *PRstatic* values of sandstone rocks has been developed based on petrophysical well log data, i.e., *RHOB*, Δ*tcomp*, and Δ*tshear* using artificial neural networks (ANN). The model is presented in a white-box mode by developing a new empirical equation to estimate *PRstatic* values of sandstone rocks directly from the log data without running the ANN model.

The rest of the paper is structured as follows: Section 2 contains materials and methods used for developing the new approach, Section 3 includes the obtained results from the optimization process of the developed model in addition to the procedure required to be followed to use the developed model, performance analysis and the validation process. Finally, Section 4 comprises a summary of the findings of this study listed as conclusions.
