**Case Number 2**

For this well, wire-lined log data (*RHOB*, Δ*tcomp* , and Δ*tshear*) for an interval of 300 ft of sandstone formation are used as inputs. In addition, five experimentally measured core data points of *PRstatic* are available from the same interval to compare with the results obtained from the ANN model. Figure 15 shows very good agreement between the values measured in the laboratory and predicted *PRstatic* values, with *R* of 0.92 and an MAPE of 2.53% between the predicted and the actual values.

**Figure 15.** Comparison of the *PRstatic* values predicted by the ANN model with the measured values for cores from well number 2 (*R* = 0.92, MAPE = 2.53%).

3.5.2. Phase 2: Validation by Comparing the Predictions of the ANN Model with Common Previous Approaches

As mentioned before the most reliable measurements of *PRstatic* values are provided by the lab measurements of core samples representing the desired interval. However, due to the difficulty and complexity to get samples for the depth interval of interest, it is common in the oil and gas industry to use correlations to predict *PRstatic* values via a standard workflow. These correlations are normally obtained by relating the *PRstatic* values measured in the laboratory to the calculated *PRdynamic* from well logs. The dynamic Poisson's ratio values can be estimated using *Vp* and *Vs* via Equation (1). Then *PRstatic* values can be related to *PRdynamic* values by plotting *PRstatic* vs. *PRdynamic.* In this study, the correlation between the actual *PRstatic* and the calculated *PRdynamic* is developed using the same dataset used for building the ANN model resulting in Equation (9) which relates *PRstatic* with *PRdynamic.* Thereafter this correlation can be then used to predict *PRstatic* for other datasets.

Equations (9) is determined by identifying the best fit equation when plotting *PRstatic* vs. *PRdynamic*, as shown in Figure 16. The extracted equation shows low coefficient of determination (*R*2) between *PRstatic* and *PRdynamic* of 0.58.

$$PR\_{static} = 1.3 \times PR\_{dynamic} - 0.006 \tag{9}$$

**Figure 16.** Relationship between *PRstatic* vs. *PRdynamic* using well log data (*Vp* and *Vs*) for sandstone sections in the same area.

After that another (unseen) dataset representing sandstone sections within the same area is then used to estimate *PRstatic* using the developed ANN model and Equation (9) and compare the accuracy of the results relative to the actual *PRstatic* values. Figure 17a,b show comparison between the actual *PRstatic* and those estimated using the developed ANN model and Equation (9). The developed ANN is found to outperform with *R*<sup>2</sup> of 0.96 compared to *R*<sup>2</sup> of 0.5 using Equation (9). More details about this standard workflow to predict *PRstatic* can be found in [61–63].

**Figure 17.** Comparison between the measured values of *PRstatic* vs. the estimated values using (**a**) *PRdynamic* values via Equation (9) (**b**) the developed ANN model.

For further confirmation on the superiority of the developed ANN model to predict *PRstatic*, it is compared with the model developed by Kumar [25]. Kumar developed a correlation relating *PRstatic* with *Vp* and *Vs* stated in Equation (2). Then, *PRstatic* values are estimated using Kumar's model (using the same dataset used for validating the ANN model vs. the aforementioned standard workflow) and the results are compared to actual *PRstatic* values. The performance of the developed ANN model, the standard workflow, and Kumar's model is evaluated in terms of *R*, MAPE, and *R*<sup>2</sup> between the estimated and measured *PRstatic* values, as listed in Table 4 and shown in Figure 18.


**Table 4.** The optimized weight and biases for the developed ANN model.

**Figure 18.** Comparison between the prediction efficiency of *PRstatic* values using previous approaches vs. the developed ANN model in terms of MAPE.
