Abstract
Rock mechanical properties play a crucial role in fracturing design, wellbore stability and in situ stresses estimation. Conventionally, there are two ways to estimate Young’s modulus, either by conducting compressional tests on core plug samples or by calculating it from well log parameters. The first method is costly, time-consuming and does not provide a continuous profile. In contrast, the second method provides a continuous profile, however, it requires the availability of acoustic velocities and usually gives estimations that differ from the experimental ones. In this paper, a different approach is proposed based on the drilling operational data such as weight on bit and penetration rate. To investigate this approach, two machine learning techniques were used, artificial neural network (ANN) and support vector machine (SVM). A total of 2288 data points were employed to develop the model, while another 1667 hidden data points were used later to validate the built models. These data cover different types of formations carbonate, sandstone and shale. The two methods used yielded a good match between the measured and predicted Young’s modulus with correlation coefficients above 0.90, and average absolute percentage errors were less than 15%. For instance, the correlation coefficients for ANN ranged between 0.92 and 0.97 for the training and testing data, respectively. A new empirical correlation was developed based on the optimized ANN model that can be used with different datasets. According to these results, the estimation of elastic moduli from drilling parameters is promising and this approach could be investigated for other rock mechanical parameters.
Highlights
Correlation between static and dynamic Young’s modulus has been built using machine learning methods and presented in a previous publication (Elkatatny et al 2019). This correlation has been used to fill the gap between the static values, and a continuous profile of static Young’s modulus is obtained
support vector machine (SVM) was introduced in the 1960s as a linear classifier and modified in the 1990s for nonlinear problems by using kernel function (Boser et al 1992; Cortes and Vapnik 1995)
Kernel function was proposed by Aizerman et al (Aizerman et al 1964), and there are different kernels such as homogenous and inhomogeneous polynomial, Gaussian and hyperbolic tangent
Summary
The models that correlate the static with the dynamic properties are presented in Table A1 in the Appendix A Part of the equations presented in Table A1 were derived with relatively small numbers of samples or for a certain type of rock. They require the knowledge of dynamic elastic properties which is not always guaranteed. Different techniques were used to develop the presented models such as functional network (FN), adaptive neuro-fuzzy inference system (ANFIS), alternating conditional expectation (ACE) and fuzzy logic (FL) A complete workflow to obtain a continuous static Young’s modulus profile using drilling operational parameters is presented using different AI techniques
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