Unconfined compressive strength (UCS) is the key parameter to; estimate the insitu stresses of the rock, design optimal hydraulic fracture geometry and avoid drilling problems like wellbore instability. UCS can be estimated by rock mechanical tests on core plugs retrieved from the depth of interest but retrieving reservoir rock samples throughout the depth of the reservoir section and performing laboratory tests on them are extremely expensive as well as time consuming. In absence of core plugs, UCS can be estimated from empirical correlations. Most of the empirical correlations for UCS prediction reported in the literature are based on elastic parameters or on compressional wave velocity. These correlations were developed using linear or non-linear regression techniques. Artificial intelligence tools once optimized for training can successfully model UCS since these tools can capture highly complex and non-linear relationship between input parameters and the output parameter. The objective of this research study is to accurately predict UCS of rock using basic geophysical well logs namely; bulk density, compressional, and shear wave velocities, by applying different artificial intelligence techniques namely; Support Vector Machine (SVM), Adaptive neuro fuzzy inference system (ANFIS) and Artificial neural network (ANN). The data set used in this study, comprised of 200 laboratory measured UCS values on core plugs and their corresponding well logs. The data were collected from 10 wells which were located in a giant carbonate reservoir. Based on minimum average absolute percentage error (AAPE) and highest coefficient of determination (R2) between actual and predicted data, ANN model proposed as the best model to predict UCS. A rigorous empirical correlation was developed using the weights and biases of ANN model to predict without the need of any software incorporating AI. A comparison of proposed model with other correlations to predict UCS on new data set also suggested that the proposed model gives less AAPE. Therefore, the proposed model seems very promising and can serve as a handy tool to help geo-mechanical engineers to determine the UCS of the carbonate rock.
Ultrasonic elastic‐wave velocities, as well as the stress‐strain behavior, were measured on dry dune sand from Saudi Arabia under hydrostatic loading from 0 to 50 MPa. The samples came from the dune's crest, limb, and base. The experiments included several loading and unloading cycles. All samples exhibited irreversible deformation and porosity reduction during the tests due to grain repacking in low‐stress regimes and grain breakage at higher stress. The loading behavior was plastic, while the unloading/reloading behavior was elastic. In spite of noticeable porosity variations during the experiments, the elastic‐wave velocities mainly depended on the stress rather than on porosity. Our velocity versus stress data is very close to earlier published results, although the provenance of the sand is very different, pointing at a universality of such behavior in loose sand. Our results were matched by the contact Hertz‐Mindlin theory with varying coordination number and shear‐stiffness adjustment. We also offer a new theoretical model for the static bulk modulus measured in these experiments. This model is based on the concept of stress heterogeneity (stress chains or patches) in a granular pack and uses elastic bound averaging of the respective moduli of stressed and unstressed parts of the pack. The same model is used to describe the velocity versus stress behavior. These results and theory constitute a new installment into the published sparse data of the mechanical properties of unconsolidated sand as well as theoretical analyses thereof and are the first ever such data generated in Saudi Arabia.
Total organic carbon (TOC) is an essential parameter used for unconventional shale resources evaluation. The current methods for TOC determination are based on conducting time-consuming laboratory experiments or by using empirical correlations; the later are developed based on assumptions that restrict their applicability. This study provides a new robust model for TOC estimation based on conventional well logs. The model was developed using an adaptive neuro-fuzzy inference system with subtractive clustering (ANFIS-SC). Four conventional well logs of deep resistivity, sonic transit time, gamma ray, and formation bulk density collected from Barnett shale formation were used to develop the ANFIS-SC model for TOC estimation. A dataset consists of 645 records of the four well logs and TOC were used to develop the new model. The model was optimized for the different combinations of the ANFIS-SC’ design parameters and for training/testing data ratio. The optimum predictability of the ANFIS-SC TOC model was reached after 400 iterations using a cluster radius of 0.3 and a training/testing data ratio of 70/30. The statistical analysis showed that TOC is a strong function of the bulk density, moderate function of the sonic transit time and gamma ray, and a weak function of the deep resistivity. The training and testing results proved that the developed ANFIS-SC model is able to predict the TOC based on the four mentioned well log data with high accuracy. For the training data set, the TOC was estimated with an average absolute percentage error (AAPE) of 8.62%, a coefficient of determination (R2) of 0.91, and a correlation coefficient (R) of 0.96. For the testing data set, the associated AAPE in predicting the TOC is 9.57%, while R2 and R between the actual and predicted TOC are 0.89 and 0.94, respectively.
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