Predicting the Rock Hardness of Unconventional Shales Based on Elemental Compositions by Employing Artificial Neuron Networks

Understanding rock strength has profound significance in the petroleum industry. It assists in predicting the success of hydraulic fracturing in tight reservoirs, evaluates wellbore stability, and predicts drilling progress. Rock hardness is one of the most critical factors in assessing rock strength and durability. Different techniques are used to determine rock hardness including measurements and modeling approaches. However, these approaches suffer from several drawbacks, including time and cost of measurements. Hence, available information like rock composition can be utilized to produce reliable predictions of rock hardness. In this work, for the first time, rock hardness is estimated based on rock elemental analysis using X-ray Fluorescence (XRF) spectroscopy on a suite of carbonate mudrocks. In this work, hardness measurements were made using the Equotip hardness test, and more than 700 samples were used to construct the predictive models, using artificial neuron networks (ANN). Measured data were grouped into two main sets which are training and testing groups, in order to build and test the ANN models. The predicted data were compared with HLD values measured by Leeb hardness tests, and different types of error indexes were determined to indicate the prediction performance. Before developing the ANN models, statistical analysis was carried out to establish the relationship between hardness and rock mineralogy. The impact of model inputs on the prediction performance was assessed. Three different ANN models of various inputs are discussed in this paper. The correlation coefficient analysis was used to classify and rank the inputs based on their importance. The inputs were classified based on their importance on the hardness into three groups; high, moderate, and low impact. The developed ANN models showed very acceptable performance with percentage errors of 7 to 7.7%, based on the model inputs. The ANN model structure was optimized in order to minimize prediction error, and the optimum ANN models are reported in this paper. Thereafter, a new equation was extracted from the developed ANN model to allow fast and better estimations of rock hardness. The developed equation can be applied to carbonate mudrocks to estimate the hardness based on the elements of Ca, Si, Al, Fe, Ti, and Mo. This work is the first time that hardness values have been modeled based on different rock elements using artificial neuron networks. The developed model can predict the hardness in a time-efficient manner and with high reliability compared to conventional hardness tests that may take longer measurement time.