Evaluation of brittleness index (BI) is a fundamental principle of a hydraulic fracturing design. A wide variety of BI calculations often baffle field engineers. The traditional value comparison may also not make the best of BI. Moreover, it is often mixed up with the fracability in field applications, thus causing concerns. We, therefore, redefine fracability as the fracturing pressure under certain rock mechanical (mainly brittleness), geological and injecting conditions to clarify the confusion. Then, we propose a data-driven workflow to optimize BIs by con- trolling the geological and injecting conditions. The machine learning (ML) workflow is employed to predict the fracability (fracturing pressure) based on field measurement. Three representative ML algorithms are applied to average the prediction, aiming to restrict the interference of algorithm performances. The contribution of brit- tleness on pressure/fracability prediction by error analysis (rather than the traditional method of BI-value comparison) is proposed as the new criterion for optimization. Six classic BI correlations (mineral-, logging- and elastic-based) are evaluated, three of which are optimized for the derivation of a new BI using the backward elimination strategy. The stress ratio (ratio of minimum and maximum horizontal principal stress), representing the geological feature, is introduced into the derived calculation based on the independent variable analysis. The reliability of the new BI is verified by error analyses using data of eight fracturing stages from seven different wells. Approximately 40% –50% of the errors are reduced based on the new BI. The differences among the performances of algorithms are also significantly restrained. The new brittleness index provides a more reliable option for evaluating the brittleness and fracability of the fracturing formation. The machine learning workflow also proposes a promising application scenario of the BI for hydraulic fracturing, which makes more efficient and broader usages of the BI compared with the traditional value comparison. 1.Introduction Brittleness index (BI), an essential parameter to evaluate the mineral, mechanical and failure characteristics of formations, is commonly applied in mining (e.g. rock cutting) and petroleum engineering (e.g. drilling and fracturing).1–3 For hydraulic fracturing, it is an essential criterion for the optimization of “sweet point ” that is easy to crack and tends to create complex fracture networks – namely the evaluation of fracability (how easy the reservoir can be cracked).4–6 Initiating from the mineral component analysis, the BI calculations for hydraulic frac- turing are involving more and more rock mechanical and engineering features.7,8 Dozens of BI calculations are proposed for various formations with unique lithological and elastic properties, which could be roughly classified into (i) the mineral-based brittleness index (MBI),9,10 (ii) the logging-based brittleness index (LBI),11 and (iii) the elastic-based brit- tleness index (EBI).12,13 Current efforts evaluate the BI calculations mainly based on numerical simulation,14 logging data,15 and static tests.16 Limited test at field-practical scales is presented, thus restricting the reliability and persuasion of these BI calculations. However, the successful applications of machine learning techniques in petroleum engineering have paved a potential data-driven approach for BI opti- mization at field-practical scales.17,18 The primary application of BI is to evaluate the fracability for hy- draulic fracturing. However, the BI is often mixed up with the fracability in many fracturing applications, which has caused concerns about misleading the brittleness and ductility recognization of the targeting formation.19–21 Some researchers believe that the BI is more like a rock *Corresponding author. **Corresponding author. E-mail addresses: leihou.upc@gmail.com (L. Hou), yi.fang@sdsmt.edu (Y. Fang). Contents lists available at ScienceDirect International Journal of Rock Mechanics and Mining Sciences u{�~zkw! s{yo| kro>! ÐÐÐ1 ow�o�to~1m{y2 w{mk�o2tu~ yy�! https://doi.org/10.1016/j.ijrmms.2022.105207 Received 15 November 2021; Received in revised form 9 May 2022; Accepted 11 August 2022 International Journal of Rock Mechanics and Mining Sciences 159 (2022) 105207 2type indicator. The geological properties should also play an important role in the evaluation of fracability, for instance, the in-situ confining stress, pore pressure, natural fractures and faults.22–24 To distinguish fracability from BI, we propose that fracability should be an even broader concept that involves the injection parameters (pump rate, fluid and proppant properties) as well. Therefore, we redefine fracability as the fracturing pressure, a more comprehensive response of the cracked reservoir under certain geolog - ical, rock mechanical and hydraulic injecting conditions. Then, a ma- chine learning (ML) workflow is proposed for optimizing BIs by predicting the fracability/pressure based on field measurements. The prediction errors are analyzed to evaluate the contribution of each BI via a control variate method (controlling the interferences of geological, hydraulic and ML algorithm conditions). A new BI is derived by inte- grating the geological feature based on the optimization, variable analysis (optimizing variables according to their significance to the prediction) and backward elimination strategy (starting with all candi - dates and eliminating one at a time until minimizing the error), which significantly improves the predictions of fracability/pressure compared with classic BIs. Our optimization work clarifies the confusion between BI and fracability, promotes the calculation of BI and provides a more reliable option of BI for the recognition of targeting formation and design of fracturing schedule. It also demonstrates a promising appli - cation scene of BI based on the data-driven approach, which takes better advantage of BI than the traditional value comparisons. 2.Methodology The field measurements of hydraulic fracturing are collected and used as the Basic dataset for comparisons. By appending the brittleness index to the Basic dataset, the BI datasets are built for data processing. Three classic machine learning algorithms, Multiple Linear Regression (MLR), Support Vector Regression (SVR), and Artificial Neural Network (ANN) are used for data processing to mitigate the interference of al- gorithm performances on the predicted fracability. The mean absolute error (MAE) and root mean squared error (RMSE) are deployed for the prediction analyses and BI optimization. The backward elimination strategy and variable analysis are applied for the derivation of the new BI, as shown in Fig. 1. 2.1. Data preparation We collect 76 stages of shale gas fracturing and logging measure - ments (11,860 groups of data at minute level) in 7 wells (denoted as W1 to W7) from the Sichuan Basin (Longmaxi shale gas formation), China, as shown in Table 1. Each group of data involves parameters of fluid types (hydrochloric acid – HCL, slickwater, and gel), pump rate, prop- pant concentration, proppant mesh, and fracturing pressure. The log- ging interpretations for calculating BIs contain mineral components (Clay, Quartz, Carbonate and total organic carbon – TOC), Young ’s modulus, Poisson ratio, density, porosity, wave velocities and compressional slowness (DTC). The training and predicting stages are specially designed (Table 1). There are 68 stages from wells W1~W4 used for algorithm training. The first four predicting stages (Stage 3, 5, 7 and 9) are selected successively from the same wells (W1~W4), aiming to control the uncertainties from geological heterogeneity in the shale formation. As a result, the opti- mization of BI based on the prediction is more reliable by minimizing the interference of geological uncertainties. Four more predicting stages are selected from the first and second halves of the fracturing stages in two new wells, as shown in Table 1. W5 and W3 are neighbour wells. W6 is a distant well far from all others. W7 drills through different subdivided formations from all other wells. We choose representative stages from the first and second halves of a fracturing operation to restrict the po- tential influence of human factors on fracturing pressures because op- erators usually learn experiences from precedents and perform better in subsequent fracturing stages. The categorical data encoding and feature scaling are carried out during the data pre-processing. There are three fluid types and one special fluid condition (the pump off, denoted as N/A) in our dataset, which are string variables and can not be used for algorithm training directly. Therefore, the fluid type is encoded by the OneHotEncoder and transformed into a combination of three binary digits (i.e. 0, 0 and 1) after deleting the dummy variable.25 The fluid type used to be one column of strings is then transformed into three columns of binary code when they are fed into the algorithm. The proppant type is presented by its averaged diameter. All input variables are standardized by removing the mean and scaling to unit variance. The datasets, inputs and outputs are summarized in Table 2. The pump rate, fluid type, proppant con- centration, averaged proppant diameter and BI are used as inputs for the algorithm training, in which the hydraulic parameters are set as control variables. The machine learning algorithm is trained by the inputs to predict fracturing pressures. The predictions are then compared with field records for error analyses. Both the Basic and BI datasets contain all stages in Table 1. 2.2. Brittleness index for optimization Six representative BI calculations are selected from MBI, LBI and EBI categories for evaluations, as summarized in Table 3. BI1 and BI2, widely used for shale gas fracturing, are usually obtained by laboratory tests and reflect the mechanical properties of the rock. BI3 are empirical equations based on data from the shale gas wells in the Permian Basin (U.S.), which evaluates the BI based on the logging response of under - ground formations. The sum of the calculations is utilized for BI3. BI4 is the energy dissipation per unit area during the process of new fracture creation. The fracture toughness (KIC) represents the resistance of rock to fracture propagation. BI5 and BI6 are deformations and extensions of BI2. The correlations in Table 3 assess the brittleness from different as- pects (mineral components, rock mechanism, energy dissipation, log- ging interpretation, etc.) using various data sources (from both surface and subsurface). The calculation biases are inevitable because the brit- tleness is the synthetical result of multifactor. Therefore, the machine learning workflow is applied to evaluate the performances of BIs. Each BI is calculated by original data and fed into the algorithm as an input feature. Then, the prediction errors based on each correlation are Fig. 1.The structure for data processing and BI optimization. L. Hou et al. International Journal of Rock Mechanics and Mining Sciences 159 (2022) 105207 3analyzed and used as the criterion for BI optimization. 2.3. Machine learning algorithm and workflow Three different machine learning algorithms are deployed to restrict the potential interferences induced by the algorithm performances. The MLR is used for both pressure prediction and variable analysis. The SVR, with a radial basis function (RBF) kernel, is capable of both linear and non-linear regression.30,31 A three-layer ANN (input, hidden and output layers) is constructed under the Tensorflow frame with 20 neural units in the first and hidden layers referring to previous research.32,33 The dropout regularization (the rate of 0.2) is set after the first and hidden layers to avoid overfitting.34 The Adam routine is selected as the opti- mizer to compile the model, where a callback function is applied to return and automatically update the learning rate.35 Other hyper - parameters are optimized by the Grid search and K-fold cross- - validation,36,37 including the training epochs (30) and batch size (50). The detailed data processing workflow, integrating BI calculations and machine learning algorithms, is illustrated in Fig. 2. The original data is pre-processed by the calculations in Table 3 for BIs. Considering the division design in Tables 1 and 2, the geological and hydraulic ef- fects on fracturing pressure/fracability are restricted, thus boosting the Table 1 Division of training and predicting stages for data processing workflow. Well No. W1 W2 W3 W4 W5 W6 W7 For Training/Number of stages 14 17 17 20 / / / For Testing/Stage no. Stage 3 Stage 5 Stage 7 Stage 9 Stage 11 Stage 18 Stages 10 & 15 Notes / / / / Neighbour well Distant well Different formation Table 2 Summary of datasets, inputs and outputs for the data processing workflow. Inputs Outputs Error Analyses (Refer to Field Record) BI Optimization and Derivation Brittleness Hydraulic Parameters (Control Variates) Basic Dataset / Pump rate; fluid type; proppant concentration and mesh Pressure (Baseline) Baseline error / / BI Dataset Brittleness Index Pump rate; fluid type; proppant concentration and mesh Pressure (BI- based) BI-based error Error improvement New BI and verification Table 3 Summary of the BI correlations for evaluation. No. Correlation Category Original parameters collected for calculations