Crack initiation pressure prediction for SC-CO2 fracturing by integrated meta-heuristics and machine learning algorithms.

• A large number of supercritical carbon dioxide fracturing laboratory tests were carried out. • Three hybrid AI models were proposed for predicting the CIP of SCDF. • PSO was used to optimize the hyper-parameters of BPNN, ELM, and SVM. • The PSO-SVM intelligent model has better prediction ability for crack initiation pressure. The replacement of water by supercritical carbon dioxide in coal and rock mass fracturing has shown excellent development prospects. However, large-scale industrial implementation of supercritical carbon dioxide fracturing (SCDF) requires an accurate estimation of crack initiation pressure, while laboratory test methods are time-consuming and involve too complicated testing and sample preparation procedures. To better predict the SCDF crack initiation pressure, this study applied three hybrid artificial intelligence models, which alternatively combined the particle swarm optimization algorithm (PSO) with the BP neural network (BPNN), extreme learning machine (ELM), and support vector machine (SVM). Their prediction results were compared with each other and with those of the conventional linear multivariate regression analyses (L-MRA). Data samples for the prediction models' training were experimentally obtained via the SCDF indoor tests with various influencing factors, including vertical principal stress, horizontal maximum principal stress, horizontal minimum principal stress, fracturing fluid injection rate, fracturing fluid temperature, coal and rock mass tensile strength, coal and rock mass elastic modulus, and coal and rock mass Poisson's ratio. The models' output variable was the SCDF crack initiation pressure. The correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) were used to evaluate and compare the performance of the predictive models. Their prediction accuracy can be ranked in the decreasing order as PSO-SVM, PSO-ELM, PSO-BPNN, and L-MRA, with corresponding R values of 0.9339, 0.9135, 0.6971, and 0.6057, respectively. The PSO-SVM hybrid intelligent model was found to provide the most efficient SCDF crack initiation pressure prediction. The results obtained are quite instrumental in the promotion and application of SCDF technology. [ABSTRACT FROM AUTHOR]