An efficient method for predicting the morphology of proppant packs based on a surrogate model

In the volume fracturing of unconventional oil and gas reservoirs, many proppant particles are injected underground along with the fracturing fluid, and their placement patterns determine the propping effect and conductivity of fractures. Accurate prediction of the in-fracture proppant placement patterns can help optimize the fracturing design and improve fracturing efficiency. Currently, experimental and numerical methods are the main approaches for reproducing the proppant accumulation process and placement patterns in fractures. These methods are still confined by limited simulation scales, time-consuming computations, and high-cost operations. In this paper, the two-fluid method was employed for numerical simulations, with a primary focus on the effects of drag, virtual mass, and lift forces on the momentum exchange between phases. The numerical simulations were conducted on the Fluent platform, and the simulation results were validated against experimental data to ensure reliability and accuracy. The numerical simulation results of proppant transport would be adopted as data sets for input, training, and testing. To characterize the intricate accumulation and packing dynamics of proppants, we distilled key parameters, specifically the concentration distribution and accumulation height profiles. Through correlation analysis, the primary factors influencing these characteristic parameters were identified. Intelligent proxy models for the prediction of proppant placement patterns were established on the basis of the cascade neural network, including a time-concentration model for predicting particle volume fraction and a displacement-height model for predicting particle placement height. The former model enabled predictions of the distribution of proppant concentrations within the fracture at different times, whereas the latter allowed estimation of how the stacking heights of proppants varied with the injection rate. Furthermore, the grid precisions of the prediction models were optimized to enhance their accuracy and performance. The data were allocated to the training, validation, and testing phases of the surrogate model at a ratio of 6∶2∶2, respectively. Specifically, 60% of the data was used for training the models, 20% was used for validation to fine-tune the models’ parameters, and another 20% was used for testing to evaluate the models’ performance on unseen data. The results showed that the predictions of proppant placement patterns were highly consistent with the numerical simulation results. For the time-concentration model, the prediction results were closely aligned with the numerical simulation outcomes, successfully capturing the characteristics of a constant placement height and a progressive increase in placement length after reaching the equilibrium height. For the displacement-height model, although the predicted placement profile lacked detailed irregularities of the proppant accumulation surface because of model simplification, it accurately described the characteristic variation in placement morphology with changes in injection rate, demonstrating that the surrogate model for predicting particle placement height can also efficiently capture the proppant placement morphology within the fracture. Additionally, the time consumed by a single prediction step was only 0.14% of the time consumed by a single simulation step. The model and approach proposed in this study accelerated the speed of proppant transport simulation and greatly shortened the prediction time of the proppant placement patterns, which could be widely applied in fracturing in the field after further improvement.