Theoretical and experimental determination of proppant-crushing ratio and fracture conductivity with different particle sizes

Crushing ratio and fracture conductivity are two key indicators for proppant evaluation. The most common way to evaluate these two indicators is physical testing, but physical testing is costly and time-consuming, and the results are unstable. Therefore, a method for calculating proppant-crushing ratio and fracture conductivity is proposed to replace repetitive physical experiments. However, in past attempts, only mathematical models using the same particle size have been established, while the particle-size distribution in actual proppant arrangement is within a certain numerical range. Therefore, in order to establish a mathematical model more consistent with the actual situation of proppant arrangement, firstly, the Monte Carlo method was used to simulate proppant particles arranged with different particle sizes, and then a mathematical model was established describing the force of proppant particles. Secondly, according to the sparse, ill-conditioned, and asymmetric characteristics of the coefficient matrix, an improved singular value decomposition method is proposed to improve the accuracy and efficiency of calculation. Finally, the crushing ratio and fracture conductivity of proppant were calculated through the new model in this paper. It was found that the results calculated by the new model in this paper are closer to actual test results.