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Proppant is an important material for hydraulic fracturing that impacts the production and production cost of oil and gas wells. The key properties of proppant are crushing rate and fracture conductivity. The most common way to evaluate the key properties of proppant is physical testing, but this method is time-consuming and costly, and it may result in different results under the same experimental conditions. This paper presents a method for calculating proppant crushing rate and fracture conductivity, which are obtained by combining a series of simple and economical laboratory experiments with a significant amount of numerical calculations under various experimental conditions. First, the arrangement of proppant particles was simulated, and the location of particles was determined with the Monte Carlo method, the optimization model, and search algorithm in this process. Second, by mechanical analysis of proppant particles, a mathematical model of force was established, and the singular-value decomposition (SVD) method was used to calculate the force of each particle. Third, the crushing rate of proppant particles was calculated under irregular conditions using mathematical statistics. The Kozeny–Carman equation was improved on to establish a fracture conductivity model. Finally, the average fracture conductivity was calculated on the basis of the simulation results. The calculated fracture conductivity is consistent with the experimental results, which verifies the accuracy of the model.

The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.

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