Abstract Hydraulic fracturing technology is widely used in the oil and gas industry. A part of the technology consists in injecting a mixture of proppant and fluid into the fracture. Proppant significantly increases the viscosity of the injected mixture and can cause plugging of the fracture. In this paper we propose a numerical model of hydraulic fracture propagation within the framework of the radial geometry taking into account the proppant transport and possible plugging. The finite difference method and the singularity subtraction technique near the fracture tip are used in the numerical model. Based on the simulation results it was found that depending on the parameters of the rock, fluid, and fluid injection rate, the plugging can be caused by two reasons. A parameter was introduced to separate these two cases. If this parameter is large enough, then the plugging occurs due to reaching the maximum possible concentration of proppant far from the fracture tip. If its value is small, then the plugging is caused by the proppant reaching a narrow part of the fracture near its tip. The numerical experiments give an estimate of the radius of the filled with proppant part of the fracture for various injection rates and leakages into the rock.

中文翻译：

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在径向水力压裂模型框架内模拟支撑剂输送和裂缝封堵

摘要 水力压裂技术在油气工业中应用广泛。该技术的一部分包括将支撑剂和流体的混合物注入裂缝中。支撑剂显着增加了注入混合物的粘度，并可能导致裂缝堵塞。在本文中，我们提出了在径向几何框架内考虑支撑剂输送和可能堵塞的水力压裂扩展数值模型。数值模型采用裂缝尖端附近的有限差分法和奇异减法技术。根据模拟结果发现，根据岩石、流体和流体注入速率的参数，堵塞可能由两个原因引起。引入了一个参数来分隔这两种情况。如果该参数足够大，则由于支撑剂在远离裂缝尖端的地方达到最大可能浓度而发生堵塞。如果它的值很小，那么堵塞是由支撑剂到达其尖端附近裂缝的狭窄部分引起的。数值实验给出了对于不同注入速率和岩石泄漏的裂缝的填充支撑剂部分的半径的估计。