The non-uniform temperature distribution in supercritical CO (Sc-CO) fracturing influences the density, viscosity, and volume expansion or shrinkage rate of Sc-CO, impacting proppant migration. This study presents a coupled computational fluid dynamics-discrete element method and heat transfer model to examine the effects of proppant bed shape and the heat transfers of proppant-wall, proppant-fluid, and fluid-wall on the fluid and proppant temperature fields. The Sc-CO volume expansion is assessed under various temperature conditions by evaluating the volume-averaged Sc-CO density. Several factors, including proppant size, shape, thermal conductivity, concentration, temperature difference, and injection velocity, are carefully analyzed to elucidate their impacts. The findings elucidate the existence of four distinct zones in the fluid temperature field. Each zone exhibits different magnitudes of temperature change under diverse conditions and undergoes dynamic transformations with the development of the proppant bed. The fluid-wall heat transfer and the fluid temperatures in Zones C and D are significantly subject to the fluid injection velocity (governing the heating duration), the temperature difference between fluid and formation (impacting the magnitude of heat flux), and the proppant bed shape (controlling the effective heating area). Additionally, the proppant-wall and proppant-fluid heat transfers determine the temperatures of both the proppant bed and the fluid within Zone B, showing a strong correlation with proppant thermal conductivity, proppant size, injection velocity, and temperature difference. The proposed coupled model provides valuable insights into the temperature distributions and flow behaviors of temperature-dependent fracturing fluids and proppants.

中文翻译：

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超临界CO2压裂支撑剂和流体相非均匀温度场的数值研究

超临界CO（Sc-CO）压裂中的不均匀温度分布会影响Sc-CO的密度、粘度和体积膨胀或收缩率，从而影响支撑剂运移。本研究提出了耦合计算流体动力学-离散元方法和传热模型，以研究支撑剂床形状以及支撑剂壁、支撑剂流体和流体壁的传热对流体和支撑剂温度场的影响。通过评估体积平均 Sc-CO 密度，可以在不同温度条件下评估 Sc-CO 体积膨胀。仔细分析了几个因素，包括支撑剂尺寸、形状、导热率、浓度、温差和注入速度，以阐明其影响。研究结果阐明了流体温度场中存在四个不同的区域。每个区域在不同条件下表现出不同程度的温度变化，并随着支撑剂床的发展而经历动态转变。 C 区和 D 区的流体壁传热和流体温度很大程度上受流体注入速度（控制加热持续时间）、流体与地层之间的温差（影响热通量大小）以及支撑剂床的影响。形状（控制有效加热面积）。此外，支撑剂壁和支撑剂流体传热决定了 B 区内支撑剂床和流体的温度，显示出与支撑剂导热率、支撑剂尺寸、注入速度和温差的强相关性。所提出的耦合模型为温度相关压裂液和支撑剂的温度分布和流动行为提供了有价值的见解。