Gas-water flow in propped fractures can be commonly observed in various practical applications, including hydrocarbon development, geothermal exploitation, contaminant transport, and geological carbon storage. The fluid flow in a propped fracture can be regarded as Darcy type if only the resistance from the propping materials (e.g., cement in natural fractures and proppant-pack in hydraulic fractures) accounts. However, if the fracture width is sufficiently small, the extra resistance from the viscous shear of fracture walls cannot be neglected, resulting in the appearance of Brinkman flow. In practice, during the development of a naturally fractured aquifer or a hydraulicly fractured hydrocarbon reservoir, the fracture width will be significantly reduced as the production proceeds. Therefore, the Brinkman flow can impose a strong effect on the fluid transportation within the fractures. However, the existing study about the two-phase Brinkman flow in propped fractures is still far from adequate. In this work, on the basis of a modified two-phase Brinkman equation, the authors derive a novel analytical formulation to correct the relative permeability of gas-water two-phase flow in propped fractures to account for the Brinkman effect. With the aid of the proposed formulation, the authors carry out a comprehensive investigation of the influence of Brinkman flow on the effective gas-water relative permeability and well performance. The calculated results show that the effect of Brinkman flow on the water phase (or gas phase) transportation is more significant with a larger water (or gas) saturation. A narrower propped fracture is more likely to induce Brinkman flow, thus leading to a lower relative permeability for both water and gas phases. As the propping-material permeability is increased, the fluid transportation bears more severe viscous drag from fracture walls, and the relative permeability will be consequently reduced. Only if the fracture width is significantly reduced during the production, the Brinkman flow demonstrates its influence on the well performance. Otherwise, Darcy's law can provide sufficiently accurate results in characterizing the two-phase flow in propped fractures.

中文翻译：

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考虑 Brinkman 流影响的修正支撑裂缝中气-水流相对渗透率的解析公式


支撑裂缝中的气水流动可以在各种实际应用中常见，包括碳氢化合物开发、地热开采、污染物运输和地质碳储存。如果仅考虑支撑材料（例如，天然裂缝中的水泥和水力裂缝中的支撑剂包）的阻力，则可以将支撑裂缝中的流体流动视为达西型。然而，如果裂缝宽度足够小，则不能忽视裂缝壁粘性剪切带来的额外阻力，从而导致 Brinkman 流的出现。在实践中，在自然裂缝含水层或水力裂缝碳氢化合物储层的开发过程中，随着生产的进行，裂缝宽度将显著减小。因此，Brinkman 流会对裂缝内的流体传输产生很大影响。然而，关于支撑裂缝中两相 Brinkman 流的现有研究仍远未充分。在这项工作中，基于改进的两相 Brinkman 方程，作者推导出了一种新的解析公式来校正支撑裂缝中气-水两相流的相对渗透率，以解释 Brinkman 效应。在所提出的公式的帮助下，作者对 Brinkman 流对有效气-水相对渗透率和井性能的影响进行了全面研究。计算结果表明，当水（或气）饱和度较大时，Brinkman 流对水相（或气相）传输的影响更显著。较窄的支撑裂缝更有可能诱发 Brinkman 流，从而导致水相和气相的相对渗透率较低。 随着支撑材料渗透率的增加，流体输送承受来自裂隙壁的更严重的粘性阻力，相对渗透率将因此降低。只有在生产过程中裂缝宽度显著减小时，Brinkman 流才会显示出其对油井性能的影响。否则，达西定律可以在描述支撑裂缝中的两相流方面提供足够准确的结果。