水力压裂裂缝壁面上热流密度函数的推导

许多压裂的油气井都具有较高的地层温度 .为了获得最佳的压裂效果 ,在压裂设计计算时应该考虑裂缝中温度变化对压裂液流变特性和滤失速度等的影响 .因此 ,需要建立水力压裂裂缝中的温度场模型 ,用于计算施工过程中裂缝中压裂液的温度随时间和位置的变化 .根据热能平衡方程 ,建立起了滤失和非滤失裂缝缝面附近地层中温度的偏微分方程 ,然后借助于拉普拉斯变换和逆变换 ,获得了这两种情况下 ,裂缝壁面上的热流密度函数 .通过算例分析发现 ,裂缝壁面上的热流密度随注液时间的增加而减小 ;对于滤失性裂缝壁面 ,压裂液的综合滤失系数和地层的孔隙度越高 ,热流密度越低 .

Derivation of the Heat Flux Density Expressions on the Fracture Surface of Hydraulic Fracturing

Many oil and gas wells have high formation temperature. For obtaining optimum fracturing result, it is necessary to consider the effect of the temperature change along the fracture on the properties and fluid loss speed of fracturing liquid in fracturing design. For this reason, the temperature field mode inside the fracture is established for determining the temperature distribution of the fracturing fluid at any given moment. First, two partial differential equations is established for describing the temperature distribution in the fractured formation rock based on thermal energy equilibrum, one is suitable for permeable rock, and the other is for compacted rock. Then, the heat flux density expressions of the permeable and compacted fracture surfaces are obtained by the Laplace Transform of these two partial differential equations. The calculation and analysis of an example show that the heat flux density is decreased with the increase of fracturing time, to the permeable fracture surface, the greater the fluid loss coefficient of fracturing fluid and formation porosity, the lower the heat flux density at any given moment and position. The two heat flux density expressions can be used for establishing the temperature field model of three dimensional fracture.