Numerical Simulation on Influence Parameters of Horizontal Well Hydraulic Fracturing
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摘要: 水力压裂是低渗油气藏的主要开发手段，传统数值模型所得到的基质-裂缝窜流量以及断裂参数精度不足.为此以流固耦合理论与断裂力学相结合的压裂模型为基础，模拟了水力裂缝扩展过程.在模型中分别引入离散裂缝模型和广义J积分计算基质-裂缝流量交换和断裂参数，并采用动态网格技术对裂缝尖端进行局部加密，以提高模拟的效率和精度.模型计算结果显示，影响水力压裂过程的主要参数中：基质渗透率和压裂液粘度主要影响水力裂缝的最终形态；岩石弹性模量影响裂缝宽度.对压裂车而言，最高工作压力一般都能够满足压裂增产需求，其最大输出功率和最大输出流量是限制压裂能力的主要因素.Abstract: Hydraulic fracturing is the main development method of low permeability reservoir, so it is important to the engineering to address the issue. By combining the fluid-structure interaction theory with fracture mechanics, the propagation of hydraulic fracture is simulated in this paper. Discrete fracture model and generalized J integral are introduced in the proposed model to calculate the flux across the fracture-matrix interface and fracture parameters, respectively. To ensure high precision and efficient simulation, the adaptive mesh refinement technology is introduced in the grids near the crack tip. The results show that the matrix permeability and viscosity of fracturing fluid mainly influence the final shape of hydraulic fracture, while the elastic modulus of rock mainly influence the fracture width. For fracture trucks, the maximum working pressure can generally meet the demand for fracturing production, and the maximum output power and maximum output flow are the main factors limiting the fracturing capacity.
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图 3 本文模型与无穷大空间中径向裂缝理论解对比
Fig. 3. The comparison of the proposed model and radial fracture analytic solution
图 4 基质渗透率对压裂设备工作参数的影响
Fig. 4. Influence of permeability on fracturing equipment working parameters
图 7 岩石弹性模量对压裂设备工作参数的影响
Fig. 7. Influence of elasticity modulus on fracturing equipment working parameters
图 8 压裂液粘度对压裂设备工作参数的影响
Fig. 8. Influence of fracturing fluid viscosity on fracturing equipment working parameters
图 10 压裂参数随裂缝半长的变化关系
Fig. 10. Relationship between equipment parameters and half-length of fracture
表 1 算例2.1参数取值
Table 1. Parameters of example 2.1
物性参数 取值 流体密度(kg/m3) 982.600 流体粘度(mPa·s) 0.456 井半径(m) 0.070 泊松比 0.220 断裂韧度(MPa·m1/2) 2.000 注入流量(m3/min) 0.500 弹性模量(GPa) 35.000 
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表 2 2.2节中算例参数取值
Table 2. Parameters in section 2.2
物性参数 取值 基质渗透率(mD) 2.000 流固耦合系数 0.890 流体粘度(mPa·s) 0.456 流体密度(kg/m3) 986.200 弹性模量(GPa) 35.000 泊松比 0.220 断裂韧度(MPa·m1/2) 2.000
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表 3 在不同渗透率下压裂设备工作参数达到上限时的裂缝尺寸
Table 3. Sizes of fracture for different permeability under rated working conditions
渗透率
(mD)压力达到上限 流量达到上限 功率达到上限 缝长(m) 最大缝宽(cm) 缝长(m) 最大缝宽(cm) 缝长(m) 最大缝宽(cm) 1.5 - - - - - - 2.0 - - 91.783 0.222 3 77.851 0.183 3 2.5 95.318 0.233 9 71.749 0.169 0 60.878 0.142 7 3.0 77.450 0.185 9 59.063 0.140 4 49.833 0.121 3 注：表中“-”表示在本文计算的裂缝长度范围内，压力、流量或者功率未达到压裂设备参数的上限.
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表 4 在不同弹性模量下压裂设备工作参数达到上限时的裂缝尺寸
Table 4. Sizes of fractures for different elasticity modulus under rated working conditions
弹性模量
(GPa)压力达到上限值 流量达到上限值 功率达到上限值 缝长(m) 最大缝宽(cm) 缝长(m) 最大缝宽(cm) 缝长(m) 最大缝宽(cm) 20 - - 92.776 0.383 1 78.161 0.310 8 25 - - 92.776 0.308 2 78.161 0.250 8 30 - - 92.776 0.258 8 78.161 0.221 6 35 - - 92.776 0.224 5 76.161 0.184 1 40 - - 92.776 0.199 8 78.161 0.164 2 注：表中“-”表示在本文计算的裂缝长度范围内，压力、流量或者功率未达到压裂设备参数的上限.
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表 5 在不同粘度下压裂设备工作参数达到上限时的裂缝尺寸
Table 5. Sizes of fracture for different fracturing fluid viscosity under rated working conditions
压裂液粘度
(mPa·s)压力达到上限值 流量达到上限值 功率达到上限值 缝长(m) 最大缝宽(cm) 缝长(m) 最大缝宽(cm) 缝长(m) 最大缝宽(cm) 0.356 94.841 0.231 2 70.151 0.162 9 60.134 0.138 6 0.406 - - 81.564 0.193 5 68.963 0.159 9 0.456 - - 92.366 0.223 7 77.834 0.183 1 0.506 - - - - 87.258 0.209 3 0.556 - - - - 96.597 0.235 3 注：表中“-”表示在本文计算的裂缝长度范围内，压力、流量或者功率未达到压裂设备参数的上限.
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表 6 压裂车主要参数
Table 6. Working parameters for fracturing equipment
产品型号 三一重工SYN5450TYL1860(Y) 杰瑞能源YLC140-1860 山东科瑞KTYL2500-105 设备编号 1 2 3 最大工作压力(MPa) 125 140 105 最大输出流量(m3/min) 1.90 2.17 2.46 最大输出功率(kW) 1 860 1 860 1 836 注：参数来源于三一重工、杰瑞能源和山东科瑞官网.
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