摘要：

超深井钻井液在宽温度—压力域条件下的流变行为难以用单一流变模型表征。现有方法通常按温度区间选用不同流变模型并分别回归流变参数，导致流变参数在分段温度处出现不连续的跳变，影响井筒压力计算精度。针对上述问题，本文配置了油基和水基2种类型共4种密度的钻井液体系，在20~200 ℃、0.1~200 MPa范围内开展了195组温度—压力工况的流变实验，共获取1170个剪切应力数据点。归纳出剪切应力随温度、压力和剪切速率变化的4条基本规律，据此提炼出涵盖剪切稀释特性、温压单调性、温压与剪切速率耦合效应及温度与压力相对影响程度的7项物理约束条件。在此基础上，针对标准遗传编程—符号回归方法搜索空间大、缺乏物理约束、单一误差度量对低剪切速率区不敏感3方面不足，提出注入经典本构模型骨架种子、嵌入动态加权物理约束惩罚项和构建多分量损失函数3项改进。建立了以温度、压力和剪切速率为自变量的剪切应力预测公式。该公式由屈服应力项、黏性流动项和温压耦合项3部分组成，搜索数据集和独立验证集的决定系数分别为0.9933和0.9948，平均相对误差分别为6.51%和6.21%，7项物理约束综合满足率达99.28%。采用固定公式结构、重拟合系数的迁移策略在另外5种不同类型和密度的钻井液体系上验证，各体系验证集平均相对误差为7.81%~9.70%，跨体系变异系数为0.069。将该公式应用于井筒压力计算流程，2口超深井验证表明，平均绝对误差由分段流变模式法的0.56~2.06 MPa降至0.19~1.27 MPa，降幅38%~66%，并将分段温度处的单位摩阻突变由约38%降至不足0.1%。

关键词: 超深井, 钻井液流变性, 符号回归, 物理约束, 剪切应力预测, 跨体系迁移, 井筒压力计算

Abstract:

The rheological behavior of drilling fluids in ultra-deep wells under wide temperature-pressure conditions is difficult to characterize with a single rheological model. Existing methods typically select different rheological models for different temperature intervals and regress rheological parameters separately, resulting in discontinuous jumps in rheological parameters at segmentation temperatures and compromising the accuracy of wellbore pressure calculations. To address this issue, four drilling fluid systems of oil-based and water-based with two density levels were prepared, and rheological experiments were conducted under 195 temperature-pressure conditions spanning 20~200 °C and 0.1~200 MPa, yielding a total of 1170 shear stress data points. Four fundamental patterns governing the variation of shear stress with temperature, pressure, and shear rate were identified, from which seven physical constraint conditions were distilled, covering shear-thinning characteristics, temperature-pressure monotonicity, and coupling effects between temperature-pressure and shear rate, and the relative magnitude of temperature versus pressure effects. To overcome three shortcomings of standard genetic programming-symbolic regression-a vast search space, a lack of physical constraints, and insensitivity of a single error metric to the low-shear-rate region-three improvements are proposed: Injecting classical constitutive models as skeletal seeds into the initial population, embedding seven physical constraints as dynamically weighted penalty terms in the fitness function, and constructing a multi-component loss function. A shear stress prediction formula with temperature, pressure, and shear rate as independent variables was thereby established. The formula comprises three components-a yield stress term, a viscous flow term, and a temperature-pressure coupling term-with coefficients of determination of 0.9933 and 0.9948 for the training dataset and independent validation set, respectively, mean relative errors of 6.51% and 6.21%, and an overall satisfaction rate of the seven physical constraints of 99.28%. A transfer strategy of fixing the formula structure and refitting only the coefficients was validated on five additional drilling fluid systems of different types and densities; the mean relative error for each system ranged from 7.81%~9.70%, with a cross-system coefficient of variation of 0.069. The formula was applied to the wellbore pressure calculation workflow and validated on two ultra-deep wells; the mean absolute error was reduced from 0.56~2.06 MPa with the piecewise rheological model method to 0.19~1.27 MPa, a reduction of 38%~66%, while the abrupt change in unit frictional pressure drop at segmentation temperature was reduced from approximately 38% to less than 0.1%.

Key words: ultra-deep well, drilling fluid rheology, symbolic regression, physical constraints, shear stress prediction, cross-system transfer, wellbore pressure calculation

中图分类号: 

• TE242

• TE22