融合物理约束与符号回归的宽温度—压力域钻井液剪切应力预测方法OA

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 ℃ 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 identi-fied,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 pro-posed: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%.