Model for Predicting Drilling Fluid Rheological Parameters in Wide Temperature and Pressure Range
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摘要: 钻井液流变参数的精准预测对于高温高压井水力参数及井筒压力精确计算、保证钻井安全具有重要意义。基于构建的钻井液流变性实验数据库，对不同钻井液体系大温压范围内九种流变模式进行了适用性评价，其中油基钻井液体系优选了赫巴流变模式（中低温低压）和四参数流变模式（高温高压），水基钻井液体系在大温压范围内优选了双曲流变模式。优选的流变模式是高温高压井井筒压力准确预测的基础。基于实验数据开发与多元非线性拟合，提出了一种新的适用于大温压范围下不同钻井液体系、不同流变模式的流变参数预测模型，并对某高温高压井井筒压力进行了计算验证。计算结果表明：以双曲模式流变参数模型为基础计算的井底压力误差为1.31%，可以满足深层、超深层高温高压井井筒压力精确计算要求。Abstract: Accurate prediction of drilling fluid rheological parameters is of great importance to the accurate computation of high temperature high pressure (HTHP) hydraulic parameters and borehole pressure, and to maintain the safety of drilling operation. Based on the database of drilling fluid rheological parameters obtained in laboratory experiments, nine flow models were evaluated for their adaptability to different drilling fluid systems in a wide temperature and pressure range. Among these models, the Herschel-Bulkley model (medium and low temperature, low pressure) and the four-parameter flow model were selected for evaluating their adaptability to oil based drilling fluids, the hyperbolic flow model was selected for evaluating its adaptability in a wide temperature and pressure range to water based drilling fluids. The selected flow models are the bases for accurately predicting the borehole pressures in HTHP wells. Based on the experiment data development and multivariate nonlinear fitting, a new model was established for predicting the rheological parameters of different drilling fluid systems with different flow models in a wide temperature and pressure range. This new model was then verified with borehole pressure data obtained from an HTHP well. The verification results show that the error existed for using the hyperbolic flow model as the basis to calculate the bottom hole pressure is 1.31%, indicating that the new model has satisfied the needs for accurate computation of borehole pressures in deep and ultra-deep HTHP wells.
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表 1 钻井液流变性的实验数据库
序号 数据源 时间 实验组数 T/ ℃ P/MPa 1 赵怀珍[18] 2009 5 90.00～240.00 100.00 2 Steve Young[19] 2012 24 4.44～65.56 10.34～51.71 3 Khaled J. Hassiba[20] 2012 8 20.00～232.22 0～241.39 4 Emanuel Stamatakis[21] 2013 10 65.56～315.56 0～275.79 5 Kumapayi Olamide[22] 2014 16 48.89～82.22 3.40 6 H. Fan[15] 2015 48 20.00～180.00 0～4.00 7 Kay A. Galindo[23] 2015 6 48.89～204.44 13.79 8 P K S Sairam[24] 2015 4 23.89～148.89 6.89～68.95 9 滕学清[14] 2015 30 20.00～180.00 1.00～8.00 10 许洁[25] 2015 13 60.00～200.00 6.00 11 马光曦[26] 2016 16 20.00～180.00 6.00～8.00 12 Erna Kakadjian[27] 2019 11 4.44～121.11 0.10～137.90 13 周号博[28] 2019 48 20.00～180.00 0～8.00 14 Vikrant Wagle[29] 2020 9 65.56～166.11 13.47～64.11 15 Ashok Santra[30] 2021 21 65.56～232.22 68.95 
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表 2 钻井液的流变模式分类
类别 流变模式 表达式 双参数 宾汉模式 $ \tau = {\tau _0} + {\mu _p}\gamma $ 幂律模式 $ \tau = K{\gamma ^n} $ 卡森模式 $ {\tau ^{1/2}} = \tau _c^{1/2} + \eta _\infty ^{1/2}{\gamma ^{1/2}} $ 三参数 赫巴模式 $ \tau = {\tau _0} + K{\gamma ^n} $ 罗斯模式 $ \tau = A{\left( {\gamma + C} \right)^B} $ Sisko模式 $ \tau = a\gamma + b{\gamma ^c} $ 双曲模式 $\tau = {\tau _0} + \dfrac{ {a\gamma } }{ {1 + b\gamma } }$ 林伯亨模式 $\tau = {\tau _s} + {\eta _P}\gamma {\left( {1 + \dfrac{\beta }{\gamma } } \right)^{1/2} }$ 四参数 四参数模式 $ \tau = {\tau _0} + a\gamma + b{\gamma ^c} $
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表 3 不同钻井液流变模式R2统计表
流变模式 油基钻井液R2范围/% 水基钻井液R2范围/% <0.95 0.95～
0.998>0.998 <0.95 0.95～
0.998>0.998 宾汉模式 3.14 64.55 32.31 17.65 57.84 24.51 幂律模式 16.40 64.55 9.53 26.47 65.69 7.84 卡森模式 1.59 59.79 38.62 13.73 72.55 13.72 赫巴模式 0.53 15.96 83.51 0 39.22 60.78 罗斯模式 1.59 42.33 56.08 0.98 47.06 52.94 Sisko模式 0.53 16.93 82.54 4.90 44.12 50.98 双曲模式 0.53 25.40 74.07 0 46.08 53.92 林伯亨模式 0.74 14.08 85.18 6.56 44.26 49.18 四参数模式 1.59 20.21 78.25 13.73 49.02 37.25
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表 4 钻井液流变模式的优选结果
钻井液类型 温压范围
（以150 ℃、69 MPa为界）流变模式优选结果 油基钻井液 中低温低压 赫巴模式 油基钻井液 高温高压 四参数模式 水基钻井液 大温压范围 双曲模式
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表 5 不同流变参数预测模型的决定系数R2对比
数据源 流变模式 钻井液类型 流变参数 本文模型 赵胜英 高禹 蒋官澄[33] 宾汉 水基 AV
PV0.999
0.9990.998
0.9990.999
0.998谢春林[34] 宾汉 油基 AV
PV
YP0.995
0.995
0.9750.994
0.992
0.9620.995
0.995
0.968Emanuel Stamatakis 宾汉 油基 AV
PV
YP0.978
0.975
0.9820.977
0.971
0.9810.973
0.965
0.982Ashok Santra 宾汉 油基 PV
YP0.985
0.9840.974
0.9680.975
0.974Erna Kakadjian 宾汉 油基 PV
YP0.992
0.9770.994
0.9650.991
0.978H. Fan 赫巴 油基 YP 0.981 0.942 0.957 稠度系数 0.923 0.952 0.979 流性指数 0.916 滕学清 赫巴 油基 YP 0.972 0.965 0.970 稠度系数 0.984 0.946 0.972 流性指数 0.935 Ashok Santra 四参数 油基 YP 0.977 0.9644 0.971 黏度系数 0.981 0.952 0.981 稠度系数 0.992 0.985 0.979 流性指数 0.948 Erna Kakadjian 四参数 油基 YP 0.985 0.983 0.983 黏性系数 0.995 0.997 0.991 稠度系数 0.985 0.963 0.972 流性指数 0.922 Emanuel Stamatakis 四参数 油基 YP 0.991 0.976 0.982 黏性指数 0.983 0.986 0.980 稠度系数 0.987 0.982 0.976 流性指数 0.956 Khaled J. Hassiba 双曲 水基 YP 0.986 0.969 0.982 稠度系数 0.939 0.921 0.921 剪切稀释系数 0.894 周号博 双曲 水基 YP 0.979 0.958 0.986 稠度系数 0.998 0.987 0.998 剪切稀释系数 0.931 许洁 双曲 水基 YP 0.979 0.984 0.979 稠度系数 0.979 0.984 0.979 剪切稀释系数 0.923
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