﻿ 起下钻过程中井筒稳态波动压力计算方法

Improved Calculation of Wellbore Steady Fluctuation Pressure in Tripping Operations
PENG Qi, FAN Honghai, LIU Jin'ge, HAN Fuxin, FU Suiyi
MOE Key Laboratory of Petroleum Engineering(China University of Petroleum(Beijing)), Beijing, 102249, China
Abstract: To eliminate the possibility of kicks, lost circulation and other complicated situations during tripping operations, it is necessary to enhance the accuracy of calculation for the wellbore fluctuation pressure. Based on the slot flow model and considering the actual velocity distribution in the wellbore, fluctuation pressure at laminar flows and turbulence flows was investigated in accordance with the continuity of wellbore fluids and corresponding boundary conditions. Eventually, steady fluctuation pressure calculation methods were established and numerical solutions were also introduced. Field production data were used to verify these models. When the velocity of the drilling string was increased from 0.2 m/s to 0.6 m/s, fluctuation pressures increased from 0.21 MPa to 0.27 MPa. Under stable drilling strings velocity and fluid rheology, fluctuation pressure of the wellbore increased from 0.3MPa to 0.5 MPa when ID/OD ratio increased from 0.55 to 0.9. Through comparison with experiment data in published literatures, calculation errors from the Burkhardt model was over 8%, while the calculation error from the new model was less than 5%. The new model met pressures accuracy requirements in drilling operations. Research results show that the high-precision steady fluctuation pressure calculation method could be used for accurate analysis of wellbore pressures during non-drilling operations and might provide necessary guidance for secure operation onsite.
Key words: fluctuation pressure     slot flow model     tripping     pressure-controlled drilling

1 环空中波动压力计算模型

 图 1钻柱运动引起井筒流场示意 Fig.1Schematic drawing for wellbore flows induced by movements of drilling strings

1.1 第一速度剪切区

 (1)

 (2)

1.2 第二速度剪切区

l2lH时，称为Ⅲ区域，随着半径增大，流体所受切应力逐渐增大，此时有：

 (3)

 (4)

1.3 流核区域

l1≤l＜l2时，为Ⅱ区域，该部分为流核区域，流体流速均相等，即。根据流体受力平衡，Δps(l2-l1)W=2τ0WL，可得：

 (5)

 (6)
 (7)

c=l2-l1，则由(5)可变为：

 (8)

 (9)

 (10)
1.4 环空总流量

 (11)

 (12)
2 钻柱内波动压力计算模型

 (13)

 (14)
 (15)
 (16)
 (17)

 (18)
3 模型的求解

 (19)
 (20)

 (21)

 (22)

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 (24)
 (25)

 图 2波动压力计算流程 Fig.2Flow chart for calculation of fluctuation pressures
4 实例计算

 图 3波动压力与钻柱运动速度的关系曲线 Fig.3Correlation between fluctuation pressure and the velocity of drilling string
 图 4井筒各区域流量与钻柱运动速度的关系曲线 Fig.4Correlation between flow rates and velocities of drilling strings in various parts of the wellbore

vp=0.4 m/s、其他参数不变的情况下，井筒中各区域的流量随环空内外径之比Φ(Φ=Dpo/Dh)的变化关系如图 5所示。

 图 5井筒各流动区域流量与环空内外径之比的关系曲线 Fig.5Correlation between flow rates and the ID/OD ratios of annular spaces in various parts of the wellbore

 图 6不同流速下波动压力与环空内外径的关系曲线 Fig.6Correlation between fluctuation pressures and the ID/OD ratios of annular spaces under various flow rates

 图 7井筒波动压力与钻柱运动速度的关系 Fig.7Correlation between fluctuation pressure and the velocity of drilling strings

 图 8波动压力计算值与文献测量值的对比曲线 Fig.8Comparison of calculated values of fluctuation pressure with measured values specified in relevant references
 图 9波动压力计算误差分析 Fig.9Errors in the calculation of fluctuation pressures
5 结论

1) 以槽流模型为基础，根据起下钻过程中井筒的真实流动情况，采用通用流量计算方法，建立了稳态波动压力计算模型，并采用数值解法求解，提高了模型计算结果的精度。

2) 与前人波动压力的计算方法相比，新模型在计算井筒流量的过程中未作简化处理，井筒流体流动规律更加符合真实情况；由于采用迭代求解的数值解法，导致新模型的求解过程相对复杂。

3) 井筒波动压力随着钻柱运动速度的增加而增加，随钻柱运动速度增加环空近管壁处剪切区的厚度增加，而流核区厚度减小。此外，在其他条件不变时，随着环空内外径之比增大，井筒波动压力也逐渐增大。

4) 采用文献数据对提出的波动压力计算模型进行了验证，结果表明：波动压力计算新模型的计算结果与实测值具有较高的吻合度，研究结果对于后续波动压力的研究具有一定的指导作用。

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#### 文章信息

PENG Qi, FAN Honghai, LIU Jin'ge, HAN Fuxin, FU Suiyi

Improved Calculation of Wellbore Steady Fluctuation Pressure in Tripping Operations

Petroleum Drilling Techniques, 2016, 44(04): 35-40.
http://dx.doi.org/10.11911/syztjs.201604007