WO2022011700A1 - 一种井眼轨迹自适应测斜计算方法 - Google Patents

一种井眼轨迹自适应测斜计算方法 Download PDF

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WO2022011700A1
WO2022011700A1 PCT/CN2020/102782 CN2020102782W WO2022011700A1 WO 2022011700 A1 WO2022011700 A1 WO 2022011700A1 CN 2020102782 W CN2020102782 W CN 2020102782W WO 2022011700 A1 WO2022011700 A1 WO 2022011700A1
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measurement
measuring
section
point
angle
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PCT/CN2020/102782
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English (en)
French (fr)
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黄根炉
于凡
李伟
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中国石油大学(华东)
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Priority to US17/522,791 priority Critical patent/US11319796B2/en
Publication of WO2022011700A1 publication Critical patent/WO2022011700A1/zh

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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells
    • E21B47/02—Determining slope or direction
    • E21B47/022—Determining slope or direction of the borehole, e.g. using geomagnetism
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/25—Methods for stimulating production
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/30—Specific pattern of wells, e.g. optimising the spacing of wells
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

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  • the invention relates to the technical field of oil and gas drilling, in particular to a wellbore trajectory adaptive inclination measurement calculation method.
  • the inclination calculation of the wellbore trajectory in oil drilling usually needs to assume the curve type of the measurement section between the two measurement points, and then determine the coordinate increment of the measurement section according to the characteristics of the curve and the wellbore direction constraints at both ends, so as to determine The coordinates of each measuring point on the borehole trajectory.
  • the latest inclination calculation method takes the inclination and azimuth of each measuring point obtained by actual measurement as sample points, and adopts cubic spline interpolation to obtain the cubic spline interpolation function of inclination and azimuth of each measurement section.
  • the wellbore trajectory is obtained by numerical integration.
  • this processing method reduces the calculation error of the wellbore trajectory to a certain extent, but the cubic spline interpolation requires the interpolation function to have continuous second derivative at the sample point (measurement point), and the actual drilling may be due to the drilling tool combination. , formation, drilling method (slip drilling or rotary drilling), drilling parameters, etc.
  • the method is also very sensitive to the error of the sample point, and the shorter the length of the measurement segment, the higher the sensitivity, and even unreasonable oscillation will occur.
  • the invention provides a wellbore trajectory adaptive inclination measurement calculation method, aiming at solving the problem of poor inclination calculation accuracy in the prior art.
  • parameters identify the curve characteristics of the calculated measurement section, and select the appropriate curve to calculate the coordinate increment of the measurement section, which can adaptively match the curve characteristic parameters that are closer to the shape of the wellbore trajectory of the measurement section to be calculated, and can significantly improve the wellbore trajectory The accuracy of the inclinometer calculation.
  • the present invention provides a wellbore trajectory adaptive inclination measurement calculation method comprising:
  • the conventional inclination calculation method is used to calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the first measurement section;
  • the conventional inclination calculation method is used to calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the last measurement section;
  • the vertical depth, N coordinate, E coordinate, horizontal projection length, horizontal displacement, translation azimuth and apparent translation in the wellbore trajectory parameters of each measuring point are calculated according to the coordinate increment of the lower measuring point relative to the upper measuring point in all measuring sections.
  • the coordinate increment includes vertical depth increment, horizontal projection length increment, N coordinate increment and E coordinate increment.
  • calculating the coordinate increment of the lower measurement point relative to the upper measurement point in the second measurement section according to the first measurement section, the second measurement section and the third measurement section specifically includes:
  • inclination angle and azimuth angle of the three measuring points corresponding to the first and second measuring sections calculate the predicted values of borehole curvature, torsion and tool face angle of the measuring points on the second measuring section;
  • inclination angle and azimuth angle of the three measuring points corresponding to the second and third measuring sections calculate the predicted values of borehole curvature, torsion and tool face angle of the measuring points under the second measuring section;
  • the average change rate of the borehole curvature and torsion between the upper and lower measuring points of the second measuring section is the reference value, and the upper and lower fluctuations of the reference value are 5% to determine the borehole curvature change rate,
  • the coordinate increase of the lower measurement point in the second measurement section relative to the upper measurement point is calculated. quantity.
  • the calculation of the coordinate increment of the lower measurement point relative to the upper measurement point in the first measurement section by using a conventional inclination measurement calculation method specifically includes:
  • ⁇ D 01 is the increment of the vertical depth of the first measurement section
  • ⁇ L p01 is the increment of the horizontal projection length of the first measurement section
  • ⁇ N 01 is the increment of the N coordinate of the first measurement section
  • ⁇ E 01 is the increment of the E coordinate of the first measurement section Increment
  • R 01 is the curvature radius of the arc of the first measuring segment.
  • calculating the coordinate increment of the lower measurement point relative to the upper measurement point of the last measurement section by using a conventional inclination measurement calculation method specifically includes:
  • the formula Calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the first measurement section, where L m is the well depth of the mth measurement point, L m-1 is the well depth of the m-1th measurement point, and ⁇ D (m-1)m is the well depth of the mth measurement point.
  • the increment of the vertical depth of the m measurement section ⁇ L p(m-1)m is the increment of the horizontal projection length of the mth measurement section, ⁇ N (m-1)m is the increment of the N coordinate of the mth measurement section, ⁇ E (m-1 )m is the increment of the E coordinate of the mth measurement section;
  • the formula Calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the mth measurement section, where ⁇ D (m-1)m is the vertical depth increment of the mth measurement section, and ⁇ L p(m-1)m is the horizontal projection of the mth measurement section
  • ⁇ N (m-1)m is the increment of the N coordinate of the mth measurement section
  • ⁇ E (m-1)m is the increment of the E coordinate of the mth measurement section
  • R (m-1)m is the increment of the E coordinate of the mth measurement section
  • the radius of curvature of the arc of the m measurement segment The radius of curvature of the arc of the m measurement segment.
  • the calculation of the estimated borehole curvature, the average rate of change of torsion and the tool face angle increment between the upper measurement point and the lower measurement point of the i-th measurement section is specifically:
  • the beneficial effect of the present invention is: firstly, according to the inclination measurement data of the 0th measuring point and the 1st measuring point of the borehole trajectory, according to the currently commonly used inclination calculation method (minimum curvature method or curvature radius method) ) to calculate the coordinate increment of the first measuring section; then assuming that the curvature and torsion of the second measuring section to the penultimate second measuring section are both linear changes, first the 0th measuring point, the first measuring point Calculate the curvature, torsion and tool face angle at the first measuring point with the inclination data of the second measuring point, and determine the second measuring section with the inclination angle and azimuth angle at the second measuring point as constraints
  • the rate of change of curvature and torsion on this basis, numerical integration to obtain the coordinate increment of the second measurement section, and so on, until the coordinate increment of the penultimate second measurement section is calculated;
  • the oblique calculation method calculates the coordinate increment of the last measurement section; finally, the
  • FIG. 1 is a schematic flowchart of a wellbore trajectory adaptive inclination calculation method according to an embodiment of the present invention.
  • an embodiment of the present invention provides a wellbore trajectory adaptive inclination calculation method
  • Step 110 Receive and process the inclination measurement data, and number the measurement points and measurement sections according to the inclination measurement data.
  • the first measuring point whose well deviation is not 0 is the first measuring point, and then the number of the measuring points increases successively until the last measuring point; the well depth above the first measuring point is 25m smaller than the well depth of the first measuring point It is the 0th measuring point. If the well depth of the first measuring point is less than 25m, the 0th measuring point is the wellhead. And the measurement segment between the 0th measurement point and the 1st measurement point is the 1st measurement segment, and so on, the measurement segment between the i-1th measurement point and the i-th measurement point is the i-th measurement point Measurement segment, where i is a positive integer greater than or equal to 1.
  • the first measuring point whose well deviation is not 0 is the first measuring point, followed by the second measuring point, the third measuring point..., until the last measuring point is the mth measuring point; the first measuring point
  • the well depth above the measuring point is 25m smaller than the well depth of the first measuring point is the 0th measuring point. If the well depth of the first measuring point is less than 25m, the 0th measuring point is the wellhead, namely
  • L 0 is the well depth at the 0th measurement point, m
  • L 1 is the well depth at the 1st measurement point, m.
  • ⁇ 0 is the inclination angle of the 0th measuring point, °; is the azimuth angle of the 0th measuring point, °; D 0 is the vertical depth of the 0th measuring point, m; L p0 is the horizontal projection length of the 0th measuring point, m; N 0 is the N coordinate of the 0th measuring point, m; E 0 is The E coordinate of the 0th measuring point, m; S 0 is the closing distance of the 0th measuring point, m; ⁇ 0 is the closed azimuth of the 0th measuring point, °.
  • the measurement segment between the i-1th measurement point and the i-th measurement point is the i-th measurement segment, and i can vary from 1 to m.
  • Step 120 Calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the first measurement section by using the conventional inclination measurement calculation method.
  • the coordinate increments include vertical depth increments, horizontal projection length increments, N coordinate increments, and E coordinate increments.
  • L 0 is the well depth at the 0th measurement point, m
  • L 1 is the well depth at the first measurement point, m
  • ⁇ D 01 is the increment of the vertical depth of the first measurement section, m
  • ⁇ L p01 is the increment of the horizontal projection length of the first measurement section , m
  • ⁇ N 01 is the increment of the N coordinate of the first measurement section, m
  • ⁇ E 01 is the increment of the E coordinate of the first measurement section, m;
  • ⁇ D 01 is the increment of the vertical depth of the first measuring section, m
  • ⁇ L p01 is the increment of the horizontal projection length of the first measuring section, m
  • ⁇ N 01 is the increment of the N coordinate of the first measuring section, m
  • ⁇ E 01 is the 1
  • R 01 is the curvature radius of the arc of the first measuring section, m.
  • R 01 (L 1 -L 0 )/ ⁇ 01 (5)
  • Step 130 Calculate the coordinate increment of the lower measurement point in the second measurement section relative to the upper measurement point according to the first measurement section, the second measurement section and the third measurement section, and calculate the relative upper measurement point of the lower measurement point in other measurement sections by analogy.
  • the coordinate increment of the point is calculated until the coordinate increment of the lower measurement point relative to the upper measurement point of the penultimate section is calculated.
  • step 130 includes the following sub-steps:
  • ⁇ 1 is the inclination angle of the first measuring point
  • k 1e is the estimated value of the borehole curvature at the first measuring point
  • k ⁇ 1 is the first measuring point.
  • the rate of change of inclination at one measuring point is the azimuth change rate at the first measuring point
  • ⁇ 1e is the estimated value of the torsion rate of the wellbore at the first measuring point
  • ⁇ 1e is the estimated value of the tool face angle at the first measuring point, is the azimuth angle increment of the first survey section, is the azimuth angle increment of the second survey section
  • ⁇ 1 is the well inclination angle of the first survey point
  • ⁇ 0 is the well inclination angle of the 0th survey point
  • ⁇ 2 is the well inclination angle of the second survey point
  • ⁇ 01 is the well inclination angle of the second survey point.
  • ⁇ 12 is the dogleg angle of the second measurement segment.
  • the process of calculating the estimated borehole curvature, the average rate of change of torsion, and the tool face angle increment between the upper and lower measurement points of the second survey section is as follows:
  • a k12 is the average rate of change of borehole curvature in the second logging interval, °/m2;
  • a ⁇ 12 is the average rate of change of borehole tortuosity in the second logging interval, °/m2;
  • ⁇ 12 is the tool in the second logging interval Increment of face angle, °; other parameters are the same as before.
  • the corresponding predicted value of the measuring section fluctuates above and below the reference value. 10% of the range is used as the upper and lower limits, that is, there are
  • k 1max k 1e +A k12 ⁇ (L 2 -L 1 ) ⁇ 10% (36)
  • ⁇ 1max ⁇ 1e +A ⁇ 12 ⁇ (L 2 -L 1 ) ⁇ 10% (38)
  • ⁇ 1min ⁇ 1e -A ⁇ 12 ⁇ (L 2 -L 1 ) ⁇ 10% (39)
  • ⁇ 1max ⁇ 1e + ⁇ 12 ⁇ 10% (40)
  • ⁇ 1min ⁇ 1e - ⁇ 12 ⁇ 10% (41)
  • k 1max is the upper limit of the borehole curvature search interval at the first measuring point, °/m
  • k 1min is the lower limit of the borehole curvature search interval at the first measuring point, °/m
  • ⁇ 1max is the first measuring point
  • ⁇ 1min is the lower limit of the search interval for wellbore torsion at the first measurement point, °/m
  • ⁇ 1max is the upper limit of the search interval for the tool face angle at the first measurement point
  • ⁇ 1min is the lower limit of the tool face angle search interval at the first measuring point, °
  • other parameters are the same as before.
  • the average change rate of borehole curvature and torsion between the upper and lower measuring points of the second measuring section is the reference value, and the upper and lower fluctuations of the reference value are 5% to determine the borehole curvature of the second measuring section
  • the value range of the change rate and torsion rate change rate is the reference value, and the upper and lower fluctuations of the reference value are 5% to determine the borehole curvature of the second measuring section.
  • the upper and lower fluctuations of the reference value are 5% to determine the second measuring section.
  • a ⁇ min is the lower limit of the search interval for the change rate of the borehole torsion rate in the second logging interval, °/m; other parameters are the same as before.
  • the borehole curvature, torsion, tool face angle, and measuring section curvature change for the measuring points on the second measuring section are used to calculate the well inclination angle, azimuth angle, borehole curvature, torsion rate and tool face angle of the measuring point in the second measuring section.
  • the specific calculation process is as follows:
  • the measurement segment is divided into several segments n, and the segment length is ds;
  • k 1c , ⁇ 1c , ⁇ 1c , A kc , and A ⁇ c are the borehole curvature, borehole tortuosity, tool face angle and borehole curvature change rate of the second logging interval at the measuring points on the second logging interval, respectively.
  • the face angle, when s takes different values, is the corresponding parameter at different depths.
  • ⁇ 2c , k 2c , ⁇ 2c , ⁇ 2c are respectively the inclination angle at the lower measurement point calculated according to a set of values (k 1c , ⁇ 1c , ⁇ 1c , A kc , A ⁇ c ) at the upper measurement point of the second survey section , azimuth, borehole curvature, borehole torsion, tool face angle.
  • the error values ⁇ 1 and ⁇ 2 for any set of values (k 1c , ⁇ 1c , ⁇ 1c , A kc , A ⁇ c ) are calculated using the following equations.
  • a set of values that satisfy ⁇ 1 ⁇ 0.0002 and ⁇ 2 is the smallest, (k 1c , ⁇ 1c , ⁇ 1c , A kc , A ⁇ c ) are determined as the optimal value (k ) 1opt , ⁇ 1opt , ⁇ 1opt , A kopt , A ⁇ opt ).
  • the measurement segment is divided into several segments n, and the segment length is ds;
  • Step 140 Calculate the coordinate increment of the lower measurement point relative to the upper measurement point of the last measurement section by using the conventional inclination measurement calculation method
  • the formula Calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the first measurement section, where L m is the well depth of the mth measurement point, m; L m-1 is the well depth of the m-1th measurement point, m; ⁇ D (m-1 )m is the vertical depth increment of the mth measurement section, m; ⁇ L p(m-1)m is the increment of the horizontal projection length of the mth measurement section, m; ⁇ N (m-1)m is the N coordinate of the mth measurement section Increment, m; ⁇ E (m-1)m is the increment of the E coordinate of the mth measurement section, m.
  • the formula Calculate the coordinate increment of the lower measurement point relative to the upper measurement point in the mth measurement section, where ⁇ D (m-1)m is the vertical depth increment of the mth measurement section, m; ⁇ Lp (m-1)m is the level of the mth measurement section The increment of the projection length, m; ⁇ N (m-1)m is the increment of the N coordinate of the mth measurement section, m; ⁇ W (m-1)m is the increment of the E coordinate of the mth measurement section, m; R ( m-1)m is the radius of curvature of the arc of the mth measurement section, m.
  • ⁇ (m-1)m is the dogleg angle of the mth measuring section, °; ⁇ m-1 is the well inclination angle of the m-1th measuring point, °; is the azimuth angle of the m-1 measuring point, °; DN (m-1)m is the increment of the vertical depth of the m-th measuring section, m; ⁇ L p(m-1)m is the increment of the horizontal projection length of the m-th measuring section, m; ⁇ N (m-1)m is the increment of the N coordinate of the mth measurement section, m; ⁇ E (m-1)m is the increment of the E coordinate of the mth measurement section, m; R (m-1)m is The radius of curvature of the arc of the mth measurement segment, m; other parameters are the same as before.
  • Step 150 Calculate the vertical depth, N coordinate, E coordinate, horizontal projection length, horizontal displacement, translation azimuth and Panning.
  • the wellbore trajectory parameters such as the vertical depth of the lower measurement point, the horizontal projection length, the N coordinate, the E coordinate, the horizontal displacement, the translation azimuth, and the apparent translation are calculated.
  • L pi L p(i-1) + ⁇ L p(i-1)i (79)
  • N i N i-1 + ⁇ N (i-1)i (80)
  • V i S i ⁇ cos( ⁇ i - ⁇ TB ) (85)
  • D i, L pi, N i, E i, S i, ⁇ i, V i are the i-th measuring point of vertical depth, the length of the horizontal projection, N coordinates, E coordinates from the closure, the closure and the azimuth angle of view Translation;
  • D i-1 , L p(i-1) , N i-1 , and E i-1 are the vertical depth, horizontal projection length, N coordinate, and E coordinate of the i-1th measuring point, respectively;
  • ⁇ D (i- 1)i , ⁇ L p(i-1)i , ⁇ N (i-1)i , ⁇ E (i-1)i are the vertical depth increment, horizontal projection length increment, and N coordinate increment of the i-th measurement section, respectively , E coordinate increment;
  • ⁇ TB is the design azimuth of the well.
  • a wellbore trajectory adaptive inclination calculation method firstly follows the currently commonly used inclination calculation methods (minimum curvature method or Radius method) to calculate the coordinate increment of the first measurement section; then assuming that the curvature and torsion from the second measurement section to the penultimate second measurement section are linear changes, the 0th measurement point, the first Calculate the curvature, torsion and tool face angle at the first measuring point with the inclination data of the measuring point and the second measuring point, and determine the second The rate of change of the curvature and torsion of the measuring section, on this basis, the numerical integration is used to obtain the coordinate increment of the second measuring section, and so on, until the coordinate increment of the second-to-last measuring section is calculated; Calculate the coordinate increment of the last measuring section by using the inclinometer calculation method; finally, according to the full trajectory parameters at the 0th measuring point and the coordinate increment of each measuring section, the full trajectory parameters of all measuring points can be calculated;
  • the curve type closest to the trajectory is used to calculate the inclination measurement, which avoids the error caused by the mismatch between the assumed curve type and the actual drilling trajectory curve, and significantly improves the accuracy of the inclination measurement calculation of the wellbore trajectory.
  • Parallel horizontal wells and dense wellbore anti-collision are of great significance.

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Abstract

一种井眼轨迹自适应测斜计算方法，通过计算测段及其前、后两个测段对应的四个测点测量参数，识别所计算测段的曲线特征，从而选择合适的曲线计算测段的坐标增量，能够根据所计算测段及其前、后两个测段的井斜角、方位角变化规律，自动优选出与所计算测段井眼轨迹形状较为接近的曲线特征参数，自动拟合出与实钻井眼轨迹最接近的曲线类型并进行测斜计算，避免了由于假定的曲线类型与实钻井眼轨迹曲线不匹配造成的误差，显著提高了井眼轨迹测斜计算的精度，在救援井、连通井、平行水平井和密集井眼防碰等方面有重要意义。

Description

一种井眼轨迹自适应测斜计算方法 技术领域
本发明涉及油气钻井技术领域，尤其涉及一种井眼轨迹自适应测斜计算方法。
背景技术
石油钻井中井眼轨迹的测斜计算通常需要假设两个测点之间测段的曲线类型，然后根据该类曲线的特征和两端的井眼方向约束，确定该测段的坐标增量，从而确定井眼轨迹各测点的坐标。
然而，由于两个测点之间实际井眼轨迹为何种曲线是未知的，针对任何轨迹的所有测段假设为一种曲线类型进行测斜计算，在假设曲线与测段实际曲线不一致时必然会导致较大的轨迹计算误差。
针对此问题，最新的测斜计算方法以实际测量得到的各测点井斜角和方位角为样本点，采取三次样条插值得到各测段的井斜角和方位角三次样条插值函数，通过数值积分得到井眼轨迹。从理论上看，这样的处理方法一定程度上降低了井眼轨迹的计算误差，但三次样条插值要求插值函数在样本点(测点)处二阶导数连续，而实际钻井可能由于钻具组合、地层、钻进方式(滑动钻进或旋转钻进)、钻进参数等变化，使得井斜角和方位角的一阶、二阶导数发生显著变化，这种情况可能会导致插值函数的震荡，产生远超预期的误差。此外，该方法对样本点的误差也非常敏感，且测段长度越短，敏感度越高，甚至会发生不合理的震荡。
发明内容
本发明提供一种井眼轨迹自适应测斜计算方法，旨在解决已有技术中测斜计算精度差的问题，通过计算测段及其前、后两个测段对应 的四个测点测量参数，识别所计算测段的曲线特征，从而选择合适的曲线计算测段的坐标增量，可以自适应匹配与待计算测段井眼轨迹形状较为接近的曲线特征参数，可以显著提高井眼轨迹测斜计算的精度。
本发明采用的技术方案如下：
本发明提供一种井眼轨迹自适应测斜计算方法包括：
接收测斜数据并对其进行处理，根据测斜数据对测点和测段进行编号；
采用常规测斜计算方法计算第1测段下测点相对上测点的坐标增量；
根据第1测段及第2测段和第3测段计算第2测段下测点相对上测点的坐标增量，并以此类推计算其他测段的下测点相对上测点的坐标增量，直至计算出倒数第2个测段的下测点相对上测点的坐标增量；
采用常规测斜计算方法计算最后一个测段下测点相对上测点的坐标增量；
根据所有测段的下测点相对上测点的坐标增量，计算各测点井眼轨迹参数中的垂深、N坐标、E坐标、水平投影长度、水平位移、平移方位角和视平移。
可选的，所述坐标增量包括垂深增量、水平投影长度增量、N坐标增量和E坐标增量。
可选的，所述根据第1测段及第2测段和第3测段计算第2测段下测点相对上测点的坐标增量，具体包括：
根据第1测段和第2测段对应的三测点井深、井斜角和方位角，计算第2测段上测点的井眼曲率、挠率和工具面角预估值；
根据第2测段和第3测段对应的三测点井深、井斜角和方位角，计算第2测段下测点的井眼曲率、挠率和工具面角预估值；
计算第2测段的上测点、下测点之间预估的井眼曲率、挠率的平均变化率和工具面角增量；
以第2测段上测点预估的井眼曲率、挠率和工具面角为参考值，以第2测段上测点、下测点之间的井眼曲率、挠率和工具面角增量的±10％为波动范围，确定第2测段的井眼曲率、挠率和工具面角的取值范围；
以第2测段上测点、下测点之间的井眼曲率、挠率的平均变化率为参考值，以参考值上、下波动5％确定第2测段的井眼曲率变化率、挠率变化率的取值范围；
在确定的第2测段的井眼曲率变化率、挠率变化率的取值范围内，针对第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率，计算第2测段下测点的井斜角、方位角、井眼曲率和挠率；
计算第2测段下测点处井斜角和方位角的计算值与实测值的综合角度偏差和第2测段上测点、下测点处曲率、挠率的计算值和预估值的综合偏差，在满足第2测段下测点角度偏差小于规定值0.0002的前提下，按照第2测段上测点、下测点处曲率、挠率的综合偏差最小原则确定第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率最优值；
根据第2测段上测点井眼曲率、挠率、工具面角和第2测段曲率变化率、挠率变化率最优值，计算第2测段下测点相对上测点的坐标增量。
可选的，所述采用常规测斜计算方法计算第1测段下测点相对上测点的坐标增量，具体包括：
根据公式
Figure PCTCN2020102782-appb-000001
Figure PCTCN2020102782-appb-000002
计算第1测段的狗腿角，其中，γ01为第1测段的狗腿角；α0为第0测点井斜角，α 1为第1测点井斜角，
Figure PCTCN2020102782-appb-000003
为第0测点方位角，
Figure PCTCN2020102782-appb-000004
为第1测点方位角；
若第1测段的狗腿角等于零，则采用如下公式计算第1测段下测点相对上测点的坐标增量
Figure PCTCN2020102782-appb-000005
其中，L 0为第0测点井深，m；L 1为第1测点井深，ΔD 01为第1测段垂深的增量，ΔL p01为第1测段水平投影长度的增量，ΔN 01为第1测段N坐标的增量，ΔE 01为第1测段E坐标的增量；
若第1测段的狗腿角大于零，则采用如下公式计算第1测段下测点相对上测点的坐标增量
Figure PCTCN2020102782-appb-000006
其中，ΔD 01为第1测段垂深的增量，ΔL p01为第1测段水平投影长度的增量，ΔN 01为第1测段N坐标的增量，ΔE 01为第1测段E坐标的增量，R 01为第1测段圆弧的曲率半径。
可选的，所述采用常规测斜计算方法计算最后一个测段下测点相对上测点的坐标增量，具体包括：
根据公式
Figure PCTCN2020102782-appb-000007
计算最后一个测段的狗腿角，其中，γ (m-1)m为第m测段的狗腿角， α m为第m测点井斜角，
Figure PCTCN2020102782-appb-000008
为第m测点方位角，α m-1为第m-1测点井斜角，
Figure PCTCN2020102782-appb-000009
为第m-1测点方位角；
若第m测段的狗腿角等于零，则采用公式
Figure PCTCN2020102782-appb-000010
计算第1测段下测点相对上测点的坐标增量，其中，L m为第m测点井深，L m-1为第m-1测点井深，ΔD (m-1)m为第m测段垂深的增量，ΔL p(m-1)m为第m测段水平投影长度的增量，ΔN (m-1)m为第m测段N坐标的增量，ΔE (m-1)m为第m测段E坐标的增量；
若第m测段的狗腿角大于零，则采用公式
Figure PCTCN2020102782-appb-000011
计算第m测段下测点相对上测点的坐标增量，其中，ΔD (m-1)m为第m测段垂深的增量，ΔL p(m-1)m为第m测段水平投影长度的增量，ΔN (m-1)m为第m测段N坐标的增量，ΔE (m-1)m为第m测段E坐标的增量，R (m-1)m为第m测段圆弧的曲率半径。
可选的，所述根据第1测段和第2测段对应的三测点井深、井斜角和方位角，计算第2测段上测点的井眼曲率、挠率和工具面角预估值，具体为：
根据公式
Figure PCTCN2020102782-appb-000012
计算第2测段上测点的井眼曲率的预估值，其中，α1为第1测点的井斜角，k 1e为第1个测点处 井眼曲率的预估值，k α1为第1个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000013
为第1个测点处的方位变化率；
根据公式
Figure PCTCN2020102782-appb-000014
计算第2测段上测点的挠率的预估值，其中，α1为第1测点的井斜角，k 1e为第1个测点处井眼曲率的预估值，k α1为第1个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000015
为第1个测点处的方位变化率，
Figure PCTCN2020102782-appb-000016
为第1个测点处井斜变化率的变化率，
Figure PCTCN2020102782-appb-000017
为第1个测点处方位变化率的变化率,τ 1e为第1个测点处井眼挠率的预估值；
根据公式
Figure PCTCN2020102782-appb-000018
计算第2测段上测点的工具面角的预估值，其中，ω 1e为第1个测点处工具面角的预估值，
Figure PCTCN2020102782-appb-000019
为第1测段的方位角增量，
Figure PCTCN2020102782-appb-000020
为第2测段的方位角增量，α 1为第1测点的井斜角，α 0为第0测点的井斜角，α 2为第2测点的井斜角，γ 01为第1测段的狗腿角，γ 12为第2测段的狗腿角。
可选的，所述根据第2测段和第3测段对应的三测点井深、井斜角和方位角，计算第2测段下测点的井眼曲率、挠率和工具面角预估值，具体为：
根据公式
Figure PCTCN2020102782-appb-000021
计算第2测段下测点的井眼曲率的预估值，其中，α2为第2测点的井斜角，k 2e为第2个测点处井眼曲率的预估值，k α2为第2个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000022
为第2个测点处的方位变化率；
根据公式
Figure PCTCN2020102782-appb-000023
计算第2测段下测点的挠率的预估值，其中，α2为第2测点的井斜角，k 2e 为第2个测点处井眼曲率的预估值，k α2为第2个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000024
为第2个测点处的方位变化率，
Figure PCTCN2020102782-appb-000025
为第2个测点处井斜变化率的变化率，
Figure PCTCN2020102782-appb-000026
为第2个测点处方位变化率的变化率,τ 2e为第2个测点处井眼挠率的预估值；
根据公式
Figure PCTCN2020102782-appb-000027
计算第1测段上测点的工具面角的预估值，，其中，ω 2e为第2个测点处工具面角的预估值，
Figure PCTCN2020102782-appb-000028
为第2测段的方位角增量，
Figure PCTCN2020102782-appb-000029
为第3测段的方位角增量，α 2为第3测点的井斜角，α 1为第1测点的井斜角，α 23为第4测点的井斜角，γ 12为第2测段的狗腿角，γ 23为第3测段的狗腿角。
可选的，所述计算第i测段的上测点、下测点之间预估的井眼曲率、挠率的平均变化率和工具面角增量，具体为：
根据公式
Figure PCTCN2020102782-appb-000030
计算第i测段的上测点、下测点之间预估的井眼曲率，其中，A k12为第2测段井眼曲率的平均变化率，L 1为第1测点井深，L 2为第2测点井深，k 1e为第1个测点处井眼曲率的预估值，k 2e为第2个测点处井眼曲率的预估值；
根据公式
Figure PCTCN2020102782-appb-000031
计算第i测段的上测点、下测点之间预估的挠率的平均变化率，其中，A τ12为第2测段井眼挠率的平均变化率，τ 1e为第1个测点处井眼挠率的预估值，τ 2e为第2个测点处井眼挠率的预估值；
根据公式
Figure PCTCN2020102782-appb-000032
计算第i测段的上测点、下测点之间预估的工具面角增量，其中，Δω 12为 第2测段工具面角的增量，ω 1e为第1个测点处工具面角的预估值，ω 2e为第2个测点处工具面角的预估值。
与现有技术相比，本发明的有益效果是：首先根据井眼轨迹第0个测点和第1个测点的测斜数据按照目前常用的测斜计算方法(最小曲率法或曲率半径法)计算第1个测段的坐标增量；然后假设从第2个测段到倒数第2个测段的曲率和挠率均为线性变化，先由第0个测点、第1个测点和第2个测点的测斜数据计算第1个测点处的曲率、挠率和工具面角，并以第2个测点处的井斜角和方位角为约束确定第2个测段曲率和挠率的变化率，在此基础上，数值积分得到第2个测段的坐标增量，以此类推，直至计算出倒数第2个测段的坐标增量；再次按照目前常用的测斜计算方法计算最后一个测段的坐标增量；最后根据第0个测点处的全轨迹参数和各测段的坐标增量就可以计算出全部测点处的全轨迹参数；能够根据所计算测段及其前、后两个测段的井斜角、方位角变化规律，自动优选出与所计算测段井眼轨迹形状较为接近的曲线特征参数，自动拟合出与实钻井眼轨迹最接近的曲线类型并进行测斜计算，避免了由于假定的曲线类型与实钻井眼轨迹曲线不匹配造成的误差，显著提高了井眼轨迹测斜计算的精度，在救援井、连通井、平行水平井和密集井眼防碰等方面有重要意义。
附图说明
图1为本发明实施例的一种井眼轨迹自适应测斜计算方法的流程示意图。
具体实施方式
为使本发明的目的、技术方案和优点更加清楚，下面对本发明实施方式作进一步地详细描述：
下面将结合图1对本发明实施例的一种井眼轨迹自适应测斜计算方法进行详细的说明。
参考图1所示，本发明实施例提供的一种井眼轨迹自适应测斜计算方法
步骤110：接收测斜数据并对其进行处理，根据测斜数据对测点和测段进行编号。
具体的，第1个井斜不为0的测点为第1测点，其后测点编号依次增加，直至最后一个测点；第1测点之上井深比第1测点井深小25m处为第0测点，若第1测点井深小于25m，则第0测点为井口。并且第0个测点和第1个测点之间的测段为第1个测段，以此类推，第i-1个测点和第i个测点之间的测段为第i个测段，其中，i为大于等于1的正整数。
示例的，第1个井斜不为0的测点为第1测点，其后依次为第2测点、第3测点……，直至最后一个测点为第m测点；第1个测点之上井深比第1测点井深小25m处为第0测点，若第1测点井深小于25m，则第0测点为井口，即
Figure PCTCN2020102782-appb-000033
其中，L 0为第0测点井深，m；L 1为第1测点井深，m。
第0测点的其他参数为：
Figure PCTCN2020102782-appb-000034
其中，α 0为第0测点井斜角，°；
Figure PCTCN2020102782-appb-000035
为第0测点方位角，°；D 0为第0测点垂深，m；L p0为第0测点水平投影长度，m；N 0为第0测点N坐标，m；E 0为第0测点E坐标，m；S 0为第0测点闭合距，m；θ 0为第0测点闭合方位角，°。
在测点编号的基础上，第i-1个测点和第i个测点之间的测段为第i个测段，i可以从1变化到m。
步骤120：采用常规测斜计算方法计算第1测段下测点相对上测点的坐标增量。
其中，坐标增量包括垂深增量、水平投影长度增量、N坐标增量和E坐标增量。
根据公式
Figure PCTCN2020102782-appb-000036
Figure PCTCN2020102782-appb-000037
计算第1测段的狗腿角，其中，γ01为第1测段的狗腿角，°；α0为第0测点井斜角，°；α1为第1测点井斜角，°；
Figure PCTCN2020102782-appb-000038
为第0测点方位角，°；
Figure PCTCN2020102782-appb-000039
为第1测点方位角，°；
若第1测段的狗腿角等于零，则采用如下公式计算第1测段下测点相对上测点的坐标增量
Figure PCTCN2020102782-appb-000040
其中，L 0为第0测点井深，m；L 1为第1测点井深，m；ΔD 01为第1测段垂 深的增量，m；ΔL p01为第1测段水平投影长度的增量，m；ΔN 01为第1测段N坐标的增量，m；ΔE 01为第1测段E坐标的增量，m；
若第1测段的狗腿角大于零，则采用如下公式计算第1测段下测点相对上测点的坐标增量
Figure PCTCN2020102782-appb-000041
其中，ΔD 01为第1测段垂深的增量，m；ΔL p01为第1测段水平投影长度的增量，m；ΔN 01为第1测段N坐标的增量，m；ΔE 01为第1测段E坐标的增量，m；R 01为第1测段圆弧的曲率半径，m。
Figure PCTCN2020102782-appb-000042
当γ 01＝0时：
Figure PCTCN2020102782-appb-000043
当γ 01>0时：
R 01＝(L 1-L 0)/γ 01             (5)
Figure PCTCN2020102782-appb-000044
其中，γ 01为第1测段的狗腿角，°；α 1为第1测点井斜角，°；
Figure PCTCN2020102782-appb-000045
为第1测点方位角，°；ΔD 01为第1测段垂深的增量，m；ΔL p01为第1测段水平投影长度的增量，m；ΔN 01为第1测段N坐标的增量，m；ΔE 01为第1测段E坐标的增量，m；R 01为第1测段圆弧的曲率半径，m；其他参数同前。
步骤130：根据第1测段及第2测段和第3测段计算第2测段下测点相对上测点的坐标增量，并以此类推计算其他测段的下测点相对上测点的坐标增量，直至计算出倒数第2个测段的下测点相对上测点的坐标增量。
具体的，步骤130包括如下子步骤：
(1)根据第1测段和第2测段对应的三测点井深、井斜角和方位角，计算第2测段上测点的井眼曲率、挠率和工具面角预估值；
根据公式
Figure PCTCN2020102782-appb-000046
计算第2测段上测点的井眼曲率的预估值，其中，α1为第1测点的井斜角，k 1e为第1个测点处井眼曲率的预估值，k α1为第1个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000047
为第1个测点处的方位变化率；
根据公式
Figure PCTCN2020102782-appb-000048
计算第2测段上测点的挠率的预估值，其中，α1为第1测点的井斜角，k 1e为第1个测点处井眼曲率的预估值，k α1为第1个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000049
为第1个测点处的方位变化率，
Figure PCTCN2020102782-appb-000050
为第1个测点处井斜变化率的变化率，
Figure PCTCN2020102782-appb-000051
为第1个测点处方位变化率的变化率,τ 1e为第1个测点处井眼挠率的预估值；
根据公式
Figure PCTCN2020102782-appb-000052
计算第2测段上测点的工具面角的预估值，其中，ω 1e为第1个测点处工具面角的预估值，
Figure PCTCN2020102782-appb-000053
为第1测段的方位角增量，
Figure PCTCN2020102782-appb-000054
为第2测段的方位角增量，α 1为第1测点的井斜角，α 0为第0测点的井斜角，α 2为第2测点的井斜角，γ 01为第1测段的狗腿角，γ 12为第2测段的狗腿角。
具体的，采用如下公式根据第1测段和第2测段对应的三测点井深、井斜角和方位角，计算第2测段上测点的井眼曲率、挠率和工具面角预估值。
Figure PCTCN2020102782-appb-000055
Figure PCTCN2020102782-appb-000056
Figure PCTCN2020102782-appb-000057
Figure PCTCN2020102782-appb-000058
Figure PCTCN2020102782-appb-000059
Figure PCTCN2020102782-appb-000060
Figure PCTCN2020102782-appb-000061
Figure PCTCN2020102782-appb-000062
Figure PCTCN2020102782-appb-000063
Figure PCTCN2020102782-appb-000064
Figure PCTCN2020102782-appb-000065
Figure PCTCN2020102782-appb-000066
Figure PCTCN2020102782-appb-000067
Figure PCTCN2020102782-appb-000068
Figure PCTCN2020102782-appb-000069
其中，
Figure PCTCN2020102782-appb-000070
为第1测段的方位角增量，°；
Figure PCTCN2020102782-appb-000071
为第2测段的方位角增量，°；γ 12为第2测段的狗腿角，°；k α01为第1测段的平均井斜变化率，°/m；
Figure PCTCN2020102782-appb-000072
为第1测段的平均方位变化率，°/m；k α12为第2测段的平均井斜变化率，°/m；
Figure PCTCN2020102782-appb-000073
为第2测段的平均方位变化率，°/m；k α1为第1个测点处的井斜变化率，°/m；
Figure PCTCN2020102782-appb-000074
为第1个测点处的方位变化率，°/m；
Figure PCTCN2020102782-appb-000075
为第1个测点处井斜变化率的变化率，°/m2；
Figure PCTCN2020102782-appb-000076
为第1个测点处方位变化率的变化率，°/m2；k 1e为第1个测点处井眼曲率的预估值，°/m；τ 1e为第1个测点处井眼挠率的预估值，°/m；ω 1e为第1个测点处工具面角的预估值，°；其它参数同前。
(2)根据第2测段和第3测段对应的三测点井深、井斜角和方位角，计算第2测段下测点的井眼曲率、挠率和工具面角预估值。
根据公式
Figure PCTCN2020102782-appb-000077
计算第2测段下测点的井眼曲率的预估值，其中，α2为第2测点的井斜角，k 2e为第2个测点处井眼曲率的预估值，k α2为第2个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000078
为第2个测点处的方位变化率；
根据公式
Figure PCTCN2020102782-appb-000079
计算第2测段下测点的挠率的预估值，其中，α2为第2测点的井斜角，k 2e为第2个测点处井眼曲率的预估值，k α2为第2个测点处的井斜变化率，
Figure PCTCN2020102782-appb-000080
为第2个测点处的方位变化率，
Figure PCTCN2020102782-appb-000081
为第2个测点处井斜变化率的变化率，
Figure PCTCN2020102782-appb-000082
为第2个测点处方位变化率的变化率,τ 2e为第2个测点处井眼挠率的预估值；
根据公式
Figure PCTCN2020102782-appb-000083
计算第1测段上测点的工具面角的预估值，，其中，ω 2e为第2个测点处工具 面角的预估值，
Figure PCTCN2020102782-appb-000084
为第2测段的方位角增量，
Figure PCTCN2020102782-appb-000085
为第3测段的方位角增量，α 2为第3测点的井斜角，α 1为第1测点的井斜角，α 23为第4测点的井斜角，γ 12为第2测段的狗腿角，γ 23为第3测段的狗腿角。
具体的，采用如下公式根据第2测段和第3测段对应的三测点井深、井斜角和方位角，计算第2测段下测点的井眼曲率、挠率和工具面角预估值。
Figure PCTCN2020102782-appb-000086
Figure PCTCN2020102782-appb-000087
Figure PCTCN2020102782-appb-000088
Figure PCTCN2020102782-appb-000089
Figure PCTCN2020102782-appb-000090
Figure PCTCN2020102782-appb-000091
Figure PCTCN2020102782-appb-000092
Figure PCTCN2020102782-appb-000093
Figure PCTCN2020102782-appb-000094
Figure PCTCN2020102782-appb-000095
Figure PCTCN2020102782-appb-000096
式中，
Figure PCTCN2020102782-appb-000097
为第3测段的方位角增量，°；γ 23为第3测段的狗腿角，°；k α23为第3测段的平均井斜变化率，°/m；
Figure PCTCN2020102782-appb-000098
为第3测段的平均方位变化率，°/m；k α2为第2个测点处的井斜变化率，°/m；
Figure PCTCN2020102782-appb-000099
为第2个测点处的方位变化率，°/m；
Figure PCTCN2020102782-appb-000100
为第2个测点处井斜变化率的变化率，°/m2；
Figure PCTCN2020102782-appb-000101
为第2个测点处方位变化率的变化率，°/m2；k 2e为第2个测点处井眼曲率的预估值，°/m；τ 2e为第2个测点处井眼挠率的预估值，°/m；ω 2e为第2个测点处工具面角的预估值，°；其它参数同前。
(3)计算第2测段的上测点、下测点之间预估的井眼曲率、挠率的平均变化率和工具面角增量。
根据公式
Figure PCTCN2020102782-appb-000102
计算第i测段的上测点、下测点之间预估的井眼曲率，其中，A k12为第2测段井眼曲率的平均变化率，L 1为第1测点井深，L 2为第2测点井深，k 1e为第1个测点处井眼曲率的预估值，k 2e为第2个测点处井眼曲率的预估值；
根据公式
Figure PCTCN2020102782-appb-000103
计算第i测段的上测点、下测点之间预估的挠率的平均变化率，其中，A τ12为第2测段井眼挠率的平均变化率，τ 1e为第1个测点处井眼挠率的预估值，τ 2e为第2个测点处井眼挠率的预估值；
根据公式
Figure PCTCN2020102782-appb-000104
计算第i测段的上测点、下测点之间预估的工具面角增量，其中，Δω 12为第2测段工具面角的增量，ω 1e为第1个测点处工具面角的预估值，ω 2e为第2个测点处工具面角的预估值。
具体的，计算第2测段的上测点、下测点之间预估的井眼曲率、挠率的平均变化率和工具面角增量的过程如下：
Figure PCTCN2020102782-appb-000105
Figure PCTCN2020102782-appb-000106
Figure PCTCN2020102782-appb-000107
式中，A k12为第2测段井眼曲率的平均变化率，°/m2；A τ12为第2测段井眼挠率的平均变化率，°/m2；Δω 12为第2测段工具面角的增量，°；其它参数同前。
(4)以第2测段上测点预估的井眼曲率、挠率和工具面角为参考值，以第2测段上测点、下测点之间的井眼曲率、挠率和工具面角增量的±10％为波动范围，确定第2测段的井眼曲率、挠率和工具面角的取值范围。
具体的，以第2测段上测点(第1测点)处的井眼曲率、挠率和工具面角预估值为参考，在参考值上、下波动该测段相应预估值变化范围的10％作为上、下限，即有
k 1max＝k 1e+A k12·(L 2-L 1)·10％              (36)
k 1min＝k 1e-A k12·(L 2-L 1)·10％              (37)
τ 1max＝τ 1e+A τ12·(L 2-L 1)·10％              (38)
τ 1min＝τ 1e-A τ12·(L 2-L 1)·10％              (39)
ω 1max＝ω 1e+Δω 12·10％                      (40)
ω 1min＝ω 1e-Δω 12·10％                      (41)
式中，k 1max为第1测点处井眼曲率搜索区间的上限，°/m；k 1min为第1测点处井眼曲率搜索区间的下限，°/m；τ 1max为第1测点处井眼挠率搜索区间的上限，°/m；τ 1min为第1测点处井眼挠率搜索区间的 下限，°/m；ω 1max为第1个测点处工具面角搜索区间的上限，°；ω 1min为第1个测点处工具面角搜索区间的下限，°；其它参数同前。
(5)以第2测段上测点、下测点之间的井眼曲率、挠率的平均变化率为参考值，以参考值上、下波动5％确定第2测段的井眼曲率变化率、挠率变化率的取值范围。
具体的，以第2测段上测点、下测点之间的井眼曲率、挠率的平均变化率为参考值，根据如下公式以参考值上、下波动5％确定第2测段的井眼曲率变化率、挠率变化率的取值范围。
A kmax＝1.05·A k12                        (42)
A kmim＝0.95·A k12                        (43)
A τmax＝1.05·A τ12                        (44)
A τmin＝0.95·A τ12                        (45)
式中，A kmax为第2测段井眼曲率变化率搜索区间上限，°/m；A kmin为第2测段井眼曲率变化率搜索区间下限，°/m；A τmax为第2测段井眼挠率变化率搜索区间上限，°/m；A τmin为第2测段井眼挠率变化率搜索区间下限，°/m；其它参数同前。
(6)在确定的第2测段的井眼曲率变化率、挠率变化率的取值范围内，针对第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率，计算第2测段下测点的井斜角、方位角、井眼曲率和挠率。
具体的，在确定的第2测段的井眼曲率变化率、挠率变化率的取值范围内，针对第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率，采用如下公式计算第2测段下测点的井斜角、方位角、井眼曲率、挠率和工具面角等参数。具体计算过程如下：
①将该测段分成若干段n，段长为ds；
②第1段的起点s＝0处的参数为
α(0)＝α 1                       (46)
Figure PCTCN2020102782-appb-000108
k(0)＝k 1c                       (48)
τ(0)＝τ 1c                       (49)
ω(0)＝ω 1c                       (50)
式中，k 1c、τ 1c、ω 1c、A kc、A τc分别为第2测段上测点处的井眼曲率、井眼挠率、工具面角和第2测段井眼曲率变化率、井眼挠率在其搜索区间内的某一取值；α(0)、
Figure PCTCN2020102782-appb-000109
k(0)、τ(0)、ω(0)分别为第2测段上距离上测点沿井深长度s＝0处的井斜角、方位角、井眼曲率、井眼挠率和工具面角，当s取不同值时就是不同深度处的相应参数。
③由s＝i·ds处的参数计算s＝(i+1)·ds处的参数
α((i+1)·ds)＝α(i·ds)+k(i·ds)·cosω(i·ds)·ds    (51)
Figure PCTCN2020102782-appb-000110
k((i+1)·ds)＝k(i·ds)+A kc·ds           (53)
τ((i+1)·ds)＝τ(i·ds)+A τc·ds           (54)
ω((i+1)·ds)＝ω(i·ds)+[τ(i·ds)-k(i·ds)·sinω(i·ds)/sinαi·ds·cosαi·ds·ds                 (55)
(i＝0，…，n-1)
④第2测段的下测点(第2测点)处的参数即为第n段终点s＝n·ds处的参数
α 2c＝α(n·ds)                      (56)
Figure PCTCN2020102782-appb-000111
k 2c＝k(n·ds)                         (58)
τ 2c＝τ(n·ds)                         (59)
ω 2c＝ω(n·ds)                         (60)
式中，α 2c、
Figure PCTCN2020102782-appb-000112
k 2c、τ 2c、ω 2c分别为根据第2测段上测点处的一组取值(k 1c，τ 1c，ω 1c，A kc，A τc)计算出的下测点处井斜角、方位角、井眼曲率、井眼挠率、工具面角。
示例的，先将第2测段分成若干段，由第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率，按照公式(46)-(50)确定迭代初值，按照公式(51)-(55)的迭代格式由上一点参数计算下一点参数，直至第2测段的下测点，即可计算得到下测点的井斜角、方位角、井眼曲率和挠率。
(7)计算第2测段下测点处井斜角和方位角的计算值与实测值的综合角度偏差和第2测段上测点、下测点处曲率、挠率的计算值和预估值的综合偏差，在满足第2测段下测点角度偏差小于规定值0.0002的前提下，按照第2测段上测点、下测点处曲率、挠率的综合偏差最小原则确定第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率最优值。
采用如下公式计算针对任一组取值(k 1c，τ 1c，ω 1c，A kc，A τc)的误差值Δ 1和Δ 2。
Figure PCTCN2020102782-appb-000113
Figure PCTCN2020102782-appb-000114
(8)根据第2测段上测点井眼曲率、挠率、工具面角和第2测段曲率变化率、挠率变化率最优值，计算第2测段下测点相对上测点的坐标增量。
具体的，在给定的取值范围内，满足Δ 1＜0.0002且Δ 2最小的一组取值，(k 1c，τ 1c，ω 1c，A kc，A τc)确定为最优值(k 1opt，τ 1opt，ω 1opt，A kopt，A τopt)。
之后以第2测段上测点(第1测点)的最优值(k 1opt，τ 1opt，ω 1opt，A kopt，A τopt)计算第2测段下测点相对上测点的坐标增量。具体的计算过程如下：
①将该测段分成若干段n，段长为ds；
②第1段的起点s＝0处的参数为
α(0)＝α 1                                  (63)
Figure PCTCN2020102782-appb-000115
k(0)＝k 1opt                            (65)
τ(0)＝τ 1opt                            (66)
ω(0)＝ω 1opt                            (67)
③由s＝i·ds处的参数计算s＝(i+1)·ds处的参数
α((i+1)·ds)＝α(i·ds)+k(i·ds)·cosω(i·ds)·ds      (68)
Figure PCTCN2020102782-appb-000116
k((i+1)·ds)＝k(i·ds)+A kopt·ds         (70)
τ((i+1)·ds)＝τ(i·ds)+A τopt·ds         (71)
ω((i+1)·ds)＝ω(i·ds)+[τ(i·ds)-k(i·ds)·sinω(i·ds)/sinαsi·ds·cosαi·ds·ds              (72)
(i＝0，…，n-1)
④第2测段的下测点相对上测点的坐标增量
Figure PCTCN2020102782-appb-000117
式中，ΔD 12为第2测段垂深的增量，m；ΔL p12为第2测段水平投影长度的增量，m；ΔN 12为第2测段N坐标的增量，m；ΔE 12为第2测段E坐标的增量，m；其他参数同前。
示例的，先将第2测段分成若干段，由第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率的最优值，按照公式(63)-(67)确定迭代初值，按照公式(68)-(72)的迭代格式由上一点参数计算下一点参数，直至第2测段的下测点，最后按照公式(73)计算第2测段下测点相对上测点的坐标增量。
步骤140：采用常规测斜计算方法计算最后一个测段下测点相对上测点的坐标增量；
其中，根据公式
Figure PCTCN2020102782-appb-000118
计算最后一个测段的狗腿角，其中，γ (m-1)m为第m测段的狗腿角，α m为第m测点井斜角，
Figure PCTCN2020102782-appb-000119
为第m测点方位角，αm -1为第m-1测点井斜角，
Figure PCTCN2020102782-appb-000120
为第m-1测点方位角；
若第m测段的狗腿角等于零，则采用公式
Figure PCTCN2020102782-appb-000121
计算第1测段下测点相对上测点的坐标增量，其中，L m为第m测点井深，m；L m-1为第m-1测点井深，m；ΔD (m-1)m为第m测段垂深的增量，m；ΔL p(m-1)m为第m测段水平投影长度的增量，m；ΔN (m-1)m为第m测段N坐标的增量，m；ΔE (m-1)m为第m测段E坐标的增量，m。
若第m测段的狗腿角大于零，则采用公式
Figure PCTCN2020102782-appb-000122
计算第m测段下测点相对上测点的坐标增量，其中，ΔD (m-1)m为第m测段垂深的增量，m；ΔLp (m-1)m为第m测段水平投影长度的增量，m；ΔN (m-1)m为第m测段N坐标的增量，m；ΔW (m-1)m为第m测段E坐标的增量，m；R (m-1)m为第m测段圆弧的曲率半径，m。
示例的，具体的计算公式如下：
Figure PCTCN2020102782-appb-000123
当γ (m-1)m＝0时：
Figure PCTCN2020102782-appb-000124
当γ (m-1)m>0时：
R (m-1)m＝(L m-L m-1)/γ (m-1)m                            (76)
Figure PCTCN2020102782-appb-000125
其中，γ (m-1)m为第m测段的狗腿角，°；α m-1为第m-1测点井斜角，°；
Figure PCTCN2020102782-appb-000126
为第m-1测点方位角，°；DN (m-1)m为第m测段垂深的增量，m；ΔL p(m-1)m为第m测段水平投影长度的增量，m；ΔN (m-1)m为第m测段N坐标的增量，m；ΔE (m-1)m为第m测段E坐标的增量，m；R (m-1)m为第m测段圆弧的曲率半径，m；其他参数同前。
步骤150：根据所有测段的下测点相对上测点的坐标增量，计算各测点井眼轨迹参数中的垂深、N坐标、E坐标、水平投影长度、水平位移、平移方位角和视平移。
具体的，由上测点的参数和测段的坐标增量数据，计算下测点垂深、水平投影长度、N坐标、E坐标、水平位移、平移方位角、视平移等井眼轨迹参数。
D i＝D i-1+ΔD (i-1)i                                (78)
L pi＝L p(i-1)+ΔL p(i-1)i                           (79)
N i＝N i-1+ΔN (i-1)i                                (80)
E i＝E i-1+ΔE (i-1)i                                (81)
Figure PCTCN2020102782-appb-000127
Figure PCTCN2020102782-appb-000128
V i＝S i·cos(θ i-θ TB)            (85)
其中，D i、L pi、N i、E i、S i、θ i、V i分别为第i测点的垂深、水平投影长度、N坐标、E坐标、闭合距、闭合方位角和视平移；D i-1、L p(i-1)、N i-1、E i-1分别为第i-1测点的垂深、水平投影长度、N坐标、E坐标；ΔD (i-1)i、ΔL p(i-1)i、ΔN (i-1)i、ΔE (i-1)i分别为第i测段的垂深增量、水平投影长度增量、N坐标增量、E坐标增量；θ TB为该井的设计方位角。
本发明实施例的一种井眼轨迹自适应测斜计算方法首先根据井眼轨迹第0个测点和第1个测点的测斜数据按照目前常用的测斜计算方法(最小曲率法或曲率半径法)计算第1个测段的坐标增量；然后假设从第2个测段到倒数第2个测段的曲率和挠率均为线性变化，先由第0个测点、第1个测点和第2个测点的测斜数据计算第1个测点处的曲率、挠率和工具面角，并以第2个测点处的井斜角和方位角为约束确定第2个测段曲率和挠率的变化率，在此基础上，数值积分得到第2个测段的坐标增量，以此类推，直至计算出倒数第2个测段的坐标增量；再次按照目前常用的测斜计算方法计算最后一个测段的坐标增量；最后根据第0个测点处的全轨迹参数和各测段的坐标增量就可以计算出全部测点处的全轨迹参数；能够根据所计算测段及其前、后两个测段的井斜角、方位角变化规律，自动优选出与所计算测段井眼轨迹形状较为接近的曲线特征参数，自动拟合出与实钻井眼轨迹最接近的曲线类型并进行测斜计算，避免了由于假定的曲线类型与实钻 井眼轨迹曲线不匹配造成的误差，显著提高了井眼轨迹测斜计算的精度，在救援井、连通井、平行水平井和密集井眼防碰等方面有重要意义。
显然，本领域的技术人员可以对本发明实施例进行各种改动和变型而不脱离本发明实施例的精神和范围。这样，倘若本发明实施例的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。

Claims (8)

  1. 一种井眼轨迹自适应测斜计算方法，其特征在于，所述井眼轨迹自适应测斜计算方法包括：
    接收测斜数据并对其进行处理，根据测斜数据对测点和测段进行编号；
    采用常规测斜计算方法计算第1测段下测点相对上测点的坐标增量；
    根据第1测段及第2测段和第3测段计算第2测段下测点相对上测点的坐标增量，并以此类推计算其他测段的下测点相对上测点的坐标增量，直至计算出倒数第2个测段的下测点相对上测点的坐标增量；
    采用常规测斜计算方法计算最后一个测段下测点相对上测点的坐标增量；
    根据所有测段的下测点相对上测点的坐标增量，计算各测点井眼轨迹参数中的垂深、N坐标、E坐标、水平投影长度、水平位移、平移方位角和视平移。
  2. 根据权利要求1所述的井眼轨迹自适应测斜计算方法，其特征在于，所述坐标增量包括垂深增量、水平投影长度增量、N坐标增量和E坐标增量。
  3. 根据权利要求1所述的井眼轨迹自适应测斜计算方法，其特征在于，所述根据第1测段及第2测段和第3测段计算第2测段下测点相对上测点的坐标增量，具体包括：
    根据第1测段和第2测段对应的三测点井深、井斜角和方位角，计算第2测段上测点的井眼曲率、挠率和工具面角预估值；
    根据第2测段和第3测段对应的三测点井深、井斜角和方位角，计算第2测段下测点的井眼曲率、挠率和工具面角预估值；
    计算第2测段的上测点、下测点之间预估的井眼曲率、挠率的平均变化率和工具面角增量；
    以第2测段上测点预估的井眼曲率、挠率和工具面角为参考值，以第2测段上测点、下测点之间的井眼曲率、挠率和工具面角增量的±10％为波动范围，确定第2测段的井眼曲率、挠率和工具面角的取值范围；
    以第2测段上测点、下测点之间的井眼曲率、挠率的平均变化率为参考值，以参考值上、下波动5％确定第2测段的井眼曲率变化率、挠率变化率的取值范围；
    在确定的第2测段的井眼曲率变化率、挠率变化率的取值范围内，针对第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率，计算第2测段下测点的井斜角、方位角、井眼曲率和挠率；
    计算第2测段下测点处井斜角和方位角的计算值与实测值的综合角度偏差和第2测段上测点、下测点处曲率、挠率的计算值和预估值的综合偏差，在满足第2测段下测点角度偏差小于规定值0.0002的前提下，按照第2测段上测点、下测点处曲率、挠率的综合偏差最小原则确定第2测段上测点井眼曲率、挠率、工具面角和测段曲率变化率、挠率变化率最优值；
    根据第2测段上测点井眼曲率、挠率、工具面角和第2测段曲率变化率、挠率变化率最优值，计算第2测段下测点相对上测点的坐标增量。
  4. 根据权利要求2所述的井眼轨迹自适应测斜计算方法，其特征在于，所述采用常规测斜计算方法计算第1测段下测点相对上测点的坐标增量，具体包括：
    根据公式
    Figure PCTCN2020102782-appb-100001
    Figure PCTCN2020102782-appb-100002
    计算第1测段的狗腿角，其中，γ 01为第1测段的狗腿角；α 0为第0测点井斜角，α 1为第1测点井斜角，
    Figure PCTCN2020102782-appb-100003
    为第0测点方位角，
    Figure PCTCN2020102782-appb-100004
    为第1测点方位角；
    若第1测段的狗腿角等于零，则采用如下公式计算第1测段下测点相对上测点的坐标增量
    Figure PCTCN2020102782-appb-100005
    其中，L 0为第0测点井深，m；L 1为第1测点井深，ΔD 01为第1测段垂深的增量，ΔL p01为第1测段水平投影长度的增量，ΔN 01为第1测段N坐标的增量，ΔE 01为第1测段E坐标的增量；
    若第1测段的狗腿角大于零，则采用如下公式计算第1测段下测点相对上测点的坐标增量
    Figure PCTCN2020102782-appb-100006
    其中，ΔD 01为第1测段垂深的增量，ΔL p01为第1测段水平投影长度的增量，ΔN 01为第1测段N坐标的增量，ΔE 01为第1测段E坐标的增量，R 01为第1测段圆弧的曲率半径。
  5. 根据权利要求2所述的井眼轨迹自适应测斜计算方法，其特征在于，所述采用常规测斜计算方法计算最后一个测段下测点相对上测点的坐标增量，具体包括：
    根据公式
    Figure PCTCN2020102782-appb-100007
    计算最后一个测段的狗腿角，其中，γ (m-1)m为第m测段的狗腿角， α m为第m测点井斜角，
    Figure PCTCN2020102782-appb-100008
    为第m测点方位角，α m-1为第m-1测点井斜角，
    Figure PCTCN2020102782-appb-100009
    为第m-1测点方位角；
    若第m测段的狗腿角等于零，则采用公式
    Figure PCTCN2020102782-appb-100010
    计算第1测段下测点相对上测点的坐标增量，其中，L m为第m测点井深，L m-1为第m-1测点井深，ΔD (m-1)m为第m测段垂深的增量，ΔL p(m-1)m为第m测段水平投影长度的增量，ΔN (m-1)m为第m测段N坐标的增量，ΔE (m-1)m为第m测段E坐标的增量；
    若第m测段的狗腿角大于零，则采用公式
    Figure PCTCN2020102782-appb-100011
    计算第m测段下测点相对上测点的坐标增量，其中，ΔD (m-1)m为第m测段垂深的增量，ΔL p(m-1)m为第m测段水平投影长度的增量，ΔN (m-1)m为第m测段N坐标的增量，ΔE (m-1)m为第m测段E坐标的增量，R (m-1)m为第m测段圆弧的曲率半径。
  6. 根据权利要求3所述的井眼轨迹自适应测斜计算方法，其特征在于，所述根据第1测段和第2测段对应的三测点井深、井斜角和方位角，计算第2测段上测点的井眼曲率、挠率和工具面角预估值，具体为：
    根据公式
    Figure PCTCN2020102782-appb-100012
    计算第2测段上测点的井眼曲率的预估值，其中，α1为第1测点的井斜角，k 1e为第1个测点处 井眼曲率的预估值，k α1为第1个测点处的井斜变化率，
    Figure PCTCN2020102782-appb-100013
    为第1个测点处的方位变化率；
    根据公式
    Figure PCTCN2020102782-appb-100014
    计算第2测段上测点的挠率的预估值，其中，α1为第1测点的井斜角，k 1e为第1个测点处井眼曲率的预估值，k α1为第1个测点处的井斜变化率，
    Figure PCTCN2020102782-appb-100015
    为第1个测点处的方位变化率，
    Figure PCTCN2020102782-appb-100016
    为第1个测点处井斜变化率的变化率，
    Figure PCTCN2020102782-appb-100017
    为第1个测点处方位变化率的变化率,τ 1e为第1个测点处井眼挠率的预估值；
    根据公式
    Figure PCTCN2020102782-appb-100018
    计算第2测段上测点的工具面角的预估值，其中，ω 1e为第1个测点处工具面角的预估值，
    Figure PCTCN2020102782-appb-100019
    为第1测段的方位角增量，
    Figure PCTCN2020102782-appb-100020
    为第2测段的方位角增量，α 1为第1测点的井斜角，α 0为第0测点的井斜角，α 2为第2测点的井斜角，γ 01为第1测段的狗腿角，γ 12为第2测段的狗腿角。
  7. 根据权利要求3所述的井眼轨迹自适应测斜计算方法，其特征在于，所述根据第2测段和第3测段对应的三测点井深、井斜角和方位角，计算第2测段下测点的井眼曲率、挠率和工具面角预估值，具体为：
    根据公式
    Figure PCTCN2020102782-appb-100021
    计算第2测段下测点的井眼曲率的预估值，其中，α2为第2测点的井斜角，k 2e为第2个测点处井眼曲率的预估值，k α2为第2个测点处的井斜变化率，
    Figure PCTCN2020102782-appb-100022
    为第2个测点处的方位变化率；
    根据公式
    Figure PCTCN2020102782-appb-100023
    计算第2测段下测点的挠率的预估值，其中，α2为第2测点的井斜角，k 2e为第2个测点处井眼曲率的预估值，k α2为第2个测点处的井斜变化率，
    Figure PCTCN2020102782-appb-100024
    为第2个测点处的方位变化率，
    Figure PCTCN2020102782-appb-100025
    为第2个测点处井斜变化率的变化率，
    Figure PCTCN2020102782-appb-100026
    为第2个测点处方位变化率的变化率,τ 2e为第2个测点处井眼挠率的预估值；
    根据公式
    Figure PCTCN2020102782-appb-100027
    计算第1测段上测点的工具面角的预估值，其中，ω 2e为第2个测点处工具面角的预估值，
    Figure PCTCN2020102782-appb-100028
    为第2测段的方位角增量，
    Figure PCTCN2020102782-appb-100029
    为第3测段的方位角增量，α 2为第3测点的井斜角，α 1为第1测点的井斜角，α 23为第4测点的井斜角，γ 12为第2测段的狗腿角，γ 23为第3测段的狗腿角。
  8. 根据权利要求3所述的井眼轨迹自适应测斜计算方法，其特征在于，所述计算第i测段的上测点、下测点之间预估的井眼曲率、挠率的平均变化率和工具面角增量，具体为：
    根据公式
    Figure PCTCN2020102782-appb-100030
    计算第i测段的上测点、下测点之间预估的井眼曲率，其中，A k12为第2测段井眼曲率的平均变化率，L 1为第1测点井深，L 2为第2测点井深，k 1e为第1个测点处井眼曲率的预估值，k 2e为第2个测点处井眼曲率的预估值；
    根据公式
    Figure PCTCN2020102782-appb-100031
    计算第i测段的上测点、下测点之间预估的挠率的平均变化率，其中，A τ12为第2测段井眼挠率的平均变化率，τ 1e为第1个测点处井眼挠率的预估值，τ 2e为第2个测点处井眼挠率的预估值；
    根据公式
    Figure PCTCN2020102782-appb-100032
    计算第i测段的上测点、下测点之间预估的工具面角增量，其中，Δω 12为第2测段工具面角的增量，ω 1e为第1个测点处工具面角的预估值，ω 2e为第2个测点处工具面角的预估值。
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