Shale gas horizontal well stratified flow array holdup meter eccentric state water holdup calculation method

Abstract

The invention discloses a shale gas horizontal well stratified flow array holdup instrument eccentric state water holdup calculation method, which comprehensively considers the spatial distribution of array probes and the influence of instrument rotation in the logging process, and adopts a Newton interpolation method to carry out interpolation processing on water holdup data of different areas in the gravity direction. Therefore, the spatial distribution transition of the water holdup in the section of the shaft is smoother, and the matching degree between the well logging interpretation result and the actual working condition is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of horizontal well water holdup monitoring, and in particular to a method for calculating the water holdup of a shale gas horizontal well laminar flow array holdup meter in an eccentric state. Background Art

[0002] With increasing global demand for oil and gas resources and the depletion of conventional reservoirs, unconventional reservoirs, such as tight oil and gas and shale oil and gas, have become a hotspot for exploration and development. Volumetric fracturing (VF) in horizontal wells is a key technology currently used to exploit these reservoirs. During horizontal well development, accurately monitoring and evaluating the oil, gas, and water production dynamics of each well's development sub-layers is crucial for optimizing and adjusting oil and gas field development plans. Water holdup is one of the key parameters for accurately determining the oil, gas, and water content of each producing layer.

[0003] During multiphase fluid flow in horizontal wells, gravity and the wellbore structure influence the flow, causing gravity differentiation in the horizontal section. This results in heavy fluids concentrating primarily at the bottom of the wellbore, while light fluids accumulate primarily at the top, leading to distinct stratification. Array flow imaging logging tools are the primary technical means of accurately monitoring horizontal well production dynamics. Existing instruments for monitoring water holdup in horizontal wells include SONDEX's array capacitance water holdup logging tool (CAT) and array resistance water holdup logging tool (RAT), and Schlumberger's fluid scanning imaging tool (FSI). The CAT and RAT tools consist of 12 evenly distributed spring arms with capacitance and resistance water holdup probes fixed to them. These tools are deployed in series with a centralizer to monitor water holdup in multiphase fluids in horizontal wells. However, during actual horizontal well logging, array capacitance holdup logging (CAT) and array resistivity holdup logging (RAT) tools still experience a certain degree of eccentricity within the wellbore due to factors such as instrument length, gravity, and wellbore structure. The water holdup information detected by each probe does not reflect the water holdup at the probe's location when the instrument is centered. Furthermore, during the processing of array water holdup data, the eccentricity of the water holdup probe is often overlooked, resulting in overstated water holdup values ​​for horizontal well sections. This seriously affects the accuracy of quantitative calculations of water holdup for multiphase fluids in horizontal wells and can mislead the optimal design of horizontal well development plans. Summary of the Invention

[0004] The present invention provides a method for calculating the water holdup in the eccentric state of a shale gas horizontal well laminar flow array holdup instrument, so as to solve the problem that in the existing array water holdup data processing, the eccentricity effect of the water holdup probe is often ignored, resulting in an overcalculated water holdup value in the horizontal well section, which affects the accuracy of the quantitative calculation of the water holdup of the multiphase fluid in the horizontal well.

[0005] According to the first aspect, an embodiment provides a method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter, the method comprising: Project each probe of the array holdup meter in an eccentric state in a horizontal well onto the vertical axis of the wellbore center in the horizontal direction to obtain multiple projection points, number each probe and each projection point, and obtain the water holdup value at each probe position; A rectangular coordinate system is established with the center of the array ratemeter in an eccentric state as the origin and the horizontal and vertical directions as the X-axis and Y-axis respectively; Based on the established rectangular coordinate system, the vertical coordinate of the projection point and the water holdup Y of the probe position corresponding to the projection point are used. wi Construct two-dimensional coordinates (y i ,Y wi ), where y i is the ordinate corresponding to the i-th projection point, Y wi is the water holding capacity corresponding to the i-th projection point; According to the two-dimensional coordinates (y i ,Y wi ), the Newton interpolation method is used to perform interpolation fitting to obtain the Newton interpolation function, and based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated.

[0006] Furthermore, each probe and each projection point is numbered, specifically including: The 12 probes of the array rate meter are numbered in a clockwise direction, with the angle between two adjacent probes and the center of the instrument being 30°. The projection points of the 12 probes are numbered in order from top to bottom.

[0007] Furthermore, the water holdup value at each probe position is obtained, specifically including: The array probe monitoring signal is the capacitance or resistivity response value at the local position of the probe. Combined with the probe's response values ​​in pure water, pure oil, and pure gas, the water holdup value at the probe position is calculated and expressed as:

[0008] Where Y w,k is the water holding capacity of the kth array probe, k = 1, 2, …, 12; CPS k is the measured response value of the kth array probe; CPS w,k is the response value of the kth array probe under full water conditions; CPS h,k is the response value of the kth array probe under pure oil or pure gas conditions.

[0009] Furthermore, a rectangular coordinate system is established with the center of the array ratemeter in the eccentric state as the origin and the horizontal and vertical directions as the X-axis and Y-axis, respectively, including: Due to the eccentricity of the instrument, the upper half of the array probe is approximately distributed in an elliptical manner, and the lower half close to the well wall is approximately distributed in a circular manner; The equation of the ellipse in the upper half of the eccentric region is:

[0010] The equation of the circle in the lower half of the eccentric area is:

[0011] In the parametric coordinate system, the ellipse equation is:

[0012] In the parametric coordinate system, the circle equation is:

[0013] Where x is the abscissa of the rectangular coordinate system; y is the ordinate of the rectangular coordinate system; R is the radius of the wellbore; d is the eccentric distance between the instrument center and the wellbore center; It is the angle between the line connecting the array probe and the wellbore center (i.e., the origin) and the positive direction of the X-axis.

[0014] Furthermore, according to the two-dimensional coordinates (y i ,Y wi ), use Newton interpolation method to perform interpolation fitting to obtain Newton interpolation function, specifically including: Suppose there are k projection points. The two-dimensional coordinates from projection point 1 to projection point k are interpolated and fitted using Newton interpolation to obtain the function:

[0015] Where y is the y coordinate of a point in the interpolation area on the vertical axis of the wellbore center; Y w is the interpolation result of a certain point in the interpolation area on the vertical axis of the wellbore center; P(y) is the Newton interpolation function; The Newton interpolation function P(y) is defined as follows:

[0016] in, is the difference quotient of each order, and the calculation process is as follows:

[0017]

[0018]

[0019]

[0020]

[0021] Where y i is the ordinate of the i-th projection point; Y wi is the water holding capacity value corresponding to the i-th projection point.

[0022] Furthermore, based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated, specifically including: When the array holdup meter does not rotate in the wellbore or the rotation angle is a multiple of 30°, there is a water holdup probe at the top of the wellbore. The 12 probes are projected onto the vertical axis to form a total of 7 projection points. In this case, the Newton interpolation formula is:

[0023] Under this distribution, the interpolation range of the Newton interpolation method is the area between the lowest point of the wellbore section and the highest point of the wellbore section (-R+d, R+d). The average water holdup of the entire wellbore section is calculated as follows:

[0024] Convert x to y using the ellipse equation:

[0025] Where, for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

[0026] Furthermore, based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated, specifically including: When the array holdup meter rotates in the wellbore and the rotation angle is an odd multiple of 15°, the 12 probes are symmetrical about the vertical axis, with 6 probes on each side of the vertical axis. The 12 probes are projected onto the vertical axis to form a total of 6 projection points. The Newton interpolation formula obtained in this case is:

[0027] In this distribution state, the interpolation range of the Newton interpolation method is the ordinate area (a, b) between the lowest projection point and the highest projection point, where:

[0028]

[0029] Where a is the ordinate of the lowest projection point in the rectangular coordinate system; b is the ordinate of the topmost projection point in the rectangular coordinate system; The water holdup is calculated using the linear interpolation method for the wellbore cross-section area outside the interpolation interval of the Newton interpolation method. The water holdup at the highest point of the wellbore cross-section is assumed to be The water holding capacity at the lowest point is , and the ordinate of the highest point of the wellbore section is The vertical coordinate of the lowest point is , then the average water holdup of the entire wellbore section is:

[0030] in:

[0031]

[0032]

[0033]

[0034] Where y1 and y6 are the ordinates of the first and sixth projection points in the rectangular coordinate system respectively; y w1 and y w6 are the water holding rates corresponding to the 1st and 6th projection points respectively; f1(y) is the linear interpolation function between the lowest point of the wellbore section and the lowest projection point; f2(y) is the Newton interpolation function between the bottom projection point and the top projection point; f3(y) is the linear interpolation function between the highest point of the wellbore section and the topmost projection point; for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

[0035] Furthermore, based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated, specifically including: When the array holdup meter rotates in the wellbore and the rotation angle is not a multiple of 15°, the 12 probes are projected onto the vertical axis to form a total of 12 projection points. In this case, the Newton interpolation formula is:

[0036] In this distribution state, the interpolation range of the Newton interpolation method is the ordinate area (c, d) between the lowest projection point and the highest projection point, where:

[0037]

[0038] Where, is the angle between the top probe and the vertical axis; c is the ordinate of the lowest projection point in the rectangular coordinate system; d is the ordinate of the topmost projection point in the rectangular coordinate system; The water holdup is calculated using linear interpolation for the wellbore area outside the interpolation interval of the Newton interpolation method. The water holdup at the highest point of the wellbore section is assumed to be The water holding capacity at the lowest point is , and the ordinate of the highest point of the wellbore section is The vertical coordinate of the lowest point is , then the average water holdup of the entire wellbore section is:

[0039] in:

[0040]

[0041]

[0042]

[0043] Where y1 and y 12 are the ordinates of the 1st and 12th projection points in the rectangular coordinate system respectively; y w1 and y w12 are the water holding rates corresponding to the 1st and 12th projection points respectively; f1(y) is the linear interpolation function between the lowest point of the wellbore section and the lowest projection point; f2(y) is the Newton interpolation function between the bottom projection point and the top projection point; f3(y) is the linear interpolation function between the highest point of the wellbore section and the topmost projection point; for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

[0044] According to the second aspect, an embodiment provides a system for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter, the system comprising: The projection module is used to project each probe of the array holdup meter in the eccentric state in the horizontal well onto the vertical axis of the wellbore center in the horizontal direction to obtain multiple projection points, number each probe and each projection point, and obtain the water holdup value of each probe position; A coordinate system establishment module is used to establish a rectangular coordinate system with the center of the array ratemeter in an eccentric state as the origin and the horizontal and vertical directions as the X-axis and Y-axis respectively; Interpolation point establishment module is used to use the vertical coordinate of the projection point and the water holdup Y of the probe position corresponding to the projection point based on the established rectangular coordinate system wi Construct two-dimensional coordinates (y i ,Y wi ), where y i is the ordinate corresponding to the i-th projection point, Y wi is the water holding capacity corresponding to the i-th projection point; Interpolation calculation module, used to construct the two-dimensional coordinates (y i ,Y wi ), the Newton interpolation method is used to perform interpolation fitting to obtain the Newton interpolation function, and based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated.

[0045] The present invention provides a method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter, which has the following beneficial effects: (1) High calculation accuracy and more realistic results. This method comprehensively considers the spatial distribution of the array probe and the influence of the instrument rotation during the logging process. The Newton interpolation method is used to interpolate the water holdup data of different regions in the gravity direction, thereby making the spatial distribution transition of the water holdup in the wellbore section smoother and improving the matching degree between the logging interpretation results and the actual working conditions.

[0046] (2) Strong adaptability and wide application range. This method constructs an inversion model of the fluid distribution in the wellbore cross section based on the spatial position information of the array probe and the corresponding water holdup data. It can be applied to the water holdup measurement of horizontal wells under different well types and logging conditions, and has good versatility and operability.

[0047] (3) High computational efficiency, automated processing, and visualization of the water holdup of the wellbore cross section. By programming this method, the water holdup at multiple depth points within the wellbore can be quickly and batch-calculated, significantly improving interpretation efficiency and meeting the needs of large-scale data processing in actual engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flow chart of a method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter provided in one embodiment of the present invention; Figure 2 The probe distribution positions of the array holdup meter in the initial state in a method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter provided by one embodiment of the present invention; Figure 3 The probe distribution positions of the array holdup meter in distribution state 1 in a method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter provided by one embodiment of the present invention; Figure 4 The probe distribution positions of the array holdup meter in distribution state 2 in a method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter provided by one embodiment of the present invention; Figure 5 The probe distribution positions of the array holdup meter in distribution state 3 in a method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter provided by one embodiment of the present invention; Figure 6 A Newton interpolation effect of array holdup logging data in an example of a method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter provided by one embodiment of the present invention; Figure 7 The present invention provides a method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter in an embodiment of the present invention, and provides a Newton interpolation imaging effect of array holdup logging data. DETAILED DESCRIPTION

[0049] The present invention will be further described in detail below by means of specific embodiments in conjunction with the accompanying drawings. Similar elements in different embodiments are numbered with associated similar elements. In the following embodiments, many detailed descriptions are provided to enable the present invention to be better understood. However, those skilled in the art will readily appreciate that some of the features may be omitted under different circumstances, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the present invention are not shown or described in the specification. This is to avoid the core of the present invention being overwhelmed by excessive descriptions, and for those skilled in the art, it is not necessary to describe these related operations in detail. They can fully understand the related operations based on the description in the specification and the general technical knowledge in the art.

[0050] In addition, the features, operations, or characteristics described in the specification may be combined in any appropriate manner to form various embodiments. Furthermore, the steps or actions in the method description may be reordered or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various sequences in the specification and drawings are provided solely for the purpose of clearly describing a particular embodiment and are not intended to be mandatory, unless otherwise specified.

[0051] The first embodiment of the present invention provides a method for calculating the water holdup of a shale gas horizontal well laminar flow array holdup instrument in an eccentric state. Based on the calculation results, understandings and conclusions obtained by this method, the calculation method of the horizontal wellbore water holdup using the monitoring data after the array holdup instrument is eccentric is enriched. The horizontal wellbore water holdup calculated based on the present invention has the highest consistency with the actual fluid distribution in the wellbore, thereby improving the accuracy of the gas and water dynamic evaluation of each production layer in the development of horizontal wells in shale gas reservoirs. Figure 1 Provide detailed explanation.

[0052] like Figure 1 As shown, in step S100, each probe of the array holdup meter in an eccentric state in a horizontal well is projected horizontally onto the vertical axis of the wellbore center to obtain multiple projection points, each probe and each projection point is numbered, and the water holdup value of each probe position is obtained. The above steps specifically include: S110: Initially number the 12 water holdup probes of the array holdup instrument in a clockwise direction, with the angle between adjacent probes and the instrument center at 30°. Project the 12 probes horizontally onto the vertical axis of the wellbore center and number them sequentially from top to bottom. There are k projection points, and the water holdup at each projection point is the average water holdup of the corresponding probes. Figure 2 The probe distribution positions of the array rate meter in the initial state, where probe No. 1 is at the highest point of all probes on the central axis of the wellbore section, and probe No. 7 is at the lowest point of the wellbore section.

[0053] S120, for the array holdup meter, the array probe monitoring signal is the capacitance or point resistivity response value at the local position of the probe. Combined with the probe's response values ​​in pure water, pure oil, and pure gas, the water holdup value at the probe position can be calculated and expressed as,

[0054] Where Y w,k is the water holding capacity of the kth array probe, k = 1, 2, …, 12; CPS k is the measured response value of the kth array probe; CPS w,k is the response value of the kth array probe under full water conditions; CPSh,k is the response value of the kth array probe under pure oil or pure gas conditions.

[0055] like Figure 1 As shown, in step S200, a rectangular coordinate system is established with the instrument center of the array ratemeter in an eccentric state as the origin, and the horizontal and vertical directions as the X-axis and Y-axis respectively.

[0056] The above steps specifically include: S210, with the center of the eccentric instrument as the origin, the horizontal and vertical directions as the X-axis and Y-axis to establish a rectangular coordinate system, the wellbore radius is , the instrument eccentricity distance is Due to the eccentricity of the instrument, the upper half of the array probe can be approximately distributed in an elliptical manner, while the lower half can be approximately distributed in a circular manner due to its close contact with the well wall.

[0057] S220, the ellipse equation of the upper half of the eccentric area is:

[0058] The equation of the circle in the lower half of the eccentric area is:

[0059] In the parametric coordinate system, the ellipse equation is:

[0060] In the parametric coordinate system, the circle equation is:

[0061] Where x is the abscissa of the rectangular coordinate system; y is the ordinate of the rectangular coordinate system; R is the radius of the wellbore; d is the eccentric distance between the instrument center and the wellbore center; It is the angle between the line connecting the array probe and the origin and the positive direction of the X-axis.

[0062] like Figure 1 As shown, in step S300, based on the established rectangular coordinate system, the vertical coordinate of the projection point and the water holdup Y of the probe position corresponding to the projection point are used. wi Construct two-dimensional coordinates (y i ,Y wi ), where y i is the ordinate corresponding to the i-th projection point, Y wi is the water holding capacity corresponding to the i-th projection point.

[0063] The above steps specifically include: S310, from the ellipse equation and circle equation in the parametric coordinate system, the coordinates of each probe can be substituted into the corresponding angle to obtain the value. i The water holding capacity Y corresponding to the projection point wi Combined into a new two-dimensional coordinate (y i ,Y wi ) for subsequent interpolation calculation. i Y is the vertical coordinate corresponding to the i-th projection point, meters (m); wi is the water holding capacity corresponding to the i-th projection point, a decimal.

[0064] like Figure 1 As shown, in step S400, the two-dimensional coordinates (y i ,Y wi ), the Newton interpolation method is used to perform interpolation fitting to obtain the Newton interpolation function, and based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated.

[0065] The above steps specifically include: S410: Use Newton interpolation to interpolate the coordinates of projection point 1 to projection point k to obtain a function. Since Newton interpolation uses a high-order polynomial to fit the data points, it approximates well within the known point interval, but Runge phenomenon may occur outside the interval, resulting in distorted prediction values. Therefore, the interpolation range is limited to between probe 1 and probe k:

[0066] Where y is the y coordinate of a point in the interpolation area on the vertical axis of the wellbore center; Y w is the interpolation result of a certain point in the interpolation area on the vertical axis of the wellbore center; P(y) is the Newton interpolation function.

[0067] Among them, the Newton interpolation function P(y) is defined as follows:

[0068] is the difference quotient of each order, and the calculation process is as follows:

[0069]

[0070]

[0071]

[0072]

[0073] Where y i is the ordinate of the i-th projection point; Y wi is the water holding capacity value corresponding to the i-th projection point.

[0074] Since the range of water holdup is [0,1], the calculation results of the Newton interpolation method need to be constrained to be limited within this interval.

[0075] S420: Since the array holdup meter may rotate during downhole monitoring, causing the water holdup probe to deviate from its original state, the array holdup meter can be distributed in three states within the wellbore based on the instrument deflection angle obtained from monitoring: (1) Distribution state 1: When the array holdup meter does not rotate in the wellbore or the rotation angle is a multiple of 30°, there is a water holdup probe at the top of the wellbore, and the 12 probes are projected onto the vertical axis to form a total of 7 projection points. Figure 3 The probe distribution position of the array rate meter in distribution state 1, wherein the probes are symmetrically distributed with respect to the central axis of the wellbore section, and there are two probes on the axis. The probes have 7 projection points on the central axis of the wellbore.

[0076] The Newton interpolation formula obtained in this case is:

[0077] Under this distribution, the interpolation range of the Newton interpolation method is the area between the lowest point of the wellbore section and the highest point of the wellbore section (-R+d, R+d). The average water holdup of the entire wellbore section is:

[0078] Convert x to y using the ellipse equation:

[0079] Where, for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

[0080] (2) Distribution state 2: When the array holdup meter rotates in the wellbore and the rotation angle is an odd multiple of 15°, the 12 probes are symmetrical about the vertical axis, and there are 6 probes on each side of the vertical axis. The 12 probes are projected onto the vertical axis to form a total of 6 projection points. Figure 4 The probe distribution positions of the array rate meter in distribution state 2, where there are 6 probes at both ends of the wellbore central axis and they are symmetrically distributed. The probes have 6 projection points on the wellbore central axis.

[0081] The Newton interpolation formula obtained in this case is:

[0082] In this distribution state, the interpolation range of the Newton interpolation method is the ordinate area (a, b) between the lowest and highest projection points. The ordinates of these projection points are used as inputs of the Newton interpolation function (equivalent to the new abscissa) to interpolate and calculate the water holdup (new ordinate), where:

[0083]

[0084] Where a is the ordinate of the lowest projection point in the rectangular coordinate system; b is the vertical coordinate of the topmost projection point in the rectangular coordinate system.

[0085] The water holdup is calculated using the linear interpolation method for the wellbore cross-section area outside the interpolation interval of the Newton interpolation method. The water holdup at the highest point of the wellbore cross-section is assumed to be The water holding capacity at the lowest point is , and the ordinate of the highest point of the wellbore section is The vertical coordinate of the lowest point is , then the average water holdup of the entire wellbore section is:

[0086] in:

[0087]

[0088]

[0089]

[0090] Where y1 and y6 are the ordinates of the first and sixth projection points in the rectangular coordinate system respectively; y w1 and y w6 are the water holding rates corresponding to the 1st and 6th projection points respectively; f1(y) is the linear interpolation function between the lowest point of the wellbore section and the lowest projection point; f2(y) is the Newton interpolation function between the bottom projection point and the top projection point; f3(y) is the linear interpolation function between the highest point of the wellbore section and the topmost projection point; for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

[0091] (3) Distribution state three: When the array holdup meter rotates in the wellbore and the rotation angle is not a multiple of 15°, the 12 probes are projected onto the vertical axis to form a total of 12 projection points. Figure 5 The probe distribution position of the array rate meter in distribution state 3, wherein the probe is not symmetrically distributed with respect to the central axis of the wellbore, and the probe has 12 projection points on the central axis of the wellbore.

[0092] The Newton interpolation formula obtained in this case is:

[0093] In this distribution state, the interpolation range of the Newton interpolation method is the ordinate area (c, d) between the lowest projection point and the highest projection point, where:

[0094]

[0095]

[0096]

[0097] Where, is the angle between the top probe and the vertical axis; c is the ordinate of the lowest projection point in the rectangular coordinate system; d is the ordinate of the topmost projection point in the rectangular coordinate system.

[0098] The water holdup is calculated using linear interpolation for the wellbore area outside the interpolation interval of the Newton interpolation method. The water holdup at the highest point of the wellbore section is assumed to be The water holding capacity at the lowest point is , and the ordinate of the highest point of the wellbore section is The vertical coordinate of the lowest point is , then the average water holdup of the entire wellbore section is:

[0099] in:

[0100]

[0101]

[0102]

[0103] Where y1 and y 12 are the ordinates of the 1st and 12th projection points in the rectangular coordinate system respectively; y w1 and y w12 are the water holding rates corresponding to the 1st and 12th projection points respectively; f1(y) is the linear interpolation function between the lowest point of the wellbore section and the lowest projection point; f2(y) is the Newton interpolation function between the bottom projection point and the top projection point; f3(y) is the linear interpolation function between the highest point of the wellbore section and the topmost projection point; for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

[0104] Figure 6 In order to obtain the Newton interpolation effect of array holdup logging data, the area between the projection points uses the Newton interpolation method, and the other areas use the linear interpolation method, and the result of Newton interpolation is limited to [0,1]. Figure 7 This is the Newton interpolation imaging effect of the array holdup logging data. The imaging effect from green to blue is used to show the change of water holdup from 0 to 1, making the change of water holdup in the wellbore section intuitive.

[0105] Application examples: First, a multiphase flow simulation experimental system was used to simulate gas-water two-phase flow at a 90° well inclination (horizontal). Stratified gas-water two-phase flow was obtained under six simulated conditions. Monitoring was performed using a combination of an array turbine flowmeter, an array capacitance water holdup meter, and an array resistance water holdup meter. During the logging process, the array probe was fully extended. The array probe responses are shown in Table 1.

[0106] Table 1 Monitoring responses of the array capacitance probe in laminar flow under six simulation conditions

[0107] Then, based on the array probe response values, the water holdup value of each array probe is calculated. The response values ​​of each array probe in pure water and pure gas are as follows: Pure water environment: CPS w,1 =42, CPS w,2 =51, CPS w,3 =50, CPS w,4 =58, CPS w,5 =47, CPS w,6 =45, CPS w,7 =54, CPS w,8=52, CPS w,9 =59, CPS w,10 =57, CPS w,11 =47, CPS w,12 =56.

[0108] Pure gas environment: CPS g,1 =148, CPS g,2 =177, CPS g,3 =132, CPS g,4 =176, CPS g,5 =170, CPS g,6 =162, CPS g,7 =144, CPS g,8 =151, CPS g,9 =142, CPS g,10 =154, CPS g,11 =173, CPS g,12 =195.

[0109] Finally, the new method of the embodiment of the present invention was used to correct for the effect of probe eccentricity. The water holdup values ​​at the six measuring points were calculated, as shown in Table 2. The water holdup values ​​calculated using the monitoring data from the array water holdup meter ranged from 67.90% to 86.29%, while the water holdup values ​​calculated using shut-in wells ranged from 61.94% to 81.59%. The overall relative error was less than 9.0%, meeting the actual application requirements of mines.

[0110] Table 2 Comparison of calculated water holdup after eccentricity correction and actual shut-in water holdup

[0111] Corresponding to the above-disclosed method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter, an embodiment of the present invention further discloses a system for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter, which specifically includes: The projection module is used to project each probe of the array holdup meter in the eccentric state in the horizontal well onto the vertical axis of the wellbore center in the horizontal direction to obtain multiple projection points, number each probe and each projection point, and obtain the water holdup value of each probe position; A coordinate system establishment module is used to establish a rectangular coordinate system with the center of the array ratemeter in an eccentric state as the origin and the horizontal and vertical directions as the X-axis and Y-axis respectively; Interpolation point establishment module is used to use the vertical coordinate of the projection point and the water holdup Y of the probe position corresponding to the projection point based on the established rectangular coordinate system wi Construct two-dimensional coordinates (y i ,Y wi ), where yi is the ordinate corresponding to the i-th projection point, Y wi is the water holding capacity corresponding to the i-th projection point; Interpolation calculation module, used to construct the two-dimensional coordinates (y i ,Y wi ), the Newton interpolation method is used to perform interpolation fitting to obtain the Newton interpolation function, and based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated.

[0112] It should be noted that for the detailed description of the eccentric state water holdup calculation system of the stratified flow array holdup meter for shale gas horizontal wells provided in an embodiment of the present invention, reference can be made to the relevant description of the eccentric state water holdup calculation method of the stratified flow array holdup meter for shale gas horizontal wells provided in an embodiment of the present invention, which will not be repeated here.

[0113] The above examples are used to illustrate the present invention, which are only used to help understand the present invention and are not intended to limit the present invention. Those skilled in the art can make several simple deductions, modifications or substitutions based on the concept of the present invention.

Claims

1. A method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter, characterized in that: The method comprises: Project each probe of the array holdup meter in an eccentric state in a horizontal well onto the vertical axis of the wellbore center in the horizontal direction to obtain multiple projection points, number each probe and each projection point, and obtain the water holdup value at each probe position; A rectangular coordinate system is established with the center of the array ratemeter in an eccentric state as the origin and the horizontal and vertical directions as the X-axis and Y-axis respectively; Based on the established rectangular coordinate system, the vertical coordinate of the projection point and the water holdup Y of the probe position corresponding to the projection point are used. wi Construct two-dimensional coordinates (y i ,Y wi ), where y i is the ordinate corresponding to the i-th projection point, Y wi is the water holding capacity corresponding to the i-th projection point; According to the two-dimensional coordinates (y i ,Y wi ), the Newton interpolation method is used to perform interpolation fitting to obtain the Newton interpolation function, and based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated.

2. The method for calculating the water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 1, characterized in that: Number each probe and each projection point separately, including: The 12 probes of the array rate meter are numbered in a clockwise direction, with the angle between two adjacent probes and the center of the instrument being 30°. The projection points of the 12 probes are numbered in order from top to bottom.

3. The method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 1, wherein: Obtain the water holdup value at each probe position, including: The array probe monitoring signal is the capacitance or resistivity response value at the local position of the probe. Combined with the probe's response values ​​in pure water, pure oil, and pure gas, the water holdup value at the probe position is calculated and expressed as: Where, Y w,k For the k The water holding capacity of each array probe, k =1,2,…,12; CPS k For the k The measured response value of each array probe; CPS w,k For the k The response value of each array probe under full water conditions; CPS h,k For the k The response value of each array probe under pure oil or pure gas conditions.

4. The method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 1, wherein: A rectangular coordinate system is established with the center of the array ratemeter in an eccentric state as the origin, and the horizontal and vertical directions as the X-axis and Y-axis, respectively. Specifically, it includes: Due to the eccentricity of the instrument, the upper half of the array probe is approximately distributed in an elliptical manner, and the lower half close to the well wall is approximately distributed in a circular manner; The equation of the ellipse in the upper half of the eccentric region is: The equation of the circle in the lower half of the eccentric area is: In the parametric coordinate system, the ellipse equation is: In the parametric coordinate system, the circle equation is: Where x is the abscissa of the rectangular coordinate system; y is the ordinate of the rectangular coordinate system; R is the radius of the wellbore; d is the eccentric distance between the instrument center and the wellbore center; It is the angle between the line connecting the array probe and the wellbore center (i.e., the origin) and the positive direction of the X-axis.

5. The method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 4, characterized in that: According to the two-dimensional coordinates (y i ,Y wi ), use Newton interpolation method to perform interpolation fitting to obtain Newton interpolation function, specifically including: Suppose there are k projection points. The two-dimensional coordinates from projection point 1 to projection point k are interpolated and fitted using Newton interpolation to obtain the function: Where y is the y coordinate of a point in the interpolation area on the vertical axis of the wellbore center; Y w is the interpolation result of a certain point in the interpolation area on the vertical axis of the wellbore center; P(y) is the Newton interpolation function; The Newton interpolation function P(y) is defined as follows: in, is the difference quotient of each order, and the calculation process is as follows: Where y i is the ordinate of the i-th projection point; Y wi is the water holding capacity value corresponding to the i-th projection point.

6. The method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 5, characterized in that: Based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated, including: When the array holdup meter does not rotate in the wellbore or the rotation angle is a multiple of 30°, there is a water holdup probe at the top of the wellbore. The 12 probes are projected onto the vertical axis to form a total of 7 projection points. In this case, the Newton interpolation formula is: Under this distribution, the interpolation range of the Newton interpolation method is the area between the lowest point of the wellbore section and the highest point of the wellbore section (-R+d, R+d). The average water holdup of the entire wellbore section is calculated as follows: Convert x to y using the ellipse equation: Where, for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

7. The method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 5, characterized in that: Based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated, including: When the array holdup meter rotates in the wellbore and the rotation angle is an odd multiple of 15°, the 12 probes are symmetrical about the vertical axis, with 6 probes on each side of the vertical axis. The 12 probes are projected onto the vertical axis to form a total of 6 projection points. The Newton interpolation formula obtained in this case is: In this distribution state, the interpolation range of the Newton interpolation method is the ordinate area (a, b) between the lowest projection point and the highest projection point, where: Where a is the ordinate of the lowest projection point in the rectangular coordinate system; b is the ordinate of the topmost projection point in the rectangular coordinate system; The water holdup is calculated using the linear interpolation method for the wellbore cross-section area outside the interpolation interval of the Newton interpolation method. The water holdup at the highest point of the wellbore cross-section is assumed to be The water holding capacity at the lowest point is , and the ordinate of the highest point of the wellbore section is The vertical coordinate of the lowest point is , then the average water holdup of the entire wellbore section is: in: Where y1 and y6 are the ordinates of the first and sixth projection points in the rectangular coordinate system respectively; y w1 and y w6 are the water holding rates corresponding to the 1st and 6th projection points respectively; f1(y) is the linear interpolation function between the lowest point of the wellbore section and the lowest projection point; f2(y) is the Newton interpolation function between the bottom projection point and the top projection point; f3(y) is the linear interpolation function between the highest point of the wellbore section and the topmost projection point; for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

8. The method for calculating water holdup in an eccentric state of a shale gas horizontal well laminar flow array holdup meter according to claim 5, characterized in that: Based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated, including: When the array holdup meter rotates in the wellbore and the rotation angle is not a multiple of 15°, the 12 probes are projected onto the vertical axis to form a total of 12 projection points. In this case, the Newton interpolation formula is: In this distribution state, the interpolation range of the Newton interpolation method is the ordinate area (c, d) between the lowest projection point and the highest projection point, where: Where, is the angle between the top probe and the vertical axis; c is the ordinate of the lowest projection point in the rectangular coordinate system; d is the ordinate of the topmost projection point in the rectangular coordinate system; The water holdup is calculated using linear interpolation for the wellbore area outside the interpolation interval of the Newton interpolation method. The water holdup at the highest point of the wellbore section is assumed to be The water holding capacity at the lowest point is , and the ordinate of the highest point of the wellbore section is The vertical coordinate of the lowest point is , then the average water holdup of the entire wellbore section is: in: Where y1 and y 12 are the ordinates of the 1st and 12th projection points in the rectangular coordinate system respectively; y w1 and y w12 are the water holding rates corresponding to the 1st and 12th projection points respectively; f1(y) is the linear interpolation function between the lowest point of the wellbore section and the lowest projection point; f2(y) is the Newton interpolation function between the bottom projection point and the top projection point; f3(y) is the linear interpolation function between the highest point of the wellbore section and the topmost projection point; for , the total area of ​​the wellbore cross section; is the average water holdup of the entire wellbore section.

9. A shale gas horizontal well laminar flow array holdup meter eccentric state water holdup calculation system, characterized in that: The system comprises: The projection module is used to project each probe of the array holdup meter in the eccentric state in the horizontal well onto the vertical axis of the wellbore center in the horizontal direction to obtain multiple projection points, number each probe and each projection point, and obtain the water holdup value of each probe position; A coordinate system establishment module is used to establish a rectangular coordinate system with the center of the array ratemeter in an eccentric state as the origin and the horizontal and vertical directions as the X-axis and Y-axis respectively; Interpolation point establishment module is used to use the vertical coordinate of the projection point and the water holdup Y of the probe position corresponding to the projection point based on the established rectangular coordinate system wi Construct two-dimensional coordinates (y i ,Y wi ), where y i is the ordinate corresponding to the i-th projection point, Y wi is the water holding capacity corresponding to the i-th projection point; Interpolation calculation module, used to construct the two-dimensional coordinates (y i ,Y wi ), the Newton interpolation method is used to perform interpolation fitting to obtain the Newton interpolation function, and based on the obtained Newton interpolation function, the average water holdup of the entire wellbore section is calculated.

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