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CN112943198B - A calculation method of non-uniform stress field in deep shale complex structural strata - Google Patents

A calculation method of non-uniform stress field in deep shale complex structural strata Download PDF

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CN112943198B
CN112943198B CN202110236279.3A CN202110236279A CN112943198B CN 112943198 B CN112943198 B CN 112943198B CN 202110236279 A CN202110236279 A CN 202110236279A CN 112943198 B CN112943198 B CN 112943198B
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赵金洲
任岚
林然
李真祥
蒋廷学
付永强
宋毅
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Abstract

本发明公开一种深层页岩复杂构造地层非均匀应力场计算方法，包括计算各井位置局部坐标下的地层三轴应力梯度；计算各井位置储层中部局部坐标下的地层三轴应力值；计算各井位置储层中部全局坐标下的地层应力张量分量；计算目标区域内任意位置储层中部全局坐标下的地层应力张量分量；计算目标区域内任意位置储层中部局部坐标下的地层三轴应力值与最大主应力方向。本发明可无需进行大规模地质构造力学建模，仅依靠目标区域内已钻设井的地层三轴应力值与最大水平主应力方向等有限数据，即可计算目标区域内任意位置处地层三轴应力场非均匀分布情况，解决了深层页岩复杂地层应力场在较小区域内变化较快，缺乏快速准确的非均匀地层应力场计算方法的问题。

Figure 202110236279

The invention discloses a method for calculating the non-uniform stress field of deep shale complex structure formation, which includes calculating the formation triaxial stress gradient under the local coordinates of each well position; Calculate the formation stress tensor component under the global coordinates of the middle of the reservoir at each well position; calculate the formation stress tensor component under the global coordinates of the middle of the reservoir at any position in the target area; Triaxial stress value and direction of maximum principal stress. The invention can calculate the formation triaxiality at any position in the target area by only relying on limited data such as the formation triaxial stress value and the maximum horizontal principal stress direction of the drilled wells in the target area without the need for large-scale geological structural mechanics modeling The non-uniform distribution of the stress field solves the problem that the stress field of the deep shale complex formation changes rapidly in a small area and lacks a fast and accurate calculation method for the non-uniform formation stress field.

Figure 202110236279

Description

Method for calculating inhomogeneous stress field of deep shale complex formation
Technical Field
The invention relates to a method for calculating a heterogeneous stress field of a deep shale complex formation, and belongs to the technical field of shale gas development.
Background
Hydraulic fracturing is one of the major stimulation practices for oil and gas reservoirs. In recent years, the method is widely applied to development of unconventional oil and gas reservoirs represented by shale gas reservoirs. In the shale fracturing process, the minimum level main stress value of the stratum is closely related to the fracturing construction pressure; determining an extension path of the hydraulic fracture according to the maximum horizontal principal stress direction of the stratum; the stress difference affects the construction problem of the complex fracture network, and further affects the production effect of the fractured oil-gas well. Therefore, the hydraulic fracturing construction pressure range and the hydraulic fracture extension path can be accurately predicted through stratum stress field calculation, and guidance is provided for deep shale fracturing optimization design and site construction.
Because of the different degrees of severity of the movement of the geological structure, the distribution of the stratum stress is different. For areas where formation motion is gradual, such as successive sedimentary zones of shallower formations, formation motion has less of an effect on formation stress. The traditional stratum stress calculation method is mainly characterized in that the minimum horizontal principal stress value of a stratum is accurately measured through a hydraulic fracturing test method, the maximum horizontal principal stress value of the stratum is calculated according to a construction coefficient, the orientation of a well wall induced crack is observed through imaging logging, and the direction of the maximum horizontal principal stress is determined. In 2008, the poplar and the Liugong Biao establish a stratum level principal stress explanation chart by utilizing a stratum stress mechanical model under a complex construction condition on the basis of inversion of stratum rock parameters by logging data. In 2016, Yangxiangqiang et al determined the functional relationship between the stratum stress and the rock parameters and the lateral pressure coefficient by geological three-dimensional modeling and adopting orthogonal numerical analysis and genetic programming algorithm, and inversely calculated the stratum stress field. In 2020, the Dong et al propose a three-dimensional modeling-based stratum stress field inversion method, which inverts the stratum stress distribution characteristics by establishing a large-scale three-dimensional geological structure numerical model and by parallel calculation. In 2021, Lijing et al characterized the geologic structure characteristics based on a box-dimension method, and further calculated the formation stress by optimal inversion of boundary constraints using a neural network method.
In summary, most of the existing stratum stress calculation methods mainly aim at the situations that the movement of a geological structure is smooth and the geological structure is simple; the geological structure of the deep shale stratum is usually complex, the stratum principal stress value and the principal stress direction change rapidly in a small area, a large-scale three-dimensional geological structure numerical model needs to be established, model calibration is carried out by depending on a large amount of field measurement data, the workload is large, and the time consumption is long. Therefore, a calculation method for the inhomogeneous stress field of the stratum with the deep shale complex structure needs to be established urgently, large-scale geological structure mechanical modeling is not needed, the inhomogeneous distribution condition of the triaxial stress field of the stratum at any position in a target area can be calculated only by means of a small amount of field measurement data, a foundation is provided for predicting the hydraulic fracturing construction pressure range, the hydraulic fracture extension path and the fracture network complexity, the deep shale fracturing optimization design and the field construction are guided, and the fracturing yield-increasing effect is effectively improved.
Disclosure of Invention
The invention provides a method for calculating a heterogeneous stress field of a deep shale complex formation, aiming at solving the problems that the stress field of the deep shale complex formation in the prior art changes rapidly in a small area and a rapid and accurate calculation method of the heterogeneous stress field is lacked.
The technical scheme provided by the invention for solving the technical problems is as follows: a method for calculating the inhomogeneous stress field of deep shale complex stratum includes
Determining a stratum triaxial stress gradient under local coordinates of each well position according to stratum stress data and well position coordinate data of drilled wells in a target area;
determining a stratum stress tensor under the central local coordinate of the reservoir at each well position according to the stratum triaxial stress gradient under the local coordinate of each well position and the vertical depth data of the central part of the reservoir in the target area;
determining the formation stress tensor under the central global coordinate of the reservoir at each well position according to the formation stress tensor under the central local coordinate of the reservoir at each well position and a tensor coordinate system conversion algorithm;
determining a stratum stress tensor under the central global coordinate of the reservoir at any position in a target area and a stratum stress tensor component distribution cloud picture under the central global coordinate in the target area according to the stratum stress tensor under the central global coordinate of the reservoir at each well position and a natural adjacent point three-dimensional interpolation method;
determining a stratum triaxial main stress value and a direction component thereof under the middle local coordinate of the reservoir at any position in the target area according to the stratum stress tensor under the middle global coordinate of the reservoir at any position in the target area;
according to stratum triaxial main stress values and direction components of the stratum triaxial main stress values under the middle part local coordinates of the reservoir at any position in the target region, drawing a stratum maximum horizontal main stress value, a stratum minimum horizontal main stress value, a stratum vertical main stress value distribution cloud chart and maximum and minimum horizontal stress direction vector charts under the local coordinates in the target region;
and determining the non-uniform distribution condition of the triaxial stress field of the stratum at any position in the target region according to the distribution cloud graph of the maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum under the local coordinate in the target region and the direction vector graphs of the maximum horizontal stress and the minimum horizontal stress.
The further technical scheme is that the method for determining the triaxial stress gradient of the stratum under the local coordinate of each well position according to the stratum stress data and the well position coordinate data of the drilled well in the target area comprises the following steps:
collecting stratum stress data obtained by measuring drilled wells in a target area, wherein the stratum stress data comprises a maximum horizontal main stress value, a minimum horizontal main stress value and a vertical main stress value;
collecting coordinate data of drilled well positions in a target area and the vertical depth of each well stratum stress measuring point, and drawing a well position distribution diagram;
respectively calculating three-axis stress gradients of the stratum under the local coordinates of each well position by using the following formula, wherein the three-axis stress gradients of the stratum comprise a maximum horizontal main stress gradient, a minimum horizontal main stress gradient and a vertical main stress gradient;
Figure BDA0002960311050000031
in the formula: gi H、Gi h、Gi vThe maximum horizontal main stress gradient, the minimum horizontal main stress gradient and the vertical main stress gradient of the stratum at the No. i well position are Pa/m; sigmaiH、σi h、σi vThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum at the I-type well position are Pa; diMeasuring the vertical depth m of a formation stress data measuring point of a No. i well; and i is the number of the formation stress value measuring well.
The further technical scheme is that the step of determining the stratum stress tensor of each well position under the central local coordinate of the reservoir according to the triaxial stress gradient of the reservoir under the local coordinate of each well position and the vertical depth data of the central part of the reservoir in the target area comprises the following steps:
collecting vertical depth data of the middle part of a reservoir in a target area;
respectively calculating the stratum triaxial stress values under the middle local coordinates of the reservoir at each well position by using the following formula;
Figure BDA0002960311050000041
in the formula: gi H、Gi h、Gi vThe maximum horizontal main stress gradient, the minimum horizontal main stress gradient and the vertical main stress gradient of the stratum at the No. i well position are Pa/m; sigmai Hmid、σi hmid、σi vmidThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum under the middle local coordinate of the reservoir at the position of the No. i well are Pa; dmidThe vertical depth m of the middle part of the reservoir in the target area;
assembling stratum triaxial stress values under the central local coordinates of the reservoir at each well position into a tensor form by using the following formula;
Figure BDA0002960311050000042
in the formula: sigmai Hmid、σi hmid、σi vmidThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum under the middle local coordinate of the reservoir at the position of the No. i well are Pa; sigmai mid|localIs the stratum stress tensor Pa under the central local coordinate of the reservoir at the position of the No. i well.
The further technical scheme is that the step of determining the formation stress tensor under the central global coordinate of the reservoir at each well position according to the formation stress tensor under the central local coordinate of the reservoir at each well position and a tensor coordinate system conversion algorithm comprises the following steps:
collecting the maximum horizontal main stress direction of each well position obtained by the measurement of the drilled well in the target area, and calculating the included angle between the maximum horizontal main stress direction and the x axis of the global coordinate system;
respectively calculating stratum stress tensor components under the central global coordinates of the reservoir at each well position by using a tensor coordinate system conversion algorithm according to the following formula;
Figure BDA0002960311050000051
in the formula: sigmai xx、σi yy、σi xy、σi xz、σi yz、σi zzThe method comprises the following steps of (1) forming a formation stress tensor component Pa under the central global coordinate of a reservoir at the position of a well I; thetaiThe included angle between the maximum horizontal main stress of the No. i well and the x axis of the global coordinate system is degree; sigmai Hmid、σi hmid、σi vmidThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum under the middle local coordinate of the reservoir at the position of the No. i well are Pa;
assembling stratum stress tensor components under the central global coordinate of the reservoir at each well position into a tensor form by using the following formula;
Figure BDA0002960311050000052
in the formula: sigmai xx、σi yy、σi xy、σi xz、σi yz、σi zzThe method comprises the following steps of (1) forming a formation stress tensor component Pa under the central global coordinate of a reservoir at the position of a well I; pa; sigmai mid|globalAnd the formation stress tensor is Pa under the central global coordinate of the reservoir at the position of the No. i well.
The further technical scheme is that the method for determining the stratum stress tensor of the reservoir at any position in the target area under the global coordinate in the middle of the reservoir at each well position and the component distribution cloud pictures of the stratum stress tensor under the global coordinate in the target area according to the stratum stress tensor under the global coordinate in the middle of the reservoir at each well position and the three-dimensional interpolation method of the natural adjacent points comprises the following steps:
according to the stratum stress tensor component under the central global coordinate of the reservoir at each well position, calculating the stratum stress tensor component under the central global coordinate of the reservoir at any position in the target area by a natural adjacent point three-dimensional interpolation method by using the following formula;
Figure BDA0002960311050000061
in the formula: sigmai mid|globalThe method comprises the steps of (1) forming a formation stress tensor Pa under the global coordinate of the middle part of a reservoir at any position in a target area; sigmaxx、σyy、σxy、σxz、σyz、σzzThe method comprises the following steps of (1) forming a formation stress tensor component Pa under the global coordinate of the middle part of a reservoir at any position in a target area; interp3N is a natural neighboring point three-dimensional interpolation operator;
assembling the formation stress tensor components under the central global coordinate of the reservoir at any position in the target area into a tensor form by using the following formula;
Figure BDA0002960311050000062
in the formula: sigmai mid|globalThe method comprises the steps of (1) forming a formation stress tensor Pa under the global coordinate of the middle part of a reservoir at any position in a target area; sigmaxx、σyy、σxy、σxz、σyz、σzzThe method comprises the following steps of (1) forming a formation stress tensor component Pa under the global coordinate of the middle part of a reservoir at any position in a target area;
and drawing a distribution cloud picture of the formation stress tensor components under the global coordinate in the target area.
The further technical scheme is that the stratum triaxial principal stress value under the central local coordinate of the reservoir at any position in the target area is determined according to the stratum stress tensor under the central global coordinate of the reservoir at any position in the target area, and the directional components of the stratum triaxial principal stress value comprise:
according to the stratum stress tensor under the central global coordinate of the reservoir at any position in the target area, calculating the stratum stress tensor eigenvalue and eigenvector matrix under the central local coordinate of the reservoir at any position in the target area by utilizing the following formula through the matrix eigenvalue and eigenvector operation;
[V,D]＝eig(σmid|global)
in the formula: eig is a matrix eigenvalue and eigenvector operator; v is a stratum stress tensor eigenvalue matrix Pa under the middle local coordinate of the reservoir at any position in the target area; d is a formation stress tensor eigenvector matrix under the middle local coordinate of the reservoir at any position in the target area, and is dimensionless; sigmamid|globalThe method comprises the steps of (1) forming a formation stress tensor Pa under a global coordinate in the middle of a reservoir;
extracting the maximum horizontal main stress value, the minimum horizontal main stress value, the vertical main stress value and each main stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area from the stratum stress tensor eigenvalue and eigenvector matrix under the middle local coordinate of the reservoir at any position in the target area by using the following formula;
V＝[σhmid,σHmid,σvmid]
Figure BDA0002960311050000071
in the formula: v is the characteristic moment of formation stress tensor under the middle local coordinate of the reservoir at any position in the target areaArray, Pa; d is a formation stress tensor eigenvector matrix under the middle local coordinate of the reservoir at any position in the target area, and is dimensionless; sigmaHmid、σhmid、σvmidThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value Pa of the stratum under the middle local coordinate of the reservoir at any position in the target area are obtained; x is the number ofhmid、yhmid、zhmidThe minimum horizontal principal stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area is dimensionless; x is the number ofHmid、yHmid、zHmidThe method is characterized in that the method is a formation maximum horizontal principal stress direction component under the middle local coordinate of a reservoir at any position in a target region and is dimensionless; x is the number ofvmid、yvmid、zvmidThe vertical principal stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area is dimensionless.
The invention has the following beneficial effects: compared with the prior art, the method is specially used for solving the problem that the acquisition means of stress field data of the deep shale complex formation is insufficient, and a tensor coordinate system conversion algorithm and a natural adjacent point three-dimensional interpolation method are combined, so that a calculation method of the non-uniform stress field of the deep shale complex formation is provided; because the method can calculate the inhomogeneous distribution condition of the triaxial stress field of the stratum at any position in the target area only by depending on limited data such as the triaxial stress value, the maximum horizontal main stress direction and the like of the stratum drilled with the well in the target area without large-scale geological structure mechanical modeling, the method solves the problems that the stratum stress field of the complex structure of the deep shale changes faster in a smaller area and a fast and accurate inhomogeneous stratum stress field calculation method is lacked.
Drawings
FIG. 1 is a block diagram of the computational flow of the method of the present invention;
FIG. 2 is a diagram of the location of a drilled well within a target area of an embodiment;
FIG. 3 is a cloud of the distribution of the components of the formation stress tensor at the global coordinates of the middle of the reservoir in the target region of the embodiment;
FIG. 4 is a cloud chart of distribution of maximum and minimum horizontal principal stress values of the formation at the local coordinates of the middle portion of the reservoir in the target region according to the embodiment;
FIG. 5 is a diagram of the direction vector of the maximum and minimum horizontal principal stresses of the formation at the local coordinates of the middle portion of the reservoir in the target region according to an embodiment.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in FIG. 1, the method for calculating the inhomogeneous stress field of the deep shale complex formation stratum comprises the following steps:
step A, calculating a stratum triaxial stress gradient under local coordinates of each well position according to drilled well data in a target area;
step A, calculating a flow:
collecting formation stress data obtained by measuring drilled wells in a target area, wherein the formation stress data comprises a maximum horizontal main stress value, a minimum horizontal main stress value and a vertical main stress value;
collecting coordinate data of drilled well positions in the target area and the vertical depth of the stratum stress measuring points of each well, and drawing a well position distribution diagram;
thirdly, calculating three-axis principal stress gradients of the stratum at each well position respectively by using an equation (1), wherein the three-axis principal stress gradients of the stratum comprise a maximum horizontal principal stress gradient, a minimum horizontal principal stress gradient and a vertical principal stress gradient;
Figure BDA0002960311050000091
in the formula: gi H、Gi h、Gi vThe maximum horizontal main stress gradient, the minimum horizontal main stress gradient and the vertical main stress gradient of the stratum at the No. i well position are Pa/m; sigmai H、σi h、σi vThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum at the I-type well position are Pa; diMeasuring the vertical depth m of a formation stress data measuring point of a No. i well; and i is the number of the formation stress value measuring well.
B, calculating the maximum horizontal principal stress value, the minimum horizontal principal stress value and the vertical principal stress value of the stratum under the local coordinate of the middle part of the reservoir at each well position based on the triaxial principal stress gradient of the stratum and the vertical depth data of the middle part of the reservoir in the target area in the step A, and assembling the maximum horizontal principal stress value, the minimum horizontal principal stress value and the vertical principal stress value into a stratum stress tensor form under the local coordinate;
step B, calculating a flow:
collecting vertical depth data of the middle part of a reservoir in a target area;
secondly, calculating the stratum triaxial stress value under the middle local coordinate of the reservoir at each well position by using an equation (2), wherein the equation comprises the following steps: the maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum;
thirdly, assembling stratum triaxial stress values under the central local coordinate of the reservoir at the position of the well I into a tensor form by using an equation (3);
Figure BDA0002960311050000092
Figure BDA0002960311050000093
in the formula: sigmaiHmid、σi hmid、σi vmidThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value of the stratum under the middle local coordinate of the reservoir at the position of the No. i well are Pa; dmidThe vertical depth m of the middle part of the reservoir in the target area; sigmai mid|localThe method comprises the following steps of (1) forming a formation stress tensor Pa under a central local coordinate of a reservoir at a well position I;
step C, calculating a stratum stress tensor component under the central global coordinate of the reservoir at each well position through a tensor coordinate system conversion algorithm based on the stratum stress tensor under the central local coordinate of the reservoir at each well position obtained in the step B;
step C, calculating a flow:
collecting the maximum horizontal main stress direction of each well position obtained by drilling and setting well measurement in a target area, and calculating the included angle between the maximum horizontal main stress direction and the x axis of the global coordinate system;
respectively calculating the formation stress tensor components under the central global coordinate of the reservoir at each well position by using an equation (5) through a tensor coordinate system conversion algorithm;
thirdly, assembling the formation stress tensor components under the central global coordinate of the reservoir at each well position into a tensor form by using an equation (4);
Figure BDA0002960311050000101
Figure BDA0002960311050000102
in the formula: sigmai xx、σi yy、σi xy、σixz、σi yz、σi zzThe method comprises the following steps of (1) forming a formation stress tensor component Pa under the central global coordinate of a reservoir at the position of a well I; thetaiThe included angle between the maximum horizontal main stress of the No. i well and the x axis of the global coordinate system is degree;
step D, calculating the stratum stress tensor component under the central global coordinate of the reservoir at any position in the target area through a natural adjacent point three-dimensional interpolation method based on the stratum stress tensor under the central global coordinate of the reservoir at each well position obtained in the step C, assembling the stratum stress tensor component into a stratum stress tensor form under the global coordinate, and drawing a stratum stress tensor component distribution cloud picture under the global coordinate in the target area;
step D, calculating a flow:
calculating the stratum stress tensor component under the central global coordinate of the reservoir at any position in a target area by using an equation (7) through a natural adjacent point three-dimensional interpolation method according to the stratum stress tensor component under the central global coordinate of the reservoir at each well position;
assembling the formation stress tensor components under the global coordinate of the middle part of the reservoir at any position in the target area into a tensor form by using an equation (6);
thirdly, drawing a distribution cloud picture of stratum stress tensor components under the global coordinate in the target area;
Figure BDA0002960311050000111
Figure BDA0002960311050000112
in the formula: sigmai mid|globalThe method comprises the steps of (1) forming a formation stress tensor Pa under the global coordinate of the middle part of a reservoir at any position in a target area; sigmaxx、σyy、σxy、σxz、σyz、σzzThe method comprises the following steps of (1) forming a formation stress tensor component Pa under the global coordinate of the middle part of a reservoir at any position in a target area; interp3N is a natural neighboring point three-dimensional interpolation operator;
step E, calculating a stratum triaxial main stress value under the middle local coordinate of the reservoir at any position in the target area and a direction component thereof based on the stratum stress tensor under the middle global coordinate of the reservoir at any position in the target area obtained in the step D;
step E, calculating a flow:
according to the stratum stress tensor under the central global coordinate of the reservoir at any position in the target area, calculating the stratum stress tensor eigenvalue and eigenvector matrix under the central local coordinate of the reservoir at any position in the target area by using an equation (8) through the matrix eigenvalue and eigenvector operation;
extracting the maximum horizontal principal stress value, the minimum horizontal principal stress value, the vertical principal stress value and each principal stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area from the stratum stress tensor eigenvalue and the eigenvector matrix under the middle local coordinate of the reservoir at any position in the target area by using equations (9) and (10);
[V,D]＝eig(σmid|global) (8)
V＝[σhmid,σHmid,σvmid] (9)
Figure BDA0002960311050000121
in the formula: eig is a matrix eigenvalue and eigenvector operator; v is a stratum stress tensor eigenvalue matrix Pa under the middle local coordinate of the reservoir at any position in the target area; d is a formation stress tensor eigenvector matrix under the middle local coordinate of the reservoir at any position in the target area, and is dimensionless; sigmaHmid、σhmid、σvmidThe maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value Pa of the stratum under the middle local coordinate of the reservoir at any position in the target area are obtained; x is the number ofhmid、yhmid、zhmidThe minimum horizontal principal stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area is dimensionless; x is the number ofHmid、yHmid、zHmidThe method is characterized in that the method is a formation maximum horizontal principal stress direction component under the middle local coordinate of a reservoir at any position in a target region and is dimensionless; x is the number ofvmid、yvmid、zvmidThe vertical principal stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area is dimensionless;
f, drawing a stratum maximum horizontal main stress value, a minimum horizontal main stress value, a vertical main stress value distribution cloud chart and maximum and minimum horizontal stress direction vector charts under local coordinates in the target region;
and G, determining the non-uniform distribution condition of the triaxial stress field of the stratum at any position in the target region according to the stratum stress tensor component distribution cloud picture under the global coordinate in the target region, the stratum maximum horizontal main stress value, the minimum horizontal main stress value and the vertical main stress value distribution cloud picture under the local coordinate in the target region, and the maximum and minimum horizontal stress direction vector pictures.
Example 1
A method for calculating a nonuniform stress field of a deep shale complex formation comprises the following steps:
actual data of 6 drilled wells in a deep shale gas reservoir area with a certain complex structure are shown in table 1.
TABLE 1 actual data of 6 drilled wells in a deep shale gas reservoir area of a complex structure
Figure BDA0002960311050000131
The calculation flow diagram of the method according to the invention (as shown in fig. 1) develops an example calculation:
firstly, the triaxial stress gradient of the stratum under the local coordinate of each well position is calculated by using the drilled well data in the target area.
The method comprises the following specific steps: inputting formation stress data obtained by measuring drilled wells in a target area, wherein the formation stress data comprises a maximum horizontal main stress value, a minimum horizontal main stress value and a vertical main stress value; secondly, inputting the coordinate data of the drilled well position in the target area and the vertical depth of the stratum stress measuring point of each well, and drawing a well position distribution diagram as shown in figure 2; thirdly, calculating the three-axis principal stress gradient of the stratum at each well position by using the equation (1), comprising the following steps: maximum horizontal principal stress gradient, minimum horizontal principal stress gradient, vertical principal stress gradient, as shown in table 2.
TABLE 2 three-axis principal stress gradient of formation at each well location
Figure BDA0002960311050000132
Figure BDA0002960311050000141
And then, calculating the triaxial stress value of the stratum under the middle local coordinate of the reservoir at each well position by using the middle vertical depth data of the reservoir in the target area.
The method comprises the following specific steps: inputting vertical depth data of the middle part of a reservoir in a target area: 2200 m; secondly, calculating the stratum triaxial stress value under the middle local coordinate of the reservoir at each well position by using an equation (2), wherein the equation comprises the following steps: the maximum horizontal principal stress value, the minimum horizontal principal stress value, and the vertical principal stress value are shown in table 3; thirdly, assembling the triaxial stress values of the stratum under the local coordinates of the middle part of the reservoir at the position of the i-type well into a tensor form by using an equation (3).
TABLE 3 triaxial stress values of the formation at the middle local coordinates of the reservoir at each well location
Figure BDA0002960311050000142
And then, calculating the stratum stress tensor component under the central global coordinate of the reservoir at each well position by using a tensor coordinate system conversion algorithm.
The method comprises the following specific steps: firstly, inputting the maximum horizontal main stress direction of each well position obtained by drilling and setting well measurement in a target area, namely the included angle between the maximum horizontal main stress direction and the x axis of the global coordinate system; respectively calculating the formation stress tensor components under the central global coordinate of the reservoir at each well position by using an equation (5) through a tensor coordinate system conversion algorithm, as shown in a table 4; and thirdly, assembling the formation stress tensor components under the central global coordinate of the reservoir at each well position into a tensor form by using an equation (4).
TABLE 4 formation stress tensor components at the central global coordinates of the reservoir at each well location
Figure BDA0002960311050000151
And then, calculating the formation stress tensor component under the central global coordinate of the reservoir at any position in the target area by using a natural adjacent point three-dimensional interpolation algorithm.
The method comprises the following specific steps: calculating the stratum stress tensor component under the central global coordinate of the reservoir at any position in a target area by using an equation (7) through a natural adjacent point three-dimensional interpolation method according to the stratum stress tensor component under the central global coordinate of the reservoir at each well position, and drawing a distribution cloud picture; assembling the formation stress tensor components under the global coordinate of the middle part of the reservoir at any position in the target area into a tensor form by using an equation (6); and thirdly, drawing a distribution cloud picture of each component of the formation stress tensor under the global coordinate in the target area, as shown in fig. 3.
And then, calculating the stratum triaxial stress value and the maximum principal stress direction under the middle local coordinate of the reservoir at any position in the target area by using a tensor coordinate system conversion algorithm.
The method comprises the following specific steps: calculating a stratum stress tensor eigenvalue and an eigenvector matrix under the central local coordinate of the reservoir at any position in the target area by using an equation (8) through the matrix eigenvalue and eigenvector operation according to the stratum stress tensor under the central global coordinate of the reservoir at any position in the target area; extracting the maximum horizontal principal stress value, the minimum horizontal principal stress value, the vertical principal stress value and each principal stress direction component of the stratum under the middle local coordinate of the reservoir at any position in the target area from the stratum stress tensor eigenvalue and the eigenvector matrix under the middle local coordinate of the reservoir at any position in the target area by using equations (9) and (10); and thirdly, drawing a distribution cloud picture of the maximum horizontal principal stress value, the minimum horizontal principal stress value and the vertical principal stress value of the stratum under the local coordinate in the target area, and a direction vector picture of the maximum horizontal stress and the minimum horizontal stress respectively as shown in the figures 4 and 5.
The method is specially used for solving the problem of insufficient data acquisition means of the stress field of the deep shale complex formation, and provides a calculation method of the inhomogeneous stress field of the deep shale complex formation by combining a tensor coordinate system conversion algorithm and a natural adjacent point three-dimensional interpolation method. Because the method can calculate the inhomogeneous distribution condition of the triaxial stress field of the stratum at any position in the target area only by depending on limited data such as the triaxial stress value, the maximum horizontal main stress direction and the like of the stratum drilled with the well in the target area without large-scale geological structure mechanical modeling, the method solves the problems that the stratum stress field of the complex structure of the deep shale changes faster in a smaller area and a fast and accurate inhomogeneous stratum stress field calculation method is lacked.
Although the present invention has been described with reference to the above embodiments, it should be understood that the present invention is not limited to the above embodiments, and those skilled in the art can make various changes and modifications without departing from the scope of the present invention.

Claims (6)

1.一种深层页岩复杂构造地层非均匀应力场计算方法，其特征在于，包括：1. a deep shale complex structural formation non-uniform stress field calculation method, is characterized in that, comprises: 根据目标区域内已钻设井的地层应力数据、井位坐标数据确定各井位置局部坐标下的地层三轴应力梯度；According to the formation stress data and well position coordinate data of the drilled wells in the target area, determine the formation triaxial stress gradient under the local coordinates of each well position; 根据各井位置局部坐标下的地层三轴应力梯度和目标区域内储层中部垂直深度数据确定各井位置储层中部局部坐标下的地层应力张量；According to the formation triaxial stress gradient under the local coordinates of each well position and the vertical depth data of the middle of the reservoir in the target area, determine the formation stress tensor under the local coordinates of the middle of the reservoir at each well position; 根据各井位置储层中部局部坐标下的地层应力张量和张量坐标系转换算法确定各井位置储层中部全局坐标下的地层应力张量；According to the formation stress tensor under the local coordinates of the middle of the reservoir at each well position and the tensor coordinate system conversion algorithm, the formation stress tensor under the global coordinates of the middle of the reservoir at each well position is determined; 根据各井位置储层中部全局坐标下的地层应力张量和自然邻点三维插值方法确定目标区域内任意位置储层中部全局坐标下的地层应力张量、目标区域内全局坐标下的地层应力张量分量分布云图；According to the formation stress tensor under the global coordinates of the middle of the reservoir at each well position and the three-dimensional interpolation method of natural neighbor points, the formation stress tensor under the global coordinates of the middle of the reservoir at any position in the target area and the formation stress tensor under the global coordinates in the target area are determined. Quantitative component distribution cloud map; 根据目标区域内任意位置储层中部全局坐标下的地层应力张量确定目标区域内任意位置储层中部局部坐标下的地层三轴主应力值，及其方向分量；According to the formation stress tensor under the global coordinates of the middle of the reservoir at any position in the target area, determine the triaxial principal stress value of the formation under the local coordinates of the middle of the reservoir at any position in the target area, and its direction component; 根据目标区域内任意位置储层中部局部坐标下的地层三轴主应力值，及其方向分量绘制目标区域内局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值分布云图，以及最大、最小水平应力方向矢量图；According to the triaxial principal stress value of the formation in the local coordinate of the middle of the reservoir at any position in the target area, and its direction component, draw the maximum horizontal principal stress value, the minimum horizontal principal stress value, and the vertical principal stress value of the formation under the local coordinate in the target area. Distribution cloud map, and maximum and minimum horizontal stress direction vector diagram; 根据目标区域内局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值分布云图，以及最大、最小水平应力方向矢量图确定目标区域内任意位置处地层三轴应力场非均匀分布情况。According to the distribution cloud map of the maximum horizontal principal stress value, the minimum horizontal principal stress value, and the vertical principal stress value under the local coordinates in the target area, as well as the vector diagram of the maximum and minimum horizontal stress directions, determine the triaxial stress field of the formation at any position in the target area non-uniform distribution. 2.根据权利要求1所述的一种深层页岩复杂构造地层非均匀应力场计算方法，其特征在于，根据目标区域内已钻设井的地层应力数据、井位坐标数据确定各井位置局部坐标下的地层三轴应力梯度包括：2. The method for calculating the non-uniform stress field of a deep shale complex structural stratum according to claim 1, characterized in that, according to the stratum stress data and well position coordinate data of the drilled wells in the target area, the local position of each well is determined. The formation triaxial stress gradient in coordinates includes: 收集目标区域内已钻设井测量得到的地层应力数据，所述地层应力数据包括最大水平主应力值、最小水平主应力值、垂向主应力值；Collect formation stress data measured by drilled wells in the target area, where the formation stress data includes a maximum horizontal principal stress value, a minimum horizontal principal stress value, and a vertical principal stress value; 收集目标区域内已钻设井位坐标数据，以及各井地层应力测量点的垂直深度，绘制井位分布图；Collect the coordinate data of drilled well locations in the target area, as well as the vertical depth of the formation stress measurement points of each well, and draw the well location distribution map; 利用下式分别计算各井位置局部坐标下的地层三轴应力梯度，所述地层三轴应力梯度包括最大水平主应力梯度、最小水平主应力梯度、垂向主应力梯度；The following formula is used to calculate the formation triaxial stress gradient under the local coordinates of each well position, where the formation triaxial stress gradient includes the maximum horizontal principal stress gradient, the minimum horizontal principal stress gradient, and the vertical principal stress gradient;
Figure FDA0002960311040000021
Figure FDA0002960311040000021
 式中：Gi H、Gi h、Gi v为i号井位置地层最大水平主应力梯度、最小水平主应力梯度、垂向主应力梯度，Pa/m；σi H、σi h、σi v为i号井位置地层最大水平主应力值、最小水平主应力值、垂向主应力值，Pa；Di为i号井地层应力数据测量点垂直深度，m；i为地层应力值测量井编号。In the formula: G i H , G i h , and G i v are the maximum horizontal principal stress gradient, minimum horizontal principal stress gradient, and vertical principal stress gradient of the formation at the position of Well i, Pa/m; σ i H , σ i h , σ i v is the maximum horizontal principal stress value, minimum horizontal principal stress value and vertical principal stress value of the formation at the position of Well i, Pa; D i is the vertical depth of the measurement point of formation stress data in Well i, m; i is the formation stress value Measurement well number. 3.根据权利要求2所述的一种深层页岩复杂构造地层非均匀应力场计算方法，其特征在于，根据各井位置局部坐标下的地层三轴应力梯度和目标区域内储层中部垂直深度数据确定各井位置储层中部局部坐标下的地层应力张量包括：3. The non-uniform stress field calculation method of a deep shale complex structure formation according to claim 2, characterized in that, according to the formation triaxial stress gradient under the local coordinates of each well position and the vertical depth of the middle of the reservoir in the target area The data determines the formation stress tensor under the local coordinates in the middle of the reservoir at each well position, including: 收集目标区域内储层中部垂直深度数据；Collect vertical depth data in the middle of the reservoir in the target area; 利用下式分别计算各井位置储层中部局部坐标下的地层三轴应力值；Use the following formula to calculate the formation triaxial stress value under the local coordinates of the middle of the reservoir at each well position;
Figure FDA0002960311040000022
Figure FDA0002960311040000022
 式中：Gi H、Gi h、Gi v为i号井位置地层最大水平主应力梯度、最小水平主应力梯度、垂向主应力梯度，Pa/m；σi Hmid、σi hmid、σi vmid为i号井位置储层中部局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值，Pa；Dmid为目标区域内储层中部垂直深度，m；In the formula: G i H , G i h , and G i v are the maximum horizontal principal stress gradient, the minimum horizontal principal stress gradient, and the vertical principal stress gradient at the position of Well i, Pa/m; σ i Hmid , σ i hmid , σ i vmid is the maximum horizontal principal stress value, the minimum horizontal principal stress value, and the vertical principal stress value under the local coordinates of the middle of the reservoir at the position of Well i, Pa; D mid is the vertical depth of the middle of the reservoir in the target area, m; 利用下式将各井位置储层中部局部坐标下的地层三轴应力值组装为张量形式；Use the following formula to assemble the formation triaxial stress values at the local coordinates of the middle of the reservoir at each well position into a tensor form;
Figure FDA0002960311040000031
Figure FDA0002960311040000031
 式中：σi Hmid、σi hmid、σi vmid为i号井位置储层中部局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值，Pa；σi mid|local为i号井位置储层中部局部坐标下的地层应力张量，Pa。In the formula: σ i Hmid , σ i hmid , σ i vmid are the maximum horizontal principal stress value, the minimum horizontal principal stress value, and the vertical principal stress value of the formation under the local coordinates in the middle of the reservoir at the position of Well i, Pa; σ i mid | local is the formation stress tensor at the local coordinate in the middle of the reservoir at the position of Well i, Pa. 4.根据权利要求3所述的一种深层页岩复杂构造地层非均匀应力场计算方法，其特征在于，根据各井位置储层中部局部坐标下的地层应力张量和张量坐标系转换算法确定各井位置储层中部全局坐标下的地层应力张量包括：4. The method for calculating the non-uniform stress field of a deep shale complex structure formation according to claim 3, characterized in that, according to the formation stress tensor and the tensor coordinate system conversion algorithm under the local coordinates of the middle of the reservoir at each well position Determining the formation stress tensor under the global coordinates in the middle of the reservoir at each well position includes: 收集目标区域内已钻设井测量得到的各井位置最大水平主应力方向，计算其与全局坐标系x轴之间的夹角；Collect the maximum horizontal principal stress direction of each well position measured by the drilled wells in the target area, and calculate the angle between it and the x-axis of the global coordinate system; 通过张量坐标系转换算法，利用下式分别计算各井位置储层中部全局坐标下的地层应力张量分量；Through the tensor coordinate system transformation algorithm, the following formulas are used to calculate the formation stress tensor components in the global coordinates of the middle of the reservoir at each well position;
Figure FDA0002960311040000032
Figure FDA0002960311040000032
 式中：σi xx、σi yy、σi xy、σi xz、σi yz、σi zz为i号井位置储层中部全局坐标下的地层应力张量分量，Pa；θi为i号井最大水平主应力与全局坐标系x轴之间的夹角，°；σi Hmid、σi hmid、σi vmid为i号井位置储层中部局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值，Pa；In the formula: σ i xx , σ i yy , σ i xy , σ i xz , σ i yz , σ i zz are the formation stress tensor components in the global coordinates of the middle of the reservoir at the position of Well i, Pa; θ i is i The angle between the maximum horizontal principal stress of Well No. and the x-axis of the global coordinate system, °; σ i Hmid , σ i hmid , and σ i vmid are the maximum horizontal principal stress value of the formation under the local coordinates of the middle of the reservoir at the position of Well i, Minimum horizontal principal stress value, vertical principal stress value, Pa; 利用下式将各井位置储层中部全局坐标下的地层应力张量分量组装为张量形式；The formation stress tensor components under the global coordinates in the middle of the reservoir at each well position are assembled into a tensor form using the following formula;
Figure FDA0002960311040000041
Figure FDA0002960311040000041
 式中：σi xx、σi yy、σi xy、σi xz、σi yz、σi zz为i号井位置储层中部全局坐标下的地层应力张量分量，Pa；Pa；σi mid|global为i号井位置储层中部全局坐标下的地层应力张量，Pa。In the formula: σ i xx , σ i yy , σ i xy , σ i xz , σ i yz , σ i zz are the formation stress tensor components in the global coordinates of the middle of the reservoir at the position of Well i, Pa; Pa; σ i mid | global is the formation stress tensor in the global coordinates of the middle of the reservoir at the position of Well i, Pa. 5.根据权利要求4所述的一种深层页岩复杂构造地层非均匀应力场计算方法，其特征在于，根据各井位置储层中部全局坐标下的地层应力张量和自然邻点三维插值方法确定目标区域内任意位置储层中部全局坐标下的地层应力张量、目标区域内全局坐标下的地层应力张量各分量分布云图包括：5. The method for calculating the non-uniform stress field of a deep shale complex structure formation according to claim 4, characterized in that, according to the formation stress tensor under the global coordinates of the middle of the reservoir at each well position and the three-dimensional interpolation method of natural adjacent points Determine the formation stress tensor under the global coordinates of the middle of the reservoir at any position in the target area, and the distribution cloud map of each component of the formation stress tensor under the global coordinates in the target area, including: 根据各井位置储层中部全局坐标下的地层应力张量分量，利用下式通过自然邻点三维插值方法，计算目标区域内任意位置储层中部全局坐标下的地层应力张量分量；According to the formation stress tensor components in the global coordinates of the middle of the reservoir at each well position, the following formula is used to calculate the formation stress tensor components in the global coordinates of the middle of the reservoir at any position in the target area through the three-dimensional interpolation method of natural neighbors;
Figure FDA0002960311040000042
Figure FDA0002960311040000042
 式中：σi mid|global为目标区域内任意位置储层中部全局坐标下的地层应力张量，Pa；σxx、σyy、σxy、σxz、σyz、σzz为目标区域内任意位置储层中部全局坐标下的地层应力张量分量，Pa；interp3N为自然邻点三维插值算子；In the formula: σ i mid | global is the formation stress tensor in the global coordinates of the middle of the reservoir at any position in the target area, Pa; σ xx , σ yy , σ xy , σ xz , σ yz , σ zz are any The formation stress tensor component in the global coordinates in the middle of the position reservoir, Pa; interp3N is the natural neighbor three-dimensional interpolation operator; 利用下式将目标区域内任意位置储层中部全局坐标下的地层应力张量分量组装为张量形式；The formation stress tensor components in the global coordinates of the middle of the reservoir at any position in the target area are assembled into a tensor form using the following formula;
Figure FDA0002960311040000043
Figure FDA0002960311040000043
 式中：σi mid|global为目标区域内任意位置储层中部全局坐标下的地层应力张量，Pa；σxx、σyy、σxy、σxz、σyz、σzz为目标区域内任意位置储层中部全局坐标下的地层应力张量分量，Pa；In the formula: σ i mid | global is the formation stress tensor in the global coordinates of the middle of the reservoir at any position in the target area, Pa; σ xx , σ yy , σ xy , σ xz , σ yz , σ zz are any The formation stress tensor component in global coordinates in the middle of the location reservoir, Pa; 绘制目标区域内全局坐标下的地层应力张量分量分布云图。Plot the distribution cloud map of the formation stress tensor components in the global coordinates in the target area. 6.根据权利要求5所述的一种深层页岩复杂构造地层非均匀应力场计算方法，其特征在于，根据目标区域内任意位置储层中部全局坐标下的地层应力张量确定目标区域内任意位置储层中部局部坐标下的地层三轴主应力值，及其方向分量包括：6 . The method for calculating the non-uniform stress field of a deep shale complex structure formation according to claim 5 , wherein, according to the formation stress tensor under the global coordinates of the middle of the reservoir at any position in the target area, any arbitrary stress field in the target area is determined. 7 . The triaxial principal stress value of the formation at the local coordinates in the middle of the reservoir, and its directional components include: 根据目标区域内任意位置储层中部全局坐标下的地层应力张量，利用下式通过矩阵特征值与特征向量运算，计算目标区域内任意位置储层中部局部坐标下地层应力张量特征值与特征向量矩阵；According to the formation stress tensor under the global coordinates of the middle of the reservoir at any position in the target area, the following formula is used to calculate the eigenvalues and characteristics of the formation stress tensor under the local coordinates of the middle of the reservoir at any position in the target area through the operation of matrix eigenvalues and eigenvectors vector matrix; [V,D]＝eig(σmidglobal)[V,D]=eig(σ midglobal ) 式中：eig为矩阵特征值与特征向量算子；V为目标区域内任意位置储层中部局部坐标下地层应力张量特征值矩阵，Pa；D为目标区域内任意位置储层中部局部坐标下地层应力张量特征向量矩阵，无量纲；σmid|global为储层中部全局坐标下的地层应力张量，Pa；In the formula: eig is the matrix eigenvalue and eigenvector operator; V is the formation stress tensor eigenvalue matrix at the local coordinates of the middle of the reservoir at any position in the target area, Pa; D is the local coordinate of the middle of the reservoir at any position in the target area. eigenvector matrix of formation stress tensor, dimensionless; σ mid | global is the formation stress tensor in the global coordinate of the middle of the reservoir, Pa; 利用下式从目标区域内任意位置储层中部局部坐标下地层应力张量特征值与特征向量矩阵中，提取目标区域内任意位置储层中部局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值，以及各主应力方向分量；From the eigenvalues and eigenvector matrix of the formation stress tensor at the local coordinates of the middle of the reservoir at any position in the target area, the maximum horizontal principal stress value and the minimum horizontal principal stress of the formation under the local coordinates of the middle of the reservoir at any position in the target area are extracted by the following formula. Stress value, vertical principal stress value, and direction components of each principal stress; V＝[σhmid,σHmid,σvmid]V=[σ hmid ,σ Hmid ,σ vmid ]
Figure FDA0002960311040000051
Figure FDA0002960311040000051
 式中：V为目标区域内任意位置储层中部局部坐标下地层应力张量特征值矩阵，Pa；D为目标区域内任意位置储层中部局部坐标下地层应力张量特征向量矩阵，无量纲；σHmid、σhmid、σvmid为目标区域内任意位置储层中部局部坐标下的地层最大水平主应力值、最小水平主应力值、垂向主应力值，Pa；xhmid、yhmid、zhmid为目标区域内任意位置储层中部局部坐标下的地层最小水平主应力方向分量，无量纲；xHmid、yHmid、zHmid为目标区域内任意位置储层中部局部坐标下的地层最大水平主应力方向分量，无量纲；xvmid、yvmid、zvmid为目标区域内任意位置储层中部局部坐标下的地层垂向主应力方向分量，无量纲。In the formula: V is the eigenvalue matrix of formation stress tensor at the local coordinates of the middle of the reservoir at any position in the target area, Pa; D is the eigenvector matrix of the formation stress tensor at the local coordinates of the middle of the reservoir at any position in the target area, dimensionless; σ Hmid , σ hmid , and σ vmid are the maximum horizontal principal stress value, the minimum horizontal principal stress value, and the vertical principal stress value under the local coordinates of the middle of the reservoir at any position in the target area, Pa; x hmid , y hmid , z hmid is the directional component of the minimum horizontal principal stress of the formation under the local coordinates of the middle of the reservoir at any position in the target area, dimensionless; x Hmid , y Hmid , and z Hmid are the maximum horizontal principal stress of the formation at the local coordinates of the middle of the reservoir at any position in the target area The direction component is dimensionless; x vmid , y vmid , and z vmid are the directional components of the vertical principal stress of the formation under the local coordinates of the middle of the reservoir at any position in the target area, and are dimensionless.
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