CN107679999B - Method and system for calculating fracture pressure of coal-bed gas well - Google Patents
Method and system for calculating fracture pressure of coal-bed gas well Download PDFInfo
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Abstract
The invention provides a method and a system for calculating the fracture pressure of a coal-bed gas well, wherein the method for calculating the fracture pressure of the coal-bed gas well comprises the following steps: acquiring the fracture toughness of the coal rock of the target coal bed through an indoor experiment; obtaining coal bed fractal parameters by carrying out variable-scale analysis on logging information of coal bed gas wells in a research block; and calculating the fracture pressure of the coal-bed gas well by combining the acquired fracture toughness of the coal rock, the coal-bed fractal parameter and the coal-bed gas well fracture pressure calculation model. The scheme provided by the invention can accurately predict the fracture pressure, provide a design basis for drilling and well cementation engineering, provide reference for selection of a later-stage well completion mode and a production increasing measure, and reduce underground accidents and economic losses caused by unreasonable design.
Description
Technical Field
The invention belongs to the technical field of coal bed gas exploitation, and particularly relates to a method and a system for calculating fracture pressure of a coal bed gas well.
Background
Aiming at the international situation of low oil (gas) price and the production characteristics of low daily gas production rate and long development period of the coal-bed gas well, the coal-bed gas well is required to achieve cost reduction and efficiency improvement in the development link. Because a method for calculating the fracture pressure of the coal bed gas well is not available, the prediction result of the fracture pressure of the coal bed gas well often cannot effectively guide field operation, so that underground accidents such as unreasonable drilling design, coal bed leakage of cement slurry in a well cementation process and the like are caused, the well construction period and the production cost of the coal bed gas well are increased due to frequent accidents, the underground complicated accidents in the well drilling and completion process can be reduced by accurately predicting the fracture pressure of the coal bed gas well, the time and the economic investment of well drilling are reduced, and the method plays a vital role in realizing the efficient and low-cost development of the coal bed.
At present, the calculation of the fracture pressure of the coal-bed gas well still continues to use a calculation method based on a conventional sand-shale model, the influence of coal-rock cutting theory and fracture fractal is not considered in the conventional method, and the limitation of the model makes the coal-bed fracture pressure calculated by the conventional method inaccurate, so that the establishment of an effective and practical calculation method of the fracture pressure of the coal-bed gas well is necessary and is a key technical problem which needs to be solved urgently at present.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a method for establishing a fracture pressure calculation model of a coal-bed gas well.
The invention further aims to provide a coal-bed gas well fracture pressure calculation model established by the method.
It is a further object of the present invention to provide a method of calculating the fracture pressure of a coal bed gas well.
It is a further object of the present invention to provide a system for calculating the fracture pressure of a coal bed gas well.
In order to achieve the aim, the invention provides a method for establishing a coal bed gas well fracture pressure calculation model, which comprises the following steps:
deducing fracture toughness of the coal rock type I fracture considering fractal characteristics;
obtaining the normal resultant force of the surface cleat in any occurrence state through matrix conversion and ground stress analysis;
and establishing a fracture pressure calculation model of the coal-bed gas well according to the fracture criterion that the fracture initiation of the fracture is greater when the surface-cleavage normal resultant force is greater than the fracture toughness of the coal rock I-type fracture considering the fractal characteristics.
Unlike sand (mud) rock, coal rock develops a face-cut with very little cohesion, and the face-cut is lower in strength than the coal rock body, so that the face-cut is broken in preference to the body. The coal rock face cutting mechanism has fractal characteristics, and fractal parameters can influence the fracture toughness of the coal rock type I cracks. Therefore, in order to obtain more accurate calculation of the fracture pressure of the coal-bed gas well, the invention particularly provides the method for establishing the fracture pressure calculation model of the coal-bed gas well, which takes the influences of coal rock cleat and fracture fractal into consideration.
In the method for establishing the coal-bed gas well fracture pressure calculation model, the matrix is converted into a matrix conversion relation among different coordinate systems; the ground stress analysis is a mechanical analysis process in rock mechanics; the failure criterion is a type I fracture failure criterion in fracture mechanics.
The invention also provides a coal-bed gas well fracture pressure calculation model established by the method, which comprises the following specific steps:
wherein f isi(P) is the burst pressure objective function, MPa; p is bottom hole pressure, MPa; ppIs the formation pressure, MPa; sigmai、σj、σkThree main stresses are well wall, MPa; omega1、ω2、ω3Is the included angle between the corresponding direction vector of the three main stresses and the surface secant outer normal line, rad; eta is a biot coefficient and is dimensionless; l isfIs the face-cutting length, m; kICFracture toughness of type I crack, MPa.m1/2(ii) a r is a self-similarity coefficient; dimensionless; d is fractal dimension and is dimensionless.
The invention also provides a method for calculating the fracture pressure of the coal-bed gas well, which comprises the following steps:
acquiring fracture toughness of the I-shaped crack of the coal rock of the target coal bed through an indoor experiment;
obtaining coal bed fractal parameters by carrying out variable-scale analysis on logging information of coal bed gas wells in a research block;
and calculating the fracture pressure of the coal-bed gas well by combining the acquired fracture toughness of the coal rock, the coal-bed fractal parameters and the established coal-bed gas well fracture pressure calculation model.
In the method for calculating the fracture pressure of the coal-bed gas well, preferably, in the step of obtaining the fracture toughness of the target coal-bed coal rock through an indoor experiment, the prefabricated fracture coal rock used in the indoor experiment is prepared through the following steps:
obtaining target layer coal rock by rope coring; preparing a disc-shaped core section with the thickness of 30-50mm by a diamond slicer; and in the prefabricated crack of the disc-shaped core section, the ratio of the length of the prefabricated crack to the disc diameter is 0.1-0.3.
In the method for calculating the fracture pressure of the coal-bed gas well, preferably, in the step of obtaining the coal-bed fractal parameter by performing variable-scale analysis on logging information of the coal-bed gas well in the research block,
the fractal parameter is a fractal dimension;
the specific calculation formula of the logging data variable-scale analysis is as follows:
wherein, R is range, S is standard deviation, R (n)/S (n) is R/S value corresponding to the nth sampling point, R (n)/S (n) and n of sound wave time difference/depth resistivity/density are used for making a double logarithmic scatter diagram, the slope of a straight line is obtained by regression, and the fractal dimension is 2-H.
In the method for calculating the fracture pressure of the coal-bed gas well, preferably, the specific process of calculating the fracture pressure of the coal-bed gas well by combining the acquired fracture toughness of the coal rock, the coal bed fractal parameter and the established coal-bed gas well fracture pressure calculation model is as follows:
a. the well circumferential angle range is 0-180 degrees, and the bottom hole pressure is enabled to be from P under the premise of giving the well circumferential anglepAt 0.1PpIs increased to 10Pp；
b. Calculating three main stresses sigma of well walli、σj、σkAnd the included angles omega between the corresponding direction vectors of the three main stresses and the surface secant outer normal1、ω2、ω3；
c. Substituting all parameters into the coal-bed gas well fracture pressure calculation model, and solving a fracture pressure objective function fiA value of (P); an objective function fiAnd (P) taking the bottom hole pressure when the absolute value of the (P) is smaller than the error zeta as the fracture pressure at the current circumferential angle, finally comparing the fracture pressures in the circumferential angle range, and taking the minimum value as the borehole fracture pressure.
In the method for calculating the fracture pressure of the coal-bed gas well, the three main stresses sigma of the well wall in the fracture pressure calculation model of the coal-bed gas well are preferably calculated by adopting the following formulai、σj、σk：
Wherein: sigmaz、σθAnd σθzIs the stress component in the borehole coordinate system, MPa.
In the method for calculating the fracture pressure of the coal-bed gas well, preferably, the following formula is adopted to calculate the included angle ω between the corresponding direction vector of the three principal stresses in the fracture pressure calculation model of the coal-bed gas well and the surface secant external normal line1、ω2、ω3：
Wherein:
wherein (l)mi，mmi，nmi) { i ═ 1, 2, 3} are the direction vector coordinates of the three principal stresses; (l)p，mp，np) Is the direction vector coordinate of the surface secant outer normal;alpha is the angle of inclination, degree; beta is the azimuth angle, °; theta is the well angle, °; gamma is the angle between the main stress and the axis of the well; thetasThe direction is the dough cutting direction; thetaDIs the face-cutting inclination angle.
The invention also provides a system for calculating the fracture pressure of the coal-bed gas well, which comprises the following components:
the first module is used for acquiring fracture toughness of the I-shaped crack of the coal rock of the target coal bed through an indoor experiment;
the second module is used for carrying out variable-scale analysis on logging information of coal-bed gas wells in the research block to obtain coal-bed fractal parameters;
the third module is used for calculating the fracture pressure of the coal-bed gas well through the acquired fracture toughness of the coal rock, the coal-bed fractal parameters and the coal-bed gas well fracture pressure calculation model;
the coal bed gas well fracture pressure calculation model is as follows:
wherein f isi(P) is the burst pressure objective function, MPa; p is bottom hole pressure, MPa; ppIs the formation pressure, MPa; sigmai、σj、σkThree main stresses are well wall, MPa; omega1、ω2、ω3Is the included angle between the corresponding direction vector of the three main stresses and the surface secant outer normal line, rad; eta is a biot coefficient and is dimensionless; l isfIs the face-cutting length, m; kICFracture toughness of type I crack, MPa.m1/2(ii) a r is a self-similarity coefficient; dimensionless; d is fractal dimension and is dimensionless.
The fracture pressure is very important basic data in the whole coal bed gas well drilling and completion process, and the accuracy of the fracture pressure directly influences the rationality of the drilling and completion engineering design. According to the scheme provided by the invention, coal rock fracture toughness and face-cutting fractal parameters can be obtained through indoor fracture toughness experiments and variable-scale analysis of logging data, and on the basis of the analysis results, relevant data is brought into the coal bed gas well fracture pressure calculation model creatively established by the invention, so that the fracture pressure of the coal bed gas well in the research area (coal bed gas field) can be calculated. The scheme provided by the invention can accurately predict the fracture pressure, provide a design basis for drilling and well cementation engineering, provide reference for selection of a later-stage well completion mode and a production increasing measure, and reduce underground accidents and economic losses caused by unreasonable design.
Drawings
FIG. 1 is a flow chart of a method for calculating a fracture pressure of a coal-bed gas well according to an embodiment of the invention;
FIG. 2 is a detailed flow chart of the method for calculating burst pressure data from a model according to an embodiment of the present invention;
FIG. 3a is a time-varying time scale analysis of acoustic waves obtained by an embodiment of the present invention;
FIG. 3b is a graph of a density-scaling analysis obtained in accordance with an embodiment of the present invention;
FIG. 4 is a graph of fracture pressure versus angle of the well obtained in accordance with an embodiment of the present invention;
FIG. 5 is a graph of the fracture pressure versus wellbore orientation obtained in accordance with an embodiment of the present invention;
FIG. 6 is a graph of fracture pressure versus rake angle for a cleave plane, obtained in accordance with an embodiment of the present invention;
FIG. 7 is a graph of fracture pressure versus fractal parameter obtained in accordance with an embodiment of the present invention;
FIG. 8 is a graph of fracture pressure versus fracture length obtained in accordance with an embodiment of the present invention;
FIG. 9 is a coal-bed gas well fracturing construction diagram obtained by the embodiment of the invention.
Detailed Description
The technical solutions of the present invention will be described in detail below in order to clearly understand the technical features, objects, and advantages of the present invention, but the present invention is not limited to the practical scope of the present invention.
FIG. 1 is a flow chart of a method for calculating the fracture pressure of a coal-bed gas well according to an embodiment of the invention.
As shown in fig. 1, the method for calculating the fracture pressure of the coal-bed gas well according to the embodiment of the invention comprises the following steps:
and S101, acquiring fracture toughness of the coal rock of the target coal bed through an indoor experiment.
Preferably, in this step, the indoor experiment is a coal rock fracture toughness test experiment, and the pre-crack coal rock used in the experiment is prepared by the following steps: obtaining target layer coal rock by rope coring; preparing a disc-shaped core section with the thickness of 30-50mm by a diamond slicer; and in the prefabricated crack of the disc-shaped core section, the ratio of the length of the prefabricated crack to the disc diameter is 0.1-0.3. The fracture toughness of the coal rock is the average value of the fracture toughness of the coal rock in the research area.
And S102, carrying out variable-scale analysis on logging information of the coal-bed gas well in the research block to obtain coal-bed fractal parameters.
Preferably, in the step, variable-scale analysis is performed on the logging information of adjacent wells, wherein the adjacent wells refer to wells with the same target coal seam and the nearest linear distance from the wellhead as the prediction wells, and include both cored wells and non-cored wells; the coal bed fractal parameter refers to a fractal dimension; the variable-scale analysis of the logging information refers to R/S analysis of the logging information such as the acoustic time difference, the density, the resistivity and the like of the coal-bed gas well.
Preferably, in this step, the specific calculation formula of the well-logging data variable-scale analysis is as follows:
wherein, R is range, S is standard deviation, R (n)/S (n) is R/S value corresponding to the nth sampling point, R (n)/S (n) and n of sound wave time difference/depth resistivity/density are used for making a double logarithmic scatter diagram, the slope of a straight line is obtained by regression, and the fractal dimension is 2-H.
And 103, establishing a coal bed gas well fracture pressure calculation model.
Preferably, in this step, the specific process of establishing the coal-bed gas well fracture pressure calculation model is as follows:
a. deducing fracture toughness of the coal rock type I fracture considering fractal characteristics;
b. obtaining the normal resultant force of the surface cleat in any occurrence state through matrix conversion and ground stress analysis;
c. and establishing a fracture pressure calculation model of the coal-bed gas well according to the fracture criterion that the fracture initiation of the fracture is greater when the surface-cleavage normal resultant force is greater than the fracture toughness of the coal rock I-type fracture considering the fractal characteristics.
Wherein, the matrix is converted into a matrix conversion relation among different coordinate systems; the stress analysis is a mechanical analysis process in rock mechanics; the failure criterion is type I fracture failure criterion in fracture mechanics.
Preferably, in this step, the calculation model of the fracture pressure of the coal-bed gas well is established as follows:
wherein f isi(P) is the burst pressure objective function, MPa; p is bottom hole pressure, MPa; ppIs the formation pressure, MPa; sigmai、σj、σkThree main stresses are well wall, MPa; omega1、ω2、ω3Is the included angle between the corresponding direction vector of the three main stresses and the normal outside the cutting surface, rad; eta is a biot coefficient and is dimensionless; l isfIs the face-cutting length, m; kICFracture toughness of type I crack, MPa.m1/2(ii) a r is a self-similarity coefficient; dimensionless; d is fractal dimension and is dimensionless.
And step S104, calculating the fracture pressure of the coal-bed gas well through the coal-bed gas well fracture pressure calculation model established in the step S103 by combining the acquired fracture toughness of the coal rock and the coal-bed fractal parameters.
Preferably, in this step, fig. 2 is a flowchart of calculating the fracture pressure of the coal-bed gas well in the step S104 according to the embodiment of the present invention, and the specific process is summarized as follows:
a. the well circumferential angle range is 0-180 degrees, and the bottom hole pressure is enabled to be from P under the premise of giving the well circumferential anglepAt 0.1PpIs increased to 10Pp；
b. Calculating three main stresses sigma of well walli、σj、σkAnd the included angles omega between the corresponding direction vectors of the three main stresses and the surface secant outer normal1、ω2、ω3；
c. Substituting all parameters into the coal-bed gas well fracture pressure calculation model, and solving a fracture pressure objective function fiA value of (P); an objective function fiAnd (P) taking the bottom hole pressure when the absolute value of the (P) is smaller than the error zeta as the fracture pressure at the current circumferential angle, finally comparing the fracture pressures in the circumferential angle range, and taking the minimum value as the borehole fracture pressure.
Preferably, in the step, the following formula is adopted to calculate three main stresses sigma of the well wall in the coal-bed gas well fracture pressure calculation modeli、σj、σk：
Wherein: sigmaz、σθAnd σθzIs the stress component in the borehole coordinate system, MPa.
Preferably, in the step, the following formula is adopted to calculate the included angle ω between the corresponding direction vector of the three principal stresses and the surface secant outer normal line in the coal-bed gas well fracture pressure calculation model1、ω2、ω3：
Wherein:
wherein (l)mi，mmi，nmi) { i ═ 1, 2, 3} are the direction vector coordinates of the three principal stresses; (l)p，mp，np) Is the direction vector coordinate of the surface secant outer normal; alpha is the angle of inclination, degree; beta is the azimuth angle, °; theta is the well angle, °; gamma is the angle between the main stress and the axis of the well; thetasThe direction is the dough cutting direction; thetaDIs the face-cutting inclination angle.
The present invention will be further described with reference to the accompanying drawings and specific embodiments.
The well depth of the coal bed is 600m, the pressure of the overlying strata is 10MPa, the maximum horizontal main stress is 9MPa, the minimum horizontal main stress is 8MPa, the stratum pressure is 6MPa, the tensile strength of the coal rock is 1.2MPa, and the fracture toughness of the coal rock is 0.68 MPa-m & lt m & gt obtained through experiments1/2The surface cutting length is 0.01m, the surface cutting trend is NE32 degrees, the surface cutting inclination angle is 10 degrees, the horizontal well hole orientation is NE70 degrees, and the maximum horizontal main stress direction is consistent with the true north direction.
Fig. 3a is a time-varying scale analysis of the obtained sound waves, and fig. 3b is a density-varying scale analysis of the obtained sound waves. As can be seen from fig. 3a and 3 b: the slopes of straight lines obtained by regression after the variable-scale analysis of the acoustic wave time difference and the density logging data are respectively 0.946 and 0.987, so that the fractal dimensions are respectively 1.054 and 1.013, and the average value of the fractal dimensions is 1.034.
Fig. 4 is a curve of the obtained fracture pressure and the change of the well inclination angle, and it can be seen that the method of the embodiment is consistent with the rule obtained by the conventional method, the fracture pressure decreases along with the increase of the well inclination angle, and the fracture pressure is larger when the fracture toughness of the coal rock is larger. The reason is that the fracture toughness represents the energy required for the fracture initiation of the coal rock face cleavage tip, and the larger the fracture toughness indicates the larger the energy required for the fracture initiation of the face cleavage tip, and therefore the larger the fracture pressure.
FIG. 5 is a curve of the change of the fracture pressure and the borehole orientation, and it can be seen that the method of the present invention has the same rule as the conventional method, the fracture pressure and the borehole orientation change in a sinusoidal rule, and the fracture pressure is the smallest when the borehole orientation is the same as the direction of the maximum horizontal principal stress; the fracture pressure is greatest when the borehole orientation coincides with the direction of the minimum horizontal principal stress. If the maximum construction pump pressure during horizontal well fracturing needs to be reduced, drilling along the maximum horizontal main stress direction; if the safe density window range during drilling needs to be increased, the well can be drilled along the direction of the minimum horizontal principal stress.
Fig. 6 is a graph of the relationship between the fracture pressure and the cleat face inclination angle, and it can be seen that the fracture pressure increases with the increase of the cleat face inclination angle, the influence of the inclination angle on the fracture pressure is insignificant when the inclination angle is small, and the influence is more significant when the inclination angle is large. At low inclination, the maximum value of the fracture pressure is along the direction of the minimum horizontal principal stress; the azimuth angle corresponding to the maximum value of the burst pressure increases gradually as the inclination angle increases, and when the inclination angle reaches 90 °, the maximum value of the burst pressure occurs at an azimuth of 120 ° to the direction of the maximum horizontal principal stress.
Fig. 7 is a relation curve of the obtained rupture pressure and the fractal parameter, and it can be seen that the self-similarity ratio is unchanged, and the larger the fractal dimension is, the larger the rupture pressure is; the fractal dimension is unchanged, and the larger the self-similarity ratio, the smaller the burst pressure. The reason is that the larger the fractal dimension is, the more complex the face cutting principle is, and the more irregular the crack propagation path is; the similarity ratio represents the minimum fractal size of the crack, and the smaller the similarity ratio, the higher the measurement accuracy of the crack fractal degree, and the larger the crack length. Therefore, the larger the fractal dimension, the smaller the self-similarity ratio, and the larger the burst pressure.
Fig. 8 is a graph of the fracture pressure obtained versus the fracture length, and it can be seen that the fracture pressure decreases as the fracture length increases, and exhibits a "fast-before-slow" variation law.
FIG. 9 is an obtained actual fracturing construction curve of a coal-bed gas well in a research area, and it is seen from the graph that the actual fracture pressure of coal rock is 13.8MPa, the fracture pressure calculated by the method is 13.3MPa, and the error is 3.62%; the calculated fracture pressure according to the conventional method is 12.4MPa, and the error is 10.14 percent, so that the fracture pressure calculation method has smaller and more accurate error than the conventional method, and can better meet the requirements of coal bed gas sites.
Claims (7)
1. A method for calculating the fracture pressure of a coal-bed gas well is characterized by comprising the following steps:
acquiring fracture toughness of a coal rock type I crack of a target coal seam through an indoor experiment;
obtaining coal bed fractal parameters by carrying out variable-scale analysis on logging information of coal bed gas wells in a research block;
calculating the fracture pressure of the coal-bed gas well by combining the acquired fracture toughness of the coal rock I-type fracture, the coal bed fractal parameter and a coal-bed gas well fracture pressure calculation model;
the coal bed gas well fracture pressure calculation model is as follows:
wherein f isi(P) is the burst pressure objective function, MPa; p is bottom hole pressure, MPa; ppIs the formation pressure, MPa; sigmai、σj、σkThree main stresses are well wall, MPa; omega1、ω2、ω3Is the included angle between the corresponding direction vector of the three main stresses and the surface secant outer normal line, rad; eta is a biot coefficient and is dimensionless; l isfIs the face-cutting length, m; kICFracture toughness of type I crack, MPa.m1/2(ii) a r is a self-similarity coefficient; dimensionless; d is a fractal dimension and is dimensionless;
the method for constructing the coal-bed gas well fracture pressure calculation model comprises the following steps:
deducing fracture toughness of the coal rock type I fracture considering fractal characteristics;
obtaining the normal resultant force of the surface cleat in any occurrence state through matrix conversion and ground stress analysis;
establishing a fracture pressure calculation model of the coal-bed gas well according to a fracture criterion that fracture initiation occurs when the surface-cleated normal resultant force is larger than the fracture toughness of the coal rock I-type fracture considering the fractal characteristics;
converting the matrix into a matrix conversion relation among different coordinate systems; the ground stress analysis is a mechanical analysis process in rock mechanics; the failure criterion is a type I fracture failure criterion in fracture mechanics.
2. The method of calculating coalbed methane well fracture pressure according to claim 1,
in the step of obtaining the I-shaped fracture toughness of the coal rock of the target coal bed through the indoor experiment, the prefabricated fracture coal rock used in the indoor experiment is prepared through the following steps:
obtaining target layer coal rock by rope coring; preparing a disc-shaped core section with the thickness of 30-50mm by a diamond slicer; and in the prefabricated crack of the disc-shaped core section, the ratio of the length of the prefabricated crack to the disc diameter is 0.1-0.3.
3. The method of calculating coalbed methane well fracture pressure according to claim 1,
in the step of obtaining the coal bed fractal parameters by carrying out variable-scale analysis on the logging information of the coal bed gas well in the research block,
the fractal parameter is a fractal dimension;
the specific calculation formula of the logging data variable-scale analysis is as follows:
wherein, R is range, S is standard deviation, R (n)/S (n) is R/S value corresponding to the nth sampling point, R (n)/S (n) and n of sound wave time difference/depth resistivity/density are used for making a double logarithmic scatter diagram, the slope of a straight line is obtained by regression, and the fractal dimension is 2-H.
4. The method for calculating the fracture pressure of the coal-bed gas well as recited in any one of claims 1 to 3,
the specific process of calculating the fracture pressure of the coal-bed gas well by combining the acquired fracture toughness of the coal rock, the coal-bed fractal parameter and the coal-bed gas well fracture pressure calculation model is as follows:
a. the well circumferential angle range is 0-180 degrees, and the bottom hole pressure is enabled to be from P under the premise of giving the well circumferential anglepAt 0.1PpIs increased to 10Pp；
b. Calculating three main stresses sigma of well walli、σj、σkAnd the included angles omega between the corresponding direction vectors of the three main stresses and the surface secant outer normal1、ω2、ω3；
c. Substituting all parameters into the coal-bed gas well fracture pressure calculation model, and solving a fracture pressure objective function fiA value of (P); an objective function fiAnd (P) taking the bottom hole pressure when the absolute value of the (P) is smaller than the error zeta as the fracture pressure at the current circumferential angle, finally comparing the fracture pressures in the circumferential angle range, and taking the minimum value as the borehole fracture pressure.
5. The method of calculating coalbed methane well fracture pressure according to claim 4,
the three main stresses sigma of the well wall in the coal-bed gas well fracture pressure calculation model are calculated by adopting the following formulai、σj、σk：
Wherein: sigmaz、σθAnd σθzIs the stress component in the borehole coordinate system, MPa.
6. The method for calculating the fracture pressure of the coal-bed gas well as recited in claim 4, wherein an included angle ω between a corresponding direction vector of three principal stresses and a surface secant outer normal in a fracture pressure calculation model of the coal-bed gas well is calculated by the following formula1、ω2、ω3：
Wherein:
wherein (l)mi，mmi，nmi) { i ═ 1, 2, 3} are the direction vector coordinates of the three principal stresses; (l)p，mp，np) Is the direction vector coordinate of the surface secant outer normal; alpha is the angle of inclination, degree; beta is the azimuth angle, °; theta is the well angle, °; gamma is the angle between the main stress and the axis of the well; thetasThe direction is the dough cutting direction; thetaDIs the face-cutting inclination angle.
7. A system for calculating the fracture pressure of a coal-bed gas well, the system comprising:
the first module is used for acquiring fracture toughness of the I-shaped crack of the coal rock of the target coal bed through an indoor experiment;
the second module is used for carrying out variable-scale analysis on logging information of coal-bed gas wells in the research block to obtain coal-bed fractal parameters;
the third module is used for calculating the fracture pressure of the coal-bed gas well by combining the acquired fracture toughness of the coal rock, the coal-bed fractal parameter and the coal-bed gas well fracture pressure calculation model;
the coal bed gas well fracture pressure calculation model is as follows:
wherein f isi(P) is the burst pressure objective function, MPa; p is bottom hole pressure, MPa; ppIs the formation pressure, MPa; sigmai、σj、σkThree main stresses are well wall, MPa; omega1、ω2、ω3Is the included angle between the corresponding direction vector of the three main stresses and the surface secant outer normal line, rad; eta is a biot coefficient and is dimensionless; l isfIs the face-cutting length, m; kICFracture toughness of type I crack, MPa.m1/2(ii) a r is a self-similarity coefficient; dimensionless; d is a fractal dimension and is dimensionless;
the method for constructing the coal-bed gas well fracture pressure calculation model comprises the following steps:
deducing fracture toughness of the coal rock type I fracture considering fractal characteristics;
obtaining the normal resultant force of the surface cleat in any occurrence state through matrix conversion and ground stress analysis;
establishing a fracture pressure calculation model of the coal-bed gas well according to a fracture criterion that fracture initiation occurs when the surface-cleated normal resultant force is larger than the fracture toughness of the coal rock I-type fracture considering the fractal characteristics;
converting the matrix into a matrix conversion relation among different coordinate systems; the ground stress analysis is a mechanical analysis process in rock mechanics; the failure criterion is a type I fracture failure criterion in fracture mechanics.
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