CN111980697A - Method for calculating well casing variable of hydraulic fracturing horizontal well in natural fractured shale stratum - Google Patents

Method for calculating well casing variable of hydraulic fracturing horizontal well in natural fractured shale stratum Download PDF

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CN111980697A
CN111980697A CN202011012263.6A CN202011012263A CN111980697A CN 111980697 A CN111980697 A CN 111980697A CN 202011012263 A CN202011012263 A CN 202011012263A CN 111980697 A CN111980697 A CN 111980697A
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crack
stress
calculating
fracture
mpa
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CN111980697B (en
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路千里
郭建春
刘壮
张航
母青平
尹从彬
李彦超
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Southwest Petroleum University
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Abstract

The invention relates to a method for calculating a well casing variable of a hydraulic fracturing horizontal well in a natural fractured shale stratum, and belongs to the technical field of shale gas fracturing. The invention mainly overcomes the defects in the prior art, and provides a method for calculating the variable of a well casing of a hydraulic fracturing horizontal well in a natural fractured shale stratum, which comprises the following steps: acquiring the ground stress, rock mechanical parameters, natural crack geometric parameters and logging data of a target work area; establishing an I-II composite fracture displacement field analytical model of the superposed fluid pressure based on a complex function method; calculating to obtain the tangential relative displacement of the crack; and finally, determining the variable of the shaft sleeve according to the tangential relative displacement of the crack. The method can accurately calculate to obtain the variable of the well casing, and in the area with higher casing deformation risk, measures such as optimizing the well casing direction, strengthening the well cementation quality, properly reducing the discharge capacity, adopting a temporary plugging technology and the like can be considered to reasonably control the fluid pressure in the seam to reduce the casing deformation risk.

Description

Method for calculating well casing variable of hydraulic fracturing horizontal well in natural fractured shale stratum
Technical Field
The invention relates to a method for calculating a well casing variable of a hydraulic fracturing horizontal well in a natural fractured shale stratum, and belongs to the technical field of shale gas fracturing.
Background
The casing pipe can deform in different degrees in the shale gas fracturing process, so that the fracturing construction difficulty and the cost are increased, great difficulty is brought to follow-up operation and production, the problems of low single-well yield, short well life cycle and the like are caused, the overall economic benefit of shale gas development is seriously influenced, the casing pipe deformation (hereinafter referred to as casing deformation) can influence the integrity of a shaft, prevent a downhole tool from being lowered, reduce the fracturing segmentation effectiveness, even cause part of fracturing sections to give up transformation, and becomes one of important factors influencing the shale gas fracturing development.
With the rapid development of unconventional oil and gas, the fracturing technology is a main means for the reformation of unconventional oil and gas reservoirs, and the fracturing often occurs along with micro-earthquakes, so that the dislocation of a certain scale of a stratum is caused, the shearing force generated by the dislocation of the stratum directly acts on a sleeve, the sleeve is subjected to plastic deformation and even damage, and finally the fracturing construction cannot be continued. Therefore, when the set change occurs, the quick determination of the set variable is significant to the field engineering design. Currently, the set variables are usually based on caliper analysis or numerical simulation calculation, and there are many limitations in practical applications.
Disclosure of Invention
The invention mainly overcomes the defects in the prior art and provides a method for calculating the variable of a well casing of a hydraulic fracturing horizontal well in a natural fractured shale stratum.
The technical scheme provided by the invention for solving the technical problems is as follows: the method for calculating the well casing variable of the hydraulic fracturing horizontal well in the natural fractured shale stratum comprises the following steps:
step one, acquiring the ground stress, rock mechanical parameters, natural crack geometric parameters and logging data of a target work area, and then obtaining the data according to the groundStress calculation shear stress tau in y-direction of ground stressxyDetermining the distance x from the shaft to the center of the crack length according to the logging data;
secondly, establishing an I-II composite fracture displacement field analytical model of the superposed fluid pressure based on a complex function method;
thirdly, calculating to obtain the tangential relative displacement delta u of the crack according to the I-II composite crack displacement field analytical modelfAnd the normal relative displacement amount Deltavf；
Step four, finally, according to the tangential relative displacement delta u of the crackfAnd the normal relative displacement amount DeltavfAnd determining the comprehensive displacement S of the fracture, namely the variable of the wellbore casing.
The further technical scheme is that a calculation formula of the shear stress tau of the ground stress in the y direction in the step one is as follows:
Figure BDA0002697887880000021
in the formula: τ is the shear stress of the ground stress in the y-direction, MPa; sigmaHMaximum horizontal principal stress, MPa; sigmahMinimum horizontal principal stress, MPa; theta is an included angle between the maximum horizontal main stress direction and the crack surface along the clockwise direction.
The further technical scheme is that the rock mechanical parameters comprise a rock static Young modulus E and a rock static Poisson ratio upsilon; the natural fracture geometry parameters include fracture half-length a.
The further technical scheme is that the I-II composite fracture displacement field analysis model is as follows:
Figure BDA0002697887880000022
Figure BDA0002697887880000023
in the formula: τ being the earth stress in the y directionShear stress, MPa; Δ ufIs the tangential relative displacement of the crack, m; Δ vfIs the normal relative displacement of the crack, m; e is the static Young modulus of rock, MPa; upsilon is the static Poisson's ratio of the rock and has no dimension; edThe dynamic Young modulus of rock in the formation acoustic logging data is MPa; upsilon isdThe dynamic Poisson's ratio of the rock in the formation acoustic logging data is dimensionless; a is the half-length of the crack, m; x is the distance from the shaft to the center of the crack length, m; a is1、b1、c1、d1Fitting coefficients for a rock dynamic and static parameter relation curve; sigmabThe normal stress of the ground stress on the stress unit is MPa; p is a radical offFluid pressure in the fracture, MPa.
The further technical scheme is that the calculation formula of the comprehensive displacement S of the crack is as follows:
Figure BDA0002697887880000031
in the formula: Δ ufIs the tangential relative displacement of the crack, m; Δ vfIs the normal relative displacement of the crack, m; and S is the comprehensive displacement of the crack, m.
The invention has the following beneficial effects: the method can accurately calculate to obtain the variable of the well casing, can provide an analysis tool and a reference for quickly pre-judging the casing deformation risk and the severity of the horizontal well in the fracturing engineering design, and considers the measures of optimizing the well casing direction, strengthening the well cementation quality, properly reducing the discharge capacity, adopting a temporary plugging technology and the like to reasonably control the fluid pressure in the seam to reduce the casing deformation risk in the area with higher casing deformation risk judgment.
Drawings
FIG. 1 is a plane strain model diagram of a compound type I-II fracture;
FIG. 2 is a model calculated HX-1 casing variable distribution plot.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
In the fracturing process of a HX-1 well of a certain horizontal well of a well zone, the 20 th section of bridge plug is blocked due to deformation of a sleeve during perforation linkage. The ant tracing crack prediction graph shows that possible natural cracks (the crack length is 150m, N50 degrees E) are developed near the point of resistance, the distance between the shaft and the center of the crack length is about 30m, the borehole diameter logging shows that three-level casing change occurs at the point of resistance, and the well temperature logging shows that the temperature of the point of resistance is obviously reduced. The stress in the well is relatively stable and the direction of the maximum principal stress is predicted to be 103 deg..
Therefore, the method of the invention is adopted to calculate the variable of the casing of the HX-1, and comprises the following specific steps:
s10, acquiring the ground stress, rock mechanical parameters, natural fracture geometric parameters and logging data of a target work area, wherein the data results are shown in Table 1;
TABLE 1
Length of natural seam, m 150
Diameter of open hole, mm 215.9
Diameter of the sleeve, mm 139.7
Wall thickness of the sleeve pipe mm 12.7
Poisson ratio 0.22
Young's modulus, MPa 43500
Minimum horizontal principal stress, MPa 60
Maximum horizontal principal stress, MPa 72
Step S20, calculating the shear stress τ of the ground stress in the y direction,
Figure BDA0002697887880000041
in the formula: tau isxyIs the shear stress of the ground stress in the y direction, MPa; sigmaHMaximum horizontal principal stress, MPa; sigmahMinimum horizontal principal stress, MPa; theta is an included angle between the maximum horizontal main stress direction and the crack surface along the clockwise direction;
s30, determining the distance x from the shaft to the center of the crack length according to the logging data;
step S40, establishing an I-II composite fracture displacement field analytical model of the superimposed fluid pressure based on a complex function method:
Figure BDA0002697887880000042
Figure BDA0002697887880000043
in the formula: τ is the shear stress of the ground stress in the y-direction, MPa; Δ ufIs the tangential relative displacement of the crack, m; Δ vfIs the normal relative displacement of the crack, m; e is the static Young modulus of rock, MPa; upsilon is the static Poisson's ratio of the rock and has no dimension; edThe dynamic Young modulus of rock in the formation acoustic logging data is MPa; upsilon isdThe dynamic Poisson's ratio of the rock in the formation acoustic logging data is dimensionless; a is the half-length of the crack, m; x is the distance from the shaft to the center of the crack length, m; a is1、b1、c1、d1Fitting coefficients for a rock dynamic and static parameter relation curve; sigmabThe normal stress of the ground stress on the stress unit is MPa; p is a radical offFluid pressure, MP, in the fracture;
wherein the above model calculation results are shown in table 2:
parameter(s) E υ Ed υd a1 b1 c1 d1
Data of 43500 0.22 44257 0.29 7.81 -2.0449 -0.42 62088
Step S50, based on the above data and the following formula, HX-1 casing variable (fig. 2) can be calculated, i.e. the wellbore casing variable is 33.5 mm;
Figure BDA0002697887880000051
in the formula: Δ ufIs the tangential relative displacement of the crack, m; Δ vfIs the normal relative displacement of the crack, m; and S is the comprehensive displacement of the crack, m.
Comparing the borehole diameter logging results (shown in table 3), the maximum deformation of the casing calculated after the measured inner diameter data is centrally corrected is 31.8mm, the calculation error is 5.3%, and the calculation result of the method is accurate and reliable.
TABLE 3
Figure BDA0002697887880000052
Figure BDA0002697887880000061
The process for establishing the I-II compound fracture displacement field analytical model of the superimposed fluid pressure comprises the following steps:
the model assumes that: natural fracture being a superimposed fluid pressure p in the fracturefThe compound type I-II cracks of (1); fluid pressure p in the fracturefThe fracture is completely propped open under the action, the fluid pressure is equal at each position in the fracture, the fracturing fluid is not lost, and the fracture is not expanded. A fracture plane strain model can be established, and the tangential displacement of the fracture is calculated based on a complex function method.
The I-II composite crack Westergaard stress function can be expressed as:
Z(z)＝ZI(z)-iZII(z)
in the formula, ZI、ZIIZ is a Westergaard stress function of the compound cracks I, II and I-II respectively;
in the above formula, the Westergaard stress function for the I, II type crack is:
Figure BDA0002697887880000062
in the formula, σa、σbThe normal stress of the original stress on the stress unit; τ is the shear stress of the ground stress in the y-direction.
As shown in fig. 1, any point z in polar coordinates can be represented by the following formula:
Figure BDA0002697887880000063
in the formula, a is half crack length m; r, r1、r2The distances m from the z point to the middle point of the long axis of the crack and the two ends of the crack respectively; beta, beta1、β2Is respectively r and r1、r2Angle to the long axis of the crack.
Substituting the formula into formula, by euler's formula, the formula can be written as:
Figure BDA0002697887880000071
namely, the method comprises the following steps:
Figure BDA0002697887880000072
wherein Z' is,
Figure BDA0002697887880000073
Is to differentiate and integrate the Z function.
Based on the fracture displacement calculation method deduced by Muskhellivili and the like, the I-II compound fracture displacement full-field solution can be expressed as follows:
Figure BDA0002697887880000074
the normal displacement and the tangential displacement of the crack can be calculated by substituting the formula:
Figure BDA0002697887880000075
on the fracture surface (y is 0), θ is 0 °, θ1+θ2＝π,r1＝a-x,r2And a + x, the relative displacement of the crack surface is as follows:
Figure BDA0002697887880000081
in the formula, u and v are I-II compound fracture tangential and normal displacement field full-field solutions, m respectively; u. of+、u-Is the tangential displacement of the upper surface and the lower surface of the I-II composite crack respectively, m; v. of+、v-Is the normal displacement of the upper surface and the lower surface of the I-II composite crack respectively, m; and delta u and delta v are respectively tangential and normal relative displacement of the I-II compound type crack and m.
Fluid pressure p in the fracturefThe Westergaard stress function of (a) can be expressed as:
Figure BDA0002697887880000082
similarly, the calculation formula of the relative displacement of the fracture surface under the action of the fluid pressure can be obtained:
Figure BDA0002697887880000083
the I-II composite fracture displacement field and the fluid pressure displacement field are superposed to obtain the following components:
Figure BDA0002697887880000084
in the formula up、vpThe displacement field full-field solution is the fracture tangential and normal displacement field full-field solution m under the action of fluid pressure; Δ up、ΔvpThe displacement is the tangential and normal relative displacement of the crack under the action of fluid pressure, m; Δ uf、ΔvfThe tangential and normal relative displacement, m, of the I-II composite fracture respectively representing the superimposed fluid pressure.
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 (5)

1. The method for calculating the well casing variable of the hydraulic fracturing horizontal well in the natural fractured shale stratum is characterized by comprising the following steps of:
acquiring the ground stress, rock mechanical parameters, natural fracture geometric parameters and logging data of a target work area, calculating the shear stress tau of the ground stress in the y direction according to the ground stress, and determining the distance x from a shaft to the center of the fracture length according to the logging data;
secondly, establishing an I-II composite fracture displacement field analytical model of the superposed fluid pressure based on a complex function method;
thirdly, calculating to obtain the tangential relative displacement delta u of the crack according to the I-II composite crack displacement field analytical modelfAnd the normal relative displacement amount Deltavf；
Step four, finally, according to the tangential relative displacement delta u of the crackfAnd the normal relative displacement amount DeltavfDetermining the combined displacement S of the fracture, i.e. wellbore casing deformationAmount of the compound (A).
2. The method for calculating the wellbore casing variable of the hydraulic fracturing horizontal well of the natural fractured shale formation according to claim 1, wherein the shear stress tau of the ground stress in the y direction in the step one is calculated according to the following formula:
Figure FDA0002697887870000011
in the formula: τ is the shear stress of the ground stress in the y-direction, MPa; sigmaHMaximum horizontal principal stress, MPa; sigmahMinimum horizontal principal stress, MPa; theta is an included angle between the maximum horizontal main stress direction and the crack surface along the clockwise direction.
3. The method for calculating the wellbore casing variable of the hydraulic fracturing horizontal well in the natural fractured shale stratum according to claim 1, wherein the rock mechanical parameters comprise rock static Young modulus E and rock static Poisson ratio upsilon; the natural fracture geometry parameters include fracture half-length a.
4. The method for calculating the wellbore casing variable of the hydraulic fracturing horizontal well in the natural fractured shale formation according to claim 3, wherein the I-II composite fracture displacement field analytical model is as follows:
Figure FDA0002697887870000021
Figure FDA0002697887870000022
in the formula: τ is the shear stress of the ground stress in the y-direction, MPa; Δ ufIs the tangential relative displacement of the crack, m; Δ vfIs the normal relative displacement of the crack, m; e is the static Young modulus of rock, MPa; upsilon is rockStone static poisson ratio, dimensionless; edThe dynamic Young modulus of rock in the formation acoustic logging data is MPa; upsilon isdThe dynamic Poisson's ratio of the rock in the formation acoustic logging data is dimensionless; a is the half-length of the crack, m; x is the distance from the shaft to the center of the crack length, m; a is1、b1、c1、d1Fitting coefficients for a rock dynamic and static parameter relation curve; sigmabThe normal stress of the ground stress on the stress unit is MPa; p is a radical offFluid pressure in the fracture, MPa.
5. The method for calculating the wellbore casing variable of the hydraulic fracturing horizontal well in the natural fractured shale formation according to claim 4, wherein the calculation formula of the comprehensive fracture displacement S is as follows:
Figure FDA0002697887870000023
in the formula: Δ ufIs the tangential relative displacement of the crack, m; Δ vfIs the normal relative displacement of the crack, m; and S is the comprehensive displacement of the crack, m.
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