CN114662316A - Method for calculating friction coefficient in wall surface of spatial three-dimensional natural crack - Google Patents
Method for calculating friction coefficient in wall surface of spatial three-dimensional natural crack Download PDFInfo
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Abstract
The invention discloses a method for calculating a friction coefficient in a wall surface of a spatial three-dimensional natural crack, which comprises the steps of determining the trend of the natural crack and an included angle between the natural crack and a horizontal plane; determining a horizontal maximum principal stress orientation; determining in-situ three-dimensional main stress; determining a pore elastic constant and a formation fluid pressure; determining a natural fracture approach angle; determining a unit normal vector of a three-dimensional natural crack surface; determining normal stress and shear stress of a three-dimensional natural fracture surface; determining an effective stress; and determining the friction coefficient in the spatial natural fracture. The method considers that natural fractures in an underground reservoir are distributed in space and are subjected to combined action of an in-situ stress field and formation fluid to keep static mechanical balance; the method for calculating the internal friction angle of the three-dimensional natural crack in the rock mass containing the natural crack medium is obtained through a mathematical method, fills the blank of the method for obtaining the internal friction coefficient of the three-dimensional natural crack, and can give the influence of the trend and the inclination angle of the natural crack on the internal friction coefficient of the crack surface.
Description
Technical Field
The invention relates to a method for calculating a friction coefficient in a spatial three-dimensional natural fracture wall surface, and belongs to the technical field of unconventional oil and gas reservoir volume fracturing exploration and development.
Background
Rock mass mechanics parameters and strength parameters have very important application in the technical field of engineering. In the technology of hydraulic fracturing yield increase transformation related to the field of oil and gas exploration and development, a target reservoir is generally regarded as an isotropic uniform continuous line elastomer, and the initiation and extension of a hydraulic fracture are judged mainly by adopting a first strength theory (or called a maximum tensile stress criterion) (Liyigchuan: oil production engineering. Beijing, oil industry publisher, 2008; Wanrenzhi: oil production technology handbook. Beijing, oil industry publisher, 1998; Zengvanui et al: an open hole fracturing pressure prediction model considering percolation effect. natural gas geoscience, 2019;). The primary tensile strength is determined according to brazilian cracking tests or calculated using empirical formulas.
Since the shale gas revolution, the reconstruction of unconventional oil and gas reservoirs with a large number of weak faces of natural fracture structures by adopting fracture network volume fracturing has been greatly successful. The industrial industry has recognized through indoor experiments, theoretical analysis and mine field summarization that 'structural weak faces such as relatively developed natural fractures and the like widely exist in rock masses' are one of the most important key elements influencing fracture network fracturing modification (Huyongquan et al: fracture network fracturing control condition research, university of Petroleum, southwestern, proceedings 2013). As the fracture mechanics mechanism of the natural fracture-matrix rock mass medium restricts the network fracture propagation evolution behavior and the volume of production increase transformation (Liuyuan shuang and the like: the research on the volume fracturing complex fracture opening mechanics condition, China and foreign energy sources 2015, Liyalong and the like: the simulation research progress of the shale reservoir fracture network, the petroleum geophysical exploration 2019), the high attention of the engineering technology to the weak surface property of the natural fracture structure is promoted.
For experimental determination of shear parameters (cohesion and internal friction angle) of a continuum medium, GB/T50266-2013 'engineering rock mass test method standard' is widely adopted, and a triaxial compression test and a direct shear test are mainly adopted. The 'rock structure face shear test method and device' (201210223787) of Liujianfeng, Xie and Heng et al, and the 'rock shear strength test method and process' (201710937345) of Xurong super et al are all improvements on the continuous uniform medium shear test device and method, and the obtained mechanical parameters are the internal friction coefficient of the continuous medium body and the like. These devices and methods are not suitable for shear parameter testing of subsurface three-dimensional natural fractures multifaceted by in situ stress field loading and formation pore fluid pressure. At present, an acquisition method of the friction coefficient of the natural crack is not seen.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a method for calculating the friction coefficient in a spatial three-dimensional natural crack wall surface.
The technical scheme provided by the invention for solving the technical problems is as follows: a method of calculating a coefficient of friction in a spatial three-dimensional natural fracture wall, comprising:
determining the trend of the natural fracture and the included angle between the natural fracture and the horizontal plane according to imaging logging information of the natural fracture or the observation under a directional coring mirror;
determining a horizontal maximum principal stress azimuth according to microseism fracturing crack monitoring or core testing;
determining in-situ three-dimensional main stress according to a test fracturing method or a Kaiser effect and other core test methods;
determining a pore elastic constant and formation fluid pressure according to a rock core experiment test method;
determining a natural fracture approach angle according to the horizontal maximum principal stress azimuth and the natural fracture strike;
determining a unit normal vector of a three-dimensional natural fracture surface according to an included angle between a natural fracture and a horizontal plane and an approach angle of the natural fracture;
determining normal stress and shear stress of the three-dimensional natural fracture surface according to the unit normal vector and the in-situ three-dimensional principal stress of the three-dimensional natural fracture surface;
determining effective stress acting in the space natural fracture according to normal stress and shear stress of a three-dimensional natural fracture surface, a pore elastic constant and formation fluid pressure;
and determining the friction coefficient in the spatial natural fracture according to the effective stress acting in the spatial natural fracture.
The further technical scheme is that the in-situ three-dimensional principal stress comprises a vertical principal stress sigmazHorizontal maximum principal stress σyHorizontal minimum principal stress σx。
The further technical scheme is that the calculation formula of the unit normal vector of the three-dimensional natural crack surface is as follows:
wherein:
in the formula:
is a unit normal vector; n isxIs the unit normal vector x-direction component; n isyIs the unit normal vector y direction component; n iszIs the unit normal vector z-direction component; theta is a natural fracture approach angle;
the included angle between the natural crack and the horizontal plane.
The further technical scheme is that a calculation formula of normal stress of the three-dimensional natural fracture surface is as follows:
pn＝σxnxnx+σynyny+σznznz
in the formula: n isxIs the unit normal vector x-direction component; n is a radical of an alkyl radicalyIs the unit normal vector y direction component; n is a radical of an alkyl radicalzIs the unit normal vector z-direction component; sigmazIs a vertical principal stress; sigmayIs the horizontal maximum principal stress; sigmaxIs the horizontal minimum principal stress; p is a radical ofnNormal stress of three-dimensional natural fracture surface.
The further technical scheme is that the calculation formula of the shear stress of the three-dimensional natural fracture surface is as follows:
in the formula: p is a radical ofnNormal stress of three-dimensional natural crack surface;
acting force applied to the wall surface of the natural crack; n isxIs the unit normal vector x-direction component; n isyIs the unit normal vector y-direction component; n is a radical of an alkyl radicalzIs the unit normal vector z-direction component; sigmazIs the vertical principal stress; sigmayIs the horizontal maximum principal stress; sigmaxIs the horizontal minimum principal stress; p is a radical of formulaτIs the shear stress of the three-dimensional natural fracture surface.
The further technical scheme is that the effective stress acting in the spatial natural fracture comprises effective normal stress and effective shear stress.
The further technical scheme is that the calculation formula of the effective normal stress is as follows:
pn,e＝pn-αps
in the formula: p is a radical of formulanNormal to the three-dimensional natural fracture surfaceNormal stress; α is the pore elastic constant; p is a radical ofsIs the formation fluid pressure; p is a radical ofn,eIs the effective normal stress.
The further technical scheme is that the calculation formula of the effective shear stress is as follows:
τe＝pτ
in the formula: p is a radical ofτShear stress for three-dimensional natural fracture faces; tau iseIs the effective shear stress.
The further technical scheme is that the calculation formula of the friction coefficient in the space natural fracture is as follows:
μ＝τe/pn,e
in the formula: p is a radical ofn,eEffective normal stress; tau iseEffective shear stress; mu is the friction coefficient in the spatial natural fracture.
The invention has the following beneficial effects: the invention considers the space distribution of natural fractures in the underground reservoir, and the natural fractures are kept in static mechanical balance under the combined action of an in-situ stress field and formation fluid. The method for calculating the internal friction angle of the three-dimensional natural fracture in the rock mass containing the natural fracture medium is obtained by a mathematical method by applying a mechanical principle and a strength criterion. The method fills the blank of the method for obtaining the friction coefficient in the space three-dimensional natural crack, and can give the influence of the trend and the inclination angle of the natural crack on the friction coefficient in the crack surface.
Drawings
FIG. 1 is a force-resolved wall space of a natural fracture;
FIG. 2 is a graph illustrating the dominant natural fracture path from an imaging log;
FIG. 3 is a graph of natural fracture dip explained by imaging logs;
FIG. 4 is a horizontal maximum principal stress azimuth of a target work area determined by microseismic testing;
FIG. 5 is a graph of coefficient of friction versus approach angle for a natural fracture.
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.
The invention discloses a method for calculating a friction coefficient in a wall surface of a space three-dimensional natural crack, which comprises the following steps of:
(1) the natural fracture trend and the included angle between the natural fracture and the horizontal plane are obtained by adopting the imaging logging or the observation under the lens of the directional coring;
(2) acquiring a horizontal maximum main stress azimuth by adopting methods such as microseism monitoring, core testing and the like;
(3) determining in-situ three-dimensional main stress by a test fracturing method or a Kaiser effect and other core test methods;
(4) obtaining a pore elastic constant and formation fluid pressure through a rock core experiment test or other methods;
(5) determining a natural fracture approach angle according to the horizontal maximum principal stress azimuth and the natural fracture strike;
(6) calculating a unit normal vector of the spatially distributed natural fracture;
the spatial natural fractures formed during the formation of a hydrocarbon reservoir are shown in figure 1 under a cartesian coordinate system. Note that the unit normal vector of the natural fracture is:
wherein:
in the formula：
Is a unit normal vector; n isxIs the unit normal vector x-direction component; n is a radical of an alkyl radicalyIs the unit normal vector y direction component; n iszIs the unit normal vector z-direction component; theta is a natural fracture approach angle;
the included angle between the natural crack and the horizontal plane is formed;
(7) normal stress and shear stress of the spatially distributed natural fracture surfaces are calculated;
at this point, the forces acting on the natural fracture face are:
according to the stress decomposition principle in the theory of elastic mechanics, a normal stress and shear stress calculation formula acting on a natural fracture surface in a rock mass medium containing natural fractures can be derived.
pn＝nkek.σijnjej＝niσijnj
＝σxxnxnx+σxynynx+σxznznx+σxynxny+σyynyny
+σyznzny+σxznxnz+σyznynz+σzznznz
(8) Calculating effective stress acting in the spatial natural fracture;
the reservoir is usually filled with groundFormation fluid, corresponding formation fluid pressure ps(ii) a Because rock mass destruction is induced under the action of effective stress, the effective normal stress and the effective shear stress of the structural weak plane under the action of formation fluid pressure are calculated according to the Taisha base principle, and the expression is as follows:
pn,e＝pn-αps
τe＝pτ
in the formula: p is a radical ofnNormal stress of three-dimensional natural crack surface; α is the pore elastic constant; p is a radical ofsIs formation fluid pressure; p is a radical ofn,eEffective normal stress; p is a radical of formulaτShear stress of three-dimensional natural fracture surface; tau.eEffective shear stress;
(9) determining the friction coefficient in the space natural fracture;
the natural fracture in the rock body under the original stratum condition is considered to have no fracture to generate a new fracture surface, namely the spatial natural fracture is in a static mechanical equilibrium state. The wall surface of the natural crack meets the coulomb shear strength theory, namely when the shear force of the crack surface is greater than the shear strength, the crack is sheared and broken. The conditional expression of the strength of the destruction is as follows:
τe＝c+μ.pn,e
the internal friction coefficient of the natural fracture wall surface can be expressed as
μ＝(τe-c)/pn,e
For open natural fractures, the cohesion is approximately zero. Thus, there are:
μ＝τe/pn,e
in the formula: p is a radical ofn,eEffective normal stress; tau iseEffective shear stress; mu is the friction coefficient in the natural crack of the space; c is the cohesion of the natural fracture surface.
Examples
And (3) developing natural fractures of oil reservoirs in well sections of 691.0-713.0 m of KL-B509 wells of a certain oil field in the west, and carrying out imaging well logging, core experiment testing in-situ stress field and fracturing microseism monitoring in the well construction process.
The method is applied to calculate the friction coefficient in the natural fracture on site, and comprises the following steps:
A. collecting parameters of natural fracture strike, horizontal maximum principal stress direction, horizontal three-dimensional principal stress, pore elastic constant and the like of a natural fractured reservoir;
firstly, explaining 691.0-713.0 m well section high-conductivity natural fractures by applying an imaging well logging interpretation principle to obtain 44 natural fractures, wherein the dominant directions of the natural fractures are NE0-10 degrees, NE30-40 degrees and 24-28 degrees (shown in figures 2 and 3);
average values in this example: the dominant trend is 10 degrees and the dip angle is 25 degrees;
secondly, the horizontal maximum principal stress azimuth obtained by monitoring the microseism fracturing fracture is NE45 degrees (as shown in figure 4);
obtaining the in-situ three-direction principal stress based on the Kaiser effect and other core testing methods respectively as follows: vertical principal stress sigmazMaximum horizontal principal stress sigma of 15.0MPay13.5MPa, minimum principal stress σ horizontalx＝11.0MPa。
Testing the elastic constant alpha of the pore space to be 0.7 and the pressure of the formation fluid to be 6.8 MPa;
B. calculating the normal stress and the shear stress of the natural crack surface;
taking the trend of the dominant natural crack as NE10 degrees and the horizontal maximum main stress direction as NE45 degrees; then
The natural fracture approach angle is: NE45-NE10 is 35 °;
secondly, the inclination angle is obtained according to the imaging logging data
Computing unit normal vector
Fourthly, calculating normal stress and shear stress on natural crack surface
pn＝13.5×0.34622+11.0×0.24242+15×0.90632＝14.585MPa
C. Calculating effective stress in the natural fracture;
pn,e＝14.585-0.7×6.8＝9.825MPa
τe＝1.019MPa
G. determining the friction coefficient in the natural fracture;
μ＝1.019/9.825＝0.1037
assuming that the in-situ stress field, the formation pressure and the pore elastic constant are kept constant, similar calculation can be adopted to obtain the change relation of the friction coefficient in the natural fracture wall surface along with the approach angle when the dominant azimuth of the natural fracture changes, as shown in figure 5.
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 (9)
1. A method for calculating the friction coefficient in a spatial three-dimensional natural crack wall surface is characterized by comprising the following steps:
determining the trend of the natural fracture and the included angle between the natural fracture and the horizontal plane according to imaging logging information of the natural fracture or the observation under a directional coring mirror;
determining a horizontal maximum principal stress azimuth according to microseism fracturing crack monitoring or rock core testing;
determining in-situ three-dimensional main stress according to a test fracturing method or a Kaiser effect and other core test methods;
determining a pore elastic constant and formation fluid pressure according to a rock core experiment test method;
determining a natural fracture approach angle according to the horizontal maximum principal stress azimuth and the natural fracture strike;
determining a unit normal vector of a three-dimensional natural fracture surface according to an included angle between the natural fracture and a horizontal plane and an approach angle of the natural fracture;
determining normal stress and shear stress of the three-dimensional natural fracture surface according to the unit normal vector of the three-dimensional natural fracture surface and the in-situ three-way main stress;
determining effective stress acting in the space natural fracture according to normal stress and shear stress of a three-dimensional natural fracture surface, a pore elastic constant and formation fluid pressure;
and determining the friction coefficient in the spatial natural fracture according to the effective stress acting in the spatial natural fracture.
2. The method for calculating the in-wall friction coefficient of a spatial three-dimensional natural fracture according to claim 1, wherein the in-situ three-way principal stress comprises a vertical principal stress σzHorizontal maximum principal stress σyHorizontal minimum principal stress σx。
3. The method for calculating the friction coefficient in the wall surface of the spatial three-dimensional natural crack as claimed in claim 2, wherein the calculation formula of the unit normal vector of the three-dimensional natural crack surface is as follows:
wherein:
in the formula:
is a unit normal vector; n isxIs the unit normal vector x-direction component; n isyIs the unit normal vector y-direction component; n iszIs the z-direction component of the unit normal vector; theta is a natural fracture approach angle;
the included angle between the natural crack and the horizontal plane.
4. The method for calculating the friction coefficient in the spatial three-dimensional natural fracture wall surface according to the claim 2, characterized in that the calculation formula of the normal stress of the three-dimensional natural fracture surface is as follows:
pn＝σxnxnx+σynyny+σznznz
in the formula: n isxIs the unit normal vector x-direction component; n isyIs the unit normal vector y-direction component; n iszIs the unit normal vector z-direction component; sigmazIs the vertical principal stress; sigmayIs the horizontal maximum principal stress; sigmaxIs the horizontal minimum principal stress; p is a radical of formulanNormal stress of three-dimensional natural fracture surface.
5. The method for calculating the friction coefficient in the wall surface of the spatial three-dimensional natural crack as claimed in claim 2, wherein the calculation formula of the shear stress of the three-dimensional natural crack surface is as follows:
in the formula:pnnormal stress of three-dimensional natural crack surface;
acting force applied to the wall surface of the natural crack; n is a radical of an alkyl radicalxIs the unit normal vector x-direction component; n isyIs the unit normal vector y direction component; n is a radical of an alkyl radicalzIs the unit normal vector z-direction component; sigmazIs the vertical principal stress; sigmayIs the horizontal maximum principal stress; sigmaxIs the horizontal minimum principal stress; p is a radical of formulaτIs the shear stress of the three-dimensional natural fracture surface.
6. The method for calculating the in-wall friction coefficient of the spatial three-dimensional natural fracture according to claim 1, wherein the effective stresses acting in the spatial natural fracture comprise an effective normal stress and an effective shear stress.
7. The method for calculating the friction coefficient in the wall surface of the spatial three-dimensional natural crack according to claim 6, wherein the calculation formula of the effective normal stress is as follows:
pn,e＝pn-αps
in the formula: p is a radical ofnNormal stress of three-dimensional natural crack surface; α is the pore elastic constant; p is a radical ofsIs formation fluid pressure; p is a radical of formulan,eIs the effective normal stress.
8. The method for calculating the friction coefficient in the wall surface of the spatial three-dimensional natural crack according to claim 7, wherein the effective shear stress is calculated by the following formula:
τe＝pτ
in the formula: p is a radical of formulaτShear stress of three-dimensional natural fracture surface; tau iseIs the effective shear stress.
9. The method for calculating the friction coefficient in the wall surface of the spatial three-dimensional natural fracture according to claim 8, wherein the calculation formula of the friction coefficient in the spatial natural fracture is as follows:
μ＝τe/pn,e
in the formula: p is a radical of formulan,eEffective normal stress; tau iseEffective shear stress; mu is the friction coefficient in the spatial natural fracture.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117328861A (en) * | 2023-11-07 | 2024-01-02 | 西南石油大学 | Calculation method for simulating hydraulic fracture to pass through rock stratum |
| CN117494446A (en) * | 2023-11-09 | 2024-02-02 | 西南石油大学 | Method for judging extension behavior of two-dimensional hydraulic fracture and natural fracture after meeting |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117328861A (en) * | 2023-11-07 | 2024-01-02 | 西南石油大学 | Calculation method for simulating hydraulic fracture to pass through rock stratum |
| CN117328861B (en) * | 2023-11-07 | 2024-06-11 | 西南石油大学 | Calculation method for simulating hydraulic fracture to pass through rock stratum |
| CN117494446A (en) * | 2023-11-09 | 2024-02-02 | 西南石油大学 | Method for judging extension behavior of two-dimensional hydraulic fracture and natural fracture after meeting |
| CN117494446B (en) * | 2023-11-09 | 2024-06-04 | 西南石油大学 | Method for judging extension behavior of two-dimensional hydraulic fracture and natural fracture after meeting |
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