CN111474604A - Electrical property detection method and system for transverse isotropic rock containing rotation inclined crack - Google Patents

Electrical property detection method and system for transverse isotropic rock containing rotation inclined crack Download PDF

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CN111474604A
CN111474604A CN202010499783.8A CN202010499783A CN111474604A CN 111474604 A CN111474604 A CN 111474604A CN 202010499783 A CN202010499783 A CN 202010499783A CN 111474604 A CN111474604 A CN 111474604A
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conductivity
fracture
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cracks
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韩同城
颜韩
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China University of Petroleum East China
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Abstract

The invention relates to an electrical property detection method and system for transverse isotropic rock with a rotary inclined crack, which comprises the following steps: measuring the conductivity parameter to obtain the conductivity tensor K of the background rock0And CT scanning is carried out on transverse isotropic rock containing the cracks to obtain volume content phi of the cracks, aspect ratio α of the cracks, included angle theta between the cracks and a background isotropic face and rotation angle
Figure DDA0002524288370000011
The fracture shape is characterized through fracture aspect ratio α and an included angle theta between the fracture and a background isotropic face, an oriented fracture shape tensor H is obtained, a conductivity contribution tensor A of the fracture is calculated according to the fracture shape tensor H, a transverse isotropic rock conductivity tensor of a rotary inclined fracture is obtained based on an electrical sliding theory, and the conductivity of the rock is obtained according to the conductivity tensorThe conductivity characteristics of the actual rock can be reflected more truly.

Description

Electrical property detection method and system for transverse isotropic rock containing rotation inclined crack
Technical Field
The invention relates to an electrical property detection method and system for transverse isotropic rock containing rotary inclined crack, and belongs to the technical field of exploration geophysics.
Background
For fractured strata, establishing a proper electrical rock physical model is the basis for accurately evaluating fracture characteristics by applying electrical prospecting. To advance the development of electrical prospecting techniques, researchers have developed a number of petrophysical models that characterize the conductivity of fractured rock. For the fissured isotropic background rock, the closed form of the solution for effective thermal conductivity (similar derivation and mathematical expression to the medium conductivity) is given by Hatta and Taya when all the fissures are parallel. Shafiro and Kachanov were characterized by introducing an Orientation Distribution Function (ODF) for the thermal conductivity properties of isotropic rocks containing a variety of oriented fractures. The above models all assume that the background medium of the fractured rock is isotropic, however, actual fractured formations may exhibit significant transverse isotropy characteristics. The effect of the presence of cracks on the conductivity of the rock is further complicated when the background rock is transversely isotropic. Barthelemy gives an implicit method for deducing the permeability of anisotropic rock with arbitrarily oriented fractures (with a similar deduction process and mathematical expression form as the conductivity of the medium) by analyzing a Green function of the anisotropic medium with fractures, and provides a direction for deducing the conductivity of transversely isotropic rock with inclined fractures. Giraud et al subsequently investigated the electrical properties of transversely isotropic rock containing fractures and gave a closed solution of the effective conductivity in both the special cases of fractures parallel and perpendicular to the isotropic face of the background rock. However, in actual fractured formations, under the combined influence of various geological actions, the fracture is not simply parallel or perpendicular to the isotropic plane of the background rock, but is oblique to the isotropic plane of the rock in any direction, i.e., the fracture has a rotation around the vertical axis of the background rock under the premise of being oblique to the isotropic plane of the background rock. Therefore, the existing rock conductivity model is difficult to truly reflect the conductivity characteristics of the actual rock. In order to more accurately represent the actual conductivity characteristics of the stratum containing the rotary inclined fractures, the invention provides a method for calculating the anisotropic conductivity of the transverse isotropic rock containing the rotary inclined fractures.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a transverse isotropic rock electrical property detection method and system with a rotation inclined fracture, which can better meet the situation of a real stratum with the fracture and can more truly reflect the conductivity characteristic of the real rock by rotating the fracture around the vertical axis of a background rock.
In order to achieve the purpose, the invention provides an electrical property detection method for transverse isotropic rock with rotation inclined cracks, which comprises the following steps: s1 measuring the conductivity parameter to obtain the conductivity tensor K of the background rock0And fracture conductivity tensor K*S2 CT scanning is carried out to transverse isotropic rock containing cracks to obtain volume content phi of the cracks, aspect ratio α of the cracks, included angle theta between the cracks and a background isotropic face and rotation angle
Figure BDA0002524288350000011
S3 the crack shape is characterized by crack aspect ratio α and the included angle theta between the crack and the background isotropic surface, and the obtained value is
Figure BDA0002524288350000028
The shape tensor H of the fracture at zero time and the actual shape tensor H of the fracture at that time
Figure BDA0002524288350000029
A value is calculated for the conductivity contribution tensor a of the fracture, the formula for the conductivity contribution tensor a being:
Figure BDA0002524288350000021
wherein I is a second order unit tensor; p is the Hill tensor; s4 according to the conductivity tensor K of the background rock0Fracture conductivity tensor K*The volume content phi of the crack and the conductivity contribution tensor A of the crack are obtained, the conductivity tensor of the transverse isotropic rock of the rotation inclined crack is obtained on the basis of the electrical sliding theory, and the conductivity of the rock is obtained according to the conductivity tensor.
Further, the transverse isotropic rock conductivity tensor K of the rotated dip fracture is:
Figure BDA0002524288350000022
K11＝kx+φ(k*-kx)A11，
K22＝kx+φ(k*-kx)A22，
K33＝kz+φ(k*-kz)A33，
K12＝K21＝φ(k*-kx)A12，
K13＝K31＝φ(k*-kz)A13，
K23＝K32＝φ(k*-kx)A23，
wherein k isxHorizontal conductivity of transverse isotropic background rock without cracks; k is a radical ofzIs the vertical conductivity of the transversely isotropic background rock without fractures, k is the conductivity of the formation water in the fractures, phi is the volume content of the fractures, A11、A22、A33、A12、A13And A23Are all elements of the conductivity contribution tensor a.
Further, the formula for the calculation of the elements in the conductivity contribution tensor a is:
Figure BDA0002524288350000023
Figure BDA0002524288350000024
Figure BDA0002524288350000025
Figure BDA0002524288350000026
Figure BDA0002524288350000027
Figure BDA0002524288350000031
wherein M is11、M22、M33、M23And M32Are the non-zero elements in the inverse tensor M, which are both conductivity contribution tensors a.
Further, the non-zero elements of the inverse tensor M of the conductivity contribution tensor a are calculated as:
Figure BDA0002524288350000032
Figure BDA0002524288350000033
Figure BDA0002524288350000034
Figure BDA0002524288350000035
Figure BDA0002524288350000036
wherein, T22、T23、T32And T33Are all elements of the transformed fracture shape tensor T, T2And t3Is the eigenvalue of the transformed fracture shape tensor T, λ1、λ2And λ3Are the diagonal elements of the Eshelby conduction tensor.
Further, the transformed fracture shape tensor T is obtained from the fracture shape tensor H by the following equation:
Figure BDA0002524288350000037
wherein, T at the upper right corner of the formula represents transposition operation; the equation for transforming the fracture shape tensor T is:
Figure BDA0002524288350000038
Figure BDA0002524288350000039
Figure BDA00025242883500000310
Figure BDA00025242883500000311
Figure BDA00025242883500000312
further, the eigenvalue T of the fracture shape tensor T is converted1、t2And t3The calculation formula of (2) is as follows:
t1＝T11，
Figure BDA00025242883500000313
Figure BDA00025242883500000314
wherein (x) is a Heaviside function, which can be expressed as
Figure BDA00025242883500000315
Further, a unit feature vector q corresponding to the fracture shape tensor T is converted1、q2And q is3：
Figure BDA0002524288350000041
Figure BDA0002524288350000042
Figure BDA0002524288350000043
Further, the calculation formula of the hill tensor is as follows:
Figure BDA0002524288350000044
wherein λ is1、λ2And λ3Are the diagonal elements of the Eshelby conduction tensor.
Further, λ1、λ2And λ3The expression of (a) is:
when t is1>t2>t3When the temperature of the water is higher than the set temperature,
Figure BDA0002524288350000045
Figure BDA0002524288350000046
λ2＝1-λ1-λ3，
wherein F and E are respectively:
Figure BDA0002524288350000047
Figure BDA0002524288350000048
when t is1>t2＝t3When the temperature of the water is higher than the set temperature,
Figure BDA0002524288350000049
λ1＝1-2λ2；
when t is1＝t2>t3When the temperature of the water is higher than the set temperature,
Figure BDA00025242883500000410
λ3＝1-2λ1；
when t is1＝t2＝t3When the temperature of the water is higher than the set temperature,
Figure BDA00025242883500000411
the invention also discloses an electrical property detection system for the transverse isotropic rock with the rotation inclined crack, which comprises the following steps: the conductivity tensor acquisition module is used for measuring the conductivity parameters to acquire the conductivity tensor K of the background rock0And fracture conductivity tensor K*The crack parameter acquisition module is used for carrying out CT scanning on transverse isotropic rock containing cracks to obtain the volume content phi of the cracks, the aspect ratio α of the cracks, the included angle theta between the cracks and a background isotropic face and the rotation angle
Figure BDA00025242883500000412
And the conductivity contribution tensor acquisition module is used for representing the shape of the crack through the crack aspect ratio α and the included angle theta between the crack and the background isotropic surface and acquiring the shape of the crack
Figure BDA00025242883500000413
The shape tensor H of the fracture at zero time and the actual shape tensor H of the fracture at that time
Figure BDA00025242883500000414
A value is calculated for the conductivity contribution tensor a of the fracture, the formula for the conductivity contribution tensor a being:
Figure BDA0002524288350000051
wherein I is a second order unit tensor; p is the Hill tensor; a conductivity tensor acquisition module for acquiring the conductivity tensor K of the background rock0Fracture conductivity tensor K*The volume content phi of the crack and the conductivity contribution tensor A of the crack are obtained on the basis of an electrical sliding theoryThe conductivity tensor of the rock is obtained according to the conductivity tensor.
Due to the adoption of the technical scheme, the invention has the following advantages:
the method is characterized in that only cracks parallel or vertical to an isotropic surface are considered for an electrical rock physical model of the rock with cracks, and in an actual fractured stratum, due to the influence of ground stress, the cracks are not parallel to the isotropic surface generally but are oblique to the isotropic surface at a certain angle.
Aiming at the defects of the existing electrical rock physical model containing a crack medium, the conductivity calculation model of the transverse isotropic rock containing the rotation inclined coin-shaped crack is deduced based on the transverse isotropic background medium and the coin-shaped crack which is obliquely crossed with an isotropic surface and has a small aspect ratio based on the real characteristics of the crack-containing rock. The comparison result shows that the change of each element of the conductivity tensor obtained by the calculation of the invention along with the rotation inclination angle and the aspect ratio is in line with the expectation. The method can more effectively predict the electrical properties of the transverse isotropic rock containing the rotation inclined fracture, and can provide support for electrical prospecting, well logging identification and fracture reservoir evaluation.
Drawings
FIG. 1 is a flow chart of an electrical property detection method for a transverse isotropic rock with a rotation dip crack according to an embodiment of the invention;
FIG. 2 is a schematic structural diagram of a transversely isotropic rock with a rotational dip fracture according to an embodiment of the present invention;
FIG. 3 is a graph of the variation of elements in the conductivity tensor of a transversely isotropic rock with rotated dip fractures with fracture dip angle at four fracture rotation angles of 0, π/8, π/4, 3 π/8, π/2; wherein the crack aspect ratio is set to 0.001, and K is shown in FIG. 3(a)11A plot of variation with crack inclination angle; FIG. 3(b) is K22A plot of variation with crack inclination angle; FIG. 3(c) is K33Incline with the crackA graph of the change in angle; FIG. 3(d) is K12A plot of variation with crack inclination angle; FIG. 3(e) is K13A plot of variation with crack inclination angle; FIG. 3(f) is K23Graph of variation with crack inclination angle.
FIG. 4 is a graph of the variation of elements in the conductivity tensor of a transversely isotropic rock with rotated dip fractures as a function of fracture rotation angle at four fracture rotation angles of 0, π/8, π/4, 3 π/8, π/2; wherein the crack aspect ratio is set to 0.001, and K is shown in FIG. 4(a)11A graph of variation with fracture rotation angle; FIG. 4(b) is K22A graph of variation with fracture rotation angle; FIG. 4(c) is K33A graph of variation with fracture rotation angle; FIG. 4(d) is K12A graph of variation with fracture rotation angle; FIG. 4(e) is K13A graph of variation with fracture rotation angle; FIG. 4(f) is K23Graph of variation with crack rotation angle.
FIG. 5 is a graph of the change of elements in the conductivity tensor of a transversely isotropic rock with rotated dip fractures as a function of fracture aspect ratio at four fracture rotation angles of 0, π/8, π/4, 3 π/8, π/2; wherein the crack aspect ratio is set to 0.001, and K is shown in FIG. 5(a)11Plot of change with fracture aspect ratio; FIG. 5(b) is K22Plot of change with fracture aspect ratio; FIG. 5(c) is K33Plot of change with fracture aspect ratio; FIG. 5(d) is K12Plot of change with fracture aspect ratio; FIG. 5(e) is K13Plot of change with fracture aspect ratio; FIG. 5(f) is K23Graph of aspect ratio as a function of fracture.
Detailed Description
The present invention is described in detail by way of specific embodiments in order to better understand the technical direction of the present invention for those skilled in the art. It should be understood, however, that the detailed description is provided for a better understanding of the invention only and that they should not be taken as limiting the invention. In describing the present invention, it is to be understood that the terminology used is for the purpose of description only and is not intended to be indicative or implied of relative importance.
Example one
The embodiment discloses an electrical property detection method for a transverse isotropic rock with a rotation inclined crack, which comprises the following steps of:
s1 measuring the conductivity parameter, wherein the conductivity parameter comprises horizontal isotropy background rock horizontal conductivity k without cracksxPerpendicular conductivity kzConductivity k of formation water in the fracture*Obtaining the conductivity tensor K of the background rock0And fracture conductivity tensor K*Wherein the background rock conductivity tensor K0The formula of (1) is:
Figure BDA0002524288350000061
fracture conductivity tensor K*The formula of (1) is:
Figure BDA0002524288350000062
s2, carrying out CT scanning on transverse isotropic rock containing cracks to obtain volume content phi of the cracks, aspect ratio α of the cracks, included angle theta between the cracks and a background isotropic surface and rotation angle of the cracks
Figure BDA0002524288350000063
The included angle θ between the crack and the background isotropic surface is the rotation inclination angle of the rotation inclined crack, as shown in fig. 2, the parallel line represents the background isotropic surface, and the background isotropic surface is a transverse tangent plane of the rock. The plane where the ellipse is located is the plane where the crack is located, and the included angle between the plane where the crack is located and the background isotropic face is the included angle theta between the crack and the background isotropic face. The angle of the projection of the ellipse on the background isotropic surface to the y-axis is the rotation angle of the crack
Figure BDA0002524288350000064
The direction of the arrow in the figure is the normal direction of the plane in which the slit is located. The slit in this embodiment is a rotating inclined coin-like slit.
S3 the crack shape is characterized by crack aspect ratio α and the included angle theta between the crack and the background isotropic surface, and the obtained value is
Figure BDA0002524288350000065
The fracture shape tensor H at zero. The formula of the fracture shape tensor H is:
Figure BDA0002524288350000071
based on fracture shape tensor H and background rock conductivity tensor K0The transformed fracture shape tensor T is obtained by the following method:
Figure BDA0002524288350000072
t has the following form:
Figure BDA0002524288350000073
wherein,
Figure BDA0002524288350000074
Figure BDA0002524288350000075
Figure BDA0002524288350000076
Figure BDA0002524288350000077
after obtaining the transformed fracture shape tensor T, it is necessary to obtain an eigenvalue T of the transformed fracture shape tensor T from the transformed fracture shape tensor T1、t2、t3And corresponding unit feature vector q1、q2And q is3：
t1＝T11，
Figure BDA0002524288350000078
Figure BDA0002524288350000079
Wherein (x) is a Heaviside function, which can be expressed as
Figure BDA00025242883500000710
Figure BDA00025242883500000711
Figure BDA00025242883500000712
Figure BDA00025242883500000713
By obtaining the eigenvalues T of the transformed fracture shape tensor T1、t2And t3And corresponding unit feature vector q1、q2And q is3Conjointing reality
Figure BDA00025242883500000714
The values further yield the conductivity contribution tensor a of the fracture:
Figure BDA0002524288350000081
wherein I is a second order unit tensor; p is the hill tensor. The calculation formula of the hill tensor is as follows:
Figure BDA0002524288350000082
wherein λ is1、λ2And λ3Are the diagonal elements of the Eshelby conduction tensor.
When t is1>t2>t3When the temperature of the water is higher than the set temperature,
Figure BDA0002524288350000083
Figure BDA0002524288350000084
λ2＝1-λ1-λ3，
wherein F and E are respectively:
Figure BDA0002524288350000085
Figure BDA0002524288350000086
when t is1>t2＝t3When the temperature of the water is higher than the set temperature,
Figure BDA0002524288350000087
λ1＝1-2λ2；
when t is1＝t2>t3When the temperature of the water is higher than the set temperature,
Figure BDA0002524288350000088
λ3＝1-2λ1；
when t is1＝t2＝t3When the temperature of the water is higher than the set temperature,
Figure BDA0002524288350000089
the formula for the calculation of the elements in the conductivity contribution tensor A is:
Figure BDA00025242883500000810
Figure BDA00025242883500000811
Figure BDA00025242883500000812
Figure BDA00025242883500000813
Figure BDA0002524288350000091
Figure BDA0002524288350000092
wherein M is11、M22、M33、M23And M32Are elements in the inverse tensor M of the conductivity contribution tensor a.
To obtain the final rock conductivity tensor, the inverse tensor M of the conductivity contribution tensor A of the fracture needs to be calculated. The non-zero elements of the inverse tensor M are as follows:
Figure BDA0002524288350000093
Figure BDA0002524288350000094
Figure BDA0002524288350000095
Figure BDA0002524288350000096
Figure BDA0002524288350000097
Figure BDA0002524288350000098
s4 according to the conductivity tensor K of the background rock0Fracture conductivity tensor K*The volume content phi of the crack and the conductivity contribution tensor A of the crack are obtained on the basis of an electrical linear sliding theory, the conductivity tensor of the transverse isotropic rock of the rotation inclined crack is obtained, and the conductivity of the rock is obtained according to the conductivity tensor. The formula of the electrical linear sliding theory is as follows:
K＝K0+φ(K*-K0)A
tensor K is used for conductivity of background rock0Fracture conductivity tensor K*Substituting the volume content phi of the crack and the conductivity contribution tensor A of the crack into the formula to obtain the conductivity tensor K of the transverse isotropic rock of the rotation inclined crack, wherein the calculation formula of the conductivity tensor K of the transverse isotropic rock of the rotation inclined crack is as follows:
Figure BDA0002524288350000099
K11＝kx+φ(k*-kx)A11，
K22＝kx+φ(k*-kx)A22，
K33＝kz+φ(k*-kz)A33，
K12＝K21＝φ(k*-kx)A12，
K13＝K31＝φ(k*-kz)A13，
K23＝K32＝φ(k*-kx)A23，
wherein k isxHorizontal conductivity of transverse isotropic background rock without cracks; k is a radical ofzIs transversely isotropic background rock vertical conductivity, k, without cracks*Is the conductivity of the formation water in the fracture, phi is the volume content of the fracture, A11、A22、A33、A12、A13And A23Are all elements of the conductivity contribution tensor a.
Example two
Based on the same inventive concept, the embodiment discloses an electrical property detection system for transverse isotropic rock with rotation inclined cracks, which comprises:
the conductivity tensor acquisition module is used for measuring the conductivity parameters to acquire the conductivity tensor K of the background rock0And fracture conductivity tensor K*；
The crack parameter acquisition module is used for carrying out CT scanning on transverse isotropic rock containing cracks to obtain the volume content phi of the cracks, the aspect ratio α of the cracks, the included angle theta between the cracks and the background isotropic face and the rotation angle
Figure BDA0002524288350000101
And the conductivity contribution tensor acquisition module is used for representing the shape of the crack through the crack aspect ratio α and the included angle theta between the crack and the background isotropic surface and acquiring the shape of the crack
Figure BDA0002524288350000102
A fracture shape tensor H at zero time, and a joint of the fracture shape tensor H at that time
Figure BDA0002524288350000103
A value is calculated for the conductivity contribution tensor a of the fracture, the formula for the conductivity contribution tensor a being:
Figure BDA0002524288350000104
wherein I is a second order unit tensor; p is the Hill tensor;
a conductivity tensor acquisition module for acquiring the conductivity tensor K of the background rock0Fracture conductivity tensor K*The volume content phi of the crack and the conductivity contribution tensor A of the crack are obtained, the conductivity tensor of the transverse isotropic rock of the rotation inclined crack is obtained on the basis of the electrical sliding theory, and the conductivity of the rock is obtained according to the conductivity tensor.
EXAMPLE III
In order to better illustrate the technical solution of the present invention, this embodiment takes the actual formation rock conductivity as an example for illustration. In this embodiment, the horizontal conductivity k of the background rock is obtained according to the detection result of detecting the rock in the stratum of the certain placex0.0524S/m, vertical conductivity kzThe fracture volume content was 0.0025 when the fracture volume content was 0.0117S/m.
FIG. 3 is a graph of the variation of elements in the conductivity tensor of a transversely isotropic rock with rotated dip fractures with fracture dip angle at four fracture rotation angles of 0, π/8, π/4, 3 π/8, π/2; wherein the crack aspect ratio is set to 0.001, and K is shown in FIG. 3(a)11A plot of variation with crack inclination angle; FIG. 3(b) is K22A plot of variation with crack inclination angle; FIG. 3(c) is K33A plot of variation with crack inclination angle; FIG. 3(d) is K12A plot of variation with crack inclination angle; FIG. 3(e) is K13A plot of variation with crack inclination angle; FIG. 3(f) is K23Graph of variation with crack inclination angle.
FIG. 4 is a graph of the variation of elements in the conductivity tensor of a transversely isotropic rock with rotated dip fractures as a function of fracture rotation angle at four fracture rotation angles of 0, π/8, π/4, 3 π/8, π/2; wherein the crack aspect ratio is set to 0.001, and K is shown in FIG. 4(a)11A graph of variation with fracture rotation angle; FIG. 4(b) is K22A graph of variation with fracture rotation angle; FIG. 4(c) is K33A graph of variation with fracture rotation angle; FIG. 4(d) is K12A graph of variation with fracture rotation angle; FIG. 4(e) is K13A graph of variation with fracture rotation angle; FIG. 4(f) is K23Graph of variation with crack rotation angle.
FIG. 5 is a graph of the change of elements in the conductivity tensor of a transversely isotropic rock with rotated dip fractures as a function of fracture aspect ratio at four fracture rotation angles of 0, π/8, π/4, 3 π/8, π/2; wherein the crack aspect ratio is set to 0.001, and K is shown in FIG. 5(a)11Plot of change with fracture aspect ratio; FIG. 5(b) is K22Plot of change with fracture aspect ratio; FIG. 5(c) is K33Plot of change with fracture aspect ratio; FIG. 5(d) is K12Plot of change with fracture aspect ratio;FIG. 5(e) is K13Plot of change with fracture aspect ratio; FIG. 5(f) is K23Graph of aspect ratio as a function of fracture.
Comparing the detection results in the figures 3, 4 and 5 with the resistivity detected by the actual stratum, the fact that the non-zero elements of the conductivity tensor are consistent with the actual measurement result can be found, the detection result in the invention accords with the expected result, and the fact that the electrical rock physical model provided at this time can accurately calculate the conductivity of the rock containing the rotation inclined fracture is shown.
Aiming at the defects of the existing physical model of the electrical rock containing the crack medium, the invention deduces the conductivity calculation model of the transverse isotropic rock containing the rotation inclined coin-shaped crack based on the transverse isotropic background medium and the coin-shaped crack which is obliquely crossed with the isotropic surface and has smaller vertical and horizontal ratios based on the real characteristics of the rock containing the crack, can more effectively predict the electrical property of the rock containing the rotation inclined crack, and can provide support for electrical exploration, well logging identification and crack reservoir evaluation.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims (10)

1. The electrical property detection method for the transverse isotropic rock with the rotation inclined cracks is characterized by comprising the following steps of:
s1 measuring the conductivity parameter to obtain the conductivity tensor K of the background rock0And fracture conductivity tensor K*；
S2, carrying out CT scanning on transverse isotropic rock containing cracks to obtain volume content phi of the cracks, aspect ratio α of the cracks, included angle theta between the cracks and a background isotropic surface and rotation angle
Figure FDA0002524288340000011
S3 the crack shape is characterized by the crack aspect ratio α and the included angle theta between the crack and the background isotropic surface, and the obtained value is
Figure FDA0002524288340000012
A fracture shape tensor H at zero time, and a joint of the fracture shape tensor H at that time
Figure FDA0002524288340000013
Value calculation the conductivity contribution tensor a of the fracture:
Figure FDA0002524288340000014
wherein I is a second order unit tensor; p is the Hill tensor;
s4 according to the conductivity tensor K of the background rock0Fracture conductivity tensor K*The volume content phi of the fracture and the conductivity contribution tensor A of the fracture are obtained on the basis of an electrical sliding theory, the conductivity tensor of the transverse isotropic rock of the rotation inclined fracture is obtained, and the conductivity of the rock is obtained according to the conductivity tensor.
2. The electrical property detection method for the transverse isotropic rock with the rotation dip cracks as claimed in claim 1, wherein the transverse isotropic rock conductivity tensor K of the rotation dip cracks is as follows:
Figure FDA0002524288340000015
K11＝kx+φ(k*-kx)A11，
K22＝kx+φ(k*-kx)A22，
K33＝kz+φ(k*-kz)A33，
K12＝K21＝φ(k*-kx)A12，
K13＝K31＝φ(k*-kz)A13，
K23＝K32＝φ(k*-kx)A23，
wherein k isxHorizontal conductivity of transverse isotropic background rock without cracks; k is a radical ofzIs transversely isotropic background rock vertical conductivity, k, without cracks*Is the conductivity of the formation water in the fracture, phi is the volume content of the fracture, A11、A22、A33、A12、A13And A23Are all elements of the conductivity contribution tensor a.
3. The method for detecting the electrical property of the transverse isotropic rock with the rotation dip cracks as claimed in claim 2, wherein the calculation formula of the elements in the conductivity contribution tensor A is as follows:
Figure FDA0002524288340000021
Figure FDA0002524288340000022
Figure FDA0002524288340000023
Figure FDA0002524288340000024
Figure FDA0002524288340000025
Figure FDA0002524288340000026
wherein M is11、M22、M33、M23And M32Are elements of an inverse tensor M of the conductivity contribution tensor a.
4. The method for detecting the electrical property of the transverse isotropic rock with the rotation dip cracks as claimed in claim 3, wherein the electrical conductivity contribution tensor A is calculated by the formula of an inverse tensor M:
Figure FDA0002524288340000027
Figure FDA0002524288340000028
Figure FDA0002524288340000029
Figure FDA00025242883400000210
Figure FDA00025242883400000211
wherein, T22、T23、T32And T33Are all elements of the transformed fracture shape tensor T, T2And t3Is the eigenvalue of the transformed fracture shape tensor T, λ1、λ2And λ3Are the diagonal elements of the Eshelby conduction tensor.
5. The method for detecting the electrical property of the transverse isotropic rock with the rotation dip cracks as claimed in claim 4, wherein the converted crack shape tensor T is obtained by a crack shape tensor H through the following formula:
Figure FDA00025242883400000212
wherein, T at the upper right corner of the formula represents transposition operation;
the calculation formula of the converted fracture shape tensor T is as follows:
Figure FDA0002524288340000031
Figure FDA0002524288340000032
Figure FDA0002524288340000033
Figure FDA0002524288340000034
Figure FDA0002524288340000035
6. the method for detecting the electrical property of the transversely isotropic rock with the rotated inclined fracture as claimed in claim 5, wherein the eigenvalue T of the transformed fracture shape tensor T1、t2And t3The calculation formula of (2) is as follows:
t1＝T11，
Figure FDA0002524288340000036
Figure FDA0002524288340000037
wherein (x) is a Heaviside function expressed as
Figure FDA0002524288340000038
7. The method for detecting the electrical property of the transverse isotropic rock with the rotation dip cracks as claimed in any one of claims 1 to 6, wherein the unit eigenvector q corresponding to the transformation crack shape tensor T is1、q2And q is3：
Figure FDA0002524288340000039
Figure FDA00025242883400000310
Figure FDA00025242883400000311
8. The method for detecting the electrical property of the transverse isotropic rock with the rotation dip cracks as claimed in claim 7, wherein the calculation formula of the Hill tensor is as follows:
Figure FDA00025242883400000312
wherein λ is1、λ2And λ3Are the diagonal elements of the Eshelby conduction tensor.
9. The method for detecting the electrical property of the transversely isotropic rock with the rotation inclined cracks as claimed in claim 8, wherein the lambda is1、λ2And λ3The expression of (a) is:
when t is1>t2>t3When the temperature of the water is higher than the set temperature,
Figure FDA00025242883400000313
Figure FDA0002524288340000041
λ2＝1-λ1-λ3，
wherein F and E are respectively:
Figure FDA0002524288340000042
Figure FDA0002524288340000043
when t is1>t2＝t3When the temperature of the water is higher than the set temperature,
Figure FDA0002524288340000044
λ1＝1-2λ2；
when t is1＝t2>t3When the temperature of the water is higher than the set temperature,
Figure FDA0002524288340000045
λ3＝1-2λ1；
when t is1＝t2＝t3When the temperature of the water is higher than the set temperature,
Figure FDA0002524288340000046
10. an electrical property detection system for a transverse isotropic rock containing a rotation dip crack, comprising:
the conductivity tensor acquisition module is used for measuring the conductivity parameters to acquire the conductivity tensor K of the background rock0And fracture conductivity tensor K*；
The crack parameter acquisition module is used for carrying out CT scanning on transverse isotropic rock containing cracks to obtain the volume content phi of the cracks, the aspect ratio α of the cracks, the included angle theta between the cracks and the background isotropic face and the rotation angle
Figure FDA0002524288340000047
The conductivity contribution tensor acquisition module is used for representing the shape of the crack through the crack aspect ratio α and the included angle theta between the crack and the background isotropic face and acquiring the shape of the crack
Figure FDA0002524288340000048
A fracture shape tensor H at zero and associated with the actual fracture shape tensor H
Figure FDA0002524288340000049
Value calculation the conductivity contribution tensor a of the fracture:
Figure FDA00025242883400000410
wherein I is a second order unit tensor; p is the Hill tensor;
a conductivity tensor acquisition module for acquiring the conductivity tensor K of the background rock0Fracture conductivity tensor K*The volume content phi of the fracture and the conductivity contribution tensor A of the fracture are obtained on the basis of an electrical linear sliding theory, the conductivity tensor of the transverse isotropic rock of the rotation inclined fracture is obtained, and the conductivity of the rock is obtained according to the conductivity tensor.
CN202010499783.8A 2020-06-04 2020-06-04 Electrical property detection method and system for transverse isotropic rock containing rotation inclined crack Withdrawn CN111474604A (en)

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