CN112434413A - Method for determining hydraulic fracture support fracture conductivity - Google Patents

Method for determining hydraulic fracture support fracture conductivity Download PDF

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CN112434413A
CN112434413A CN202011294500.2A CN202011294500A CN112434413A CN 112434413 A CN112434413 A CN 112434413A CN 202011294500 A CN202011294500 A CN 202011294500A CN 112434413 A CN112434413 A CN 112434413A
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吴忠维
崔传智
韩兴源
张团
李怀亮
杨永超
苏鑫坤
王国彪
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China University of Petroleum East China
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Abstract

The invention belongs to the technical field of hydraulic fracturing development oil reservoir fracturing optimization, and discloses a method for determining the flow conductivity of a hydraulic fracturing support fracture, which comprises the steps of calculating the width of the fracture at any fracture position along the fracture; dispersing wedge-shaped cracks; determining the number of the laying layers of the propping agents in the fracture elements on the width section of the fracture; determining the pore volume of the fracture element; determining the porosity of the fracture element, the type of the pore radius of the fracture element and the equivalent radius of each pore type; the equivalent radius of the pore of the fracture element, the permeability of the fracture element and the conductivity of the fracture element are determined. For proppant-filled discrete fracture elements, the pores may be classified as non-fracture-contacting pores, fracture-contacting pores. The method can accurately determine the flow conductivity of the wedge-shaped supporting fracture with certain technical difficulty, and simultaneously, the accurate determination of the flow conductivity of the wedge-shaped supporting fracture is the key for evaluating the hydraulic fracturing transformation effect and evaluating the productivity of the hydraulic fracturing well.

Description

Method for determining hydraulic fracture support fracture conductivity
Technical Field
The invention belongs to the technical field of hydraulic fracturing exploitation oil reservoir fracturing optimization, and particularly relates to a method for determining hydraulic fracturing propping fracture conductivity.
Background
At present, unconventional resources such as dense oil gas, shale oil gas and the like in China are wide in distribution and large in reserves, and have a material basis for efficient development. The compact oil gas and shale oil gas reservoir has the characteristics of low porosity and low permeability, generally has no natural energy, and needs to adopt a hydraulic fracturing reservoir modification technology to realize economic and efficient development of unconventional resources. When the hydraulic fracturing technology is used for reservoir reconstruction, a propping agent is injected into a fracture; after the reservoir transformation is finished, the fracture is closed and propped by the injected propping agent under the influence of stratum stress, and finally a propped fracture is formed. The flow conductivity of the supporting fractures directly influences the hydraulic fracturing reservoir transformation effect, the flow conductivity of the supporting fractures is high, the fluid flowing capacity in the fractures is high, and the hydraulic fracturing reservoir transformation effect is good; otherwise, the improvement effect is not good. The hydraulic fracturing is transformed into wedge-shaped supporting cracks, namely the supporting cracks are narrow in toe end and wide in heel end, and the gaps of the cracks are filled with the propping agents. The method has certain technical difficulty in accurately determining the flow conductivity of the wedge-shaped supporting fracture, and the accurate determination of the flow conductivity of the wedge-shaped supporting fracture is the key for evaluating the hydraulic fracturing transformation effect and evaluating the productivity of a hydraulic fracturing well.
Through the above analysis, the problems and defects of the prior art are as follows: the prior art cannot accurately determine the flow conductivity of the wedge-shaped support fracture.
The difficulty in solving the above problems and defects is: not only is the width of any fracture location, the placement characteristics of the proppant in the fracture obtained, but also the pore radius size of the various pore types is determined.
The significance of solving the problems and the defects is as follows: the flow conductivity of the supporting fractures is accurately predicted, and powerful support is provided for unconventional reservoir fracturing optimization design, economic evaluation and the like.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for determining the hydraulic fracture propping fracture conductivity.
The invention is realized by a method for determining the hydraulic fracture propping fracture conductivity, which comprises the following steps:
step one, calculating the width of a crack at any crack position along the crack;
dispersing the wedge-shaped cracks, namely dispersing the cracks into N sections, wherein when the number of the discrete sections is large enough, the wedge-shaped cracks can be equivalent to N discrete crack elements with different widths, the width of the cracks in each discrete crack element is unchanged, and the width of each discrete crack element can be obtained by using the method in the S101;
determining the number of the proppant paving layers in the fracture element, the pore volume of the fracture element and the porosity of the fracture element on the fracture width section;
step four, the pore radius types of the fracture elements and the equivalent radii of all the pore types, and for discrete fracture elements at the heel end of the fracture filled with the proppant, the pores can be divided into pores not in contact with the fracture and pores in contact with the fracture; the pores not in contact with the fracture are pores surrounded by proppant; the pore in contact with the crack is a pore surrounded by the wall surface of the crack and the propping agent;
and fifthly, determining the equivalent radius of the pores of the fracture elements, the permeability of the fracture elements and the flow conductivity of the fracture elements.
Further, in the step one, the specific process of calculating the crack width is as follows:
assuming that the width of the crack is linearly reduced along the crack away from the crack heel end, on the basis of the known length of the crack as L meters and the width of the crack heel end as wf meters, obtaining the relationship between the width of the crack and the length from the crack heel end:
Figure BDA0002784804250000021
wherein L isxLength along the fracture from the heel end of the fracture, meters; w is axIs LxWidth of crack, meter.
Further, in the second step, the conductivity solving of the wedge-shaped propped fracture can be equivalent to the conductivity solving of the N discrete fracture elements, the conductivity solving method of each discrete fracture element is the same, and then the conductivity determining method of the propped fracture is described by taking the discrete fracture element at the fracture heel end as an example.
Further, in the third step, the determination process of the number of the proppant paving layers in the fracture element is as follows:
the width and the length of the discrete crack element at the crack heel end are w respectivelyiRice and
Figure BDA0002784804250000022
filling the cracks with the proppant in a staggered manner;
according to the relation between the number of layers on the fracture width section and the fracture width and the proppant radius, wherein the fracture width is equal to the proppant filling width
Figure BDA0002784804250000031
Wherein n is the number of layers of the proppant on the fracture width cross section; r is proppant radius, meters.
Further, in the third step, the determination process of the pore volume of the fracture element is as follows:
for discrete fracture elements at the heel end of the fracture, the pore volume of the fracture element can be obtained according to the fact that the pore volume of the fracture element is equal to the difference between the external surface volume of the fracture element and the total proppant volume in the fracture element：
Figure BDA0002784804250000032
Wherein phi isiPorosity at the heel end of the crack; h is reservoir thickness, meter; lfΔCalculating the length along the crack direction to obtain 1 meter;
Figure BDA0002784804250000033
the number of proppant layers in the thickness direction of the reservoir is indicated by the subscript int which is rounded down since the number of proppant layers are all integers.
Further, in the third step, the determination process of the porosity of the fracture element is as follows:
for discrete fracture elements at the heel end of the fracture, the ratio of the pore volume to the external volume is obtained according to the definition of porosity,
Figure BDA0002784804250000034
wherein phi isiPorosity at the heel end of the fracture.
Further, in the fourth step, the specific process of the pore radius types of the fracture elements and the equivalent radii of each pore type is as follows:
for the pore which is not contacted with the crack, a rhombohedral column with the height of 2R and the side length of 2R is used for cutting off the pore, and the volume of the cut-off pore is equivalent to the radius Rff1A cylinder with a height of 2R;
the pore volume obtained by interception is equal to radius rff1The length of the cylinder is 2R, and an equivalent cylinder radius calculation formula can be obtained
Figure BDA0002784804250000035
For the pore contacting with the crack, a cubic column with the height of 2R, the long side of 2R and the short side of R is used for cutting off the pore, and the volume of the cut-off pore is equivalent to the radius of rff2A cylinder with a height of 2R;
the pore volume obtained by interception is equal to radius rff2Cylinder with height of 2RObtaining the equivalent cylinder radius calculation formula
Figure BDA0002784804250000041
Further, in the fifth step, the specific process of the equivalent radius of the pores of the fracture element is as follows:
depending on the geometry of the proppant distribution, it can be seen that the number of proppant layers N has a twofold relationship with the total number of pores N1, N1 ═ 2N, and two types of pores;
respectively as follows: the sum of the number of pores in contact with the fracture (2) and the number of pores not in contact with the fracture (2N-2) is equal to the total number of pores (2N);
the average pore radius can be obtained by averaging according to the number of pores:
Figure BDA0002784804250000042
further, in the fifth step, the specific process for determining the permeability of the fracture element is as follows:
according to the Kozeny-Carman formula
Figure BDA0002784804250000043
Wherein φ is porosity; r is the pore radius; tau is the porosity tortuosity and takes a value of 1.2, and the permeability of discrete fracture elements at the heel end of the fracture filled with the proppant can be obtained
Figure BDA0002784804250000044
Wherein k isiμ m for crack heel permeability2；ψ1Is a unit conversion coefficient and takes a value of 1012。
Further, in the fifth step, the flow conductivity of the fracture element is determined by the following process:
according to the fracture conductivity definition, the conductivity is equal to the product of the fracture permeability and the fracture width, and the fracture conductivity FCD can be obtainedi＝ψ2kiwi；
Wherein FCDiThe flow guide energy of heel end crack elementForce, μm2·cm；ψ2Is a unit conversion coefficient and takes a value of 10-2；
And (4) obtaining the flow conductivity of all discrete fracture elements according to the steps so as to obtain the flow conductivity of the hydraulic fracture support fracture.
By combining all the technical schemes, the invention has the advantages and positive effects that: the method can accurately determine the flow conductivity of the wedge-shaped supporting fracture with certain technical difficulty, and simultaneously, the accurate determination of the flow conductivity of the wedge-shaped supporting fracture is the key for evaluating the hydraulic fracturing transformation effect and evaluating the productivity of the hydraulic fracturing well.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments of the present application will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained from the drawings without creative efforts.
Fig. 1 is a flow chart of a method for determining hydraulic fracture propping fracture conductivity according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of a pore that does not contact a fracture, as provided by an embodiment of the present invention.
FIG. 3 is a schematic diagram of pores in contact with a fracture provided by an embodiment of the present invention.
Figure 4 is a schematic illustration of proppant distribution in a propped fracture provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In view of the problems in the prior art, the present invention provides a method for determining the fracture conductivity of a hydraulic fracture support, which is described in detail below with reference to the accompanying drawings.
The embodiment of the invention provides a method for determining hydraulic fracture support fracture conductivity, which comprises the following steps:
s101: along the fracture, the fracture width at any fracture location is calculated.
S102: and (3) dispersing the wedge-shaped cracks, namely dispersing the cracks into N sections, wherein when the number of the discrete sections is large enough, the wedge-shaped cracks can be equivalent to N discrete crack elements with different widths, the width of the cracks in each discrete crack element is unchanged, and the width of each discrete crack element can be obtained by using the method in the S101.
S103: and determining the number of the layers of the proppants laid in the fracture element, the pore volume of the fracture element and the porosity of the fracture element on the fracture width section.
S104: the pore radius types of the fracture elements and the equivalent radius of each pore type, and for discrete fracture elements filled with the proppant, the pores can be divided into pores not in contact with the fracture and pores in contact with the fracture; the pores not in contact with the fracture are pores surrounded by proppant; the pore space contacting with the crack is a pore space surrounded by the wall surface of the crack and the propping agent.
S105: and determining the equivalent radius of the pores of the fracture elements, the permeability of the fracture elements and the flow conductivity of the fracture elements.
In S101 provided by the embodiment of the present invention, a specific process of calculating the crack width is as follows:
assuming that the crack width decreases linearly along the crack away from the crack heel, where the crack length is known to be L meters and the crack heel width is known to be wfOn the basis of meters, the relation between the width of the crack and the length from the heel end of the crack is obtained:
Figure BDA0002784804250000061
wherein L isxLength along the fracture from the heel end of the fracture, meters; w is axIs LxWidth of crack, meter.
In S102 provided in the embodiment of the present invention, the conductivity solution of the wedge-shaped propping fractures may be equivalent to the conductivity solution of N discrete fracture elements, the conductivity solution method of each discrete fracture element is the same, and then the conductivity determination method of the propping fractures is described by taking the discrete fracture elements at the fracture heel end as an example.
In S103 provided by the embodiment of the present invention, the process for determining the number of the proppant placement layers in the fracture element is as follows:
the width and the length of the discrete crack element at the crack heel end are w respectivelyiRice and
Figure BDA0002784804250000062
filling the cracks with the proppant in a staggered manner;
according to the relation between the number of layers on the fracture width section and the fracture width and the proppant radius, wherein the fracture width is equal to the proppant filling width
Figure BDA0002784804250000063
Wherein n is the number of layers of the proppant on the fracture width cross section; r is proppant radius, meters.
In S103 provided by the embodiment of the present invention, the determination process of the pore volume of the fracture element is as follows:
for discrete fracture elements at the heel end of the fracture, the pore volume of the fracture element can be obtained according to the fact that the pore volume of the fracture element is equal to the difference between the external surface volume of the fracture element and the total proppant volume in the fracture element:
Figure BDA0002784804250000064
wherein phi isiPorosity at the heel end of the crack; h is reservoir thickness, meter; lfΔLength in the direction along the fracture (1 in the calculation), m;
Figure BDA0002784804250000071
the number of proppant layers in the thickness direction of the reservoir is indicated by the subscript int which is rounded down since the number of proppant layers are all integers.
In S103 provided by the embodiment of the present invention, the determination process of the porosity of the fracture element is as follows:
for discrete fracture elements at the heel end of the fracture, the method is based on the porosityBy definition, the ratio of pore volume to external volume is obtained,
Figure BDA0002784804250000072
wherein phi isiPorosity at the heel end of the fracture.
In S104 provided by the embodiment of the present invention, the specific process of the pore radius type of the fracture element and the equivalent radius of each pore type is as follows:
for the pore which is not contacted with the crack, a rhombohedral column with the height of 2R and the side length of 2R is used for cutting off the pore, and the volume of the cut-off pore is equivalent to the radius Rff1A cylinder with a height of 2R;
the pore volume obtained by interception is equal to radius rff1The length of the cylinder is 2R, and an equivalent cylinder radius calculation formula can be obtained
Figure BDA0002784804250000073
For the pore contacted with the crack, a cubic column with the height of 2R, the long side of 2R and the short side of R is used for cutting off the pore, and the volume of the cut-off pore is equivalent to the radius of Rff2A cylinder with a height of 2R;
the pore volume obtained by interception is equal to radius rff2The height of the cylinder is 2R, and an equivalent cylinder radius calculation formula can be obtained
Figure BDA0002784804250000074
In S105 provided by the embodiment of the present invention, the specific process of the equivalent radius of the fracture element pore is as follows:
depending on the geometry of the proppant distribution (fig. 3), the number of available proppant layers N has a twofold relationship with the total number of pores N1 (N1 ═ 2N), and two types of pores;
respectively as follows: the sum of the pores (2) in contact with the fracture and the pores (2N-2) not in contact with the fracture is equal to the total number of pores (2N);
the average pore radius can be obtained by averaging according to the number of pores:
Figure BDA0002784804250000081
in S105 provided by the embodiment of the present invention, the specific process for determining the permeability of the fracture element is as follows:
according to the Kozeny-Carman formula
Figure BDA0002784804250000082
Wherein φ is porosity; r is the pore radius; tau is the porosity tortuosity and takes a value of 1.2, and the permeability of discrete fracture elements at the heel end of the fracture filled with the proppant can be obtained
Figure BDA0002784804250000083
Wherein k isiμ m for crack heel permeability2；ψ1Is a unit conversion coefficient and takes a value of 1012。
In S105 provided by the embodiment of the present invention, the process of determining the conductivity of the fracture element is as follows:
according to the fracture conductivity definition, the conductivity is equal to the product of the fracture permeability and the fracture width, and the fracture conductivity FCD can be obtainedi＝ψ2kiwi；
Wherein FCDiThe flow conductivity of heel end crack element is mum2·cm；ψ2Is a unit conversion coefficient and takes a value of 10-2；
And (4) obtaining the flow conductivity of all discrete fracture elements according to the steps so as to obtain the flow conductivity of the hydraulic fracture support fracture.
The technical solution of the present invention is further described with reference to the following specific examples.
TABLE 1 calculation of propped fracture conductivity
Figure BDA0002784804250000084
Figure BDA0002784804250000091
Figure BDA0002784804250000101
In order to verify the accuracy of the calculation model of the flow conductivity of the supported fracture, the method is used for calculating the flow conductivity of the filled fracture under the conditions of any width and any size of the propping agent (the width of the fracture and the size of the propping agent are shown in the following table 2), the calculation result is compared with the reported result of the calculation model and the application of the flow conductivity of the fractured fracture of the coal reservoir published in the journal of the coal science in 2014, and the comparison result is shown in the following table 2. As can be seen from table 2, the model of the present invention is very similar to the reported result in the article "model and application for calculating fracture conductivity of coal reservoir fracturing", published in journal of coal science in 2014, and the relative error is 5.05% at most. This comparison illustrates the accuracy of the method.
TABLE 2 comparison of the parameters used for model validation with the calculated results
Figure BDA0002784804250000102
Figure BDA0002784804250000111
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A method of determining hydraulic fracture propped fracture conductivity, the method comprising:
calculating the width of the crack at any crack position along the crack;
dispersing the wedge-shaped cracks, namely dispersing the cracks into N sections, when the number of the discrete sections is large enough, equivalent the wedge-shaped cracks into N discrete crack elements with different widths, wherein the width of the cracks in each discrete crack element is unchanged, and the width of each discrete crack element can be obtained by a method of calculating the width of the cracks at any crack position along the cracks;
determining the number of the layers of the proppants laid in the fracture element, the pore volume of the fracture element and the porosity of the fracture element on the fracture width section;
the pore radius types of the fracture elements and the equivalent radius of each pore type are that for discrete fracture elements at the heel end of the fracture filled with the proppant, the pores are divided into pores not in contact with the fracture and pores in contact with the fracture; the pores not in contact with the fracture are pores surrounded by proppant; the pore in contact with the crack is a pore surrounded by the wall surface of the crack and the propping agent;
and determining the equivalent radius of the pores of the fracture elements, the permeability of the fracture elements and the flow conductivity of the fracture elements.
2. The method for determining hydraulic fracture propping fracture conductivity of claim 1, wherein the fracture width calculation is carried out by the following specific processes: the width of the crack is linearly reduced along the crack away from the crack heel end, the length of the known crack is L meters, and the width of the crack heel end is wfOn the basis of meters, the relation between the width of the crack and the length from the heel end of the crack is obtained:
Figure FDA0002784804240000011
wherein L isxThe length along the fracture from the heel end of the fracture in meters; w is axIs LxThe width of the crack is measured in meters.
3. The method for determining the conductivity of a hydraulic fracture-propped fracture as claimed in claim 1, wherein the conductivity solution of the wedge-shaped propped fracture is equivalent to the conductivity solution of N discrete fracture elements, the conductivity solution method of each discrete fracture element is the same, and the conductivity determination method of the propped fracture is described by taking the discrete fracture element at the heel end of the fracture as an example.
4. The method for determining hydraulic fracture propped fracture conductivity of claim 1, wherein the number of proppant placement layers in the fracture element is determined by:
the width and the length of the discrete crack element at the crack heel end are w respectivelyiRice and
Figure FDA0002784804240000021
filling the cracks with the proppant in a staggered manner;
according to the relation between the number of layers on the fracture width section and the fracture width and the proppant radius, wherein the fracture width is equal to the proppant filling width
Figure FDA0002784804240000022
Wherein n is the number of layers of the proppant on the fracture width cross section; r is proppant radius, meters.
5. The method for determining hydraulic fracture-propping fracture conductivity of claim 1, wherein the pore volume of the fracture element is determined by:
for discrete fracture elements at the heel end of the fracture, the pore volume of the fracture element can be obtained according to the fact that the pore volume of the fracture element is equal to the difference between the external surface volume of the fracture element and the total proppant volume in the fracture element:
Figure FDA0002784804240000023
wherein phi isiPorosity at the heel end of the crack; h is reservoir thickness, meter; lfΔCalculating the length along the crack direction to obtain 1 meter;
Figure FDA0002784804240000024
the number of proppant layers in the thickness direction of the reservoir is indicated by the subscript int which is rounded down since the number of proppant layers are all integers.
6. The method for determining hydraulic fracture-propping fracture conductivity of claim 1, wherein the fracture element porosity determination process is as follows:
for discrete fracture elements at the heel end of the fracture, the ratio of the pore volume to the external volume is obtained according to the definition of porosity,
Figure FDA0002784804240000025
wherein phi isiPorosity at the heel end of the fracture.
7. The method for determining the hydraulic fracture-propping fracture conductivity of claim 1, wherein the specific process of the pore radius types of the fracture elements and the equivalent radii of the pore types is as follows: for the pore which is not contacted with the crack, a rhombohedral column with the height of 2R and the side length of 2R is used for cutting off the pore, and the volume of the cut-off pore is equivalent to the radius Rff1A cylinder with a height of 2R;
the pore volume obtained by interception is equal to radius rff1The length of the cylinder is 2R, and an equivalent cylinder radius calculation formula can be obtained
Figure FDA0002784804240000031
For the pore contacted with the crack, a cubic column with the height of 2R, the long side of 2R and the short side of R is used for cutting off the pore, and the volume of the cut-off pore is equivalent to the radius of Rff2A cylinder with a height of 2R;
the pore volume obtained by interception is equal to radius rff2The height of the cylinder is 2R, and an equivalent cylinder radius calculation formula can be obtained
Figure FDA0002784804240000032
8. The method for determining the hydraulic fracture-propping fracture conductivity of claim 1, wherein the equivalent radius of the fracture element pores is determined by the following specific process:
depending on the geometry of the proppant distribution, the number of proppant layers N1 available has a twofold relationship N1 to 2N with the total number of pores N1, and two types of pores;
respectively as follows: the sum of the number of pores in contact with the fracture (2) and the number of pores not in contact with the fracture (2N-2) is equal to the total number of pores (2N);
the average pore radius can be obtained by averaging according to the number of pores:
Figure FDA0002784804240000033
9. the method for determining hydraulic fracture propping fracture conductivity of claim 1, wherein the fracture element permeability is determined by the following specific process:
according to the Kozeny-Carman formula
Figure FDA0002784804240000034
Wherein φ is porosity; r is the pore radius; tau is the porosity tortuosity and takes a value of 1.2, and the permeability of discrete fracture elements at the heel end of the fracture filled with the proppant can be obtained
Figure FDA0002784804240000035
Wherein k isiμ m for crack heel permeability2；ψ1Is a unit conversion coefficient and takes a value of 1012。
10. The method for determining hydraulic fracture propping fracture conductivity of claim 1, wherein the conductivity of the fracture element is determined by:
the conductivity is equal to the permeability of the fracture andthe product of the width of the crack can obtain the crack conductivity FCDi＝ψ2kiwi；
Wherein FCDiThe flow conductivity of heel end crack element is mum2·cm；ψ2Is a unit conversion coefficient and takes a value of 10-2；
And (4) solving the flow conductivity of all discrete fracture elements to obtain the flow conductivity of the hydraulic fracture support fracture.
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