CN113221361A - Method for calculating fracture width change under shale reservoir closed pressure - Google Patents

Method for calculating fracture width change under shale reservoir closed pressure Download PDF

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CN113221361A
CN113221361A CN202110539939.5A CN202110539939A CN113221361A CN 113221361 A CN113221361 A CN 113221361A CN 202110539939 A CN202110539939 A CN 202110539939A CN 113221361 A CN113221361 A CN 113221361A
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董利飞
王苗
陈飞宇
雷刚
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Chongqing Three Gorges University
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Abstract

The invention provides a method for calculating fracture width change under shale reservoir closed pressure, which comprises the following steps: collecting the radius R of the proppant particle1Elastic modulus E1Poisson ratio v1(ii) a And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall2Poisson ratio v2Acquiring collected data; respectively calculating the extrusion force of the support agent A layer and the extrusion force of the support agent B layer under the closed pressure according to the acquired data and the Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to an extrusion force self-defined formula; and calculating to obtain the crack width variation according to the total pressure of the two A layers and the plurality of B layers. The method is based on the Hertz contact theory, a model of the propping behavior of the propping agent in the fracture under the fracture closure pressure is established, and compared with the existing model, the model considersThe injection of the proppant and the elastic compression between the proppants are considered, and the actual physical process is closer to the actual physical process; the accuracy of the obtained crack width variation is higher.

Description

Method for calculating fracture width change under shale reservoir closed pressure
Technical Field
The invention relates to a method for calculating the width change of a fracture, in particular to a method for calculating the width change of the fracture under the closing pressure of a shale reservoir.
Background
The description of the fracture width is the key for evaluating the fracture conductivity and influences the development efficiency of unconventional oil and gas resources. Typically, when proppant is filled into a fracture, the fracture will undergo a width change under closure pressure, and the proppant will resist the change in fracture width. Therefore, establishing a theoretical model for predicting the change of the crack has important significance. The hydraulic fracturing technology is common in the development of unconventional oil and gas reservoirs, a fracture network consisting of natural fractures and induced fractures is formed after the hydraulic fracturing process, a fluid seepage channel is provided, and a propping agent is injected into the fracture network along with fracturing fluid; once the well is opened and put into operation, the pore pressure can be obviously reduced, the width of the fracture can be reduced, part of the proppant can be discharged back, and part of the proppant is retained in the fracture, and the propping action is excited along with the change of the width of the fracture, so that the opening degree of the fracture is maintained; the propping action of the propping agent under the closing pressure can affect the width and the flow conductivity of the crack, and the development efficiency is related. Therefore, it is of great significance to study the compressive capacity of the proppant and describe the change of the fracture width under the closing pressure.
In fact, during the course of resistance to compression, the proppant in the fracture will be compressed or embedded, resulting in a change in fracture width; researchers in 1998 studied experimentally the relationship between the degree of proppant embedment and the closure pressure, proppant concentration, and mechanical properties of the rock; in the aspect of theoretical research, a mathematical model of the injection amount of the proppant under closed pressure is established through analysis, and the particle size of the proppant and the sensitivity of the Young modulus of the rock are discussed; deducing a proppant embedding depth model by using an elasticity theory, and carrying out sensitivity analysis on basic parameters; the numerical method is adopted to represent the influence of the particle size and the number of layers of the propping agent on the flow conductivity of the fracture.
These studies have discussed the impact of proppant embedding processes and fracture conductivity, but are mostly based on rigid ball assumptions, ignoring contact deformation between proppants. And therefore cannot accurately describe the change in fracture width under closure pressure. In particular, a theoretical model that takes into account proppant elastomechanics needs to be established.
Disclosure of Invention
The invention aims to provide a method for calculating fracture width variation under shale reservoir closing pressure, which can be used for calculating fracture width variation under shale reservoir closing pressure.
The invention is realized by the technical scheme, which comprises the following steps:
a fracture width change calculation method under shale reservoir closing pressure is characterized in that a propping agent is injected into a shale reservoir fracture, the propping agent comprises two single contact layers of upper and lower propping agent and fracture wall contact layers and a plurality of double contact layers of middle propping agent and propping agent, the single contact layer is defined as an A layer, the double contact layers are defined as B layers, and the fracture width change calculation method specifically comprises the following steps:
1) collecting the radius R of the proppant particle1Elastic modulus E1Poisson ratio v1(ii) a And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall2Poisson ratio v2Acquiring collected data;
2) respectively calculating the extrusion force of the proppant A layer and the extrusion force of the proppant B layer under the closed pressure according to the acquired data in the step 1) and a Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to an extrusion force self-defined formula;
3) calculating to obtain the variation of the crack width according to the total pressure of the two A layers and the plurality of B layers obtained in the step 2).
Further, the specific method for calculating the total compression of the proppant and the layer A of the crack wall contact layer in the step 2) is as follows:
the layer of the proppant directly contacting the fracture wall is an A layer, and according to the Hertz contact theory, the normal force N of the single A layer proppant is as follows:
Figure BDA0003071295360000021
in the formula (1), R1Radius of proppant, R2Radius of the fracture wall, E1As a proppantModulus of elasticity of (E)2Is the modulus of elasticity, v, of the fracture wall1Poisson ratio, v, as a proppant2Poisson ratio, alpha, of the crack wall1Is the compression value of the a layer;
radius R since the fracture wall tends to be flat2→ infinity, the formula (1) can be simplified as:
Figure BDA0003071295360000022
the proppants are closely arranged in multiple layers, each proppant is extruded by 8 surrounding particles, the contact area formed by extrusion of each particle is approximately a regular quadrangle, wherein any side length is 2r of the particle diameter, and the area of a single triangle is as follows:
Figure BDA0003071295360000023
total contact area:
Figure BDA0003071295360000024
the proppants are elastic spheres, and the pressure F experienced by each proppant, for a layer a of proppants, is equal to its normal force N:
Figure BDA0003071295360000025
in formula (5), F is the pressure of the proppant, P is the closure pressure, PcFor fracture closure pressure, R1Is the proppant diameter. Fracture closure pressure P from force analysiscComprises the following steps:
Pc＝Po-Pp (6)
in the formula (6), PoIs overburden pressure, PpIs the pore pressure;
the compression value alpha of the a-layer proppant1Comprises the following steps:
Figure BDA0003071295360000031
the upper and lower layers of proppant are in contact with the top and bottom layers of the fracture wall, respectively, so that the total amount of compression h caused by the A-layer proppant1Comprises the following steps:
Figure BDA0003071295360000032
further, the specific method for calculating the total compression of the proppant and the proppant contact layer B in step 2) is as follows:
the contact layer of the proppant and the proppant is a B layer, and according to the Hertz contact theory, the normal force N' of a single B layer of proppant is as follows:
Figure BDA0003071295360000033
in the formula (9), R1Radius of proppant, E1Is the elastic modulus, v, of the proppant1Is the Poisson's ratio, alpha, of the proppant2Is the compression value of a single B layer;
the stress F' of the single proppant in the B layer is obtained by stress analysis:
Figure BDA0003071295360000034
the compression value of the individual B-layer proppants, alpha2Comprises the following steps:
Figure BDA0003071295360000035
according to the fracture width L and the proppant radius R1And (3) calculating the total number of the proppants as n, wherein the total compression amount of the B layer is as follows:
Figure BDA0003071295360000036
further, the specific method for calculating the change of the crack width in the step 2) is as follows:
the fracture width change h is the sum of the total compression of the proppant and the layer A and the total compression of the layer B:
Figure BDA0003071295360000041
due to the adoption of the technical scheme, the invention has the following advantages:
1. the method is based on the Hertz contact theory, a model of the propping behavior of the propping agent in the fracture under the fracture closure pressure is established, and compared with the existing model, the model considers the injection of the propping agent and the elastic compression between the propping agents and is closer to the actual physical process.
2. This application obtains crack width variation through calculating the compressive capacity of proppant and crack contact layer and the elastic compression between the proppant, and the crack width variation accuracy that obtains is higher.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof.
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The drawings of the present invention are described below.
FIG. 1 is a schematic structural diagram of the present invention.
FIG. 2 is a compression model of proppant in a fracture under closure pressure.
Fig. 3 shows the prediction result of the change in the crack width.
Detailed Description
The invention is further illustrated by the following figures and examples.
A fracture width variation calculation method under the closing pressure of a shale reservoir is disclosed, as shown in (a) - (c) in figure 2, a proppant is injected in a fracture of the shale reservoir, the proppant in the fracture is spherical, the proppants are distributed in a connected mode, the compaction effect of the closing pressure on the proppant is elastic deformation of particles, in figure 2, (a) the proppant is not compacted and is accumulated, in figure 2, (B) the proppant is deformed under the compaction effect, in figure 2, (c) the proppant is a model after the proppant is compressed, the proppant comprises two single contact layers of an upper proppant and a lower proppant and a fracture wall contact layer and a plurality of double contact layers of an intermediate proppant and the proppant, the single contact layer is defined as an A layer, the double contact layer is a B layer, the material performance of the proppant is kept stable during the deformation process, and the compaction effect is jointly contributed by the A layer and the B layer, the stable shape of the compressed proppant is hexagonal, as shown in fig. 1, the fracture width variation calculation method specifically comprises the following steps:
1) collecting the radius R of the proppant particle1Elastic modulus E1Poisson ratio v1(ii) a And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall2Poisson ratio v2Acquiring collected data;
2) respectively calculating the extrusion force of the proppant A layer and the extrusion force of the proppant B layer under the closed pressure according to the acquired data in the step 1) and a Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to an extrusion force self-defined formula;
3) calculating to obtain the variation of the crack width according to the total pressure of the two A layers and the plurality of B layers obtained in the step 2).
As an embodiment of the present invention, a specific method for calculating the total compression amount of the proppant and the layer a of the fracture wall contact layer in the step 2) is as follows:
the layer of the proppant directly contacting the fracture wall is an A layer, and according to the Hertz contact theory, the normal force N of the single A layer proppant is as follows:
Figure BDA0003071295360000051
in the formula (14), R1Radius of proppant, R2Radius of the fracture wall, E1Is the modulus of elasticity of the proppant, E2Is the modulus of elasticity, v, of the fracture wall1Poisson ratio, v, as a proppant2Poisson ratio, alpha, of the crack wall1Is the compression value of the a layer;
radius R since the fracture wall tends to be flat2→ infinity, the formula (1) can be simplified as:
Figure BDA0003071295360000052
the proppants are closely arranged in multiple layers, each proppant is extruded by 8 surrounding particles, the contact area formed by extrusion of each particle is approximately a regular quadrangle, wherein any side length is 2r of the particle diameter, and the area of a single triangle is as follows:
Figure BDA0003071295360000053
total contact area:
Figure BDA0003071295360000054
the proppants are elastic spheres, and the pressure F experienced by each proppant, for a layer a of proppants, is equal to its normal force N:
Figure BDA0003071295360000055
in the formula (18), F is the pressure of the proppant, P is the closing pressure, PcFor fracture closure pressure, R1Proppant diameter;
under the action of fracture closure, the proppant is extruded and deformed, the pressure influence on the compressed proppant is balanced, and the fracture wall is sealed by a sealing pressure PcInfluence of a value equal to overburden pressure PoAnd pore pressure PpThe difference between the difference of the two phases,compressive force N and confining pressure P of proppantcBalance is maintained, and gravity and buoyancy of the proppant in the fracture are ignored in the compaction process; fracture closure pressure PcComprises the following steps:
Pc＝Po-Pp (19)
in the formula (19), PoIs overburden pressure, PpIs the pore pressure;
the compression value alpha of the a-layer proppant1Comprises the following steps:
Figure BDA0003071295360000061
the upper and lower layers of proppant are in contact with the top and bottom layers of the fracture wall, respectively, so that the total amount of compression h caused by the A-layer proppant1Comprises the following steps:
Figure BDA0003071295360000062
as an embodiment of the present invention, a specific method for calculating the total compression of the proppant and the proppant contact layer B in step 2) is as follows:
the contact layer of the proppant and the proppant is a B layer, and according to the Hertz contact theory, the normal force N' of a single B layer of proppant is as follows:
Figure BDA0003071295360000063
in the formula (22), R1Radius of proppant, E1Is the elastic modulus, v, of the proppant1Is the Poisson's ratio, alpha, of the proppant2Is the compression value of a single B layer;
as shown in fig. 2(d), the pressure F' to which a single proppant in layer B is subjected by force analysis is:
Figure BDA0003071295360000064
the compression value of the individual B-layer proppants, alpha2Comprises the following steps:
Figure BDA0003071295360000065
according to the fracture width L and the proppant radius R1And (3) calculating the total number of the proppants as n, wherein the total compression amount of the B layer is as follows:
Figure BDA0003071295360000066
as an embodiment of the present invention, a specific method for calculating the crack width variation in step 2) is as follows:
the fracture width change h is the sum of the total compression of the proppant and the layer A and the total compression of the layer B:
Figure BDA0003071295360000071
as shown in FIG. 3, the ceramsite proppant is selected, and has an elastic modulus of 11306MPa and a Poisson ratio of 0.2. The average diameter of the proppant was 0.55mm (20-40 mesh), 0.27mm (40-60 mesh) and 0.17mm (70-100 mesh), respectively. The modulus of elasticity and Poisson's ratio of the fracture matrix were 0.25 and 8000MPa, respectively. The closing pressure is 0-70 MPa. Using the above method, the calculation of the change in fracture width was performed, and the predicted structure is shown in FIG. 3 (Theoretical model).
In order to research the influence factor of the hydraulic fracture conductivity of the shale reservoir, the factors such as the type, the particle size, the sand content, the cyclic stress, the backflow of fracturing fluid and the like are considered in the file Liu academic Wei, the influence factor of the hydraulic fracture conductivity of the shale reservoir [ J ], the fault block oil and gas field 2020,27(3): 394-. The change in fracture width under closure pressure was studied using 0.55mm (20-40 mesh), 0.27mm (40-60 mesh) and 0.17mm (70-100 mesh) sizes of proppant as shown in fig. 3 (Liu, 2020).
As can be seen from fig. 3, for different particle sizes of the ceramsite proppant, the variation of the fracture width predicted by the method described herein at different closure pressures remains consistent with the experimental data (Liu, 2020). Thus, the model presented herein is accurate, consistent with the physical mechanism of proppant support within the fracture, facilitating prediction of fracture width under closed pressure conditions.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (4)

1. The method for calculating fracture width change under shale reservoir closing pressure is characterized in that a proppant comprises two single contact layers of an upper proppant and a lower proppant and a fracture wall contact layer and a plurality of double contact layers of a middle proppant and a proppant, wherein the single contact layer is defined as an A layer, the double contact layers are defined as B layers, and the method for calculating fracture width change specifically comprises the following steps:
1) collecting the radius R of the proppant particle1Elastic modulus E1Poisson ratio v1(ii) a And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall2Poisson ratio v2Acquiring collected data;
2) respectively calculating the extrusion force of the proppant A layer and the extrusion force of the proppant B layer under the closed pressure according to the acquired data in the step 1) and a Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to an extrusion force self-defined formula;
3) calculating to obtain the variation of the crack width according to the total pressure of the two A layers and the plurality of B layers obtained in the step 2).
2. The method for calculating the fracture width variation under the shale reservoir closing pressure as claimed in claim 1, wherein the specific method for calculating the total compression amount of the two A layers in the step 2) is as follows:
the layer of the proppant directly contacting the fracture wall is an A layer, and according to the Hertz contact theory, the normal force N of the single A layer proppant is as follows:
Figure FDA0003071295350000011
in the formula (1), R1Radius of proppant, R2Radius of the fracture wall, E1Is the modulus of elasticity of the proppant, E2Is the modulus of elasticity, v, of the fracture wall1Poisson ratio, v, as a proppant2Poisson ratio, alpha, of the crack wall1Is the compression value of the a layer;
radius R since the fracture wall tends to be flat2→ infinity, the formula (1) can be simplified as:
Figure FDA0003071295350000012
the proppants are closely arranged in multiple layers, each proppant is extruded by 8 surrounding particles, the contact area formed by extrusion of each particle is approximately a regular quadrangle, wherein any side length is 2r of the particle diameter, and the area of a single triangle is as follows:
Figure FDA0003071295350000013
total contact area:
Figure FDA0003071295350000014
the proppants are elastic spheres, and the pressure F experienced by each proppant, for a layer a of proppants, is equal to its normal force N:
Figure FDA0003071295350000015
in formula (5), F is the pressure of the proppant, P is the closure pressure, PcFor fracture closure pressure, R1Is the proppant diameter. Fracture closure pressure P from force analysiscComprises the following steps:
Pc＝Po-Pp (6)
in the formula (6), PoIs overburden pressure, PpIs the pore pressure;
the compression value alpha of the a-layer proppant1Comprises the following steps:
Figure FDA0003071295350000021
the upper and lower layers of proppant are in contact with the top and bottom layers of the fracture wall, respectively, so that the total amount of compression h caused by the A-layer proppant1Comprises the following steps:
Figure FDA0003071295350000022
3. the method for calculating the fracture width variation under the shale reservoir closing pressure as claimed in claim 2, wherein the specific method for calculating the total compression amount of the plurality of layers B in the step 2) is as follows:
the contact layer of the proppant and the proppant is a B layer, and according to the Hertz contact theory, the normal force N' of a single B layer of proppant is as follows:
Figure FDA0003071295350000023
in the formula (9), R1Radius of proppant, E1Is the elastic modulus, v, of the proppant1Is the Poisson's ratio, alpha, of the proppant2Is the compression value of a single B layer;
the stress F' of the single proppant in the B layer is obtained by stress analysis:
Figure FDA0003071295350000024
the compression value of the individual B-layer proppants, alpha2Comprises the following steps:
Figure FDA0003071295350000025
according to the fracture width L and the proppant radius R1And (3) calculating the total number of the proppants as n, wherein the total compression amount of the B layer is as follows:
Figure FDA0003071295350000026
4. the method for calculating the fracture width change under the shale reservoir closing pressure as claimed in claim 3, wherein the specific method for calculating the fracture width change in the step 3) is as follows:
the fracture width change h is the sum of the total compression of the proppant and the layer A and the total compression of the layer B:
Figure FDA0003071295350000031
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113591328A (en) * 2021-08-24 2021-11-02 西南石油大学 Deep shale hydraulic fracture long-term support opening change calculation method
CN113591328B (en) * 2021-08-24 2022-04-12 西南石油大学 Deep shale hydraulic fracture long-term support opening change calculation method

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