CN113221361B - Shale reservoir fracture width change calculation method under closing pressure - Google Patents
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Abstract
The invention provides a calculation method for the width change of a crack under shale reservoir closing pressure, which comprises the following steps: radius R of proppant particle acquisition 1 Modulus of elasticity E 1 Poisson ratio v 1 The method comprises the steps of carrying out a first treatment on the surface of the And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall 2 Poisson ratio v 2 Acquiring acquisition data; respectively calculating extrusion forces of the propping agent A layer and the propping agent B layer under closed pressure according to acquired data and a Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to a self-defined extrusion force formula; and calculating the obtained total pressure of the two layers A and the plurality of layers B to obtain the crack width variation. Based on Hertz contact theory, the method establishes a model of the propping action of the propping agent in the fracture under the fracture closing pressure, and compared with the existing model, the model considers the injection of the propping agent and the elastic compression between propping agents, and is closer to the actual physical process; the accuracy of the obtained crack width variation is higher.
Description
Technical Field
The invention relates to a fracture width change calculation method, in particular to a fracture width change calculation method under shale reservoir closing pressure.
Background
The description of the width of the crack is the key for evaluating the flow conductivity of the crack, and influences the development efficiency of unconventional oil and gas resources. Typically, when proppants are filled into a fracture, the fracture will undergo a change in width at the closing pressure, and the proppants resist the change in fracture width. Therefore, it is of great importance to build a theoretical model for predicting crack changes. The hydraulic fracturing technology is common in unconventional oil and gas reservoir development, a fracture network consisting of natural fractures and induced fractures is formed after the hydraulic fracturing process, a fluid seepage channel is provided, and propping agents are injected into the fracture network along with fracturing fluid; once the well is opened and put into production, the pore pressure can be obviously reduced, the width of the crack can be reduced, part of propping agent can be discharged back, and part of propping agent stays in the crack, and the propping effect is excited along with the change of the width of the crack, so that the opening degree of the crack is maintained; propping action of proppants under closing pressure can affect fracture width and conductivity, related to development efficiency. Therefore, it is of great importance to study the pressure resistance of proppants, describing the variation of fracture width under closure pressure.
In fact, during the compression process, proppants in the fracture may be compressed or embedded, resulting in a change in fracture width; the relation between the embedding degree of proppants and the closing pressure, the concentration of proppants and the rock mechanical properties is studied by students in 1998 as early as possible; in the aspect of theoretical research, a mathematical model of the proppant injection amount under the sealing pressure is established through analysis, and the sensitivity of the proppant particle size and the rock Young modulus is discussed; deducing a proppant embedding depth model by using an elasticity theory, and carrying out sensitivity analysis on basic parameters; the influence of the particle size and the layer number of the propping agent on the fracture conductivity is characterized by adopting a numerical method.
These studies have discussed the impact factors on the proppant's embedding process and fracture conductivity, but most are based on rigid sphere assumptions, ignoring contact deformation between proppants. The variation in slit width at closing pressure cannot be accurately described. In particular, a theoretical model that takes into account proppant elastography needs to be built.
Disclosure of Invention
The invention aims to provide a calculation method for the width change of a crack under the closing pressure of a shale reservoir, which can be used for calculating the width change of the crack under the closing pressure of the shale reservoir.
The invention aims at realizing the technical scheme, which comprises the following steps:
the method for calculating the width change of the crack of the shale reservoir under the closing pressure comprises the following specific steps of:
1) Radius R of proppant particle acquisition 1 Modulus of elasticity E 1 Poisson ratio v 1 The method comprises the steps of carrying out a first treatment on the surface of the And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall 2 Poisson ratio v 2 Acquiring acquisition data;
2) Respectively calculating extrusion forces of the propping agent A layer and the propping agent B layer under the closing pressure according to the acquired data of the step 1) and the Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to a self-defined extrusion force formula;
3) And (3) calculating the variation of the width of the crack according to the total pressure of the two layers A and the plurality of layers B obtained in the step (2).
Further, the specific method for calculating the total compression of the propping agent and the fracture wall contact layer A layer in the step 2) is as follows:
the propping agent is directly contacted with the crack wall to form a layer A, and the normal force N of the propping agent of the single layer A is as follows according to the Hertz contact theory:
in the formula (1), R 1 For radius of propping agent, R 2 Radius of crack wall, E 1 Modulus of elasticity, E, of the proppant 2 Modulus of elasticity, v, of the fracture wall 1 Poisson's ratio, v as proppant 2 Poisson ratio, alpha, of fracture wall 1 Is the compression value of layer a;
radius R because the fracture wall tends to be planar 2 → infinity, formula (1) can be simplified as:
the proppants are closely arranged in multiple layers, each propping agent is extruded by surrounding 8 particles, the contact area formed by extrusion of each particle is approximately a regular quadrangle, wherein any side length is the particle diameter of 2r, and the area of a single triangle is as follows:
total contact area:
the proppants are elastic spheres, each of which is subjected to a pressure F equal to its normal force N for the a-layer proppants:
in formula (5), F is the pressure of the proppant, P is the closing pressure, P c For crack closure pressure, R 1 Is the proppant diameter. Based on force analysis, crack closure pressure P c The method comprises the following steps:
P c ＝P o -P p (6)
in formula (6), P o To overburden pressure, P p Is pore pressure;
compression value alpha of the a-layer proppant 1 The method comprises the following steps:
the upper and lower layers of propping agent are respectively contacted with the top layer and the bottom layer of the crack wall, so the total compression amount h caused by the propping agent of the layer A 1 The method comprises the following steps:
further, the specific method for calculating the total compression of the proppants and the proppants contact layer B in the step 2) is as follows:
the propping agent and propping agent contact layer is a B layer, and according to the Hertz contact theory, the normal force N' of the propping agent of the single B layer is as follows:
in the formula (9), R 1 Radius of propping agent, E 1 As the elastic modulus of the proppant, v 1 Poisson ratio, alpha, of proppant 2 A compression value for a single B layer;
the pressure F' to which the single proppants of the layer B are subjected by stress analysis is as follows:
compression value alpha of single B layer proppant 2 The method comprises the following steps:
according to the fracture width L and the proppant radius R 1 And calculating the total number of layers of the propping agent as n, wherein the total compression amount of the layer B is as follows:
further, the specific method for calculating the crack width change in the step 2) is as follows:
the fracture width change h is the sum of the total compression of the propping agent and the layer A and the total compression of the layer B:
due to the adoption of the technical scheme, the invention has the following advantages:
1. based on Hertz contact theory, the model of the propping action of the propping agent in the fracture under the fracture closing pressure is established, and compared with the existing model, the model considers the injection of the propping agent and the elastic compression between propping agents, and is closer to the actual physical process.
2. According to the method, the fracture width variation is obtained by calculating the compression amount of the propping agent and the fracture contact layer and the elastic compression between propping agents, and the accuracy of the obtained fracture width variation 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.
Drawings
The drawings of the present invention are described below.
Fig. 1 is a schematic structural view of the present invention.
Fig. 2 is a compression model of proppant in a fracture at closure pressure.
Fig. 3 shows the predicted result of the crack width change.
Detailed Description
The invention is further described below with reference to the drawings and examples.
The method for calculating the width change of the crack under the closing pressure of the shale reservoir is shown in (a) - (c) in fig. 2, proppants are injected into the crack of the shale reservoir, the proppants in the crack are spherical, the proppants are mutually connected and distributed, the compaction effect of the closing pressure on the proppants is particle elastic deformation, the proppants are piled up in (a) in fig. 2, the proppants are deformed under the compaction effect, the proppants in (B) in fig. 2 are models after being compressed, the proppants in (c) in fig. 2 are models after being compressed, the proppants comprise two single contact layers of upper proppants and lower proppants and crack wall contact layers and a plurality of double contact layers of middle proppants, the single contact layer is defined as a layer A, the double contact layers are a layer B, the material performance of the proppants is kept stable in the deformation process, the compaction effect is contributed by the two parts of the layer A and the layer B, the stable shape of the proppants after being compressed is hexagonal, and the method for calculating the width change of the crack specifically comprises the following steps:
1) Radius R of proppant particle acquisition 1 Modulus of elasticity E 1 Poisson ratio v 1 The method comprises the steps of carrying out a first treatment on the surface of the And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall 2 Poisson ratio v 2 Acquiring acquisition data;
2) Respectively calculating extrusion forces of the propping agent A layer and the propping agent B layer under the closing pressure according to the acquired data of the step 1) and the Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to a self-defined extrusion force formula;
3) And (3) calculating the variation of the width of the crack according to the total pressure of the two layers A and the plurality of layers B obtained in the step (2).
As an embodiment of the present invention, the specific method for calculating the total compression amount of the proppants and the fracture wall contact layer a layer in the step 2) is as follows:
the propping agent is directly contacted with the crack wall to form a layer A, and the normal force N of the propping agent of the single layer A is as follows according to the Hertz contact theory:
in the formula (14), R 1 For radius of propping agent, R 2 Radius of crack wall, E 1 Modulus of elasticity, E, of the proppant 2 Modulus of elasticity, v, of the fracture wall 1 Poisson's ratio, v as proppant 2 Poisson ratio, alpha, of fracture wall 1 Is the compression value of layer a;
radius R because the fracture wall tends to be planar 2 → infinity, formula (1) can be simplified as:
the proppants are closely arranged in multiple layers, each propping agent is extruded by surrounding 8 particles, the contact area formed by extrusion of each particle is approximately a regular quadrangle, wherein any side length is the particle diameter of 2r, and the area of a single triangle is as follows:
total contact area:
the proppants are elastic spheres, each of which is subjected to a pressure F equal to its normal force N for the a-layer proppants:
in the formula (18), F is the pressure of the propping agent, P is the closing pressure, P c For crack closure pressure, R 1 Is the proppant diameter;
under the action of fracture closure, the propping agent is extruded and deformed, the influence of pressure on the compressed propping agent is balanced, and the fracture wall is subjected to the closure pressure P c Influence of a value equal to the overburden pressure P o And pore pressure P p The difference between the compression force N and the closing pressure P of the propping agent c Maintaining balance, wherein gravity and buoyancy of proppants in the fracture are ignored in the compaction process; fracture closure pressure P c The method comprises the following steps:
P c ＝P o -P p (19)
in the formula (19), P o To overburden pressure, P p Is pore pressure;
compression value alpha of the a-layer proppant 1 The method comprises the following steps:
the upper and lower layers of propping agent are respectively contacted with the top layer and the bottom layer of the crack wall, so the total compression amount h caused by the propping agent of the layer A 1 The method comprises the following steps:
as an embodiment of the present invention, the specific method for calculating the total compression of the proppant and the proppant contacting layer B layer in step 2) is:
the propping agent and propping agent contact layer is a B layer, and according to the Hertz contact theory, the normal force N' of the propping agent of the single B layer is as follows:
in the formula (22), R 1 Radius of propping agent, E 1 As the elastic modulus of the proppant, v 1 Poisson ratio, alpha, of proppant 2 A compression value for a single B layer;
as shown in fig. 2 (d), the pressure F' to which the single proppant of layer B is subjected by stress analysis is:
compression value alpha of single B layer proppant 2 The method comprises the following steps:
according to the fracture width L and the proppant radius R 1 And calculating the total number of layers of the propping agent as n, wherein the total compression amount of the layer B is as follows:
as an embodiment of the present invention, the specific method for calculating the crack width change in step 2) is as follows:
the fracture width change h is the sum of the total compression of the propping agent and the layer A and the total compression of the layer B:
as shown in fig. 3, the ceramic proppant is selected, the elastic modulus is 11306MPa, and the poisson ratio is 0.2. The average diameters of the proppants were 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. By the above method, calculation of the crack width change is performed, and the predicted structure is shown in fig. 3 (Theoretical model).
In order to study the influence factors of the hydraulic support fracture conductivity of the shale reservoir, the factors of the type of propping agent, the grain size, the sand content, the circulating stress, the fracturing fluid backflow and the like are considered in the document Liu Xuewei, namely the shale reservoir hydraulic support fracture conductivity influence factor [ J ]. The broken block oil-gas field 2020,27 (3): 394-398', and an indoor experiment is carried out. The variation of the fracture width under closing pressure was studied using proppants of sizes 0.55mm (20-40 mesh), 0.27mm (40-60 mesh) and 0.17mm (70-100 mesh), as shown in fig. 3 (Liu, 2020).
As can be seen from fig. 3, the variation in fracture width predicted by the methods described herein at different closure pressures for different particle sizes of ceramsite proppants is consistent with experimental data (Liu, 2020). Therefore, the model provided herein is accurate, conforms to the physical mechanism of propping of the proppants in the fracture, and facilitates the prediction of fracture width under closed pressure conditions.
It will be appreciated by those skilled in the art that 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 flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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: the above embodiments are only for illustrating the technical aspects of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above embodiments, it should be understood by those of ordinary skill in the art that: modifications and equivalents may be made to the specific embodiments of the invention without departing from the spirit and scope of the invention, which is intended to be covered by the claims.
Claims (2)
1. The method for calculating the width change of the crack of the shale reservoir under the closing pressure of the shale reservoir is characterized in that the propping agent comprises two single contact layers of an upper propping agent and a lower propping agent and a crack wall contact layer and a plurality of double contact layers of an intermediate propping agent and the propping agent, wherein the single contact layer is defined as an A layer, the double contact layer is defined as a B layer, and the method for calculating the width change of the crack comprises the following specific steps:
1) Radius R of proppant particle acquisition 1 Modulus of elasticity E 1 Poisson ratio v 1 The method comprises the steps of carrying out a first treatment on the surface of the And the initial width L of the crack to be filled, the modulus of elasticity E of the crack wall 2 Poisson ratio v 2 Acquiring acquisition data;
2) Respectively calculating extrusion forces of the propping agent A layer and the propping agent B layer under the closing pressure according to the acquired data of the step 1) and the Hertz contact theory; respectively calculating total pressure of the two layers A and the plurality of layers B according to a self-defined extrusion force formula;
3) Obtaining the crack width variation according to the total pressure calculation of the two layers A and the plurality of layers B obtained in the step 2);
the specific method for calculating the total compression of the two A layers in the step 2) is as follows:
the propping agent is directly contacted with the crack wall to form a layer A, and the normal force N of the propping agent of the single layer A is as follows according to the Hertz contact theory:
in the formula (1), R 1 For radius of propping agent, R 2 Radius of crack wall, E 1 Modulus of elasticity, E, of the proppant 2 Modulus of elasticity, v, of the fracture wall 1 Poisson's ratio, v as proppant 2 Poisson ratio, alpha, of fracture wall 1 Is layer AIs a compressed value of (2);
radius R because the fracture wall tends to be planar 2 → infinity, formula (1) can be simplified as:
the proppants are closely arranged in multiple layers, each propping agent is extruded by surrounding 8 particles, the contact area formed by extrusion of each particle is approximately a regular quadrangle, wherein any side length is the particle diameter of 2r, and the area of a single triangle is as follows:
total contact area:
the proppants are elastic spheres, each of which is subjected to a pressure F equal to its normal force N for the a-layer proppants:
in formula (5), F is the pressure of the proppant, P is the closing pressure, P c For crack closure pressure, R 1 Is the proppant diameter; based on force analysis, crack closure pressure P c The method comprises the following steps:
P c ＝P o -P p (6)
in formula (6), P o To overburden pressure, P p Is pore pressure;
compression value alpha of the a-layer proppant 1 The method comprises the following steps:
the upper and lower layers of propping agent are respectively contacted with the top layer and the bottom layer of the crack wall, so the total compression amount h caused by the propping agent of the layer A 1 The method comprises the following steps:
the specific method for calculating the total compression of a plurality of B layers in the step 2) is as follows:
the propping agent and propping agent contact layer is a B layer, and according to the Hertz contact theory, the normal force N' of the propping agent of the single B layer is as follows:
in the formula (9), R 1 Radius of propping agent, E 1 As the elastic modulus of the proppant, v 1 Poisson ratio, alpha, of proppant 2 A compression value for a single B layer;
the pressure F' to which the single proppants of the layer B are subjected by stress analysis is as follows:
compression value alpha of single B layer proppant 2 The method comprises the following steps:
according to the fracture width L and the proppant radius R 1 And calculating the total number of layers of the propping agent as n, wherein the total compression amount of the layer B is as follows:
2. the method for calculating the width change of the crack under the closing pressure of the shale reservoir according to claim 1, wherein the specific method for calculating the width change of the crack in the step 3) is as follows:
the fracture width change h is the sum of the total compression of the propping agent and the layer A and the total compression of the layer B:
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