CN116738685A

CN116738685A - Method for determining flow conductivity of support type crack by considering elastoplastic embedding and product

Info

Publication number: CN116738685A
Application number: CN202310574798.XA
Authority: CN
Inventors: 何柏; 谢凌志; 张瑶; 任利
Original assignee: Sichuan University
Current assignee: Sichuan University
Priority date: 2023-05-19
Filing date: 2023-05-19
Publication date: 2023-09-12

Abstract

The invention provides a method for determining the flow conductivity of a supporting type crack by considering elastoplastic embedding and a product thereof, and relates to the technical field of petroleum and natural gas exploitation. According to the embodiment of the invention, based on a C-K permeation model and a Comiti-Renaud tortuosity model, a crack flow conductivity model considering the laying characteristics of propping agents and elastoplastic embedding behaviors is established, the model is verified through a planar radial permeation test, and research results show that the model can better illustrate the relation between the crack flow conductivity and the closure stress.

Description

Method for determining flow conductivity of support type crack by considering elastoplastic embedding and product

Technical Field

The embodiment of the invention relates to the technical field of petroleum and natural gas exploitation, in particular to a method and a product for determining the flow conductivity of a support type crack by considering elastoplastic embedding.

Background

Compared with the middle shallow shale reservoir, the deep shale gas in China has high initial yield in the well test, but has fast pressure drop and lower long-term yield, and one of the main reasons is as follows: the sand laying difficulty is high, the net-sewing supporting effect is not ideal, and the flow conductivity is fast reduced.

Keeping the fracture and the permeate channel open is one of the key technologies to ensure economic development of hydrocarbon resources, while propped fracture formed by proppant pack is the main channel for hydrocarbon seepage. The penetration capacity of the cracks is rapidly reduced due to the embedding, deformation, crushing, dissolution, blocking and the like of the proppants; proppant breakage/dissolution can be generally avoided by a mode of selection, the randomness of the muddy blockage is strong, and the elucidation is difficult; while proppant placement/deformation problems are generally unavoidable, while proppant placement has negligible impact on fracture conductivity in locations such as the wellbore periphery where the proppant placement concentration is high, proppant placement will have a significant impact on conductivity in some areas where the proppant placement concentration is low. In the transformation process of the deep shale reservoir, the initial seam width of each stage of cracks is narrow, propping agents are difficult to lay, and the propping agents in the deep shale reservoir coexist in a plurality of laying characteristics such as multilayer, single-layer, sparse and the like; therefore, aiming at deep shale gas development, the proppant embedding behavior is deeply known, and the method has important significance for exploring the evolution rule of the support type fracture seepage channel and ensuring the efficient development of the reservoir.

Deep shale gas reservoirs in China often show five-high characteristics, namely high formation temperature, high overburden pressure, high horizontal ground stress difference, high cracking pressure and high closing pressure; in the high-temperature and high-pressure environment, the shale plastic-delaying property of the reservoir shale is enhanced, in addition, a larger volume of fracturing fluid is injected into the reservoir during the fracturing process, the water-shale interaction is more remarkable, and the shale is hydrated and softened. On the other hand, under the action of high closing pressure, the load born by the propping agent is increased, the phenomenon that the propping agent is embedded into the shale wall surface is obviously enhanced, and for example, a core propping agent embedding test of 3800-4000 m of the burial depth of a certain reservoir in Chuan south shows that the average embedding depth can reach 0.611mm. Meanwhile, in the process of deep reservoir fracturing transformation, in order to reduce sand blocking risk, the small-particle-size propping agent ratio needs to be greatly improved, and related technology indicates that critical yield load is in a proportional relation with the square of the particle size of the propping agent, namely that the smaller the particle size of the propping agent is, the easier elastoplastic embedding behavior occurs.

Therefore, when the deep shale gas seepage channel is constructed artificially, a series of deep features such as high closing pressure, remarkable shale ductility characteristic, small propping agent particle size and the like are necessarily faced. Therefore, when the propping agent interacts with the shale wall surface, the elastic embedding behavior of the middle shallow layer is gradually converted into the elastic-plastic or full-plastic embedding behavior of the deep part; if the middle-shallow elastic embedding depth model is directly applied to deep shale gas development engineering, the embedding depth of the propping agent is inevitably underestimated, and the fracture conductivity is overestimated; this can have adverse effects on proppant type selection during reservoir development and design, as well as on post production operation management. Therefore, aiming at the shale plasticity characteristics in the deep in-situ environment, the interaction mechanism of the propping agent and the shale and the influence rule of the interaction mechanism on the crack seepage capability are explored, and important theoretical support and technical guarantee can be provided for deep shale gas development in China.

Therefore, there is a need for a method of determining propped fracture conductivity considering elastoplastic embedding for shale.

Disclosure of Invention

The embodiment of the invention provides a method for determining the flow conductivity of a supporting type crack by considering elastoplastic embedding and a product thereof, so as to at least partially solve the problems in the related art.

The first aspect of the embodiment of the invention provides a method for determining the flow conductivity of a propped fracture by considering elastoplastic embedding, which comprises the following steps:

the propping fracture conductivity was determined using the following:

wherein D is the particle size of the propping agent, w _i Represents the number of layers laid in the width direction of the fracture, delta represents the depth of proppant embedment, phi _f Representing the porosity of the support band, K represents the distance coefficient.

Alternatively, the support band porosity φ is determined using _f ：

wherein ,n_i To propping agent layer number m in the length direction of the crack _i To support the number of layers in the fracture height direction, L _F Represents the crack length, H _F Represents the crack height, W _F Representing the crack width.

Alternatively, n is calculated using the formula _i ：

wherein ,the representation function takes an integer down, K being the distance coefficient.

Alternatively, m is calculated using the formula _i ：

Alternatively, w is calculated using the formula _i ：

A second aspect of the embodiments of the present invention provides a supporting-type fracture conductivity determining apparatus considering elastoplastic embedding, the apparatus comprising:

the determining module is used for determining the supporting type crack flow conductivity by adopting the following formula:

Alternatively, the support band porosity φ is determined using _f ：

Alternatively, n is calculated using the formula _i ：

Alternatively, m is calculated using the formula _i ：

wherein ,representing the function down integer, K is distanceCoefficients.

Alternatively, w is calculated using the formula _i ：

A third aspect of the embodiments of the present invention provides an electronic device, including a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps in the method for determining a propped fracture conductivity taking into account elastoplastic embedding according to the first aspect of the present invention when executed.

A fourth aspect of the embodiments of the present invention provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the method for determining fracture conductivity of a propped fracture taking into account elastoplastic embedding according to the first aspect of the present invention.

In the embodiment of the invention, a method for determining the flow conductivity of the support type cracks by considering elastoplastic embedding is provided, based on the method, the porosity of the support belt can be determined to rise along with the increase of the laying concentration of the propping agent and the inter-particle distance coefficient, but the laying concentration is not lower than 13kg/m ² When the laying concentration is increased, the improvement of the crack flow conductivity is mainly reflected by increasing the crack width, and the porosity of the supporting belt is hardly influenced. In addition, by adopting the method for determining the conductivity of the support type fracture taking the elastoplastic embedding into consideration, which is provided by the embodiment of the invention, the equivalent porosity of the support type fracture can be determined on the basis of considering the non-compact laying characteristics of the support agent, so that the basis is provided for the follow-up research of the permeability of the support band after the elastoplastic embedding.

In the embodiment of the invention, a crack flow conductivity model considering the laying characteristics of propping agents and elastoplastic embedding behaviors is established based on a C-K permeation model and a Comiti-Renaud tortuosity model is introduced, the model is verified through a planar radial permeation test, and the research result shows that the model can better illustrate the relation between the crack flow conductivity and the closure stress.

Based on the method for determining the propping fracture conductivity taking the elastoplastic embedding into consideration, which is provided by the embodiment of the invention, the optimal proppant laying concentration of the fracture conductivity can be determined when the closing stress of the reservoir is lower; when the closing stress is higher, the increase of the laying concentration of the propping agent (the increase of the laying layers) is beneficial to reducing the influence of the embedding of the propping agent, so that the crack keeps higher diversion capacity, and therefore, the use proportion of the propping agent with the large and small particle sizes is increased in the development process of the ultra-deep shale gas, so that the laying layers of the propping agent are increased, and the diversion capacity of the propping type crack is increased. In addition, properly increasing the distance between the proppant particles helps to increase the conductivity of the fracture. According to the invention, the influence of the laying characteristics of the propping agent and the elastoplastic embedding on the fracture conductivity is comprehensively considered, and the obtained fracture conductivity model can more truly reflect key factors influencing the fracture conductivity, so that theoretical guidance is provided for propping agent type selection in the fracturing design.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments of the present invention will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a schematic representation of proppant-shale interactions involved in an embodiment of the present invention, wherein part (a) shows a proppant-shale interaction schematic and part b shows a single proppant intercalation process schematic;

FIG. 2 is a schematic illustration of proppant mono-layer/sparse lay-up involved in an embodiment of the present invention;

FIG. 3 is a schematic diagram of a proppant placement scenario involved in an embodiment of the present invention, wherein (a) shows a multi-layered proppant placement schematic in section and (b) shows a geometric topology in section;

FIG. 4 is a graph showing the variation of the initial porosity of the support tape with distance coefficient for different number of layers of the support tape laid without consideration for proppant placement in the examples of the present invention;

FIG. 5 is the effect of depth of embedment on relative porosity when a proppant monolayer is laid down in an embodiment of the present invention;

FIG. 6 is a graph showing the relative porosity as a function of depth of embedment for 10 layers of proppant in an embodiment of the present invention;

FIG. 7 is a schematic illustration of the geometric relationship between closing stress and contact force involved in an embodiment of the present invention;

FIG. 8 is a schematic diagram of the variation of the embedding depth with closing stress involved in an embodiment of the present invention;

FIG. 9 is a schematic diagram of a support belt permeability test principle involved in an embodiment of the present invention;

FIG. 10 is a schematic diagram showing proppant embedding depth versus closure stress in a proppant embedding depth model validation result involved in an embodiment of the present invention;

FIG. 11 is a schematic diagram illustrating propped fracture conductivity versus closure pressure for a single layer lay-up feature in accordance with an embodiment of the present invention;

FIG. 12 is a schematic diagram illustrating propped fracture conductivity versus closure pressure for a multi-layered lay-up feature in accordance with an embodiment of the present invention;

FIG. 13 shows the effect of distance coefficient K on propped fracture conductivity for single layer placement of proppants in a fracture, as contemplated in an embodiment of the present invention;

FIG. 14 shows the effect of distance coefficient K on propped fracture conductivity in the case of multi-layer placement of proppants in a fracture as contemplated in an embodiment of the present invention;

fig. 15 shows the effect of the number of proppant placement layers involved in an embodiment of the invention on fracture conductivity.

Detailed Description

In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.

For ease of understanding, a proppant-shale interaction mechanics model is first explained:

After hydraulic fracturing, proppant-shale interactions are shown in fig. 1, which shows a schematic diagram of proppant-shale interactions involved in embodiments of the invention, wherein part (a) shows a schematic diagram of proppant-shale interactions and part b shows a schematic diagram of a single proppant intercalation process; since the model shown in part (a) of fig. 1 is directly used for research, and is difficult to accurately describe, most students abstract one proppant particle, and the proppant is similar to a sphere in morphology, so that the interaction behavior of the proppant and shale can be simplified into the problem of contact between single spherical particles and an infinite flat plate, as shown in part (b) of fig. 1. In order to solve the contact problem, the precondition is to accurately acquire various physical and mechanical parameters of shale, so as to effectively describe the physical and mechanical behaviors of the shale; and then combining with a nonlinear contact mechanics theory, the single spherical particle elastoplastic embedded depth model can be constructed. However, since the proppant-shale system in actual situations is shown in part (a) of fig. 1, the pore volume evolution of the support zone, the relationship between the closing pressure and the contact force, and the like are all affected by the proppant placement situation, the application of the single spherical particle elastoplastic embedded depth model to actual situations must take into account the placement characteristics of the proppant in the fracture and the inter-particle interference problem.

Proppant interactions with shale remain essentially contact problems, which, from a mechanical standpoint, are largely comprised of two aspects: (1) Mechanical properties of the contact material (shale) itself, such as its elastic, yielding, strengthening, etc., necessarily affect the deformation behavior during proppant-shale contact; (2) How the mechanical behavior of shale affects the elastoplastic embedding process of proppants.

The propped fracture conductivity is generally determined by the permeability (K) of the propped band _f ) Width of the supporting seam (W) _F ) After the proppant is embedded in the formation, the fracture width is reduced resulting in a decrease in conductivity. However, the supportAfter the agent is embedded, not only the width of the crack is reduced, but also the pore structure of the crack wall surface is changed, so that the porosity of the supporting belt is affected, and the permeability of the supporting belt is reduced. Thus, there is a need for a more accurate and rational method of determining the porosity of a support belt.

The propping type cracks formed by propping agent filling are main channels for oil and gas resource seepage, and under the action of closing pressure, propping agent particles are embedded into shale wall surfaces to reduce the width of the cracks and the evolution of pore structures of the propping bands are one of main factors for reducing the diversion capacity of the propping type cracks.

In an actual crack, a plurality of propping agents are moved and piled up to form sparse, single-layer, multi-layer and other laying modes, pore structures formed by different laying modes are different, and the contact force caused by the pore structures is different, so that the permeability of the supporting belt is affected. Although proppants generally have certain grain size distribution in actual engineering, if the influence of embedding on permeation is discussed according to actual conditions, great difficulties are faced in mathematics, so that the scholars still use an equal grain size model to discuss the problem of embedding the proppants, and the embodiment of the invention still adopts an equal grain size assumption.

The arrangement of particles of equal particle size can be generally divided into: cubic, body centered cubic, wedge tetrahedron, hexagonal close packing, etc. arrangement modes; wherein the cubic packing coordination number (the number of points of contact of each particle with other surrounding particles) is 6, the porosity is about 48%, the hexagonal close packing coordination number is 12, and the porosity is about 26%. Under the natural accumulation condition, the particles are generally in a composite arrangement mode, the porosity is about 36%, under the stress disturbance effect, the particles at the bottom layer of the container tend to be arranged in a hexagonal compact mode, and the particles at the top layer of the container are arranged in a random mode; this also shows that the hexagonal close-packed mode is the most stable one of the many alignment modes, and other alignment modes have a tendency to evolve towards hexagonal close-packing under stress disturbance. In the fracturing process, when the fracturing fluid carries propping agent to fill a crack, the migration of the fluid causes the propping agent to be in a disturbed condition, in addition, after the reservoir is fractured, the reservoir is in an unstable state, and the reservoir stress adjustment causes the crack to slip, dislocate and the like, so that the disturbance rearrangement of the propping agent can be caused. The porosity of the supporting belt under the conditions of different types of propping agents and different laying concentrations is measured through an indoor test in the related art, and the porosity is about 28% -44% and is more than 26% of the porosity of the hexagonal close arrangement; thus, embodiments of the present invention contemplate that proppants should be deployed in the fracture in a manner that will predominate in the hexagonal close-packed mode and the other modes of alignment coexist.

In order to describe the state of the propping agent in the crack more accurately and avoid the mathematical problems caused by researching the problems of propping agent laying, embedding and the like in a mixed arrangement mode, the embodiment of the invention introduces the distance coefficient K, namely the propping agent is considered to be still arranged in a hexagonal compact mode, and the mixed laying problem is equivalent to: the particles are not closely together but are present at a distance, and for mathematical simplicity, it is assumed that the spacing between any adjacent particles in the same plane is uniform, thus solving the problem of greater porosity in practical situations.

Specifically, assuming that the intervals between adjacent proppants are the same, when the intervals between proppants change, the change rules are consistent every two, and the intervals between the adjacent proppants can be KD (K is a distance coefficient, and D is the particle size of the proppants); at the crack length L _F The number of layers of proppants is n _i From the geometrical relationship in FIG. 2 (showing proppant monolayer/sparse lay-up schematic)

in the formula ：in the embodiment of the invention, the finger function takes an integer downwards.

At crack height H _F The number of layers of proppants is m _i Then the same principle can be obtained

When a double rhombohedra stacking system is adopted, the adjacent layers are affected by the regular boundary, and the particle numbers of the adjacent layers are different by 1, as shown in FIG. 2H _F In the direction, if the difference between the numbers of particles in adjacent layers is ignored, the total number of proppant particles is

N _i ＝m _i n _i (3)

This will result in an increase in the statistical particle count by m _i 2 particles;

alternatively, as shown in FIG. 2, a dashed box can be used as a cell where the total number of proppant particles is

At this time, if m _i In the case of even numbers, the use of equation (4) does not mathematically cause any error, whereas when m _i When odd, equation (4) will reduce the particle count by n _i -1 or n _i Granulating;

the maximum errors caused by the formulas (3) and (4) in the topological relation are respectively as follows:

it can be noted that even when larger particle proppants are used, such as 20 mesh, the particle size is about 0.84mm assuming a fracture length or height of 10mm, error ₁ And error ₂ The values of (2) were 4.7% and 8%, respectively. In most cases, the proppant particle size is often less than 20 mesh, while the fracture length/height is also much greater than 10mm; thus, the use of formula (3) or (4) does not have a significant impact, and in view of the simplicity of the form, the total number of proppant particles can be calculated using formula (3) in embodiments of the present invention.

For the single layer lay-up mode, the propped fracture initiation porosity can be given by equation (5)

When the propping agent is embedded into the shale wall surface under the action of closing stress, the embedding depth is delta, the deformation influence generated outside the contact area in the process of embedding the propping agent is ignored, at the moment, the sphere (propping agent) is a sphere defect in the crack, and if the deformation of the propping agent is not considered, the volume in the crack after embedding is

Thus, when considering proppant insertion effects, the support band porosity is

When the number of layers of the propping agent is large, a single-layer paving model can be still adopted for the contact layer with the shale wall surface, and the propping agent is still stacked in a similar manner to a single-layer paving rule in the width direction of the crack, a schematic diagram of the propping agent paving condition is shown in fig. 3, the propping agent paving characteristics and the geometric topological relation of the propping agent paving characteristics are shown in fig. 3 in the section perpendicular to the wall surface of the crack, wherein part (a) shows the schematic diagram of the propping agent multi-layer paving, and part (b) shows the geometric topological relation. The length of OD, i.e., h, can be obtained _i Is that

Similarly, the number of layers w of the propping agent laid in the width direction of the crack _i Is that

For multilayer paving, the range of the distance coefficient should be 1.ltoreq.K.ltoreq.1.5 whenWhen the gaps between adjacent particles are increased, the particles in the middle layer are inevitably moved to a contact layer with the wall surface of the crack, and then the particles are degenerated into a single-layer or sparse arrangement mode; when->During the time, the proppant penetration phenomenon, namely 2h, will occur _i <D, which is not possible in practice.

Similarly, ignoring the differences in proppant particles from layer to layer, the total number of proppant particles can be given by formula (10)

N _i ＝m _i n _i w _i (10)

For multilayer laying applications, the support belt pores are formed by wall contact layer pores and intermediate layer pores, the contact layer pores have a volume similar to that of a single layer, e.g

The pore volume of the intermediate layer is

When proppant intercalation occurs, the intermediate layer pore volume does not change with increasing intercalation depth, and the intercalation behavior only affects the contact layer pore volume V _c0 The method comprises the steps of carrying out a first treatment on the surface of the When the proppant embedding depth is delta, the contact layer pore volume is reduced to

From this, the porosity of the support band was found to be

It can be found that when w _i When =1, i.e. when the proppant is laid in a single layer, formula (14) is degenerated to formula (7), so single layer laying is a special case when multi-layer laying, but it should be noted that the distance coefficient K cannot be greater than 1.5 when multi-layer laying, while there is no restriction on this condition when single layer laying.

In the embodiment of the invention, the values of the porosity models (7) and (14) are also assigned so as to more intuitively obtain the influence of the laying characteristics on the pore structure. Assuming a sphere particle diameter of 0.63mm, the fracture geometry L _F 、H _F 23mm and 45mm, respectively, and the crack width (w _i -1)h _i +D，h _i Obtained from equation (8).

When the number of layers of the support agent is different, the change rule of the initial porosity of the support belt (the porosity when the embedding depth is 0) along with the distance coefficient is shown in fig. 4, and fig. 4 shows the change rule of the initial porosity of the support belt along with the distance coefficient without considering the number of layers of the support belt when the support agent is embedded. As can be seen from fig. 4, the number of layers and the distance coefficient of the laying layer have a great influence on the porosity of the supporting belt, the porosity of the supporting belt tends to decrease as the number of layers increases, but the influence thereof decreases as the number of layers increases, when the number of layers is not less than 10 layers, the porosity hardly changes as the number of layers changes, and the permeability generally has a positive correlation with the porosity, that is, when the number of layers is not less than 10 layers, the influence of the number of layers on the flow conductivity is mainly reflected by changing the width of the crack. For the compact arrangement (k=1.0) the maximum porosity achieved when the single layer is laid up is about 40.7%; when the number of layers of the propping agent is more than or equal to 15, the porosity gradually reaches the minimum value, about 28 percent, and less than 70 percent when the propping agent is arranged in a single layer. On the other hand, the porosity of the support belt increases monotonically with increasing distance coefficient, and when k=1.5, the porosity is about 1.8 to 1.9 times that when k=1.0, and the porosity increases significantly.

To quantitatively discuss the effect of embedding depth on porosity, a relative porosity is defined as the ratio of the support band porosity at embedding depth δ to the porosity at δ=0, as shown in equation (15). When propping agent is arranged in a single layer or sparsely in the crack, the change rule of the relative porosity of the propping belt along with the embedding depth under the condition of different distance coefficients is shown in fig. 5, and fig. 5 shows the influence of the embedding depth on the relative porosity when the propping agent is laid in a single layer. As can be seen from fig. 5, the smaller the distance coefficient, the greater the effect of the proppant embedding depth on the relative porosity, and after the distance coefficient exceeds 1.3, the effect of the embedding depth on the relative porosity no longer changes with the change of the distance coefficient. And when K is less than or equal to 1.3, the relative porosity is reduced in an approximately exponential manner along with the embedding depth, and when K is more than 1.3, the relative porosity is attenuated in a linear manner along with the embedding depth. When δ=0.2 mm (about 31.7% of particle size), the minimum relative porosity is about 13.5% (k=1.0) and the maximum relative porosity is about 32.5% (k=1.7), it can be seen that for single or sparse arrangements, proppant intercalation will result in a sharp decrease in support band porosity.

When the proppants are laid in multiple layers (taking 10 layers as an example), the change rule of the relative porosity with the embedded depth is shown in fig. 6, and fig. 6 shows the change rule of the relative porosity with the embedded depth when the proppants are laid in 10 layers. As can be seen from fig. 6, the effect of proppant insertion depth on porosity is significantly reduced when the layers are laid up, with a minimum relative porosity of 82.2% still when δ=0.2 mm. And when K=1.1, 1.2 and 1.3, the three have no obvious difference along with the change rule of the embedding depth. Further, unlike in the case of single-layer laying, when δ is 0.1mm (about 15.9% of the particle diameter), the close arrangement is most affected by the embedding depth, and then the arrangement at a distance coefficient of 1.5 is most affected by the arrangement at k=1.3. When delta is more than or equal to 0.1mm, the arrangement condition is the arrangement condition when K=1.5, and the arrangement condition is the tight arrangement condition; this is mainly due to the fact that when the distance coefficient is large, a large number of voids exist between the propping agent and the shale wall surface contact layer, the contact layer void volume occupies the whole supporting belt void volume proportion to rise, the embedding depth is increased, the voids are rapidly reduced, and accordingly the relative porosity is obviously reduced.

The Kozeny-Carman model is a common model describing the porosity-permeability relationship of porous media materials, and the KC model is represented by the following formula:

wherein: phi is the porosity of the supporting belt, A _s To support the surface area of the belt pores, V _s To support the volume of the solid phase of the belt c ₀ Is KC constant.

In practical cases, the pore structure is in a meandering distribution, and the KC constant can be represented by the following formula:

c ₀ ＝1/2τ ² (18)

wherein: τ is the tortuosity of the pore.

When no intercalation of the proppant occurs, M _s 6/D; when the propping agent is embedded into the shale wall surface, the propping agent volume and the pore surface area can be obtained by the following formula:

A _s ＝πm _i n _i (w _i D ² -Dδ) (20)

then

If w _i When 1, the formula (21) is M in single-layer or sparse laying _s Values.

Taking equations (21), (18) into equation (16) yields a support band permeability model that takes into account proppant embedment:

in the formula (22), the parameters are known except for the tortuosity τ which needs to be further determined.

Tortuosity is an important indicator reflecting the tortuosity of a seepage channel, although the tortuosity is strictly defined in mathematics, namely the ratio of the length of an actual seepage path to the length of a seepage direction straight line. However, due to complex pore morphology, heterogeneity and the like in the actual pore structure, it is difficult to accurately obtain the change rule of tortuosity, and a great deal of researches show that the tortuosity and the porosity of the porous medium are in negative correlation, namely, the tortuosity is reduced along with the increase of the porosity, and the difficulty brought by measuring the seepage path can be avoided by constructing the relation between the tortuosity and the porosity, so that a plurality of tortuosity models are obtained in various modes such as theory, numerical value, experiment and the like in the related technology.

In the embodiment of the present invention, for the propping agent, the shape of the propping agent can be similar to spherical particles, and the porosity formed by filling is generally 0.1-0.7, so in the embodiment of the present invention, the relationship between the tortuosity and the porosity is:

τ＝1+α ₂ 1n(1/φ _f ) (23)

the supporting belt permeability considering the effects of proppant embedding and tortuosity can be obtained by taking formula (23) into formula (22):

when the number of layers of the propping agent is large, a single-layer paving model can be adopted for the contact layer with the shale wall surface, and the propping agents are still stacked in a mode similar to a single-layer paving rule in the width direction of the crack, the contact force born by each propping agent is balanced with the pressure on the regular hexagon area, as shown in fig. 7, a schematic diagram showing the geometrical relationship between the closing stress and the contact force is shown, and the relationship between the closing stress and the contact force can be represented by the formula (25) from the geometrical relationship of the propping agent is not difficult to obtain:

in the formula ：σ_c Is a closing stress.

In the embodiment of the invention, the contact area of the propping agent and shale is divided into an elastic contact area, a plastic strengthening area and a strengthening limit area, and the stress distribution of the propping agent and shale in the elastic contact area still meets the Hertz theory, the stress distribution in the plastic strengthening area has the same form in the Hertz stress distribution, but the parameters are different, and a single-particle propping agent elastoplastic embedding model is constructed based on the shale strengthening parameters and on the basis of the full-scale theory:

When the embedding depth is smaller than the critical embedding depth (delta is smaller than or equal to delta) _y )

When the depth of the embedment is greater than the critical embedment depth, but less than the shale ultimate strength depth (delta _y ≤δ≤δ _pp )

When the depth of embedment is greater than the shale ultimate strength depth (delta _pp ≤δ)

wherein ,

f represents a contact force; r represents the radius of the proppant particle; delta represents the depth of embedding, delta _y Representing a critical embedding depth; delta _pp Represents the shale ultimate strength depth, a represents the radius of the contact circle of shale and proppant particles, E ^* V is poisson's ratio, which is the integrated elastic modulus; p is p _py Is made of materialIs used as a measure of the strength of the steel,p _mc the contact pressure of the proppant particles with the shale contact center point when the rock just yields, Y is the material constant of the D-P yield criterion.

Specifically, in the embodiment of the invention, the plastic characteristics can be described by using a stress strain curve obtained by a conventional triaxial compression test.

Shale typically has a triaxial compressive stress-strain curve that can be generally characterized by 4 key points (crack closure point sigma _cc Crack initiation point sigma _ci Injury starting point sigma _cd Peak stress point sigma _p ) It is divided into 5 phases: crack closure stage (0)<σ≤σ _cc ) Stage of elastic deformation (sigma) _cc <σ≤σ _ci ) Crack stabilization and propagation stage (sigma) _ci <σ≤σ _cd ) Crack unsteady propagation stage (sigma) _cd <σ≤σ _p ) Post-peak deformation stage (sigma) _p <σ)。

In general, among the 4 key points, the peak stress point (σ _p ) As a parameter for distinguishing the integral instability of the rock, the point is taken as a distinguishing point before and after the peak to be consensus; for hard rock with high density and low porosity such as shale, the crack closing stage is not obvious, and the stage is not directly related to the characteristics of damage, plasticity, strength and the like, so the crack closing point (sigma) can be ignored in shale _cc ) Is a function of (a) and (b). The inflection point of the volume change is used as a critical point for the transition of the microcrack from stable expansion to unstable expansion, and therefore, the point can be used as a damage starting point (sigma _cd ). Crack initiation point (sigma) _ci ) There is no significant feature on the stress-strain curve, precisely, σ _ci Almost impossible, but sigma _ci As the end point of the linear elastic phase, the end point of the linear segment is generally regarded as the initial yield point in plastic mechanics, so that although the crack start point and the initial yield point are physically different, both values reflect the linear elastic phase of the rock materialThe state of transition to the nonlinear phase, it can be seen that this value has significance for building strength criteria for rock, engineering design, etc.

In the deformation and destruction process of the rock, if the influence of an external heat source is not considered, the work of the rock by the external force is converted into elastic strain energy, plastic deformation energy, surface energy and the like. From the first law of thermodynamics, it is known that:

U＝U ^d +U ^e

wherein U is the density of the external input strain energy, U ^d Dissipation energy density, energy dissipation mainly due to plastic deformation and damage, U ^e Is the elastic strain energy density.

The external input strain energy density is given by:

elastic strain energy density U ^e From generalized hooke's law:

defining an energy dissipation ratio U ^r To dissipate energy density U ^d And the ratio of the input total strain energy density U.

When the energy dissipation ratio reaches a minimum value, the crack starting point of the material is:

in the micro-defect closing stage, part of the work done by the external force is converted into elastic strain energy to be stored in the rock sample, part of the elastic strain energy is dissipated due to the micro-defect closing, and the elastic strain energy and the dissipation energy are synchronously increased, but the elastic strain energy is mainly increased. In the elastic stage, the existing microdefect of the rock sample is basically closed, the new microdefect is not generated, the work done by the external force is completely converted into elastic strain energy, the change characteristic of the dissipation energy along with the axial strain in the stage is a straight line approximately parallel to the coordinate axis, and the energy dissipation ratio is continuously reduced; when the elastic phase is finished, new micro defects start to be generated, part of work done by external force is dissipated in the forms of plastic deformation energy, surface energy and the like, namely, the dissipation energy starts to be newly increased, and along with the increase of stress, the increase speed of the dissipation energy is gradually increased until the dissipation energy is destroyed, and at the end point of the elastic phase, the energy dissipation ratio reaches a minimum value.

No matter how the rock deforms and the energy evolves, the energy dissipation caused by plastic deformation, damage and the like is basically still the initiation and evolution of the microdefect, that is, the evolution of the microdefect determines the trend of dissipation energy, and in the embodiment of the invention, the end point of the straight section of the dissipation energy is taken as the crack starting point; since the end point of the dissipation energy flat section is still affected by human factors, the minimum point of the energy dissipation ratio is used as the crack starting point (sigma _ci ). In the embodiment of the invention, the crack initiation point (sigma _ci ) The determined fracture initiation strength is taken as the initial yield point of the shale.

In the embodiment of the invention, the initial yield point sigma is obtained through a triaxial compression test of shale ₁ 、σ ₃ Converted into I1, J ₂ The D-P straight line fitting indication of the shale initial yield points with different bedding inclination angles can be obtained. Furthermore, according to the invention, the alpha of shale with 0 degree, 30 degree, 60 degree and 90 degree is 0.1096, 0.0817, 0.1527 and 0.114 respectively, and Y is 37.44MPa, 43.33MPa, 28.52MPa and 48.06MPa respectively.

Ignoring crack closure stress (sigma _cc ) The influence on the plasticity of the material is unified and considered in a crack stable expansion stage and a non-stable expansion stage, so that the stress-strain curve of shale can be simply divided into a linear elastic section, a nonlinear strengthening section and a damage softening section; in proppant embedment problems, the effects of shale softening may not be considered, then only the elastic and reinforcing sections of shale may be considered. Can be simply put by the theory of total plastic The stress-strain curve of shale is given by:

wherein: sigma is stress; sigma (sigma) _s Is the yield stress of the material; b, m is the power hardening coefficient of the material, since the stress strain point is at σ=σ _s The process is continuous, so that B, m only has one independent quantity, m is taken as an independent variable, the value range of m is 0-1, m=0 is an ideal elastoplastic material, and m=1 is an elastic material.

By analyzing the shale stress-strain curve of the embodiment, the key mechanics of shale for analyzing the analysis of the elastic-plastic embedding model of the propping agent can be obtained as shown in the following table:

therefore, in the embodiment of the invention, the embedding depth of the propping agent can be calculated.

Substituting formulas (26) - (28) into (25) and introducing a factor that increases proppant insertion depth due to inter-particulate interference: equation (29) can obtain the relation between the closing stress and the embedding depth after the proppants are elastoplastically embedded under different paving characteristics.

K _R ＝AK ^-C (29)

in the formula ：K_R For embedding depth enhancement coefficients, A, C is a fitting parameter, for embodiments of the present invention, a=1.14, c=0.179 is preferable

As shown in fig. 8, which shows the law of change of embedding depth with closing stress (θ=0°), the graph shows the law of change of embedding depth with closing stress in order of k=1.0, 1.1, 1.2, 1.3, 1.4, and 1.5 from left to right, and it is known that the smaller the distance coefficient between proppants is, the smaller the embedding depth is under the same closing pressure, and the more the inter-particle interference is caused when the distance between proppants is smaller, the more the proppant particles are arranged in a unit area, and the smaller the contact force is caused when the proppants are arranged closely, so that the influence of embedding of the proppants is reduced when the proppants are arranged closely. It should be noted, however, that the proppants are difficult to make k=1.0 during the laying process, and that a certain distance must exist between the proppants. As can be seen from fig. 8, when the closing pressure is 60MPa, the average particle diameter of the proppant is about 0.63mm (20/40 mesh), the embedding depth at k=1.0 is about 0.1mm, and when K is 1.1, 1.2, 1.3, 1.4, 1.5, respectively, the embedding depths are 0.12, 0.14, 0.16, 0.18, 0.21mm, respectively, and it can be seen that the distance coefficient can cause an increase in the embedding depth by at most 110%. If the influence of the distance coefficient is not considered in the practical engineering application, the embedding amount of the propping agent is inevitably underestimated, and the crack width is overestimated, so that adverse effects are brought to the aspects of propping agent type selection, fracturing construction and the like.

As can be seen from equation (9), the initial seam width of the seam can be expressed as W _F ＝(w _i -1)h _i +D, when proppant is embedded in delta, its fracture width can be expressed as

W _f ＝(w _i -1)h _i +D-2δ (30)

According to the definition of the diversion capability, the diversion capability of the propping agent laying characteristics and the elastoplastically embedded propping type cracks is considered as

In the embodiment of the invention, the support type crack flow conductivity determination model (formula 31) with the support agent laying characteristics and the elastoplastic embedding is also verified, and the method is specifically as follows:

in order to measure the influence of proppant embedding on permeability, in the embodiment of the present invention, gas seepage upper end shale and die steel (HRC 55) are processed into a thick-wall cylindrical structure with an outer diameter of 50mm, an inner diameter of about 5mm and a height of about 50mm, and the lower end is processed into a cylindrical structure with a diameter of 50mm and a height of about 50mm (the shale layer adopted in the embodiment of the present invention has an inclination angle of 0 °, and will not be described in detail below). Laying 1.3kg/m between the upper and lower sections of the test piece ² And 9.0kg/m ² Is 20/40 mesh, wherein the laying concentration is 1.3kg/m ² When the number of the laying layers is verified to be about 1; then, a steel wire mesh and a heat shrinkage film are sequentially wrapped outside the test piece to prevent the confining pressure oil from leaking into the test piece, as shown in fig. 9, fig. 9 shows a schematic diagram of the supporting belt permeability test principle (black dotted lines in the figure are the flow paths of the fluid). The test piece is arranged in a TOP2518 rock mechanics comprehensive test system, confining pressure is applied to 5MPa by using a confining pressure pump at a speed of 2MPa/min, axial pressure is applied to 5, 10, 15, 25, 35, 45, 55 and 65MPa by using an axial pressure pump, the change rule of the permeability is measured in real time by using nitrogen as a permeation medium, and in the process, the change condition of displacement is measured in real time by using a high-precision LVDT.

When the mold steel test piece in fig. 9 is replaced by shale, the displacement of the mold steel test piece is subtracted from the displacement data of the shale, so that the embedding depth of the propping agent under the action of different closing pressures can be obtained.

Since the distance coefficient K is not known in advance, it is often obtained by back-pushing it only by the indentation position afterwards. The related technology proposes: the method comprises the steps of paving 20/40 mesh propping agent (ceramsite) between two shale discs with the diameter of 25.4mm, exploring the embedding behavior of the propping agent by applying axial compression, obtaining the indentation condition of the propping agent by using a three-dimensional morphology instrument, and randomly selecting 4 line segments in a morphology graph, wherein the result shows that the length of the 4 line segments is 2.45-2.74 mm, each line segment comprises 2-3 indentation points, namely the inter-particle distance coefficient of the propping agent is about 1.2-1.4, and the average value is 1.34. Thus, in embodiments of the present invention, the proppant inter-particle distance coefficient laid down is approximately 1.34.

By combining equations (25) - (28) and letting k=1.34, the relation between the proppant embedding depth and the closure stress considering the laying characteristics and elastoplastic embedding behavior can be obtained, as shown in fig. 10, which shows the relation between the proppant embedding depth and the closure stress in the result of the proppant embedding depth model verification, in which point-like data are the embedding depths obtained by the test. As can be seen from FIG. 10, when σ _c <When the closing stress is higher than 30MPa, the agreement between the experimental value and the theoretical value is higher, which is mainly formed by the fact that the theoretical predicted value and the experimental value are larger, and the experimental measured embedding depth is slightly lower than the theoretical valueAt the low stress level, the embedding amount of the propping agent is low, and at the moment, the deformation amount of the connecting part of the test system is large, so that the test error at the stage is large, the embedding amount is difficult to accurately obtain, and the actually measured embedding amount is low. However, when the stress level is higher, the embedding amount of the propping agent is increased, the test error is effectively reduced, and when the closing stress is more than 30MPa, the difference between the theoretical value and the laboratory is about 0.2-10.2%; therefore, the model provided by the embodiment of the invention can be used for predicting the rule of the elastoplastic embedding depth and the closing stress of the propping agent better.

Using equation (31), and letting k=1.34, the relationship between the propped fracture conductivity and the closing pressure considering the proppant embedding and placement characteristics can be obtained, as shown by the solid lines in fig. 11 and 12, where fig. 11 shows the relationship between the propped fracture conductivity and the closing pressure for the single layer placement characteristics, and fig. 12 shows the relationship between the propped fracture conductivity and the closing pressure for the multiple layer placement characteristics, where the point-like data is the conductivity tested by the test.

For single layer, the measured test data can be directly utilized; however, in the case of multilayer placement, since the problem of proppant placement is only considered in the formula (31), the data measured at the time of the experiment is the permeability value of the comprehensive influence of proppant compaction, placement, etc., and therefore, in order to avoid the influence of proppant compaction, correction of the measured data is required, and the correction formula is that

in the formula ：k_δ In order to only consider the permeability of the proppant during embedding, k is the permeability under the comprehensive influence of compaction, embedding and the like of a proppant-shale system, and k _y Permeability, k, for the combined effects of compaction, embedding, etc. of proppant-die steel systems ₀ Is the initial permeability of the proppant-die steel system.

The permeability calculated by equation (32) is multiplied by the measured fracture width after the change to obtain fracture conductivity data when the proppant is multi-layered, as shown in the dotted data in fig. 12.

As can be seen from fig. 11, the change rule of the propping fracture conductivity with the closing stress can be better explained by using the model proposed herein, no matter the propping agent is laid in a single layer or in multiple layers. In FIG. 12, when σ _c <At 20MPa, the actual measured flow conductivity change rule and the theoretical predicted value have large difference, which is mainly due to large proppant embedding test error under the condition of low stress level.

Meanwhile, after the elastic-plastic embedding of the propping agent and the inter-particle distance coefficient are considered, the change rule of the fracture conductivity along with the closing stress is shown in fig. 13 and 14, wherein fig. 13 shows the influence of the distance coefficient K on the fracture conductivity of the propping agent under the condition that the propping agent is paved in a single layer in the fracture, wherein point-shaped data from bottom to top show the change rule of the fracture conductivity along with the closing stress under the condition that k=1.0, 1.1, 1.2, 1.3, 1.4 and 1.5 are respectively shown, and fig. 14 shows the influence of the distance coefficient K on the fracture conductivity along with the closing stress under the condition that k=1.0, 1.1, 1.2, 1.3, 1.4 and 1.5 are respectively shown in point-shaped data from bottom to top. As can be seen from fig. 13, when the proppants are laid up in a single layer in the fracture, and σ _c <At 40MPa, under the same closed stress condition, the larger the inter-particle coefficient is, the higher the flow conductivity of the crack is, and the main reason is that when the inter-particle coefficient is increased, the gaps among proppants are increased, so that the permeability of the propped belt is increased. But when sigma _c >After 40MPa, the flow conductivity at k=1.4 or 1.5 is gradually lower than that at k=1.2 or 1.3, but still greater than that at k=1.0 or 1.1. When the closing stress further increases to 70, 80, 90MPa, the conductivity of k=1.5, 1.4, 1.3 decreases to 0, respectively, i.e. fracture failure. And when the closing stress exceeds 150, 120 and 100MPa, respectively, the propped cracks with K=1.0, 1.1 and 1.2 gradually fail. It can be seen that at low closure stress levels, increasing the inter-particle distance of the proppant can dramatically increase the fracture conductivity, e.g., σ _c At=20 MPa, the flow conductivity of k=1.5 is about 42 times that of k=1.0; however, as the distance coefficient increases, the contact force to which the single proppant is subjected increasesAt high closure stress levels, proppant embedment is more pronounced, and both the width of the fracture and the permeability of the support belt drop dramatically, resulting in rapid drop in fracture conductivity until failure. Furthermore, for the case of single-layer laying, and sigma _c <At 100MPa, an appropriate increase in proppant inter-particle distance has a positive impact on improving fracture conductivity, as is the case for fractures with k=1.2, where the conductivity is significantly higher than k=1.0.

As can be seen from fig. 14, when the proppants are laid in layers in the fracture, the fracture has the highest conductivity at any closure stress level when the closure stress is not more than 100MPa, k=1.4, but the fracture has a higher conductivity when k=1.3 after the closure stress reaches 100 MPa. It can be seen that proper increase in the distance between proppant particles, regardless of the concentration of proppant pack in the fracture, helps to increase the conductivity of the fracture. The fracture conductivity is lower when the propping agent particles are closely arranged, but the fracture conductivity is favorable to be maintained under the high closed stress environment.

To further investigate the effect of proppant placement concentration on conductivity, assume k=1.34, the number of fracture proppant placement layers was 1, 3, 5, 7, 10 layers, respectively (placement concentrations of about 1.3, 4, 6.5, 9, 13kg/m ² ) When the fracture conductivity is as shown in fig. 15, fig. 15 shows the influence of the number of proppant placement layers on the fracture conductivity (k=1.34), wherein the point-like data from bottom to top show the change rule of the conductivity with the closing stress in the case of the number of proppant placement layers=1, 2, 3, 5, 7, 10, respectively. As can be seen from FIG. 15, when σ _c >After 20MPa, the higher the proppant placement concentration, the higher the fracture conductivity. But when sigma _c <At 20MPa, the flow conductivity of the single layer of the propping agent is higher than that of the 3 layers of propping agent, and even higher than that of 7 layers of propping agent under the condition of lower stress level. Therefore, under the condition of high closure stress, the laying concentration of the propping agent is improved as much as possible so as to reduce the damage of the propping agent embedding to the fracture conductivity; however, when the closing stress is low, the construction process is combined, and the optimal paving concentration exists for different distance coefficients K instead of pavingThe higher the concentration, the better.

Based on the above exploration, the embodiment of the invention provides a method for determining the flow conductivity of a support type crack by considering elastoplastic embedding, which comprises the following steps:

The propping fracture conductivity was determined using the following:

Alternatively, the support band porosity φ is determined using _f ：

Alternatively, n is calculated using the formula _i ：

Alternatively, m is calculated using the formula _i ：

The representation function takes an integer down, K being the distance coefficient.

Alternatively, w is calculated using the formula _i ：

Based on the same inventive concept, the embodiment of the invention also provides a supporting type crack flow conductivity determining device considering elastoplastic embedding, which comprises:

Alternatively, the support band porosity φ is determined using _f ：

Alternatively, n is calculated using the formula _i ：

Alternatively, m is calculated using the formula _i ：

Alternatively, w is calculated using the formula _i ：

Based on the same inventive concept, an embodiment of the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and capable of running on the processor, where the processor implements the steps in the method for determining a propping fracture conductivity considering elastoplastic embedding according to any one of the embodiments described above when executing the computer program.

Based on the same inventive concept, an embodiment of the present invention provides a computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements the steps in the method for determining a propped fracture conductivity taking into account elastoplastic embedding described in any of the above embodiments.

In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described by differences from other embodiments, and identical and similar parts between the embodiments are all enough to be referred to each other.

It will be apparent to those skilled in the art that embodiments of the present invention may be provided as a method, apparatus, or computer program product. Accordingly, embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the invention may take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. 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 passive device oriented electromagnetic response optimizing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable passive device oriented electromagnetic response optimizing terminal device, 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 passive device-oriented electromagnetic response optimization terminal device 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 passive device-oriented electromagnetic response optimization terminal device to cause a series of operational steps to be performed on the computer or other programmable terminal device to produce a computer implemented process such that the instructions which execute on the computer or other programmable terminal device provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiment and all such alterations and modifications as fall within the scope of the embodiments of the invention.

Finally, it is further noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or terminal device comprising the element.

The above description is made in detail of a method and a product for determining the flow conductivity of a supporting crack by considering elastoplastic embedding, and specific examples are applied to illustrate the principles and embodiments of the present invention, and the above examples are only used to help understand the method and core idea of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.

Claims

1. The method for determining the flow conductivity of the propped fracture taking into consideration elastoplastic embedding is characterized by comprising the following steps of:

the propping fracture conductivity was determined using the following:

2. The method for determining the conductivity of a propped fracture taking into account elastoplastic embedding of claim 1, wherein the porosity Φ of the propped band is determined using the formula _f ：

3. The method for determining the conductivity of a propped fracture taking into account elastoplastic embedding of claim 1, wherein n is calculated using the formula _i ：

4. The method for determining the conductivity of a propped fracture taking into account elastoplastic embedding of claim 1, wherein m is calculated using the formula _i ：

5. The method for determining the conductivity of a propped fracture taking into account elastoplastic embedding of claim 1, wherein w is calculated using the formula _i ：

6. A propped fracture conductivity determination device considering elastoplastic embedding, the device comprising:

the determining module is used for determining the supporting type crack flow conductivity:

7. The device for determining the conductivity of a propped fracture taking into account elastoplastic embedding of claim 6, wherein the porosity Φ of the propped band is determined using the following method _f ：

8. The device for determining the conductivity of a propped fracture taking into account elastoplastic embedding of claim 6, wherein n is calculated using the formula _i ：

9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method for determining the propped fracture conductivity taking into account elastoplastic embedding of any one of claims 1-5 when executing the computer program.

10. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method for determining the conductivity of propped fracture taking into account elastoplastic embedding as claimed in any one of claims 1 to 5.