A method for predicting the embedding depth of proppants considering the elastoplastic deformation process

Abstract

This invention relates to a method for predicting proppant embedding depth considering elastoplastic deformation processes, comprising the following steps: Step 1, based on the elastoplastic deformation law of proppant and rock, the contact deformation between proppant and rock is divided into three stages, namely, an elastic stage, an elastoplastic stage, and a plastic stage; Step 2, proppant embedding depth prediction models are established for the three extremes of the elastic, elastoplastic, and plastic stages of the contact deformation between proppant and rock; Step 3, by incorporating geostress conditions, proppant physical properties, and rock physical properties, the deformation stage to which the proppant belongs is determined, and the proppant embedding depth is predicted. The method provided by this invention can consider the influence of rock elastoplastic deformation on proppant embedding, and has reference value for subsequent research on fracture conductivity.

Description

Technical Field

[0001] This invention relates to the field of oil and gas engineering technology, and in particular to a method for predicting proppant embedding depth considering elasto-plastic deformation processes. Background Technology

[0002] my country has a large proportion of unconventional oil and gas resources, but these are generally characterized by high development difficulty and low production efficiency. Hydraulic fracturing technology has a significant effect on the development and production enhancement of unconventional oil and gas reservoirs. Hydraulic fracturing can create an artificial fracture with high conductivity underground, making oil and gas flow more easily. Among these factors, proppant embedding is a direct factor affecting the fracture stimulation effect.

[0003] With the vigorous advancement of oil and gas exploration and development, unconventional methods such as shale are playing an increasingly important role in reservoir development. As formation depth increases, the confining pressure and temperature of the rocks also increase, leading to more pronounced plasticity. However, there are currently few case studies on the influence of elastoplastic deformation on proppant embedding, resulting in an incomplete understanding of the impact of rock elastoplastic deformation on proppant embedding. Therefore, analyzing the influence of different factors on proppant embedding under elastoplastic deformation conditions is of great significance. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting proppant embedding depth considering the elastoplastic deformation process, so as to provide guidance for the study of the influence of proppant embedding in the elastoplastic deformation process of rocks.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for predicting proppant embedment depth considering elastoplastic deformation processes includes the following steps:

[0007] Step 1: Based on the elastic-plastic deformation law of proppant and rock, the contact deformation of proppant and rock is divided into three stages, namely the elastic stage, the elastic-plastic stage and the plastic stage.

[0008] Step 2: Establish proppant embedding depth prediction models for the three extreme stages of proppant-rock contact deformation: elastic stage, elastoplastic stage, and plastic stage.

[0009] Step 3: Input the geostress conditions, proppant physical properties and rock physical properties to determine the deformation stage of the proppant and predict the proppant embedment depth.

[0010] Preferably, the proppant embedding depth prediction model in step two is:

[0011]

[0012] Where d is the proppant embedding depth; P c The pressure exerted on the rock; E * R is the effective elastic modulus; P is the proppant radius; c E2 is the closing pressure; E2 is the rock elastic modulus; D is the initial width of the rock.

[0013] Preferably, the proppant embedding depth prediction model in step two during the elastoplastic stage is as follows:

[0014]

[0015] Where, σ y δ1 represents the rock yield strength; δ2 represents the maximum embedment depth in the elastic stage; and δ3 represents the critical value of the embedment depth in the plastic stage.

[0016] Preferably, the proppant embedding depth prediction model in step two is:

[0017]

[0018] Where P is the contact pressure.

[0019] Preferably, the proppant properties in step three include proppant particle size, elastic modulus, and Poisson's ratio.

[0020] Preferably, the rock physical properties in step three include the rock elastic modulus, Poisson's ratio, and initial width.

[0021] Based on the same inventive concept, this invention provides a proppant embedding depth prediction system that considers the elastoplastic deformation process, comprising:

[0022] The elastic-plastic deformation classification module divides the contact deformation between the proppant and the rock into three stages based on the elastic-plastic deformation law of the proppant and the rock. The three stages include the elastic stage, the elastic-plastic stage and the plastic stage.

[0023] The model building module is used to build proppant embedding depth prediction models for the three extreme stages of proppant-rock contact deformation: elastic stage, elastoplastic stage, and plastic stage.

[0024] The judgment and prediction model is used to input geostress conditions, proppant physical parameters and rock physical parameters to determine the deformation stage of the proppant and predict the proppant embedment depth.

[0025] On the other hand, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, when the processor executes the computer program, it implements the steps of the proppant embedding depth prediction method considering the elastoplastic deformation process described in any of the preceding claims.

[0026] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of the proppant embedding depth prediction method considering the elastoplastic deformation process described in any of the preceding claims.

[0027] According to specific embodiments provided by the present invention, the present invention has the following technical effects: the method provided by the present invention divides the proppant embedding process into three stages: elastic embedding stage, elastoplastic embedding stage (with simultaneous elastic deformation and plastic deformation), and plastic embedding stage. It can take into account the influence of rock elastoplastic deformation on proppant embedding, which is of reference significance for subsequent research on fracture conductivity. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the contact between two elastic balls;

[0030] Figure 2 This is a schematic diagram of the contact between an elastic sphere and an elastic plane.

[0031] Figure 3 A schematic diagram showing the three stages of contact deformation between the rock mass and the proppant;

[0032] Figure 4 This is a graph showing the relationship between average contact stress and embedment amount.

[0033] Figure 5 Stress analysis diagram of proppant particles;

[0034] Figure 6 This is a comparison chart of the verification results of the model of this invention and the Li Kewen proppant embedding model;

[0035] Figure 7 A graph showing the relationship between the proppant-rock receding distance and the closure pressure;

[0036] Figure 8 A graph showing the relationship between proppant embedment depth and closure pressure;

[0037] Figure 9 This is a graph showing the relationship between the proppant-rock indentation distance and the proppant particle size.

[0038] Figure 10 This is a graph showing the relationship between proppant embedding depth and proppant particle size.

[0039] Figure 11 A graph showing the relationship between the proppant-rock indentation distance and the proppant's elastic modulus;

[0040] Figure 12 A graph showing the relationship between proppant embedding depth and proppant elastic modulus;

[0041] Figure 13 A graph showing the relationship between the proppant-rock indentation distance and the rock's elastic modulus;

[0042] Figure 14 A graph showing the relationship between proppant embedment depth and rock elastic modulus;

[0043] Figure 15 This is a graph showing the relationship between the proppant-rock indentation distance and the proppant's Poisson's ratio.

[0044] Figure 16 A graph showing the relationship between proppant embedding depth and proppant Poisson's ratio;

[0045] Figure 17 A graph showing the relationship between the proppant-rock indentation distance and the rock's Poisson's ratio;

[0046] Figure 18 This is a graph showing the relationship between proppant embedment depth and rock Poisson's ratio. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The purpose of this invention is to provide a proppant embedding depth prediction method that considers the elastoplastic deformation process, so as to solve the deficiency in the prior art of lacking research on the influence of rock elastoplastic deformation on proppant embedding.

[0049] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] To study the proppant embedding behavior in rock, the contact relationship between two elastic spheres was first derived based on Hertzian contact theory. The contact relationship diagram between the two elastic spheres is shown in the figure below. Figure 1 As shown.

[0051] The relationship between the force between two elastic spheres and the radius of the contact circle is as follows:

[0052]

[0053] In the formula: F is the applied force, and the unit is N;

[0054] P 0 This represents the maximum pressure distributed on the contact circle, expressed in Pa.

[0055] α is the radius of the boundary of the contact circle region, in meters.

[0056] When the contact between two elastic spheres is in an elastic state, the expressions for the boundary radius and indentation depth of their contact area are as follows:

[0057]

[0058] In the formula: α is the radius of the boundary of the contact circle region, in meters;

[0059] P max This represents the maximum pressure distributed on the contact circle, expressed in Pa.

[0060] R * The effective radius is expressed in meters (m).

[0061] E * The effective elastic modulus is expressed in Pa.

[0062] Where R is defined * :

[0063]

[0064] Define E * :

[0065]

[0066] In the formula: R1 and R2 are the radii of the two elastic spheres, in meters;

[0067] v1 and v2 are Poisson's ratios of two elastic spheres, which are dimensionless.

[0068] E1 and E2 are the elastic moduli of the two elastic spheres, with units of Pa.

[0069] Based on the above calculation formula, the relationship between the interaction force between two elastic spheres, the radius of the contact circle, and the indentation depth can be derived as follows:

[0070]

[0071] In the formula: F is the applied force, and the unit is N;

[0072] δ represents the indentation depth, measured in meters (m).

[0073] Based on the contact solution between two elastic spheres, we can deduce the solution between the elastic sphere and the plane.

[0074] When the radius of the elastic sphere 2 in the above contact conditions approaches infinity, the elastic sphere 2 transforms from an elastic sphere facing an elastic plane. The two contacting objects also change from mutually contacting elastic spheres to mutually contacting an elastic sphere and an elastic plane. The contact relationship between the elastic sphere and the elastic plane is described in [the following text is incomplete and requires further context]. Figure 2 .

[0075] The relationship between the force between the elastic sphere and the elastic plane and the radius of the contact circle and the indentation depth is as follows:

[0076]

[0077] In the formula: F is the applied force, and the unit is N;

[0078] E * This is the effective elastic modulus, expressed in Pa.

[0079] R is the radius of the elastic sphere, in meters (m).

[0080] δ represents the indentation depth, measured in meters (m).

[0081] The radius 'a' of the contact area boundary, the indentation depth 'δ', and the maximum contact pressure 'P' distributed on the contact circle. max The expression is:

[0082]

[0083]

[0084]

[0085] In the formula: F is the applied force, and the unit is N;

[0086] R is the radius of the proppant, in meters (m).

[0087] 'a' represents the radius of the circle formed by the contact area, measured in meters (m).

[0088] The relationship between the average contact pressure and the maximum contact pressure of the contact circle is as follows:

[0089]

[0090] During the process of proppant embedding into rock mass, such as Figure 3 As shown, this can be described as a contact mechanics problem between an elastic sphere and an elastic plane under a normal load. Specifically, as the proppant embedment depth increases, the local deformation at the contact point between the rock mass and the proppant undergoes three stages: elastic, elastoplastic, and plastic. The relationship between the proppant embedment depth and the average contact stress is shown in the figure. Figure 4 As shown.

[0091] During the elastic embedding stage, the stress conditions of the crack wall and proppant particles are shown in [the diagram]. Figure 5 As shown.

[0092] Relationship between load and stress of proppant particles:

[0093] P c A f =P s MNA s (11)

[0094] A f =4MNR 2 (12)

[0095] A s =πα 2 (13)

[0096] In the formula: P c The closing pressure is expressed in Pa.

[0097] P s The pressure exerted by a single proppant on the rock, measured in Pa.

[0098] A f The area of ​​the crack is measured in m². 2 ;

[0099] A s The contact area of ​​a single proppant particle, in m². 2 .

[0100] The pressure P exerted by a single proppant on the rock can be obtained from the above formula. s :

[0101]

[0102] In summary, the embedment depth δ between the proppant and the rock can be calculated as follows:

[0103]

[0104] In the formula: δ is the contact depth, in meters (m);

[0105] R is the radius of the proppant particles, in meters (m).

[0106] Ignoring rock damage, let the rock stratum be D: The rock stratum deforms under closed pressure, and the deformation is calculated using Hooke's Law:

[0107]

[0108] In the formula: D is the initial width of the rock strata, in meters;

[0109] P c The pressure exerted on the rock, measured in Pa;

[0110] E2 is the elastic modulus of rock, measured in Pa.

[0111] Therefore, the total embedding of the proppant is:

[0112]

[0113] In the formula: P c The pressure exerted on the rock, measured in Pa;

[0114] R is the radius of the proppant particles, in meters (m).

[0115] As the indentation increases, the elastic behavior continues until the object yields. According to the Tresca yield criterion or the von Mises yield criterion, the average pressure at the onset of yielding is 1.1 times the rock yield strength, i.e., p = 1.1σ. y At this point, the rock ceases its elastic behavior.

[0116] In the elastic stage, according to Hertz theory and the fundamentals of elasticity, the relationship between the proppant embedment depth and the average contact stress is as follows:

[0117]

[0118] Therefore, according to equation (2.15), the maximum embedding depth is:

[0119]

[0120] In the formula: δ1 is the maximum embedding depth in the elastic stage, in meters;

[0121] σ v The rock yield stress is expressed in Pa.

[0122] R is the radius of the proppant particles, in meters (m).

[0123] During the plastic embedding stage, for an elastic sphere made of a material with a yield limit, when the contact stress reaches the Brinell hardness of the material, the material begins to undergo plastic deformation, entering the plastic deformation stage, and is governed by the following conditions:

[0124]

[0125] In the formula: This represents the maximum contact pressure on the contact circle during the initial stage of plastic deformation, expressed in Pa.

[0126] σ y The yield strength of the material is expressed in Pa.

[0127] ψ and ε are dimensionless parameters.

[0128] The parameter ψ basically corresponds to the ratio of the material's Brinell hardness to its yield strength, and its range is between 2.6 and 3.0.

[0129] For rock materials, the contact stress that remains constant during the plastic stage is generally considered to be three times the yield stress, i.e.:

[0130] σ p =3σ y (twenty one)

[0131] During the plastic stage, the relationship between the embedding depth and the contact radius is as follows:

[0132]

[0133] When the fully plastic state begins, the pressure on the contact surface is approximately uniform, and the load increases linearly with the increase of the contact area. By integrating and other methods, the relationship between the applied pressure and the embedding depth during the plastic stage can be obtained:

[0134] F = F P +K(δ-δ p ) (twenty three)

[0135] After transformation, we obtain:

[0136]

[0137] Wherein: F P The contact pressure of the contact circle at the beginning of the plastic stage, expressed in Pa.

[0138] k is a dimensionless constant = 2πRψσ y Rock materials are generally k = 6πRσ y ;

[0139] δ P This represents the critical depth of the plastic stage, expressed in meters (m).

[0140] The critical value for proppant plastic embedding can be derived from equations (2.2) and (2.21):

[0141]

[0142] The parameter ε corresponds to the geometric relationship required to describe the moment when the pressure on the contact surface is approximately uniform. For the contact between spheres made of the same material, ε ∈ [13, 20]. For solid materials such as rocks, theoretical and experimental studies have shown that the critical embedment depth at which plastic deformation begins is generally 82.5 times the maximum embedment depth in the elastic stage (the actual embedment depth should be determined experimentally).

[0143] Therefore, based on the relationship between the proppant embedment depth in the rock and the average contact stress, the embedment depth of the proppant in the initial plastic stage of rock embedding can be derived as follows:

[0144]

[0145] Based on the above formulas, the relationship between the degree of proppant embedding and the contact pressure during the plastic stage is as follows:

[0146]

[0147] The variation in rock strata is still expressed using Hooke's Law:

[0148]

[0149] In the formula: D is the initial width of the rock strata, in meters;

[0150] P c The pressure exerted on the rock, measured in Pa;

[0151] E2 is the elastic modulus of rock, measured in Pa.

[0152] The total embedding during the plastic stage is then:

[0153]

[0154] In the formula: σ v The yield strength of the rock is expressed in Pa.

[0155] When both elastic and plastic deformation occur during the embedding stage, the embedding is in the elasto-plastic stage. The proppant embedding depth lies between the end of the elastic phase and the beginning of the plastic phase, i.e., δ. e <δ<δ p However, the mechanical mechanism is quite complex at this point.

[0156] The relationship between the average contact pressure and the amount of deformation in elastoplastic deformation is as follows:

[0157] P=α1+α2lnδ (30)

[0158] In the formula: a1 and a2 are dimensionless factors.

[0159]

[0160]

[0161] P p and P e Substituting into the formula, we get:

[0162]

[0163]

[0164] In the formula: δ1 and δ2 are the critical embedment depths between the rock and the proppant in the elastic and plastic stages, respectively, in meters.

[0165] Substituting equations (33) and (44) into equation (30) and making changes, we can obtain the relationship between the embedment depth and the contact stress on the proppant:

[0166]

[0167] The deformation of the rock strata is:

[0168]

[0169] In the formula: D is the initial width of the rock strata, in meters;

[0170] P c The pressure exerted on the rock, measured in Pa;

[0171] E2 is the elastic modulus of rock, measured in Pa.

[0172] The total embedding in the elastoplastic stage is then:

[0173]

[0174] After obtaining the prediction formulas for the embedding depth of the three stages—elastic embedding, plastic embedding, and elastoplastic embedding—in order to verify the accuracy of the model of the present invention, the relevant factors of plasticity in the model of the present invention were adjusted to have no effect, and the calculation results were compared with those of Li Kewen's proppant embedding model that did not consider the plasticity of rock (Li, KW, Gao, YP, Lyu, YC, et al. New Mathematical Models for Calculating Proppant Embedment and Fracture Conductivity.[J]. SPE Journal,2015,20(3):496-507).

[0175] Based on the basic data of the rock, calculations were performed on Li Kewen's model without considering the influence of plasticity and the degraded model in this paper. The basic parameters for calculation were: Poisson's ratio of proppant to rock was 0.13, elastic modulus of proppant was 21306 MPa, elastic modulus of rock was 1172 MPa, proppant particle size R was 0.3175, and rock layer thickness was 20 mm.

[0176] Substituting the aforementioned basic parameters of the rock and proppant, we obtain a comparison between the degradation model of this application and Li Kewen's proppant embedding model that does not consider the influence of rock plasticity, as follows: Figure 6 As shown, it can be seen that the results obtained after the model degradation in this application are the same as those obtained by Li Kewen's proppant embedding model, therefore the model in this application is feasible.

[0177] To analyze the influence of proppant embedding depth, the embedding depth was calculated using closure pressure, particle size, elastic modulus, and Poisson's ratio.

[0178] (1) Closing pressure

[0179] Calculations were performed under the following conditions: rock elastic modulus of 40000 MPa, proppant elastic modulus of 40000 MPa, Poisson's ratio of rock and proppant of 0.20, proppant particle size of 0.4 mm, and rock thickness of 20 mm. The calculation results... Figure 7 It can be seen that as the closing pressure increases, the depth of indentation between the proppant and the rock also increases.

[0180] In the elastic stage, yield strength has no effect on the proppant retraction distance. With a yield strength of 20 MPa, the proppant enters the elastoplastic stage at a closing pressure of 22 MPa; with a yield strength of 25 MPa, it enters the elastoplastic stage at a closing pressure of 27.5 MPa; with a yield strength of 30 MPa, it enters the elastoplastic stage at a closing pressure of 33 MPa; and with a yield strength of 35 MPa, it enters the elastoplastic stage at a closing pressure of 38.5 MPa. The lower the yield strength, the faster the proppant reaches the elastoplastic stage, and the greater the retraction distance in the elastoplastic stage.

[0181] Depend on Figure 8 It can be seen that as the closing pressure increases, the embedment depth between the proppant and the rock also increases. In the elastic stage, the yield strength has no effect on the proppant embedment distance; in the elastoplastic stage, the smaller the yield strength, the faster the proppant reaches the elastoplastic stage, and the greater the proppant embedment depth.

[0182] It can be seen that the greater the closing pressure, the greater the proppant recess depth and proppant embedment depth; the smaller the yield strength, the greater the proppant recess depth and proppant embedment depth.

[0183] (2) Particle size

[0184] Under the conditions of a closing pressure of 25 MPa, a rock elastic modulus of 40000 MPa, a proppant elastic modulus of 40000 MPa, a Poisson's ratio of both rock and proppant of 0.20, and a rock layer thickness of 20 mm, the relationship between the proppant-rock indentation distance and the proppant particle size was calculated. Figure 9 It can be seen that the proppant recess depth increases continuously with the increase of proppant particle size. At a yield strength of 20 MPa, the proppant recess depth increases from 0.00582 mm to 0.02040 mm as the proppant particle size increases from 0.2 mm to 0.7 mm; at a yield strength of 25 MPa, the proppant recess depth increases from 0.00410 mm to 0.01434 mm as the proppant particle size increases from 0.2 mm to 0.7 mm; at a yield strength of 30 MPa, the proppant recess depth increases from 0.00470 mm to 0.01644 mm as the proppant particle size increases from 0.2 mm to 0.7 mm; and at a yield strength of 35 MPa, the proppant recess depth increases from 0.00470 mm to 0.01644 mm as the proppant particle size increases from 0.2 mm to 0.7 mm.

[0185] Before the closing pressure reaches the elastic limit pressure, as the proppant particle size increases, the yield strength decreases and the rate of increase in indentation depth increases.

[0186] Depend on Figure 10It can be seen that the proppant embedding distance increases with the increase of proppant particle size. At a yield strength of 20 MPa, the proppant embedding depth increases from 0.01833 mm to 0.03290 mm as the proppant particle size increases from 0.2 mm to 0.7 mm; at a yield strength of 25 MPa, the proppant embedding depth increases from 0.01660 mm to 0.02684 mm as the proppant particle size increases from 0.2 mm to 0.7 mm; at a yield strength of 30 MPa, the proppant embedding depth increases from 0.01720 mm to 0.02894 mm as the proppant particle size increases from 0.2 mm to 0.7 mm; and at a yield strength of 35 MPa, the proppant embedding depth increases from 0.01720 mm to 0.02894 mm as the proppant particle size increases from 0.2 mm to 0.7 mm.

[0187] It can be seen that the larger the proppant particle size, the greater the proppant recess depth and proppant embedment depth.

[0188] (3) Elastic modulus

[0189] (3.1) Elastic modulus of proppant

[0190] Assuming a rock elastic modulus of 40,000 MPa, a proppant particle size of 0.40 mm, a Poisson's ratio of rock to proppant of 0.20, a rock layer thickness of 20 mm, and a closure pressure of 25 MPa, the relationship between the proppant-rock indentation distance and the proppant elastic modulus was calculated.

[0191] Depend on Figure 11 It can be seen that as the elastic modulus of the proppant increases, the proppant recess distance decreases. When the yield strength is 20 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant recess depth decreases from 0.01746 mm to 0.01166 mm; when the yield strength is 25 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant recess depth decreases from 0.01227 mm to 0.00819 mm; when the yield strength is 30 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant recess depth decreases from 0.01407 mm to 0.00940 mm; when the yield strength is 35 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant recess depth decreases from 0.01407 mm to 0.00940 mm.

[0192] Depend on Figure 12It can be seen that as the elastic modulus of the proppant increases, the proppant embedding distance decreases. When the yield strength is 20 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant embedding depth decreases from 0.02996 mm to 0.02416 mm; when the yield strength is 25 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant embedding depth decreases from 0.02477 mm to 0.02069 mm; when the yield strength is 30 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant embedding depth decreases from 0.02657 mm to 0.02190 mm; when the yield strength is 35 MPa, the elastic modulus of the proppant increases from 15,000 MPa to 40,000 MPa, and the proppant embedding depth decreases from 0.02657 mm to 0.02190 mm.

[0193] As the elastic modulus of the proppant increases, the proppant indentation depth and proppant embedment depth decrease.

[0194] (3.2) Rock elastic modulus

[0195] The relationship between the proppant-rock indentation distance and the rock elastic modulus was calculated under the following conditions: proppant elastic modulus of 40000 MPa, proppant particle size of 0.40 mm, Poisson's ratio of rock and proppant of 0.20, rock layer thickness of 20 mm, and closure pressure of 25 MPa.

[0196] Depend on Figure 13 It can be seen that as the elastic modulus of the rock increases, the proppant indentation distance decreases. When the yield strength is 20 MPa, the rock elastic modulus increases from 15000 MPa to 40000 MPa, and the proppant indentation depth decreases from 0.01746 mm to 0.01166 mm; when the yield strength is 25 MPa, the rock elastic modulus increases from 15000 MPa to 40000 MPa, and the proppant indentation depth decreases from 0.01227 mm to 0.00819 mm; when the yield strength is 30 MPa, the rock elastic modulus increases from 15000 MPa to 40000 MPa, and the proppant indentation depth decreases from 0.01407 mm to 0.00940 mm; when the yield strength is 35 MPa, the rock elastic modulus increases from 15000 MPa to 40000 MPa, and the proppant indentation depth decreases from 0.01407 mm to 0.00940 mm.

[0197] Depend on Figure 14It can be seen that as the rock's elastic modulus increases, the proppant embedding depth decreases. At a yield strength of 20 MPa, as the rock's elastic modulus increases from 15000 MPa to 40000 MPa, the proppant embedding depth decreases from 0.02996 mm to 0.02416 mm; at a yield strength of 25 MPa, the same applies; at a yield strength of 30 MPa, the proppant embedding depth decreases from 0.02657 mm to 0.02190 mm; and at a yield strength of 35 MPa, the same applies.

[0198] It can be seen that as the rock elastic modulus increases, the proppant recess depth and proppant embedment depth decrease.

[0199] (4) Poisson's ratio

[0200] (4.1) Poisson's ratio of the proppant

[0201] Under the conditions of a proppant elastic modulus of 20000 MPa, a rock elastic modulus of 40000 MPa, a proppant particle size of 0.40 mm, a rock Poisson's ratio of 0.20, a rock layer thickness of 20 mm, and a closure pressure of 25 MPa, the relationship between the proppant-rock indentation distance and the proppant Poisson's ratio was calculated.

[0202] Depend on Figure 15 It can be seen that as the Poisson's ratio of the proppant increases, the proppant recess depth decreases. At a yield strength of 20 MPa, as the Poisson's ratio increases from 0.1 to 0.7, the proppant recess depth decreases from 0.01548 mm to 0.01190 mm; at a yield strength of 25 MPa, the same applies; at a yield strength of 30 MPa, the same applies; and at a yield strength of 35 MPa, the same applies.

[0203] Depend on Figure 16It can be seen that as the Poisson's ratio of the proppant increases, the proppant embedding distance decreases. At a yield strength of 20 MPa, as the Poisson's ratio increases from 0.1 to 0.7, the proppant embedding depth decreases from 0.02799 mm to 0.02440 mm; at a yield strength of 25 MPa, the same applies; at 30 MPa, the same applies; and at 35 MPa, the same proppant embedding depth decreases.

[0204] It can be seen that as the Poisson's ratio of the proppant increases, the proppant recess depth and proppant embedment depth decrease.

[0205] (4.2) Poisson's ratio of rocks

[0206] Under the conditions of a proppant elastic modulus of 20000 MPa, a rock elastic modulus of 40000 MPa, a proppant particle size of 0.40 mm, a proppant Poisson's ratio of 0.20, a rock layer thickness of 20 mm, and a closure pressure of 25 MPa, the relationship between the proppant-rock indentation distance and the rock Poisson's ratio was calculated.

[0207] Depend on Figure 17 It can be seen that as the Poisson's ratio of the rock increases, the proppant recess depth decreases. At a yield strength of 20 MPa, as the Poisson's ratio of the rock increases from 0.1 to 0.7, the proppant recess depth decreases from 0.01538 mm to 0.01364 mm; at a yield strength of 25 MPa, the same applies; at a yield strength of 30 MPa, the same applies; and at a yield strength of 35 MPa, the same applies.

[0208] Depend on Figure 18It can be seen that as the Poisson's ratio of the rock increases, the proppant embedding distance decreases. At a yield strength of 20 MPa, as the Poisson's ratio increases from 0.1 to 0.7, the proppant embedding depth decreases from 0.02788 mm to 0.02614 mm; at a yield strength of 25 MPa, the same applies; at 30 MPa, the same applies; and at 35 MPa, the same proppant embedding depth decreases.

[0209] It can be seen that as the Poisson's ratio of the rock increases, the proppant recess depth and proppant embedment depth decrease.

[0210] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0211] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for predicting proppant embedment depth considering elastoplastic deformation processes, characterized in that, include: Step 1: Based on the elastic-plastic deformation law of proppant and rock, the contact deformation of proppant and rock is divided into three stages, namely the elastic stage, the elastic-plastic stage and the plastic stage. Step 2: Establish proppant embedding depth prediction models for the three extreme stages of proppant-rock contact deformation: elastic stage, elastoplastic stage, and plastic stage. The proppant embedding depth prediction model in step two is as follows: in, d For the proppant embedding depth; The pressure exerted on the rock; The effective elastic modulus; For the proppant radius; For closing pressure; The elastic modulus of the rock; The initial width of the rock; The proppant embedding depth prediction model in step two is as follows: in, The yield strength of the rock; This represents the maximum embedding depth during the elastic phase. This represents the critical value for the embedding depth during the plastic stage. The proppant embedding depth prediction model in step two is as follows: in, P For contact pressure; Step 3: Input the geostress conditions, proppant physical properties and rock physical properties to determine the deformation stage of the proppant and predict the proppant embedment depth.

2. The proppant embedding depth prediction method considering the elastoplastic deformation process according to claim 1, wherein the proppant physical properties in step three include proppant particle size, elastic modulus, and Poisson's ratio.

3. The proppant embedding depth prediction method considering the elastoplastic deformation process according to claim 1, wherein the rock physical properties in step three include the rock elastic modulus, Poisson's ratio, and initial width.

4. A proppant embedding depth prediction system considering the elastoplastic deformation process, for implementing the method according to any one of claims 1-3, characterized in that, include: The elastic-plastic deformation classification module divides the contact deformation between the proppant and the rock into three stages based on the elastic-plastic deformation law of the proppant and the rock. The three stages include the elastic stage, the elastic-plastic stage and the plastic stage. The model building module is used to build proppant embedding depth prediction models for the three extreme stages of proppant-rock contact deformation: elastic stage, elastoplastic stage, and plastic stage. The judgment and prediction model is used to input geostress conditions, proppant physical parameters and rock physical parameters to determine the deformation stage of the proppant and predict the proppant embedment depth.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the proppant embedding depth prediction method considering the elastoplastic deformation process as described in any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the proppant embedding depth prediction method considering the elastoplastic deformation process as described in any one of claims 1 to 3.

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