A method for predicting a sand production critical pressure difference of directional perforation based on a casing-cement sheath-formation coupling action

Abstract

The application discloses a kind of based on casing-cement ring-stratum coupling action directional perforation sand critical production pressure difference prediction method, main steps include measuring the rock mechanics parameters and rock strength parameters of casing, cement ring and formation rock, ground stress parameters and pore pressure;Obtain inclination and azimuth data, casing outer diameter and wall thickness, borehole size;Using the deformation control equation and the harmonic equation of "casing-cement ring-stratum combination body" are deduced under the condition of non-uniform ground stress the stress field analytical solution of surrounding rock of directional well around casing-cement ring coupling action, based on the shear failure sand production mechanism of rock, comprehensive well stress new model and perforation hole stress model, determine the critical production pressure difference of directional perforation sand production.This application uses the perforation hole stress solution determined by the well stress new solution of casing-cement ring coupling action, not only can predict the critical production pressure difference of directional perforation well sand production, but also can optimize perforation phase angle and perforation length.

Description

Technical Field

[0001] This invention belongs to the field of deep oil and gas drilling and completion technology, and in particular, it is a method for predicting the critical production pressure difference of directional perforation sand production based on the coupling effect of casing-cement sheath-formation. Background Technology

[0002] Improper selection of the critical production differential can lead to formation sand production. Excessive sand production can cause sand accumulation at the wellbore or wellhead, reservoir sand blockage, and even wellbore burial, forcing prolonged well shutdown, reducing oil (gas) well productivity and economic benefits. Sand production in gas wells also has a significant impact on surface choke manifolds and gathering and transportation equipment. A wellbore stress field is crucial for evaluating formation sand stability. For casing-cement sheath-formation assemblies formed by casing completion, the cement sheath-casing is not only affected by the in-situ formation stress field, but also reacts to the open-hole formation rock formed during drilling, leading to a redistribution of the surrounding rock stress field. Furthermore, the perforation stress within the formation after casing perforation is a core control parameter for determining the critical production differential for perforation sand production. The determination of the perforation stress field also depends on the surrounding rock stress field resulting from the coupling effect of the casing and cement sheath. However, the linear elastic solution of the surrounding rock of conventional open-hole wells cannot reflect the influence of the casing-cement sheath coupling effect on the stress field of the surrounding rock, and therefore cannot accurately predict the critical production pressure differential for perforation and sand production.

[0003] There are many existing methods for predicting the critical production pressure differential for sand production in formations. For example, patent CN115522918A discloses a method for predicting the sand production pressure differential profile of perforated wells in deep sandstone reservoirs. This method calculates rock mechanical parameters from target well logging data to obtain a rock mechanical parameter profile along the well trajectory; calculates the geostress field distribution of the target well to obtain a profile of the three principal stress values ​​along the well trajectory; calculates geostress values ​​under different formation pressures based on changes in reservoir pressure; establishes a wellbore stress distribution model; calculates the wellbore stress distribution at each point in the well section; substitutes the wellbore stress values ​​at each point in the well section into the rock failure criterion to calculate the critical sand production pressure differential profile of the target well, thus obtaining the sand-producing well section; calculates the magnitude of geostress values ​​under different reservoir pressures and substitutes them into the sand production pressure differential model to calculate the critical sand production pressure differential for each production stage. This method solves the problem of unreasonable sand production pressure differential profile prediction methods in existing technologies. Patent CN 110566171 A discloses a method for predicting sand production in ultra-high pressure tight fractured sandstone gas reservoirs. This method mainly considers the influence of factors such as strong tectonic stress in the sand-producing reservoir of high pressure tight fractured gas reservoirs, perforation blockage, additional pressure difference, and reservoir fractures.

[0004] While these existing methods have achieved certain technical results, they do not take into account the influence of the actual casing-cement sheath on the stress field of the surrounding rock, and therefore cannot accurately predict the critical production pressure differential for perforation. Summary of the Invention

[0005] To address the problem that existing critical production pressure differential prediction methods do not consider the influence of the actual casing-cement sheath on the stress field of the surrounding rock, and therefore cannot accurately predict the critical production pressure differential of perforation, this invention provides a method for predicting the critical production pressure differential of directional perforation sand production based on the coupling effect of casing-cement sheath-formation.

[0006] The present invention provides a method for predicting the critical production pressure differential of directional perforation sand production based on the coupling effect of casing-cement sheath-formation, the steps of which are as follows:

[0007] S1. The mechanical parameters and rock strength parameters of cement stone and formation rock were tested using a triaxial compression test. The mechanical parameters included elastic modulus and Poisson's ratio; the rock strength parameters included cohesion and internal friction angle.

[0008] S2. Calculate the tectonic stress coefficient using the geostress data measured by acoustic emission tests, and statistically analyze the measured pore pressure data. The geostress data includes the maximum and minimum horizontal geostress; the tectonic stress coefficient includes the tectonic stress coefficients corresponding to the maximum and minimum horizontal geostresses.

[0009] S3. Correct the fitting coefficients of empirical prediction formulas for rock mechanics and strength parameters using experimental measurement data. Experimental measurement data includes elastic modulus, Poisson's ratio, internal friction angle, and cohesion.

[0010] S4. Use well logging data to obtain in-situ stress, original pore pressure, rock mechanical parameters, and rock strength parameters at the downhole research location. Well logging data includes sonic transit time, density, and gamma ray value; in-situ stress data includes overlying strata pressure, maximum horizontal in-situ stress, and minimum horizontal in-situ stress.

[0011] S5. Compile wellbore structural data, well inclination data, and casing mechanical parameters. Wellbore structural data includes casing outer diameter, wall thickness, and wellbore dimensions; well inclination data includes inclination angle and azimuth angle; casing mechanical parameters include the casing's elastic modulus and Poisson's ratio.

[0012] S6. Using the deformation control equation of the casing-cement sheath-formation combination, the analytical solution of the stress field of the surrounding rock of a directional well under non-uniform geostress conditions under the coupling effect of the casing-cement sheath is derived.

[0013] The analytical solution of the stress field of the rock surrounding the directional well under the coupling effect of casing and cement sheath is as follows:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, p3 is the contact force at the cement sheath-formation interface, MPa; r is the radial distance from the wellbore center to a certain location inside the formation, m; r3 is the wellbore radius, m; and These are the in-plane radial stress, tangential stress, axial stress, and shear stress distributed in the surrounding rock of the well, in MPa; and P0 is the out-of-plane shear stress, MPa; P0 and S0 are the formation mean stress and shear stress, MPa, respectively; v3 is the Poisson's ratio of the formation rock, dimensionless; θ is the wellbore angle, and the radius vector at the research location is related to the maximum horizontal in-situ stress σ. H The angle of orientation, °; ​​θ r Define as an intermediate quantity for angle conversion K3 and M3 are unknown coefficients related to the internal stress of the ground plane; B3 and D3 are unknown coefficients related to the external shear stress of the ground plane. and These represent the principal stress components and shear stress components in the wellbore coordinate system, respectively, in MPa.

[0021] S7. A new solution for the peri-wellbore stress based on the casing-cement sheath coupling effect is used to derive the peri-wellbore stress solution for directional perforations. The formula for calculating the stress field around the directional perforation channel is as follows:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] In the formula: p w θ is the fluid column pressure at the perforation orifice, MPa; θ′ is the perforation wellbore angle, °; the stress field components around the perforation channel include radial stress. Tangential stress Axial stress The shear stress in the θ′-z plane, The shear stress in the r-θ′ plane, Let be the shear stress in the zr plane, in MPa.

[0028] S8. Based on the stress solution around the directional perforation hole and the three-dimensional rock strength criterion, the critical production pressure differential for sand production in directional perforated wells is predicted, and the perforation phase angle and perforation length are optimized.

[0029] The process of predicting the critical production pressure differential for sand production in directional perforated wells is as follows:

[0030] S81, Define the well inclination angle γ bi =i°(i=0:i:90), azimuth angle Ω bj =j° (j=0:j:360), well perimeter angle θ k =k° (k=0:k:360), pressure array Used to determine the final required bottom hole flowing pressure; where Set as the maximum horizontal ground stress σ H Or even greater stress values;

[0031] S82, Given matrix (γ) bi Ω bj Pressure p ml Incrementing from 0 to 1 in intervals of 1 When the judgment condition is met Obtain the well perimeter angle θ k Corresponding collapse pressure matrix In the formula, m is a positive number that is infinitely close to 0, and c and These correspond to the inherent cohesion and internal friction angle of the rock, respectively; τ oct For octahedral shear stress, σ m This represents the average effective stress.

[0032] S83, Filter out the matrix The maximum value in Given the well inclination and azimuth (γ) bi Ω bj The corresponding bottom hole flowing pressure value;

[0033] S84. Use the formation pore pressure p0 minus the bottom hole flowing pressure as the critical production pressure differential for sand production in directional perforation completion.

[0034] Compared with the prior art, the advantages of the present invention are:

[0035] (1) The method for predicting the critical production pressure difference for sand production in directional perforated well completion proposed in this invention derives the analytical solution of the stress field of the surrounding rock under non-uniform geostress conditions under the coupling effect of the casing-cement sheath using the deformation control equation and harmonic equation of the "casing-cement sheath-formation assembly". When solving for the in-plane (related to the r-θ plane) and out-of-plane (related to the rz and θ-z planes) stress and displacement solutions of the casing-cement sheath, the initial in-plane displacement caused by formation deposition or tectonic movement is removed more objectively. and out-of-plane shear initial displacement w 0 The impact.

[0036] (2) The method of this invention uses a new solution for the perforation perimeter stress determined by the casing-cement sheath coupling effect. This solution can not only predict the critical production pressure differential for sand production in directional perforated wells, but also optimize the perforation phase angle and perforation length. This method is simple to understand, easy to operate, and low in cost. It provides a scientific basis for predicting the critical production pressure differential for sand production in (ultra)deep fracture directional perforated wells, effectively preventing formation sand production and avoiding downhole sand burial or wellbore sand blockage accidents. This invention provides theoretical and technical guidance for predicting sand production in directional perforated wells, and the evaluation results are highly reliable.

[0037] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method for predicting the critical production pressure difference of directional perforation sand production based on the coupling effect of casing-cement sheath-formation, according to the present invention. Detailed Implementation

[0039] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0040] The flow chart of the method for predicting the critical production pressure difference of directional perforation sand production based on the coupling effect of casing-cement sheath-formation in this invention is as follows: Figure 1 As shown. The specific steps are as follows:

[0041] S1. The mechanical parameters and rock strength parameters of cement stone and formation rock were tested using triaxial compression tests. The mechanical parameters of cement stone and formation rock include elastic modulus and Poisson's ratio. The rock strength parameters include cohesion and angle of internal friction.

[0042] S2. Calculate the tectonic stress coefficient using the geostress data measured by acoustic emission tests, and statistically analyze the measured pore pressure data. The geostress data includes the maximum and minimum horizontal geostress; the tectonic stress coefficient includes the tectonic stress coefficients corresponding to the maximum and minimum horizontal geostresses.

[0043] S3. Correct the fitting coefficients of empirical prediction formulas for rock mechanics and strength parameters using experimental measurement data. Experimental measurement data includes elastic modulus, Poisson's ratio, internal friction angle, and cohesion.

[0044] The fitting coefficients include: dynamic and static conversion coefficients A1, B1, A2 and B2 related to the elastic modulus and Poisson's ratio in rock mechanics parameters, and conversion coefficients C1, C2, D1 and D2 related to the uniaxial compressive strength and internal friction angle in strength parameters.

[0045]

[0046]

[0047] E s =A² + B²E d

[0048] v s =A1+B1E d

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] In the formula, Δt p and Δt s These represent the time differences between P-waves and S-waves, in µs / ft; ρ b Density of the rock mass, g / cm³ 3 v d and v s These are the dynamic and static Poisson ratios, respectively, dimensionless; E s E d These are the static and dynamic elastic moduli, respectively, in GPa; V. cl It refers to the clay content, dimensionless; GR, GR max and GR min These represent the natural gamma values ​​of the actual strata, pure mudstone layer, and pure sandstone layer, respectively, and are dimensionless; the GCUR index is related to the new and old strata of the underground sediments, taking values ​​of 3.7 (new strata) and 2.0 (old strata), respectively, and is dimensionless; I GR It is the normalized natural gamma value, which is dimensionless; is the internal friction angle of the rock, °; c is the cohesion of the rock, MPa; A1, B1, A2, B2, C1, C2, D1 and D2 are fitting coefficients.

[0055] S4. Obtain the in-situ stress, original pore pressure, rock mechanical parameters, and rock strength parameters at the downhole research location using well logging data. The well logging data includes sonic transit time, density, and gamma ray value. The in-situ stress data includes overlying strata pressure, maximum horizontal in-situ stress, and minimum horizontal in-situ stress.

[0056] S5. Compile wellbore structural data, well inclination data, and casing mechanical parameters. Wellbore structural data includes casing outer diameter, wall thickness, and wellbore dimensions. Well inclination data includes inclination angle and azimuth angle. Casing mechanical parameters include the casing's elastic modulus and Poisson's ratio.

[0057] S6. Using the deformation control equation of the casing-cement sheath-formation combination, the analytical solution of the stress field of the surrounding rock of a directional well under non-uniform geostress conditions under the coupling effect of the casing-cement sheath is derived.

[0058] The governing equations include constitutive equations, geometric equations, stress balance equations, harmonic equations, and related auxiliary equations.

[0059] The constitutive equation is:

[0060]

[0061] Where, σ ij (i, j ∈ r, θ, z) is the stress tensor, MPa; ε ij Let G be the strain tensor, which is dimensionless; ∈ be the volume strain, which is dimensionless; G is the shear modulus, defined as... GPa; K is the bulk modulus, defined as... GPa; E is the elastic modulus, GPa; v is Poisson's ratio, dimensionless.

[0062] The geometric equation is:

[0063]

[0064]

[0065]

[0066] In the formula, ε r ε θ and γ rθ These are the in-plane radial strain, tangential strain, and shear strain, respectively, and are dimensionless; u r and u θ These represent radial and tangential displacements, respectively, in meters; r is the radius, also in meters; θ is the wellbore angle. The relationship between the radius vector at the research location and the maximum horizontal geostress σ is investigated. H The angle between directions, °.

[0067] The stress balance equation is:

[0068]

[0069]

[0070] In the formula, σ r σ θ and τ rθ These are the in-plane radial stress, tangential stress, and shear stress, respectively, in MPa.

[0071] The harmonic equation is:

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] In the formula, ψ and ψ are stress compatibility functions; It is the Laplace operator for the r-θ plane. It is a reharmonic operator (a fourth-order partial differential operator); τ rz and τ θz It is the out-of-plane shear stress, MPa.

[0080] The auxiliary equation (out-of-plane shear displacement) is:

[0081]

[0082] In the formula, w is the out-of-plane shear displacement, m.

[0083] The above governing equations and related variables are applicable to describing the stress conditions of casing, cement sheath, or formation (surrounding rock).

[0084] The formula for calculating the stress field of the surrounding rock of the well, taking into account both the casing-cement sheath effect, is as follows:

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] In the formula, p3 is the contact force at the cement sheath-formation interface, MPa; r is the radial distance from the wellbore center to a certain location inside the formation, m; r3 is the wellbore radius, m; and These are the in-plane radial stress, tangential stress, and shear stress distributed in the surrounding rock of the well, in MPa. and P0 is the out-of-plane shear stress, MPa; P0 and S0 are the formation mean stress and shear stress, MPa, respectively; v3 is the Poisson's ratio of the formation rock, dimensionless; θ is the wellbore angle, and the radius vector at the research location is related to the maximum horizontal in-situ stress σ. H The angle of orientation, °; ​​θ r Define as an intermediate quantity for angle conversion

[0092] K3 and M3 are unknown coefficients related to the internal stress of the ground plane; B3 and D3 are unknown coefficients related to the external shear stress of the ground plane.

[0093] The contact force p3 (MPa) at the cement sheath-formation interface is defined as follows:

[0094]

[0095] Radial stress on the surrounding rock of the well Tangential stress and shear stress The relevant coefficients (K3, M3) are obtained from the following matrix.

[0096]

[0097] Shear stress on the surrounding rock of the well and tangential stress The relevant coefficients (B3, D3) are calculated from the following matrix.

[0098]

[0099] In the formula, the intermediate variable is defined as

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] β i =2G i

[0108] In this context, subscripts i = 1, 2, and 3 represent the casing, cement sheath, and formation, respectively. w R1 represents the wellbore fluid column pressure, in MPa; r1, r2, and r3 represent the inner radii of the casing, r1, r2, and r3, respectively. cas，i Outer radius r of the casing cas，o Or the inner radius r of the cement ring cem，i Outer radius r of cement ring cem，o Or formation (wellbore) radius r w， The mean formation stress P0 and shear stress S0 are denoted as m.

[0109]

[0110]

[0111] In the above formula, the principal stress components in the wellbore coordinate system and shear stress components Depend on Determined. Among them, the in-situ stress matrix σ ics In-situ stress coordinate system ICS(X) i Y i Z i ) to the geodetic coordinate system GCS(X) g Y g Z g The transformation matrix (I) from GCS to the wellbore coordinate system BCS (X) b Y b Z b The transformation matrix (b) is defined as follows:

[0112]

[0113]

[0114]

[0115] Among them, Ω i γ is the angle between the azimuth of the maximum horizontal stress and true north, in degrees; i Ω represents the angle between the pressure of the overlying strata and the vertical direction.b γ is the wellbore azimuth angle, in °; b σ is the well inclination angle, in degrees. H The maximum horizontal ground stress is expressed in MPa; σ h The minimum horizontal ground stress is given in MPa; σ v The overlying strata pressure is expressed in MPa; the intermediate conversion angle is θ. r Defined as

[0116] S7. A new solution for the peri-wellbore stress based on the casing-cement sheath coupling effect is used to derive the peri-wellbore stress solution for directional perforations. The formula for calculating the stress field around the directional perforation channel is as follows:

[0117]

[0118]

[0119]

[0120]

[0121]

[0122] In the formula: p w θ is the fluid column pressure at the perforation orifice, MPa; θ′ is the perforation wellbore angle, °.

[0123] S8. Based on the stress solution around the directional perforation hole and the three-dimensional rock strength criterion, the critical production pressure differential for sand production in directional perforated wells is predicted, and the perforation phase angle and perforation length are optimized.

[0124] The three-dimensional rock strength criterion, specifically the true triaxial Mogi-Coulomb strength criterion, is commonly used for evaluating the shear failure of rocks. It uses the octahedral shear stress τ... oct and average effective stress σ m The expression is as follows:

[0125]

[0126]

[0127]

[0128] In the formula, c and These correspond to the inherent cohesion and internal friction angle of the rock, respectively. The definitions of the maximum effective principal stress σ′1, the intermediate effective principal stress σ′2, and the minimum effective principal stress σ′3 are given in the following formula.

[0129]

[0130] In the formula, p0 is the initial pore pressure of the formation, MPa; α is the Biot effective stress coefficient, dimensionless.

[0131] For formation sand production caused by shear failure of the rock mass, based on the above-mentioned strength failure criterion and the stress field around the directional perforation hole, the calculation process for the critical production pressure differential for sand production in directional perforation completion can be determined as follows:

[0132] S81, Define the well inclination angle γ bi =i°(i=0:i:90), azimuth angle Ω bj =j° (j = 0:j:360), well perimeter angle θ k =k° (k=0:k:360), pressure array Used to determine the final required bottom hole flowing pressure; where Set as the maximum horizontal ground stress σ H Or even greater stress values;

[0133] S82, Given matrix (γ) bi Ω bj Pressure p ml Incrementing from 0 to 1 in intervals of 1 When the judgment condition is met Obtain the well perimeter angle θ k Corresponding collapse pressure matrix In the formula, m is a positive number that is infinitely close to 0.

[0134] S83, Filter out the matrix The maximum value in Given the well inclination and azimuth (γ) bi Ω bj The corresponding bottom hole flowing pressure value;

[0135] S84. Use the formation pore pressure p0 minus the bottom hole flowing pressure as the critical production pressure differential for sand production in directional perforation completion.

[0136] The smaller the values ​​of the positive real numbers i, j, k, and l, the higher the accuracy of the collapse pressure determined by the above method.

[0137] This invention uses laboratory experiments and imaging logging data to determine the mechanical and strength parameters of the cement sheath and formation rock, as well as relevant geomechanical parameters and wellbore structural data required for model calculations. It derives analytical solutions for the stress field of the surrounding rock under non-uniform geostress conditions due to the coupling effect of the casing and cement sheath using the deformation control equations and harmonic equations of the "casing-cement sheath-formation assembly". Based on the shear failure and sand production mechanism of the rock, and integrating a new wellbore stress model and a perforation peri-stress model, it determines a method for predicting the critical production pressure differential for sand production in directional perforations. Furthermore, it plots the critical production pressure differential for sand production affected by different perforation phase angles and perforation lengths, providing a scientific basis for field personnel to determine a reasonable critical production pressure differential for sand production in directional perforations, effectively preventing formation perforation sand production problems and preventing wellbore sand burial.

[0138] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting the critical production pressure differential of directional perforation sand production based on casing-cement sheath-formation coupling, characterized in that, The steps are as follows: S1. The mechanical parameters and rock strength parameters of cement stone and formation rock were tested using a triaxial compression test. S2. Calculate the tectonic stress coefficient using the geostress data measured by acoustic emission tests, and statistically analyze the measured pore pressure data. S3. Correct the fitting coefficients of empirical prediction formulas for rock mechanics and strength parameters using experimental measurement data; S4. Use well logging data to obtain the geostress, original pore pressure, rock mechanical parameters and rock strength parameters at the downhole research location; S5. Compile data on wellbore structure, well inclination, and casing mechanical parameters; S6. Using the deformation control equation of the casing-cement sheath-formation combination, the analytical solution of the stress field of the rock surrounding the directional well under non-uniform geostress conditions under the coupling effect of casing-cement sheath is derived. S7. Derive the solution of perimeter stress for directional perforation using a new solution of perimeter stress based on casing-cement sheath coupling effect; S8. Based on the stress solution around the directional perforation hole and the three-dimensional rock strength criterion, predict the critical production pressure differential for sand production in directional perforated wells, and optimize the perforation phase angle and perforation length. The process of predicting the critical production pressure differential for sand production in directional perforated wells is as follows: S81, Define the well inclination angle γ bi =i° (i = 0:i:90), azimuth Ω bj =j° (j = 0:j:360), well perimeter angle θ k =k° (k = 0:k:360), pressure array Used to determine the final required bottom hole flowing pressure; where Set as the maximum horizontal ground stress σ H Or even greater stress values; S82, Given matrix (γ) bi Ω bj Pressure p ml The interval l increases from 0 to When the judgment condition is met Obtain the well perimeter angle θ k Corresponding collapse pressure matrix In the formula, m is a positive number that is infinitely close to 0, and c and These correspond to the inherent cohesion and internal friction angle of the rock, respectively; τ oct For octahedral shear stress, σ m The average effective stress; S83, Filter out the matrix The maximum value in Given the well inclination and azimuth (γ) bi θ bj The corresponding bottom hole flowing pressure value; S84. Use the formation pore pressure p0 minus the bottom hole flowing pressure as the critical production pressure differential for sand production in directional perforation completion.

2. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 1, characterized in that, In step S1, the mechanical parameters include the elastic modulus and Poisson's ratio; the rock strength parameters include cohesion and internal friction angle.

3. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 1, characterized in that, In step S2, the geostress data includes the maximum horizontal geostress and the minimum horizontal geostress; the tectonic stress coefficient includes the tectonic stress coefficient corresponding to the maximum horizontal geostress and the minimum horizontal geostress.

4. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 1, characterized in that, In step S3, the experimental measurement data include elastic modulus, Poisson's ratio, internal friction angle, and cohesion.

5. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 1, characterized in that, In step S4, the logging data includes sonic transit time, density, and gamma value; the geostress data includes overlying strata pressure, maximum horizontal geostress, and minimum horizontal geostress.

6. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 5, characterized in that, In step S5, the wellbore structure data includes the casing outer diameter, wall thickness, and wellbore dimensions; the well inclination data includes the inclination angle and azimuth angle; and the casing mechanical parameters include the casing's elastic modulus and Poisson's ratio.

7. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 6, characterized in that, In step S6, the analytical solution of the stress field of the rock surrounding the directional well under the coupling effect of casing and cement sheath is as follows: In the formula, p3 is the contact force at the cement sheath-formation interface, MPa; r is the radial distance from the wellbore center to a certain location inside the formation, m; r3 is the wellbore radius, m; and These are the in-plane radial stress, tangential stress, and shear stress distributed in the surrounding rock of the well, in MPa. and The out-of-plane shear stress is MPa; P0 and S0 are the mean stress and shear stress of the formation, respectively, in MPa; v3 is the Poisson's ratio of the formation rocks, which is dimensionless; θ is the wellbore angle, and the radius vector of the research location is related to the maximum horizontal in-situ stress σ. H The angle of orientation, °; ​​θ r Define as an intermediate quantity for angle conversion K3 and M3 are unknown coefficients related to the internal stress of the ground plane; B3 and D3 are unknown coefficients related to the external shear stress of the ground plane. and These represent the principal stress components and shear stress components in the wellbore coordinate system, respectively, in MPa.

8. The method for predicting the critical production pressure difference of directional perforation sand production based on casing-cement sheath-formation coupling as described in claim 7, characterized in that, In step S7, the formula for calculating the stress field around the directional perforation channel is as follows: In the formula: p w θ is the fluid column pressure at the perforation orifice, MPa; θ′ is the perforation wellbore angle, °; the stress field components around the perforation channel include radial stress. Tangential stress Axial stress The shear stress in the θ′-z plane, The shear stress in the r-θ′ plane, Let be the shear stress in the zr plane, in MPa.

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