Prediction method for critical sand production pressure difference after ultra-deep ultrahigh pressure sandstone gas reservoir fracturing

Abstract

The invention provides a method for predicting critical sand production pressure difference after ultra-deep ultrahigh-pressure sandstone gas reservoir fracturing, and belongs to the technical field of gas well exploitation. The method comprises the steps that accurate reservoir parameters are obtained through logging information and indoor experiments; a pre-fracturing perforation well completion critical sand production pressure difference prediction model is established, and the critical sand production pressure difference when fracturing transformation is not conducted is calculated; a critical sand production pressure difference prediction model of the sandstone gas reservoir after fracturing transformation is established by considering the redistribution condition of stress at the hole after fracture forming; and comparing and analyzing the size relationship of the critical sand production pressure differences of the reservoir before and after fracturing transformation to obtain the critical sand production pressure difference. And gas wells with similar lithology and similar layers in the target block reservoir are guided to formulate a reasonable production system, and reservoir sand production can be reduced while high yield is ensured.

Description

Technical Field

[0001] The invention belongs to the technical field of gas well exploitation, and in particular relates to a method for predicting a critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir. Background Art

[0002] Ultra-deep high-pressure sandstone gas reservoirs have huge reserves and extremely high production capacity, and their mining prospects are very broad. The production status of gas wells that have been put into production is very optimistic. However, due to the great burial depth of such gas reservoirs, high reservoir temperature and high formation pressure, in the actual production process, once the reservoir produces sand, it will bring a series of mining difficulties, such as sand and liquid accumulation in the wellbore, damage to the wellbore pipe column, damage to ground equipment and other serious problems, which affect safe production and cause high sand control costs and huge economic losses. Taking the target block S well as an example, the previous research data shows that the reservoir structure of this block is complex, there is a high stress difference, and there is a risk of sand production.

[0003] For abnormally high-pressure sandstone gas reservoirs, natural completion methods can no longer meet the requirements. Currently, perforation completion is the mainstream completion method. At the same time, considering that the reservoir area connected by vertical wells is small, sand fracturing is carried out in the later stage. By artificially increasing cracks, the communication ability between the reservoir and the wellbore is improved, and the gas well production efficiency is improved. After fracturing, the stress of the well wall around the cracks is redistributed. Therefore, the conventional critical sand pressure difference prediction method can no longer meet the current gas well production needs. It is urgent to start from the actual needs of the mine, consider the stress deformation of the reservoir after fracturing, and establish a prediction method for the critical sand pressure difference after fracturing of high-pressure sandstone gas reservoirs, so as to guide the efficient development of gas wells and similar oil and gas reservoirs in the target block. Summary of the invention

[0004] In view of the problems existing in the above-mentioned prior art, the present invention provides a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir. The technical problem to be solved by the present invention is to address the difficulty in predicting the critical sand production pressure difference after fracturing transformation of an ultra-deep and high-pressure gas well reservoir, and to establish a method for predicting the critical production pressure difference of a gas well when artificial fractures are considered, so as to reasonably predict the critical sand production pressure difference of the gas well before and after fracturing transformation, and to guide the gas wells in the target block with similar reservoir lithology and similar formation to formulate a reasonable production system, so as to ensure high production while reducing sand production in the reservoir.

[0005] In order to solve the above technical problems, the present invention provides a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir, comprising the following steps:

[0006] Step S1: Obtain accurate reservoir parameters using logging data and indoor experiments;

[0007] Step S2: establishing a prediction model for critical sand production pressure difference of perforation completion before fracturing, and calculating the critical sand production pressure difference when no fracturing transformation is performed;

[0008] Step S3: Considering the redistribution of stress at the holes after fracture creation, a prediction model for the critical sand production pressure difference of the sandstone gas reservoir after fracturing transformation is established;

[0009] Step S4: Compare and analyze the critical sand production pressure difference of the reservoir before and after the fracturing stimulation to obtain the critical sand production pressure difference.

[0010] Furthermore, the step S1 includes the following steps:

[0011] Step H1: Based on the experimental and logging data, establish the rock mechanics parameter profile and the geostress parameter profile of the reservoir section;

[0012] Step H2: Considering the reservoir characteristics of deep, high-temperature and high-pressure gas wells, indoor rock mechanics parameter tests and ground stress test experiments are carried out to study the influence of high temperature and high pressure on rock strength. The experimental data are used for dynamic and static verification of rock mechanics parameters to obtain a set of verification coefficients suitable for the target block. The verification coefficients are used to correct the rock mechanics parameter profile and ground stress parameter profile of the reservoir section to obtain reservoir parameters.

[0013] Furthermore, in step H1, based on the well logging data, the acoustic wave curve, density, well diameter, gamma and resistivity curve are obtained, and the rock mechanical parameters and ground stress parameters are calculated using empirical formulas to establish a continuous parameter profile:

[0014] Before calculating the rock mechanical parameters and ground stress parameters, considering the influence of shear wave data on the calculation results, the acoustic wave time difference experiment was carried out to obtain the conversion formula of the longitudinal and shear wave relationship. The relationship obtained through experimental testing is:

[0015] V s =0.405V p +733.11

[0016] Where: V s — Shear wave velocity, m / s; V p —Longitudinal wave velocity, m / s.

[0017] Furthermore, the empirical formula is as follows:

[0018] Dynamic Poisson's ratio calculation formula:

[0019]

[0020] Where: ν—dynamic Poisson’s ratio, dimensionless;

[0021] The Young's modulus calculation formula is:

[0022]

[0023] Where: E—dynamic Young's modulus, GPa; ρ—rock density, g / cm 3 .

[0024] Uniaxial compressive strength calculation formula:

[0025] σ c =185165*exp(-0.037*V p )

[0026] Where: c —Uniaxial compressive strength, MPa.

[0027] The calculation formula of overburden rock pressure is:

[0028]

[0029] Where: ν —vertical stress; D TV —True vertical depth; g—gravitational acceleration; O—offset value; ρ b —bulk density; h—thickness, m;

[0030]

[0031]

[0032] Where: H —maximum horizontal ground stress, MPa; σ h —horizontal minimum ground stress, MPa; α—biot coefficient; P p — is the formation pore pressure, MPa; ε h — is the strain in the direction of minimum principal stress; ε H — is the strain in the direction of maximum principal stress.

[0033] Furthermore, in step S2, the effects of bottom hole flow pressure, wellbore fluid seepage, and temperature changes on the stress around the well are considered to construct a stress distribution model of the rock around the well. A stress distribution model of the surrounding rock of the perforated completion hole is established, and the influence of the fluid drag force on the stress around the hole is considered to form a prediction model for the critical sanding pressure difference of the perforated completion before fracturing.

[0034] Furthermore, establishing a rock stress distribution model around the well includes the following steps:

[0035] Step C1: The magnitude of the in-situ stress component of the wellbore is derived by converting the components of the stress tensor in the rectangular coordinate system and the cylindrical coordinate system:

[0036]

[0037] Where: α'—well inclination, °; ​​β'—azimuth, °σ xx—Stress in the x-axis direction in the cross section, MPa; σ yy —Stress in the y-axis direction in the cross section, MPa; σ xy —Stress in the xy plane of the cross section, MPa; σ xz —Out-of-plane shear stress in the xz plane, MPa; σ yz —Out-of-plane shear stress in the yz plane, MPa; σ zz —axial stress, MPa;

[0038] Step C2: Considering the effect of bottom hole pressure on wellbore stress, the analytical solution model in cylindrical coordinate system is obtained from the problem of elastic cylinder subjected to uniformly distributed force:

[0039]

[0040] Where: p w —Liquid column pressure in the well, MPa; σ r —Radial stress caused by fluid seepage, MPa; σ θ —Tangential stress caused by fluid seepage, MPa; σ z —Vertical stress generated by fluid seepage, MPa; R—wellbore radius, m; r—distance from the infinite edge of the well to the center of the well, m; τ rz , τ rθ , τ θz Shear stress on rz plane, rθ plane and θz plane, MPa;

[0041] Step C3: Considering the influence of temperature change on the stress distribution of the wellbore wall, when only the thermal stress generated by temperature change on the wellbore wall is considered, the thermal stress expression of the wellbore wall is obtained:

[0042]

[0043] Where: rT —Thermal stress in radial direction, MPa; σ θT —Thermal stress in the tangential direction, MPa; σ zT —Thermal stress in vertical direction, MPa; α T —Rock linear thermal expansion coefficient, 1 / ℃; ΔT—wellbore formation temperature change, ℃; μ—Rock Poisson’s ratio, dimensionless;

[0044] Step C4: Considering the radial flow of the wellbore fluid into the formation pores, the stress generated around the wellbore is:

[0045]

[0046] Where: δ—seepage coefficient, when there is seepage in the well wall, δ=1, when there is no seepage in the well wall, δ=0; φ—porosity; p p—initial pore pressure of formation, MPa; λ—Biot coefficient; N—constant, intermediate quantity, meaningless;

[0047] Step C5: The stress distribution model of the rock around the well that comprehensively considers the temperature-dependent stress, well wall seepage and temperature change is:

[0048]

[0049] In the formula, σ r —Radial stress of wellbore, MPa; θ—Angle between fracture stress field and initial coordinate, °.

[0050] Furthermore, the stress distribution model of the surrounding rock of the perforated completion hole is established as follows:

[0051]

[0052] Where: r ′—radial stress of perforation hole, MPa; σ θ ′—tangential stress of perforation hole, MPa; σ z ′—vertical stress of perforation hole, MPa; ω—hole circumference angle, °; s—distance from the infinite area of ​​the hole to the center of the hole, m; r p —Hole radius, mm.

[0053] Furthermore, considering the effect of pore fluid, the effective stress expression on the perforation wall is obtained as follows:

[0054]

[0055] Where: r1 ′—radial stress of perforation wall, MPa; σ θ1 ′—tangential stress of perforation wall, MPa; σ z1 ′—vertical stress of perforation wall, MPa;

[0056] Considering the influence of the drag force generated by gas flow on the rock strength of the hole wall, the friction drag force model of gas flow on the hole wall is established:

[0057]

[0058] Where:

[0059]

[0060]

[0061] Where: F wp —Gas friction drag, MPa; φ—porosity, %; n p—perforation density, holes / m; R—wellbore radius, m; r—distance from the hole to the wellbore center, m; r p —perforation radius, m; P wp —pore pressure, MPa; Q sc —Gas production under standard conditions, 10 4 m 3 / d;Z sc —Gas compressibility coefficient under standard conditions; P sc —Formation pressure under standard conditions, MPa; T sc —formation temperature under standard conditions, K; k—formation permeability, 10 -3 um 2 ;h p —Perforation thickness, m; L p —perforation length, m; Z—gas compressibility coefficient; P—formation pressure, MPa; T—formation temperature, K; γ g —Relative density of gas, kg / m 3 ;μ g —Gas viscosity, mPa.s; β—Inertial resistance coefficient affected by turbulence in porous media, m -1 ; A2 and B2 are both intermediate quantities and have no real meaning.

[0062] The prediction model of critical sand production pressure difference of perforation completion before fracturing is established as follows:

[0063]

[0064] Furthermore, in step S3, a prediction model for critical sand production pressure difference of a sandstone gas reservoir after fracturing transformation is established, including the following steps:

[0065] Step M1: Establish the geometric model of the fracturing channel after fracturing and the schematic diagram of stress redistribution, abstract and simplify the fracturing transformation process into the horizontal well perforation process, and establish the stress distribution model at the fracture initiation position:

[0066] Step M2: Considering the influence of fracture gas on the strength of the rock around the fracture after pressure fracturing, a friction drag force model of gas flow on the fracture is established, denoted as F wf , the friction drag force model of gas flow on the wall of approximately cylindrical fracturing cracks was derived;

[0067] Step M3: A rock stress distribution model around the well is obtained by comprehensively considering variable temperature stress, temperature change and fluid seepage, and a critical sand production pressure difference prediction model of the sandstone gas reservoir after fracturing transformation is obtained.

[0068] Furthermore, the prediction model of critical sand production pressure difference of sandstone gas reservoir after fracturing transformation is as follows:

[0069]

[0070] Finally, by calculating the stress magnitude under different conditions and bringing it into the rock failure criterion, the critical sand production pressure difference of the reservoir after fracturing transformation is calculated:

[0071] ΔP=p p -p w

[0072] Where: ΔP—production pressure difference, MPa.

[0073] The invention discloses a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir, aiming at the difficulty in predicting the critical sand production pressure difference after fracturing transformation of an ultra-deep and high pressure gas well reservoir, and establishes a method for predicting the critical production pressure difference of a gas well when artificial fractures exist. The method can reasonably predict the critical sand production pressure difference of the gas well before and after fracturing transformation, and guide the gas wells with similar reservoir lithology and close formation in the target block to formulate a reasonable production system, so as to ensure the high production of the target reservoir gas well and reduce the sand production of the reservoir. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a schematic diagram of an embodiment of a method for predicting a critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir according to the present invention.

[0075] Figure 2 It is a schematic diagram of rock mechanics parameter verification of a method for predicting critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir according to the present invention.

[0076] Figure 3 It is a schematic diagram of geostress parameter verification of a method for predicting critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir according to the present invention.

[0077] Figure 4 The diagram is a schematic diagram of the relationship between the coordinates of the perforation holes and the wellbore of a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir according to the present invention.

[0078] Figure 5 The present invention is a method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs. The geometric model of the fracturing channel after fracturing and the schematic diagram of stress redistribution are established; in the figure, a is the half length of the fracture, m; r1 is the distance from the bottom of the fracture to σ x Distance, m; r2—the distance from the top of the crack to σ y distance, m; θ—angle between the crack stress field and the initial coordinate, °; θ1—angle between the lower end of the crack and the crack stress field, °; θ2—angle between the upper end of the crack and the crack stress field, °; o—center of the crack; σ x , σ y ——The induced stress along the x-axis and the induced stress along the y-axis generated by the crack, MPa; x, y—coordinate axes. DETAILED DESCRIPTION

[0079] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0081] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0082] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0083] In order to better understand the purpose, structure and function of the present invention, a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir according to the present invention is further described in detail below in conjunction with the accompanying drawings.

[0084] Embodiment 1:

[0085] like Figure 1 As shown, the present invention provides a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir, comprising the following steps:

[0086] Step S1: Obtain accurate reservoir parameters using logging data and indoor experiments;

[0087] Step S2: establishing a prediction model for critical sand production pressure difference of perforation completion before fracturing, and calculating the critical sand production pressure difference when no fracturing transformation is performed;

[0088] Step S3: Considering the redistribution of stress at the holes after fracture creation, a prediction model for the critical sand production pressure difference of the sandstone gas reservoir after fracturing transformation is established;

[0089] Step S4: Compare and analyze the critical sand production pressure difference of the reservoir before and after the fracturing stimulation to obtain the critical sand production pressure difference.

[0090] The critical sand production prediction model after fracturing is an improvement on the perforation sand production prediction model before fracturing. It takes into account the influence of cracks on reservoir sand production after fracturing and calculates the sand production pressure difference before fracturing, which is convenient for comparison with the calculation results after fracturing.

[0091] Embodiment 2:

[0092] like Figure 1 As shown, the present invention provides a method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir, comprising the following steps:

[0093] Step S1: Obtain accurate reservoir parameters using logging data and indoor experiments;

[0094] Step S2: establishing a prediction model for critical sand production pressure difference of perforation completion before fracturing, and calculating the critical sand production pressure difference when no fracturing transformation is performed;

[0095] Step S3: Considering the redistribution of stress at the holes after fracture creation, a prediction model for the critical sand production pressure difference of the sandstone gas reservoir after fracturing transformation is established;

[0096] Step S4: Compare and analyze the critical sand production pressure difference of the reservoir before and after the fracturing stimulation to obtain the critical sand production pressure difference.

[0097] The difference between this embodiment and the first embodiment is that:

[0098] The step S1 includes the following steps:

[0099] Step H1: Based on the experimental and logging data, establish the rock mechanics parameter profile and the geostress parameter profile of the reservoir section;

[0100] Step H2: Considering the reservoir characteristics of deep, high-temperature and high-pressure gas wells, carry out indoor rock mechanics parameter tests and ground stress test experiments to study the influence of high temperature and high pressure on rock strength. The experimental data are used for dynamic and static verification of rock mechanics parameters to obtain a set of verification coefficients suitable for the target block. The verification coefficients are used to correct the rock mechanics parameter profile and ground stress parameter profile of the reservoir section to obtain reservoir parameters;

[0101] In step H1, based on the logging data, the acoustic wave curve, density, well diameter, gamma and resistivity curve are obtained, and the rock mechanical parameters and ground stress parameters are calculated using empirical formulas to establish a continuous parameter profile:

[0102] Before calculating the rock mechanical parameters and ground stress parameters, considering the influence of shear wave data on the calculation results, the acoustic wave time difference experiment was carried out to obtain the conversion formula of the longitudinal and shear wave relationship. The relationship obtained through experimental testing is:

[0103] V s =0.405V p +733.11

[0104] Where: V s — Shear wave velocity, m / s; V p —Longitudinal wave velocity, m / s.

[0105] In step H1, the empirical formula includes:

[0106] Dynamic Poisson's ratio calculation formula:

[0107]

[0108] Where: ν—dynamic Poisson’s ratio, dimensionless;

[0109] The Young's modulus calculation formula is:

[0110]

[0111] Where: E—dynamic Young's modulus, GPa; ρ—rock density, g / cm 3 .

[0112] Uniaxial compressive strength calculation formula:

[0113] σ c =185165*exp(-0.037*V p )

[0114] Where: c —Uniaxial compressive strength, MPa.

[0115] The calculation formula of overburden rock pressure is:

[0116]

[0117] Where: ν —vertical stress; D TV —True vertical depth; g—gravitational acceleration; O—offset value; ρ b —bulk density; h—thickness, m.

[0118]

[0119]

[0120] Where: H—maximum horizontal ground stress, MPa; σ h —horizontal minimum ground stress, MPa; α—biot coefficient; P p — is the formation pore pressure, MPa; ε h — is the strain in the direction of minimum principal stress; ε H — is the strain in the direction of maximum principal stress.

[0121] In the step S2, the influence of bottom hole flow pressure, well wall fluid seepage and temperature change on the stress around the well is considered to construct a stress distribution model of the rock around the well; a stress distribution model of the surrounding rock of the perforated completion hole is established, and the influence of the fluid drag force on the stress around the hole is considered to form a prediction model of the critical sand production pressure difference of the perforated completion before fracturing;

[0122] Establishing the rock stress distribution model around the well includes the following steps:

[0123] Step C1: The magnitude of the in-situ stress component of the wellbore is derived by converting the components of the stress tensor in the rectangular coordinate system and the cylindrical coordinate system:

[0124]

[0125] Where: α'—well inclination, °; ​​β'—azimuth, °σ xx —Stress in the x-axis direction in the cross section, MPa; σ yy —Stress in the y-axis direction in the cross section, MPa; σ xy —Stress in the xy plane of the cross section, MPa; σ xz —Out-of-plane shear stress in the xz plane, MPa; σ yz —Out-of-plane shear stress in the yz plane, MPa; σ zz —axial stress, MPa;

[0126] Step C2: Considering the effect of bottom hole pressure on wellbore stress, the analytical solution model in cylindrical coordinate system is obtained from the problem of elastic cylinder subjected to uniformly distributed force:

[0127]

[0128] Where: p w —Liquid column pressure in the well, MPa; σ r —Radial stress caused by fluid seepage, MPa; σ θ —Tangential stress caused by fluid seepage, MPa; σ z —Vertical stress generated by fluid seepage, MPa; R—wellbore radius, m; r—distance from the infinite edge of the well to the center of the well, m; τ rz , τ rθ , τ θzShear stress on rz plane, rθ plane and θz plane, MPa;

[0129] Step C3: Considering the influence of temperature change on the stress distribution of the wellbore wall, when only the thermal stress generated by temperature change on the wellbore wall is considered, the thermal stress expression of the wellbore wall is obtained:

[0130]

[0131] Where: rT —Thermal stress in radial direction, MPa; σ θT —Thermal stress in the tangential direction, MPa; σ zT —Thermal stress in vertical direction, MPa; α T —Rock linear thermal expansion coefficient, 1 / ℃; ΔT—wellbore formation temperature change, ℃; μ—Rock Poisson’s ratio, dimensionless;

[0132] Step C4: Considering the radial flow of the wellbore fluid into the formation pores, the stress generated around the wellbore is:

[0133]

[0134] In the formula: δ is the seepage coefficient, when there is seepage in the well wall, δ=1, when there is no seepage in the well wall, δ=0; φ is the porosity; λ is the Biot coefficient; N is a constant, an intermediate quantity, without real meaning, obtained by calculation of the formula.

[0135] Step C5: The stress distribution model of the rock around the well that comprehensively considers the temperature-dependent stress, well wall seepage and temperature change is:

[0136]

[0137] Based on the stress distribution model of the rock around the well, the stress distribution model of the surrounding rock of the perforated completion well is established as follows:

[0138]

[0139] Where: r ′—radial stress of perforation hole, MPa; σ θ ′—tangential stress of perforation hole, MPa; σ z ′—vertical stress of perforation hole, MPa; ω—hole circumference angle, °; s—distance from the infinite area of ​​the hole to the center of the hole, m; r p —Hole radius, mm.

[0140] Considering the pore fluid λ·P p The three effective stress expressions on the perforation wall can be obtained as follows:

[0141]

[0142] Where: r1 ′—radial stress of perforation wall, MPa; σ θ1 ′—tangential stress of perforation wall, MPa; σ z1 ′—vertical stress of perforation wall, MPa;

[0143] Considering the influence of the drag force generated by gas flow on the rock strength of the hole wall, the friction drag force model of gas flow on the hole wall is established and recorded as F wp :

[0144]

[0145] Where:

[0146]

[0147]

[0148] Where: F wp —Gas friction drag, MPa; φ—porosity, %; n p —perforation density, holes / m; R—wellbore radius, m; r—distance from the hole to the wellbore center, m; r p —perforation radius, m; P wp —pore pressure, MPa; Q sc —Gas production under standard conditions, 10 4 m 3 / d;Z sc —Gas compressibility coefficient under standard conditions; P sc —Formation pressure under standard conditions, MPa; T sc —formation temperature under standard conditions, K; k—formation permeability, 10 -3 um 2 ;h p —Perforation thickness, m; L p —perforation length, m; Z—gas compressibility coefficient; P—formation pressure, MPa; T—formation temperature, K; γ g —Relative density of gas, kg / m 3 ;μ g —Gas viscosity, mPa.s; β—Inertial resistance coefficient affected by turbulence in porous media, m -1 ; A2 and B2 are both intermediate quantities and have no real meaning.

[0149] The prediction model of critical sand production pressure difference of perforation completion before fracturing is established as follows:

[0150]

[0151] In step S3, a prediction model for critical sand production pressure difference of a sandstone gas reservoir after fracturing transformation is established, including the following steps:

[0152] Step M1: Establish the geometric model of the fracturing channel after fracturing and the schematic diagram of stress redistribution, see Figure 5 , the fracturing process is abstracted and simplified into the horizontal well perforation process, and the stress distribution model at the fracture initiation position is established:

[0153] Step M2: Considering the influence of fracture gas on the strength of the rock around the fracture after pressure fracturing, a friction drag force model of gas flow on the fracture is established, denoted as F wf , the friction drag force model of gas flow on the wall of approximately cylindrical fracturing cracks was derived;

[0154] Step M3: The stress distribution model of the rock around the well obtained by comprehensively considering the variable temperature stress, temperature change and fluid seepage can obtain the critical sand production pressure difference prediction model of the sandstone gas reservoir after fracturing transformation, that is:

[0155]

[0156] Finally, by calculating the stress magnitude under different conditions and bringing it into the rock failure criterion, the critical sand production pressure difference of the reservoir after fracturing transformation is calculated:

[0157] ΔP=p p -p w

[0158] Where: ΔP—production pressure difference, MPa.

[0159] Embodiment 3:

[0160] Combination Figure 1-5 The present invention provides a method for predicting the critical sand pressure difference of ultra-deep and ultra-high pressure sandstone gas reservoirs. Based on indoor rock mechanics parameter experiments and logging data, a set of calibration coefficients suitable for calculating mechanical parameters of target blocks are obtained to improve parameter accuracy. The influence of wellbore seepage and temperature change effects on the stress around the well is considered to determine the stress distribution of the perforation holes. At the same time, the influence of the pushing and dragging force of the gas well fluid is considered to construct a perforation hole stress distribution model. On the basis of the previous model, the influence of fracturing transformation on the re-stress distribution of the reservoir is considered. On the basis of theoretical research, the channel fracturing problem is approximately classified as a horizontal well section perforation problem, and a new model for predicting the critical sand pressure difference of perforation completion after fracturing transformation is established. The details are as follows:

[0161] Design a rock mechanics parameter experimental plan to obtain static rock mechanics parameter values, mainly including 3 groups of Brazilian split tensile tests and core rock samples from 3 different reservoir sections to ensure more accurate tensile strength of the entire reservoir section;

[0162] 60 sets of P-wave and S-wave scanning experiments were carried out, 20 sets in each of the three reservoir sections, and the accurate P-wave and S-wave conversion relationship was obtained by discrete data linear fitting method:

[0163] V s =0.405V p +733.11

[0164] Where: V s — Shear wave velocity, m / s; V p —Longitudinal wave velocity, m / s.

[0165] Taking into account the abnormally high temperature and high pressure gas well reservoir characteristics, in order to ensure the authenticity of the experimental data, 20 groups of triaxial experiments were carried out at 150℃ and 149MPa. Considering the influence of confining pressure on rock strength, the compressive strength was tested under 6 different ground pressure gradient conditions. Ten groups of uniaxial experiments were carried out at room temperature to finally obtain the uniaxial compressive strength of the rock.

[0166] For abnormally high temperature and high pressure formations, the stress field changes are very complex, and in subsequent calculations, the magnitude of the ground stress plays a decisive role in the sand production prediction results. Therefore, the acoustic emission Kessel effect experiment is carried out to determine the strength of the formation stress field. According to the needs, the cores are sampled at 0°, 45°, and 90°. Considering the influence of pressure depletion on ground stress, 15 groups of ground stresses under different confining pressures are tested respectively. It is assumed that the maximum formation pressure limits depletion until normal production cannot be achieved, and finally the reservoir stress field profile is obtained.

[0167] Based on the logging data, the mechanical parameters are calculated according to the empirical formula, and continuous rock mechanical parameter profiles and ground stress parameter profiles are established. The empirical formula for calculating rock mechanical parameters and ground stress parameters is:

[0168]

[0169] Where: ν—dynamic Poisson’s ratio, dimensionless;

[0170]

[0171] Where: E—dynamic Young's modulus, GPa.

[0172] σ c =185165*exp(-0.037*V p )

[0173]

[0174] Where: ν —vertical stress; D TV —True vertical depth; g—gravitational acceleration; O—offset value; ρ b —Bulk density.

[0175]

[0176]

[0177] Where: v is Poisson's ratio; E is Young's modulus; α is biot coefficient; P p — is the formation pore pressure, MPa; ε h — is the strain in the direction of minimum principal stress; ε H — is the strain in the direction of maximum principal stress.

[0178] Based on the above steps, a set of calibration coefficients suitable for calculating the mechanical parameters of the target block is formed. The calibration process is shown in Figure 2 and Figure 3 , the final calibration coefficients are shown in Tables 1 and 2;

[0179] Table 1 Rock mechanics parameter verification coefficient table

[0180]

[0181] Table 2 Geostress parameter verification coefficients

[0182] Geostress parameter name Calibration coefficient (experimental test / well logging interpretation) Vertical stress (MPa) 1 Maximum horizontal principal stress (MPa) 1.038 Minimum horizontal principal stress (MPa) 1.042

[0183] Then, a stress distribution model of the rock around the well is established. First, a schematic diagram of the coordinate transformation of the wellbore surrounding rock stress is established. Then, the magnitude of the in-situ stress component of the wellbore is derived through the conversion relationship between the components of the stress tensor in the rectangular coordinate system and the cylindrical coordinate system:

[0184]

[0185] Where: α'—well inclination, °; ​​β'—azimuth, °; σ H —maximum horizontal ground stress, MPa; σ h —Minimum horizontal ground stress, MPa; σ v —vertical stress, MPa; σ xx —Stress in the x-axis direction in the cross section, MPa; σ yy —Stress in the y-axis direction in the cross section, MPa; σ xy —Stress in the xy plane of the cross section, MPa; σ xz —Out-of-plane shear stress in the xz plane, MPa; σ yz —Out-of-plane shear stress in the yz plane, MPa; σ zz —Axial stress, MPa.

[0186] Considering the influence of bottom hole flow pressure on well wall stress, the analytical solution model in cylindrical coordinate system is obtained from the problem of elastic cylinder subjected to uniformly distributed force:

[0187]

[0188] Where: p w —Liquid column pressure in the well, MPa;

[0189] Considering the temperature during the completion process, the temperature of the injected working fluid is generally lower than the formation temperature of such ultra-deep reservoirs. The change in temperature will cause the deformation trend of the rock to produce temperature-dependent stress. According to the basic equation of thermoelasticity and heat conduction theory, when only the thermal stress generated by temperature change on the wellbore wall is considered, the thermal stress expression of the wellbore wall is obtained:

[0190]

[0191] Where: rT —Thermal stress in radial direction, MPa; σ θT —Thermal stress in the tangential direction, MPa; σ zT —Thermal stress in vertical direction, MPa; α T —Rock linear thermal expansion coefficient, 1 / ℃; ΔT—wellbore formation temperature change, ℃;

[0192] Considering the radial flow of fluid into the formation pores, the stress generated around the wellbore wall is:

[0193]

[0194] Where: r —Radial stress caused by fluid seepage, MPa; σ θ —Tangential stress caused by fluid seepage, MPa; σ z —Vertical stress generated by fluid seepage, MPa; δ—seepage coefficient, δ=1 when there is seepage on the well wall, δ=0 when there is no seepage on the well wall; φ—porosity; λ—Biot coefficient;

[0195] The stress distribution model of the rock around the well that comprehensively considers multiple factors such as temperature stress and well wall seepage is:

[0196]

[0197] Based on the above research steps, the stress distribution model of the perforation hole is derived, and the influence of the gas push and drag force of the perforation hole on the hole stress is analyzed. In this way, the stress distribution model of the surrounding rock of the perforation completion hole is established. The specific steps are as follows:

[0198] First, the perforation hole and the wellbore can be regarded as two wellbores of different sizes intersecting vertically, and the central axis of the perforation hole and the wellbore are in the same plane. The relative relationship between the perforation hole and the wellbore coordinate system is shown in Figure 4At this time, referring to the vertical wellbore stress distribution model, the surrounding rock stress distribution model of the perforated completion wellbore is obtained as follows:

[0199]

[0200] Where: r ′—radial stress of perforation hole, MPa; σ θ ′—tangential stress of perforation hole, MPa; σ z ′—vertical stress of perforation hole, MPa; σ θ —wellbore tangential stress, MPa; σ z —Vertical stress of wellbore, MPa; σ r — radial stress of wellbore wall, MPa; ω — hole circumference angle, °; r p —hole radius, mm;

[0201] Considering the pore fluid λ·P p The three effective stress expressions on the perforation wall can be obtained as follows:

[0202]

[0203] Considering the influence of the pushing and dragging force generated by gas flow on the rock strength of the hole wall, the friction drag force model of gas flow on the hole wall is established as follows:

[0204]

[0205] Where:

[0206]

[0207] In the formula: In the formula: F wp —Gas friction drag, MPa; φ—porosity, %; n p —perforation density, holes / m; R—wellbore radius, m; r—distance from the hole to the wellbore center, m; r p —perforation radius, m; P wp —pore pressure, MPa; Q sc —Gas production, 104m 3 / d;P sc —Gas production corresponding to pressure, MPa; T sc —Gas production corresponding to temperature, K; k—formation permeability, 10 -3 um 2 ;h p —Perforation thickness, m; L p —perforation length, m; Z—gas compressibility coefficient; P—formation pressure, MPa; T—formation temperature, K; γ g —Relative density of gas, kg / m 3;μ g —Gas viscosity, mPa.s; β—Inertial resistance coefficient affected by turbulence in porous media, m -1 .

[0208] The friction drag force model of gas flow on the hole wall in the cylindrical perforation hole model was derived. The calculation model of the well wall stress obtained by comprehensively considering the variable temperature stress and fluid seepage can be used to obtain the critical sand production pressure difference prediction model for perforation completion before fracturing, that is:

[0209]

[0210] Based on the prediction model of critical sand production pressure difference of perforation completion before fracturing, the magnitude of all-direction stress is calculated and brought into the rock failure criterion to obtain the critical bottom hole flow pressure under different formation conditions, and then calculate the critical production pressure difference;

[0211] Based on the above research, the stress redistribution problem of perforation holes after fracturing is considered, and the stress redistribution model around the fracture and the hole is derived to establish a prediction model for the critical sand pressure difference of perforation completion after fracturing. The specific steps are as follows:

[0212] First, the perforation channel and the fracture can be regarded as two wellbores of different sizes intersecting vertically, and the fracture initiation position and the central axis of the perforation channel are in the same plane. The geometric model of the fracturing channel after fracturing and the schematic diagram of stress redistribution are established, see Figure 5 , the fracturing process is abstracted and simplified into the horizontal well perforation process, and the stress distribution model at the fracture initiation position is established:

[0213]

[0214] Considering the influence of fracture gas on the strength of the rock around the fracture after pressure fracturing, the friction drag force model of gas flow on the fracture is established and recorded as F wf :

[0215] The friction drag force model of gas flow on the wall of a cylindrical fracture is derived. The calculation model of the wellbore stress is obtained by comprehensively considering the temperature-varying stress and fluid seepage, and the prediction model of the critical sand production pressure difference of the sandstone gas reservoir after fracturing can be obtained, that is:

[0216]

[0217] Finally, by calculating the stress magnitude under different conditions and bringing it into the rock failure criterion, the critical sand production pressure difference of the reservoir after fracturing transformation is calculated.

[0218] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for predicting the critical sand production pressure difference after fracturing of an ultra-deep and ultra-high pressure sandstone gas reservoir, characterized in that: The following steps are involved: Step S1: Obtain accurate reservoir parameters using logging data and indoor experiments; Step S2: establishing a prediction model for critical sand production pressure difference of perforation completion before fracturing, and calculating the critical sand production pressure difference when no fracturing transformation is performed; Step S3: Considering the redistribution of stress at the holes after fracture creation, a prediction model for the critical sand production pressure difference of the sandstone gas reservoir after fracturing transformation is established; Step S4: Compare and analyze the critical sand production pressure difference of the reservoir before and after the fracturing stimulation to obtain the critical sand production pressure difference.

2. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 1, characterized in that: The step S1 includes the following steps: Step H1: Based on the experimental and logging data, establish the rock mechanics parameter profile and the geostress parameter profile of the reservoir section; Step H2: Considering the reservoir characteristics of deep, high-temperature and high-pressure gas wells, indoor rock mechanics parameter tests and ground stress test experiments are carried out to study the influence of high temperature and high pressure on rock strength. The experimental data are used for dynamic and static verification of rock mechanics parameters to obtain a set of verification coefficients suitable for the target block. The verification coefficients are used to correct the rock mechanics parameter profile and ground stress parameter profile of the reservoir section to obtain reservoir parameters.

3. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 2, characterized in that: In step H1, based on the logging data, the acoustic wave curve, density, well diameter, gamma and resistivity curve are obtained, and the rock mechanical parameters and ground stress parameters are calculated using empirical formulas to establish a continuous parameter profile: Before calculating the rock mechanical parameters and ground stress parameters, considering the influence of shear wave data on the calculation results, the acoustic wave time difference experiment was carried out to obtain the conversion formula of the longitudinal and shear wave relationship. The relationship obtained through experimental testing is: V s =0.405V p +733.11 Where: V s — Shear wave velocity, m / s; V p —Longitudinal wave velocity, m / s.

4. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 3, characterized in that: The empirical formula is as follows: Dynamic Poisson's ratio calculation formula: Where: ν—dynamic Poisson’s ratio, dimensionless; The Young's modulus calculation formula is: Where: E—dynamic Young's modulus, GPa; ρ—rock density, g / cm 3 ; Uniaxial compressive strength calculation formula: σ c =185165*exp(-0.037*V p ) Where: c —Uniaxial compressive strength, MPa; The calculation formula of overburden rock pressure is: Where: ν —vertical stress; D TV —True vertical depth; g—gravitational acceleration; O—offset value; ρ b —bulk density; h—thickness, m; Where: H —maximum horizontal ground stress, MPa; σ h —horizontal minimum ground stress, MPa; α—biot coefficient; P p — is the formation pore pressure, MPa; ε h — is the strain in the direction of minimum principal stress; ε H — is the strain in the direction of maximum principal stress.

5. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 1, characterized in that: In step S2, the influence of bottom hole flow pressure, well wall fluid seepage and temperature change on the stress around the well is considered to construct a stress distribution model of the rock around the well; a stress distribution model of the surrounding rock of the perforation completion hole is established, and the influence of the fluid drag force on the stress around the hole is considered to form a prediction model of the critical sanding pressure difference of the perforation completion before fracturing.

6. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 5, characterized in that: Establishing the rock stress distribution model around the well includes the following steps: Step C1: The magnitude of the in-situ stress component of the wellbore is derived by converting the components of the stress tensor in the rectangular coordinate system and the cylindrical coordinate system: Where: α'—well inclination, °; ​​β'—azimuth, °σ xx —Stress in the x-axis direction in the cross section, MPa; σ yy —Stress in the y-axis direction in the cross section, MPa; σ xy —Stress in the xy plane of the cross section, MPa; σ xz —Out-of-plane shear stress in the xz plane, MPa; σ yz —Out-of-plane shear stress in the yz plane, MPa; σ zz —axial stress, MPa; Step C2: Considering the effect of bottom hole pressure on wellbore stress, the analytical solution model in cylindrical coordinate system is obtained from the problem of elastic cylinder subjected to uniformly distributed force: Where: p w —Liquid column pressure in the well, MPa; σ r —Radial stress caused by fluid seepage, MPa; σ θ —Tangential stress caused by fluid seepage, MPa; σ z —Vertical stress generated by fluid seepage, MPa; R—wellbore radius, m; r—distance from the infinite edge of the well to the center of the well, m; τ rz , τ rθ , τ θz Shear stress on rz plane, rθ plane and θz plane, MPa; Step C3: Considering the influence of temperature change on the stress distribution of the wellbore wall, when only the thermal stress generated by temperature change on the wellbore wall is considered, the thermal stress expression of the wellbore wall is obtained: Where: rT —Thermal stress in radial direction, MPa; σ θT —Thermal stress in the tangential direction, MPa; σ zT —Thermal stress in vertical direction, MPa; α T —Rock linear thermal expansion coefficient, 1 / ℃; ΔT—wellbore formation temperature change, ℃; μ—Rock Poisson’s ratio, dimensionless; Step C4: Considering the radial flow of the wellbore fluid into the formation pores, the stress generated around the wellbore is: Where: δ—seepage coefficient, when there is seepage in the well wall, δ=1, when there is no seepage in the well wall, δ=0; φ—porosity; p p —initial pore pressure of formation, MPa; λ—Biot coefficient; N—constant, intermediate quantity, meaningless; Step C5: The stress distribution model of the rock around the well that comprehensively considers the temperature-dependent stress, well wall seepage and temperature change is: In the formula, σ r —Radial stress of wellbore, MPa; θ—Angle between fracture stress field and initial coordinate, °.

7. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 6, characterized in that: The stress distribution model of the surrounding rock of the perforated completion hole is established as follows: Where: r ′—radial stress of perforation hole, MPa; σ θ ′—tangential stress of perforation hole, MPa; σ z ′—vertical stress of perforation hole, MPa; ω—hole circumference angle, °; s—distance from the infinite area of ​​the hole to the center of the hole, m; r p —Hole radius, mm.

8. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 7, characterized in that: Taking into account the effect of pore fluid, the effective stress expression on the perforation wall is obtained as follows: Where: r1 ′—radial stress of perforation wall, MPa; σ θ1 ′—tangential stress of perforation wall, MPa; σ z1 ′—vertical stress of perforation wall, MPa; Considering the influence of the drag force generated by gas flow on the rock strength of the hole wall, the friction drag force model of gas flow on the hole wall is established: Where: Where: F wp —Gas friction drag, MPa; φ—porosity, %; n p —perforation density, holes / m; R—wellbore radius, m; r—distance from the hole to the wellbore center, m; r p —perforation radius, m; P wp —pore pressure, MPa; Q sc —Gas production under standard conditions, 10 4 m 3 / d;Z sc —Gas compressibility coefficient under standard conditions; P sc —Formation pressure under standard conditions, MPa; T sc —formation temperature under standard conditions, K; k—formation permeability, 10 -3 um 2 ; h p —Perforation thickness, m; L p —perforation length, m; Z—gas compressibility coefficient; P—formation pressure, MPa; T—formation temperature, K; γ g —Relative density of gas, kg / m 3 ;μ g —Gas viscosity, mPa.s; β—Inertial resistance coefficient affected by turbulence in porous media, m -1 ; A2 and B2 are both intermediate quantities and have no real meaning; The prediction model of critical sand production pressure difference of perforation completion before fracturing is established as follows:

9. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 8, characterized in that: In step S3, a prediction model for critical sand production pressure difference of a sandstone gas reservoir after fracturing transformation is established, including the following steps: Step M1: Establish the geometric model of the fracturing channel after fracturing and the schematic diagram of stress redistribution, abstract and simplify the fracturing transformation process into the horizontal well perforation process, and establish the stress distribution model at the fracture initiation position: Step M2: Considering the influence of fracture gas on the strength of the rock around the fracture after pressure fracturing, a friction drag force model of gas flow on the fracture is established, denoted as F wf , the friction drag force model of gas flow on the wall of approximately cylindrical fracturing cracks was derived; Step M3: A rock stress distribution model around the well is obtained by comprehensively considering variable temperature stress, temperature change and fluid seepage, and a critical sand production pressure difference prediction model of the sandstone gas reservoir after fracturing transformation is obtained.

10. The method for predicting the critical sand production pressure difference after fracturing of ultra-deep and ultra-high pressure sandstone gas reservoirs according to claim 9, characterized in that: The prediction model of critical sand production pressure difference of sandstone gas reservoir after fracturing transformation is as follows: Finally, by calculating the stress magnitude under different conditions and bringing it into the rock failure criterion, the critical sand production pressure difference of the reservoir after fracturing transformation is calculated: ΔP=p p -p w Where: ΔP—production pressure difference, MPa.

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