A method and device for predicting anisotropic reservoir fracture pressure

Abstract

The present invention discloses a method and device for predicting the fracture pressure of anisotropic reservoirs, including: collecting basic parameters required for calculation; solving by adopting high-order mixed partial differential characteristic equation method, stress decomposition and superposition method, establishing a horizontal wellbore stress model, and calculating stress components at any position; using a three-dimensional displacement discontinuity method to solve the strain dislocation of surrounding rocks caused by perforation holes to generate additional induced stress, and then superimposing the total stress distribution parameters of the horizontal wellbore, and obtaining the induced stress of the perforation holes through the stress decomposition and superposition principle; calculating the stress distribution around the perforation holes according to the corresponding reservoir parameters of the perforation holes; calculating the anisotropic tensile strength using the tensile strength of vertical bedding and parallel bedding, and further calculating the fracture pressure of the anisotropic reservoir based on the anisotropic failure criterion. The anisotropic reservoir fracture pressure prediction model provided by the present application has more complete considerations than the prior art, and the calculation results are more accurate.

Description

Technical Field

[0001] The invention relates to the field of petroleum and natural gas engineering, and in particular to a method and a device for predicting anisotropic reservoir fracture pressure. Background Art

[0002] Accurately predicting the fracture pressure is the basis for optimizing construction parameters such as fracturing operation displacement and sand-to-liquid ratio, and is also a prerequisite for the preparation of completion string, fracturing vehicle power, fracturing wellhead and surface manifold. If the fracture pressure prediction is inaccurate, it will lead to a series of problems such as the construction displacement failing to meet the design requirements, the small safety pressure window for fracturing construction, or even the inability to complete the fracturing construction, which will lead to property losses. Accurately predicting the fracture pressure is very important for fracturing projects.

[0003] Due to the development of anisotropic reservoir bedding fractures, there are anisotropic characteristics in which the mechanical characteristics of the layered strata are approximately the same, but the mechanical parameters of the strata at different vertical positions are different. The prediction technology of anisotropic reservoir fracture pressure is an important link in regulating fracturing construction parameters and achieving the expected fracturing effect, and has been widely used in major oil fields. The key to the success of this process is whether the fracture pressure can be accurately predicted.

[0004] However, the existing fracture pressure prediction models are mainly aimed at isotropic and linear elastic media, and are studied through experimental physical simulation, finite element, and mathematical methods. The dynamic damage constitutive model of strongly anisotropic rocks with developed bedding is currently less studied, incomplete, and still unclear. In addition, factors such as formation anisotropy, pore pressure distribution, in situ stress, cement sheath induced stress, perforation hole induced stress, and horizontal wellbore trajectory have not been fully considered to establish a horizontal wellbore stress prediction model that comprehensively considers rock mechanics, casing / cement sheath mechanical characteristics, percolation characteristics of fracturing fluid during injection, fluid disturbance, etc., and then based on the anisotropic formation rock failure criterion, an anisotropic reservoir fracture pressure prediction model is established. Summary of the invention

[0005] In view of this, an object of the embodiments of the present invention is to provide a method and device for predicting anisotropic reservoir fracture pressure.

[0006] On the one hand, the present application provides a method for predicting anisotropic reservoir fracture pressure, comprising the following steps:

[0007] Collect basic parameters required for calculation;

[0008] Calculate the anisotropic induced stress generated by the difference in anisotropic mechanical parameters of the anisotropic reservoir, superimpose the in situ stress induced stress and the casing cement sheath induced stress, and obtain the total stress distribution parameters of the horizontal wellbore through the principle of stress component superposition. The total stress distribution parameters of the horizontal wellbore include normal stress and shear stress;

[0009] The three-dimensional displacement discontinuity method is used to solve the additional induced stress caused by the strain dislocation of the surrounding rocks caused by the perforation holes, and then the total stress distribution parameters of the horizontal wellbore and the induced stress of the fracturing fluid percolation are superimposed. The induced stress of the perforation holes is obtained through the stress decomposition and superposition principle; the perforation hole induced stress distribution parameters include radial stress, circumferential stress, axial stress, and tangential stress around the perforation holes;

[0010] According to the reservoir parameters corresponding to the perforation holes, the radial stress, circumferential stress, axial stress and tangential stress around the perforation holes are calculated; further based on the rock body cracking criterion and natural fracture initiation criterion, the anisotropic reservoir fracture pressure is calculated; the calculated fracture pressures under different failure criteria are compared to predict the anisotropic reservoir fracture pressure.

[0011] Furthermore, the basic parameters required for calculation include reservoir parameters, anisotropic mechanical parameters, fracturing parameters, and completion parameters.

[0012] Furthermore, the reservoir parameters include original formation pressure, reservoir thickness, reservoir permeability, reservoir porosity, ground stress, comprehensive compression coefficient, and fracture zone parameters; the anisotropic mechanical parameters include Young's modulus parallel to bedding, Young's modulus perpendicular to bedding, Poisson's ratio parallel to bedding, Poisson's ratio perpendicular to bedding, rock tensile strength, weak plane cohesion, formation dip, formation inclination, and internal friction angle parameters; the fracturing parameters include construction displacement, fracturing fluid viscosity, cluster number, perforation depth, hole radius, perforation length, perforation density, and perforation phase angle parameters; and the completion parameters include Young's modulus of casing, Poisson's ratio of casing, outer diameter of casing, inner diameter of casing, and wellbore radius.

[0013] Furthermore, the intelligent regulation of the non-equilibrium expansion of multiple fractures in unconventional reservoir fracturing also includes:

[0014] Based on the equilibrium equation, strain-displacement equation, strain compatibility equation, and high-order mixed partial differential characteristic equation method, the stress distribution relation of anisotropic reservoir wellbore is established.

[0015] Based on anisotropic induced stress, superimposed on in situ stress induced stress and casing cement sheath induced stress, the total stress relationship of horizontal wellbore is established;

[0016] Based on the total stress of the horizontal wellbore, the stress distribution of the perforation holes is converted through the stress decomposition and superposition principles. Then, the perforation holes are superimposed to cause the surrounding rocks to produce additional induced stress due to strain dislocation and fracturing fluid infiltration induced stress, and the perforation hole stress relationship is established.

[0017] Furthermore, the anisotropic reservoir fracture pressure prediction also includes:

[0018] Anisotropic tensile strength is calculated using perpendicular-to-bedding and parallel-to-bedding tensile strengths;

[0019] Based on the rock body fracture initiation criterion and the perforation hole stress relationship, the anisotropic reservoir fracture pressure is calculated;

[0020] Based on the tensile fracture criterion of natural fractures and the stress relationship of perforation holes, the anisotropic reservoir fracture pressure is calculated.

[0021] Based on the shear failure criterion of natural fractures and the perforation hole stress relationship, the anisotropic reservoir failure pressure is calculated;

[0022] The anisotropic reservoir fracture pressures calculated based on three anisotropic failure criteria are compared, and the one with the minimum fracture pressure is used to predict the anisotropic reservoir fracture pressure.

[0023] On the other hand, the present application provides an anisotropic reservoir fracture pressure prediction device, comprising:

[0024] Basic parameter acquisition module, used to collect basic parameters required for calculation;

[0025] Anisotropic induced stress acquisition module, used to establish anisotropic reservoir wellbore stress distribution model and calculate anisotropic induced stress components through high-order mixed partial differential characteristic equation method;

[0026] The horizontal wellbore total stress acquisition module is used to obtain the total stress distribution parameters of the horizontal wellbore by superimposing the anisotropic induced stress generated by the difference in anisotropic mechanical parameters and the in-situ stress induced stress and the casing cement sheath induced stress through the principle of stress component superposition;

[0027] The perforation hole induced stress acquisition module is used to calculate the additional induced stress caused by the strain dislocation of the surrounding rocks caused by the perforation holes, and then superimpose the total stress distribution parameters of the horizontal wellbore and the induced stress of the fracturing fluid percolation to obtain the hole induced stress parameters around the perforation holes;

[0028] The anisotropic reservoir fracture pressure prediction module is used to calculate the radial stress, circumferential stress, axial stress and tangential stress around the perforation holes according to the reservoir parameters corresponding to the perforation holes; further calculate the anisotropic reservoir fracture pressure based on the rock body cracking criterion and the natural fracture cracking criterion; compare the calculated fracture pressures under different failure criteria to predict the anisotropic reservoir fracture pressure.

[0029] Furthermore, the basic parameters required for calculation include reservoir parameters, anisotropic mechanical parameters, fracturing parameters, and completion parameters.

[0030] Furthermore, the anisotropic reservoir fracture pressure prediction also includes:

[0031] The minimum value of the minimum rupture pressure is calculated based on the anisotropic failure criterion, and the judgment method is:

[0032]

[0033] Where: is the anisotropic reservoir fracture pressure calculated based on the rock body fracture criterion, MPa; is the anisotropic reservoir fracture pressure calculated based on the natural fracture shear fracture criterion, MPa; is the anisotropic reservoir fracture pressure calculated based on the natural fracture tensile fracture criterion, MPa.

[0034] Furthermore, it also includes:

[0035] The three-dimensional displacement discontinuity calculation unit is used to solve the three-dimensional displacement discontinuity of the discrete unit in the perforation hole direction, and then calculate the additional induced stress caused by the strain dislocation of the surrounding rock caused by the perforation hole.

[0036] Furthermore, it also includes:

[0037] Fracturing fluid percolation induced stress calculation unit, used to establish the perforation hole stress distribution relationship;

[0038] The poroelastic coefficient calculation unit is used to establish the anisotropic fracture criterion relationship.

[0039] The present application provides a dynamic damage constitutive model of highly anisotropic rocks taking into account the development of bedding, comprehensively considering the influence of factors such as anisotropic characteristics of formations, pore pressure distribution, in situ stress, cement sheath induced stress, perforation hole induced stress, and horizontal wellbore trajectory, and provides an anisotropic reservoir fracture pressure prediction model, which takes into account more complete factors and has more accurate calculation results than the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The relationship between the Young's modulus and the water content of rock in the embodiment of the present invention is a schematic diagram.

[0041] Figure 2 Schematic diagram of the variation of fracture pressure under different ratios of Young's modulus parallel to bedding and Young's modulus perpendicular to bedding in an embodiment of the present invention.

[0042] Figure 3 Schematic diagram of the variation of fracture pressure under different ratios of the Poisson's ratio of parallel bedding to the Poisson's ratio of vertical bedding in an embodiment of the present invention.

[0043] Figure 4 Schematic diagram of the change of fracture pressure of different original formation pore pressures in an embodiment of the present invention.

[0044] Figure 5 Schematic diagram of the variation of fracture pressure of different reservoir permeabilities in an embodiment of the present invention.

[0045] Figure 6 Schematic diagram of the variation of bursting pressure at different displacements in an embodiment of the present invention.

[0046] Figure 7 Schematic diagram of the change of fracture pressure at different viscosities in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The details of the present invention can be more clearly understood by combining the accompanying drawings and the description of the specific embodiments of the present invention. However, the specific embodiments of the present invention described herein are only used for the purpose of explaining the present invention and cannot be construed as limiting the present invention in any way. Under the guidance of the present invention, technicians can conceive of any possible variations based on the present invention, which should all be considered to belong to the scope of the present invention.

[0048] The present invention proposes a method and device for predicting anisotropic reservoir fracture pressure, which comprises the following steps:

[0049] 1. Collect the basic parameters required for calculation. The basic parameters required for calculation include reservoir parameters, anisotropic mechanical parameters, fracturing parameters, and completion parameters. Reservoir parameters include original formation pressure, reservoir thickness, reservoir permeability, reservoir porosity, geostress, comprehensive compression coefficient, and fracture zone parameters. Anisotropic mechanical parameters include Young's modulus parallel to bedding, Young's modulus perpendicular to bedding, Poisson's ratio parallel to bedding, Poisson's ratio perpendicular to bedding, rock tensile strength, weak plane cohesion, formation dip, formation dip, and internal friction angle parameters. Fracturing parameters include construction displacement, fracturing fluid viscosity, cluster number, perforation depth, hole radius, perforation length, perforation density, and perforation phase angle parameters. Completion parameters include Young's modulus of casing, Poisson's ratio of casing, outer diameter of casing, inner diameter of casing, and wellbore radius.

[0050] 2. Calculate the anisotropic induced stress generated by the difference in anisotropic mechanical parameters of the anisotropic reservoir, superimpose the in situ stress induced stress and the casing cement sheath induced stress, and obtain the total stress distribution parameters of the horizontal wellbore through the principle of stress component superposition. The total stress distribution parameters of the horizontal wellbore include normal stress and shear stress.

[0051] (1) Physical model of anisotropic reservoir fracturing

[0052] An effective way to initiate rock fracturing on site is to pump fracturing fluid into the wellbore to redistribute stress around the horizontal wellbore and perforation holes to reach the rock tensile strength, causing the formation to fracture and produce hydraulic fractures. Figure 1 It describes the stress redistribution caused by the pressure change in the horizontal wellbore and perforation holes after the fracturing fluid is pumped into the horizontal wellbore. The stress distribution model involves five coordinate systems: ① the global coordinate system (X, Y, Z), also known as the geodetic coordinate system; ② the geostress coordinate system (X s , Ys , Z s ), maximum horizontal principal stress σ H , minimum horizontal principal stress σ h , the angle between the minimum horizontal stress and the north coordinate is βs; ③ borehole coordinate system (x, y, z), the angle between the borehole and the Z direction is the well inclination angle ψ; the angle between the borehole projection and the true north direction is the azimuth angle β; the three coordinate directions correspond to the principal stress ④ Cylindrical coordinate system (R, θ, z), with the borehole coordinate system as reference, θ is also the perforation azimuth; ⑤ Borehole coordinate system (x p ,y p , z p ), ⑥ Stratigraphic coordinate system (x w ,y w , z w ), where the formation bedding dip is α w , tends to be β w .

[0053] (2) Horizontal wellbore stress distribution

[0054] This patent mainly uses high-order mixed partial differential characteristic equation method, stress decomposition and superposition method to solve the stress distribution of horizontal wellbore. For a cylindrical wellbore in an infinite reservoir, the stress acting on the wellbore surface is taken as follows: For anisotropic rock and transversely isotropic formation, according to the generalized Hooke's law, under the condition of small deformation, the constitutive equation reflecting the stress and strain in the elastic body is:

[0055]

[0056] Where: E is the elastic modulus parallel to the bedding plane, MPa; E' is the elastic modulus perpendicular to the bedding plane, MPa; v is the Poisson's ratio parallel to the bedding plane, dimensionless; v' is the Poisson's ratio perpendicular to the bedding plane, dimensionless.

[0057] Based on the above assumptions, the equilibrium equation can be written as:

[0058]

[0059] The strain-displacement equation is:

[0060]

[0061] The strain compatibility equation is:

[0062]

[0063] Combined with the generalized plane assumption ε z = 0 and the constitutive equation (1), σ z It can be expressed by the following formula:

[0064]

[0065] Two stress functions F(x, y) and Ψ(x, y) are introduced to solve these equations. The stress components can be expressed as functions of F(x, y) and Ψ(x, y):

[0066]

[0067] Substituting equations (5) and (6) into the constitutive equation (1), strain can be expressed by F(x, y) and Ψ(x, y). Substituting them into the compatibility equation (4), the Beltrami Michel compatibility equation is obtained:

[0068]

[0069] L2, L3, and L4 are second-order, third-order, and fourth-order differential operators, which are defined as follows:

[0070]

[0071] In the formula where a ij It is a component of the flexibility matrix.

[0072] The general solution of equation (7) is given by using the high-order mixed partial differential characteristic equation method:

[0073]

[0074] Where Re represents the real part of its parameter; F i (z i )(i=1,2,3) is the complex variable z i =x+μ i y, where (x, y) is the location of the point at which the stress component is calculated. i (i=1,2,3) and formation azimuth β w and formation dip angle α w Transformed to the wellbore coordinate system, the value is the three roots of equation (10):

[0075]

[0076] Among them, l2, l3 and l4 are the characteristic equations of the three differential operators L2, L3, L4 respectively:

[0077]

[0078] Lekhnitskii proved that equation (10) has only complex roots or purely imaginary roots. Three of these roots are complex conjugates of the other three. Therefore, let μ i (i=1,2,3) are the three roots of equation (10).i (i=1,2,3) can be defined as:

[0079]

[0080] Lekhnitskii then introduced three analytic functions φ i (z i )(i=1,2,3), which are defined as follows:

[0081]

[0082] Combining equations (12) and (13), we obtain:

[0083]

[0084] Therefore, the anisotropic stress components can be expressed as functions of F(x, y) and Ψ(x, y). i '(z i )(i=1,2,3) indicates that the analytical solution of the stress distribution around the anisotropic reservoir is:

[0085]

[0086] Where:

[0087]

[0088] The coefficient D W 、E W 、F W for:

[0089]

[0090] Where: θ is the perforation azimuth, °; p w Bottom hole pressure, MPa.

[0091] Stress component caused by wellbore formation. If the internal pressure is not considered, the wellbore wall stress is 0 after the wellbore is formed. Then for any point on the wellbore wall (R w ,θ), and its boundary conditions are:

[0092]

[0093] The pressure inside a circular hole in a transversely isotropic medium is zero. For any point along the hole wall (R w ,θ), the boundary conditions can be written as:

[0094]

[0095] Then equation (19) can be expressed as the analytical function φ i (zi )(i=1,2,3) three equations:

[0096]

[0097] The anisotropic induced stress in equation (15) is transformed into the wellbore coordinate system:

[0098]

[0099] (2) In situ stress induced stress

[0100] The in-situ stress state of the formation includes three mutually orthogonal principal stresses, namely the vertical in-situ stress σ v , minimum horizontal principal stress σ h and the maximum horizontal principal stress σ H The angle between the axis of the horizontal wellbore and the Z axis of the geodetic coordinate system is the well inclination angle ψ (ψ = π / 2), and the angle β between the axis of the wellbore and the true north direction is the azimuth. The normal stress component and shear stress component of the in-situ stress around the wellbore are:

[0101]

[0102] Where: H , σ h , σ v ——maximum and minimum horizontal principal stresses and vertical stresses, MPa; ψ, β——well inclination and azimuth, °.

[0103] (3) Casing cement sheath induced stress

[0104] For anisotropic reservoirs with casing perforation completion, since the mechanical properties of the casing, such as Young's modulus and Poisson's ratio, are quite different from those of the formation, when high-pressure fracturing fluid is continuously injected into the wellbore, stress and strain are generated due to the displacement between the casing and the formation, which induces casing cement sheath stress.

[0105] Along the radial distance, the induced stress distribution in the rock around the cased hole can be written as follows:

[0106]

[0107] Where: —Radial stress and circumferential stress induced by casing around the wellbore, MPa; TF—transmission coefficient, representing the transmission of pressure in the wellbore to the formation rock.

[0108]

[0109] Where: R o , R i are the outer diameter and inner diameter of the casing, m; E, Ec Young's modulus of formation and casing, MPa; v, v c —Poisson's ratio of formation and casing, dimensionless.

[0110] (4) Total stress in horizontal wellbore

[0111] Considering the influence of anisotropic reservoir in situ stress and casing cement sheath, the total stress distribution of horizontal wellbore can be obtained by superimposing the comprehensive effect of anisotropic induced stress and bottom hole pressure:

[0112]

[0113] Where: —Radial, circumferential, and axial normal stresses, radial and circumferential, circumferential and axial, and radial and axial shear stresses in the horizontal wellbore coordinate system, MPa.

[0114] 3. The three-dimensional displacement discontinuity method is used to solve the additional induced stress caused by the strain dislocation of the surrounding rocks caused by the perforation holes, and then the total stress distribution parameters of the horizontal wellbore are superimposed. The induced stress of the perforation holes is obtained through the stress decomposition and superposition principles; the perforation hole induced stress distribution parameters include radial stress, circumferential stress, axial stress, and tangential stress around the perforation holes.

[0115] (1) Perforation hole induced stress

[0116] During casing hydraulic fracturing, perforations are often required to create weak surfaces and advantageous channels for fluid inflow. The perforations cause stress and strain in the surrounding rocks, resulting in perforation-induced stress concentration, which leads to stress redistribution in the rocks near the perforation channels. The solution of stress distribution along the perforation channels is relatively complex and requires semi-analytical, analytical, numerical simulation and other methods to solve.

[0117] The perforation holes cause strain dislocation in the surrounding rocks, generating additional induced stress. The three-dimensional displacement discontinuity method is used to solve the redistribution of stress in the rocks near the perforation holes:

[0118]

[0119] Among them C r for:

[0120]

[0121] Where f(x1,x2,x3) is:

[0122]

[0123] like Equal partial derivatives mean that f(x1,x2,x3) first takes the partial derivative with respect to x1 and then takes the partial derivative with respect to x3.

[0124] First, the length direction of the perforation channel is discretized into N symmetric planes. At the initial moment, the normal stress and shear stress near the perforation channel are both the injection pore pressure p w Substituting into equation (26), the three-dimensional displacement discontinuity of the discrete unit in the perforation hole direction can be solved: and Then, the additional induced stress caused by the strain dislocation of the surrounding rocks caused by the perforation holes is calculated.

[0125] The total stress of the horizontal wellbore is converted to the stress distribution of the perforation holes through the principle of stress decomposition and superposition. The perforation holes are then superimposed to cause the surrounding rocks to undergo strain dislocation and generate additional induced stress, and the total perforation hole induced stress is obtained:

[0126]

[0127] Where: rp , σ θp , σ zp , τ θzp , τ rθp , τ rzp — radial, circumferential, and axial normal stresses, circumferential and axial, radial and circumferential, and radial and axial shear stresses in the perforation hole coordinate system, MPa; θ * —axis σ zp The angle of rotation of the cross section after being projected onto the perforation hole section, °; ​​subscript p—perforation hole.

[0128] (2) Fracturing fluid seepage induced stress

[0129] By introducing the pressure diffusion equation, the formation pressure change during fracturing is considered. When the fracturing fluid is injected into the wellbore, an external radial flow stress will be induced in the permeable rock. The formation is considered to be homogeneous and permeable, and the characteristics of the pore fluid are consistent with the fracturing fluid. The infiltration induced stress generated by fluid infiltration is:

[0130]

[0131] Where: superscript f is the radial, circumferential, axial and tangential induced stresses generated by fracturing fluid infiltration, MPa; R(t) is the excitation radius, m; r is w —perforation hole radius, m; p e —original formation pressure, MPa; r—the distance from any point in the formation to the perforation hole, m.

[0132] The pore pressure p and the excitation radius R(t) depend on the pore pressure distribution of the formation. iWhen injected into the formation, the fracturing fluid percolates through the porous medium rock, causing the pore pressure p distribution around the wellbore to change. According to Darcy's one-dimensional radial seepage model:

[0133]

[0134] Where: k—rock permeability; —formation porosity, dimensionless; μ—viscosity of fracturing fluid, mPa·s; c—compression coefficient of fracturing fluid, MPa -1 ; t—injection time, s.

[0135] The corresponding initial and boundary conditions are as follows:

[0136] Initial conditions:

[0137] t=0,p(r)=p e (32)

[0138] Internal boundary conditions:

[0139]

[0140] External boundary conditions:

[0141] r→∞,p(r,Q i )=p e ,t>0 (34)

[0142] Where: Q i —Fracturing fluid injection rate of the ith perforation cluster, m 3 / min; N p,i —Number of holes in the ith perforation cluster, dimensionless; L p,i —Depth of perforation holes in the ith perforation cluster, m.

[0143] Regarding formula (31), Lhomme et al. proposed a complex integral calculation method, which is difficult and cumbersome to solve. Therefore, a point source solution is used to solve the one-dimensional radial seepage problem. The pore pressure at the i-th cluster perforation position is:

[0144]

[0145] In formula (35), Ei is the power integral function:

[0146]

[0147] The excitation radius R(t) of the pressure distribution is associated with the pressure excitation front. Considering the time change, the pore pressure distribution at different times and positions is obtained; when moving a certain radius from the point source position to the formation boundary, the pore pressure gradually decreases; the condition for obtaining the excitation radius R(t) is that the pore pressure is equal to the original formation pressure.

[0148] (3) Stress distribution of perforation holes

[0149] On the wall R w The total stress of the perforation hole can be obtained by superimposing the in-situ stress, anisotropic induced stress, casing cement sheath induced stress, perforation hole induced stress, and fracturing fluid percolation induced stress components to obtain the radial stress σ around the perforation hole. rp , circumferential stress σ θp , axial stress σ zp , tangential stress τ θzp , τ rθp and τ rzp :

[0150]

[0151] 4. Calculate the radial stress, circumferential stress, axial stress and tangential stress around the perforation holes according to the corresponding reservoir parameters of the perforation holes; calculate the anisotropic tensile strength using the tensile strengths of the vertical and parallel layers, and further calculate the anisotropic reservoir fracture pressure based on the anisotropic failure criteria, which include the rock body cracking criteria and the natural fracture cracking criteria.

[0152] Anisotropic reservoirs are affected by natural fractures and inclination angles, and there are two ways of hydraulic fracture initiation at the horizontal wellbore wall, namely, fracture in the rock body and fracture along the natural fracture surface. Therefore, according to the formation stress state and the occurrence of natural fractures, a method for distinguishing the hydraulic fracture initiation mode and fracture pressure of two types of fractures, namely, the development of natural fractures in rock bedding and the development of hydraulic fractures in horizontal wells, was established.

[0153] (1) Rock body cracking criteria

[0154] Tensile failure is usually used to predict the fracture initiation pressure. It assumes that when the maximum principal stress component at any point on the wellbore reaches the rock tensile strength, the perforation hole will crack. The corresponding three principal stresses are as follows:

[0155] σ1=σ rp (38)

[0156]

[0157]

[0158] By comparing formulas (38)-(40), we can see that σ3 represents the maximum tensile stress (negative value) at the hole wall. When the hole elastic coefficient is considered, the effective maximum tensile stress will be reduced:

[0159]

[0160] When rocks absorb water, the Young's modulus of the formation rocks will change, which will in turn affect the poroelastic coefficient of the rocks. The poroelastic coefficient α is defined as:

[0161]

[0162] Where: K ma —Rock skeleton bulk modulus, MPa.

[0163] In order to obtain the relationship between Young's modulus and water content, a water absorption experiment of Longmaxi shale was carried out. The experimental temperature was 25℃ and the pressure was 1 atmosphere. First, the prepared 25mm×50mm standard rock sample was dried in a drying oven for 24 hours, and then weighed, recorded as the mass of the dry rock sample m0; then the rock sample was completely immersed in the slick water fracturing fluid (fresh water + 0.1% drag reducer + 0.1% anti-swelling agent + 1% drainage agent), and then a rock sample was taken out every 6 hours to measure the mass of the rock sample m at this time. After the measurement, a triaxial compression test (confining pressure 40MPa) was carried out to obtain Young's modulus and Poisson's ratio, and the water content ω was calculated according to ω=(m-m0) / m0×100%. Table 1 shows the Young's modulus data obtained from the triaxial experiment of the Longmaxi shale sample after water absorption. The results show that with the increase of water content, Young's modulus decreases and Poisson's ratio does not change much.

[0164] Table 1 Changes of Young's modulus and Poisson's ratio of Longmaxi Formation shale after water absorption

[0165]

[0166] In order to further clarify the relationship between Young's modulus and water content, a curve showing the relationship between Young's modulus and water content is drawn, such as Figure 1 shown.

[0167] Fitting the relationship between Young's modulus E and water content ω, we get:

[0168] E=-2708.5ω+34034 (43)

[0169] The water content near the perforation hole during the fracturing process can be defined as the ratio of the mass of the fracturing fluid injected in a certain period of time to the mass of the rock within the range of the excitation radius. When the rock is not saturated with water, the water content is a function of the injection volume; when the rock is saturated with water, the water content does not change, that is:

[0170]

[0171] Where: s is the density of fracturing fluid, kg / m 3 ρ r is the rock skeleton density, kg / m 3 .

[0172] Substituting equation (44) into equation (43) and then into equation (42), the expression of the poroelastic coefficient is obtained as follows:

[0173]

[0174] The volume balance during fluid injection also follows that the injection volume of the fracturing well per unit time is equal to the change in the compression of the elastic fluid in the disturbance area. The average pressure in the agitated area is:

[0175]

[0176] The maximum tensile stress criterion is used to determine the fracture initiation pressure:

[0177] σ f ≤-σ t (47)

[0178] Where: t —Tensile strength of rock, MPa.

[0179] The direction of crack initiation is determined by using Mohr's circle:

[0180]

[0181] Where: γ—crack initiation angle, rad.

[0182] The tensile strength of anisotropic reservoirs is considered as a combination of the tensile strengths parallel to the bedding and perpendicular to the bedding, that is:

[0183]

[0184] Where: T is the tensile strength tensor, MPa; ξ is the tensile strength margin, MPa.

[0185] The tensile strength tensor is:

[0186]

[0187] Where ξ is:

[0188] ξ=T 11 T 22 T 33 -T 11 T 23 T 32 -T 21 T 12 T 33 +T 31 T 12 T 23 +T 21 T 13 T 32 -T 31 T13 T 22 (51)

[0189] Where: α m , β m is the azimuth and dip of the transversely isotropic plane stratum, °; T m is the vertical bedding tensile strength, MPa; T b is the parallel bedding tensile strength, MPa.

[0190] Then, when the injection of fracturing fluid causes the bottom hole pressure to gradually increase to a level that satisfies equation (47), the rock body breaks, and the breaking pressure is recorded as

[0191] (2) Natural fracture initiation criteria

[0192] For formations with developed natural fractures, the hydraulic fracture initiation forms are divided into shear failure along natural fractures and tensile fracture along natural fractures. NF , the weak plane failure criterion can be used to study the shear failure problem of hydraulic fractures along natural fractures.

[0193] The shear failure criterion expression of natural fractures is:

[0194]

[0195] Where: σ1—maximum principal stress, MPa; σ3—minimum principal stress, MPa; C—weak surface cohesion; μ w —internal friction coefficient of weak surface; α w — is the angle between the weak plane normal and the horizontal maximum ground stress azimuth.

[0196] For fractured formations, C = 0, and the shear failure criterion of hydraulic fractures along natural fractures is:

[0197]

[0198] When the injection of fracturing fluid causes the bottom hole pressure to gradually increase to a level that satisfies equation (52), the hydraulic fracture shears along the natural fracture and the fracture pressure is recorded as

[0199] The tensile fracture criterion of natural fractures, the maximum horizontal stress orientation is β s , the expression of normal stress on the crack surface is:

[0200]

[0201] in:

[0202]

[0203] In the formula: TR - the trend of the natural fracture zone is TR degrees north-east.

[0204] The criterion for tensile rupture of hydraulic fractures along natural fractures is:

[0205]

[0206] (3) Fracture pressure prediction model

[0207] For anisotropic formations with developed natural fractures, the initiation of hydraulic fractures may be one of the following three forms: hydraulic fractures initiating in the rock body; hydraulic fractures initiating along natural fractures by tension; hydraulic fractures shearing along natural fractures. For a specific natural fracture formation, the fracture mode and fracture pressure p of hydraulic fractures are f The minimum value of the minimum rupture pressure calculated based on the anisotropic failure criterion is taken, and the judgment method is:

[0208]

[0209] 5. Computational Examples and Analysis

[0210] Taking an actual calculation example as an example, based on the method disclosed in this application, the fracture pressure parameters are predicted, and the influence of construction parameters and formation parameters on the fracture pressure is analyzed.

[0211] (1) Basic parameters

[0212] Table 2 Basic parameters

[0213]

[0214]

[0215] (2) Analysis of influencing factors

[0216] Reservoir mechanical parameters are important factors affecting anisotropic rock fracture pressure and safe construction. Therefore, the influence of mechanical parameters such as Young's modulus anisotropy, Poisson's ratio anisotropy, and pore pressure on fracture pressure was analyzed.

[0217] from Figure 2 It can be seen that when the ratio of the Young's modulus parallel to the bedding and perpendicular to the bedding (Est / En) is 1 ( Figure 2 a) The model in this paper degenerates into an isotropic stratum, and there is no anisotropic induced stress, so the fracture pressure does not change with the stratum dip and dip angle; when the ratio of the Young's modulus of parallel bedding to that of vertical bedding (Est / En) is 1.5, 2.5 (, Figure 2 b and Figure 2c) is anisotropic strata. The anisotropic stress induced by the difference in Young's modulus changes periodically with the formation dip and inclination, and the fracture pressure changes accordingly. When the formation inclination is less than 60°, the fracture pressure along the direction of the minimum horizontal principal stress is smaller, while the fracture pressure along the direction of the maximum horizontal principal stress is larger; when the formation inclination is greater than 60°, the fracture pressure along the direction of the minimum horizontal principal stress is larger, while the fracture pressure along the direction of the maximum horizontal principal stress is larger; and as the ratio of the Young's modulus parallel to the bedding and perpendicular to the bedding gradually increases, the fracture pressure gradually decreases. This is because, on the one hand, the difference in rock body strength in the directions perpendicular to the bedding and parallel to the bedding is greater and the strength is lower, and on the other hand, the anisotropy-induced normal stress increases and the shear stress decreases, the effective stress decreases, and it is more likely to be damaged.

[0218] from Figure 3 It can be seen that when the ratio of the Poisson's ratio of parallel bedding to vertical bedding (vst / vn) is 1 ( Figure 3 a) The model in this paper degenerates into an isotropic formation, there is no anisotropic induced stress, and the fracture pressure does not change with the formation dip and dip angle; when the ratio of the Poisson's ratio of parallel bedding to vertical bedding (vst / vn) is 1.5 and 2.5 ( Figure 3 b and Figure 3 c) For anisotropic strata, the anisotropic stress induced by the difference in Poisson's ratio changes periodically with the stratum dip and inclination, and the fracture pressure changes accordingly. The fracture pressure is larger along the direction of the maximum horizontal principal stress, while the fracture pressure is smaller along the direction of the minimum horizontal principal stress. As the ratio of the Poisson's ratio parallel to the bedding to the Poisson's ratio perpendicular to the bedding gradually increases, the fracture pressure gradually increases. This is because, on the one hand, the difference in rock body strength in the directions parallel to the bedding and perpendicular to the bedding is not obvious, and on the other hand, the anisotropy-induced normal stress decreases and the shear stress increases, the effective stress increases, and it is less likely to be damaged.

[0219] from Figure 4 It can be seen that as the original formation pore pressure decreases from 33.43MPa to 25MPa, the formation fracture pressure gradually increases. This is because the original formation pore pressure decreases, which, on the one hand, increases the effective stress of the injected fluid on the rock skeleton and requires more injected fluid energy to fracture the formation rock; on the other hand, the difference in anisotropic stress components at different inclinations and dips in the formation increases (low-angle bedding fracture pressure increases, high-angle bedding fracture pressure decreases), which in turn leads to an increase in high fracture pressure tendency and dip area, and a relative decrease in low fracture pressure tendency and dip area.

[0220] Reservoir physical parameters such as permeability are important factors affecting the fracturing fluid absorption capacity, fracturing fluid percolation and thus the anisotropic rock fracture pressure. Therefore, the influence of reservoir permeabilities of 0.0014mD, 0.005mD, 0.05mD and 0.5mD on the anisotropic fracture pressure was analyzed.

[0221] from Figure 5 It can be seen that as the permeability gradually increases from 0.0014mD to 0.5mD, the fracture pressure gradually decreases from 65.4MPa to 53.3MPa, and as the permeability gradually increases, the fracture reduction amplitude gradually decreases. This is because the greater the permeability, the faster the fluid transfers pressure to the formation, and it is easier to affect the reservoir, resulting in a larger excitation radius, a greater pore pressure, a smaller effective stress, and a smaller fracture pressure.

[0222] The established fracture pressure prediction model for horizontal wells in anisotropic reservoirs takes the influence of construction parameters into consideration, and can analyze the influence of construction displacement and fracturing fluid viscosity on anisotropic fracture pressure.

[0223] from Figure 6 It can be seen that when the perforation azimuth is 60°, the construction displacement is from 10m 3 / min gradually increased to 16m 3 / min, the fracture pressure increased from 57.7MPa to 65.4MPa. This is because the construction displacement increased and the fracturing fluid injection rate increased, which, on the one hand, would cause some microcracks at the beginning of the fracture, leading to higher hydrodynamic losses and crack growth in the form of shear failure; on the other hand, the rock absorbed water, resulting in an increase in water content, a decrease in Young's modulus, and a decrease in the poroelastic coefficient, which increased the normal stress in the axial direction of the perforation hole, increased the effective stress, and gradually increased the fracture pressure.

[0224] from Figure 7 It can be seen that as the viscosity gradually increases from 5mPa·s to 20mPa·s, the fracture pressure increases rapidly from 60MPa to 69MPa, but the fracture pressure growth rate gradually decreases; and as the viscosity gradually increases from 20mPa·s to 40mPa·s, the fracture pressure does not increase significantly. This is due to the difference between the velocity of fracturing fluid loss caused by viscosity and the formation's fluid absorption capacity; in the case of low viscosity, the viscosity increases, and the dominant fracturing fluid loss rate is much greater than the formation's fluid absorption rate, which increases the energy loss of the viscous fluid in the formation, causing the pore pressure to decrease, the effective stress to increase, and the fracture pressure to rise; in the case of high viscosity, the viscosity of the fracturing fluid increases, and the fracturing fluid loss rate does not increase significantly, so that the fracture pressure does not rise significantly.

[0225] The present invention is specifically described above through the embodiments. It is necessary to point out that the embodiments are only preferred embodiments of the present invention, and do not limit the present invention in any way, nor are they limited to the forms disclosed herein, and should not be regarded as excluding other embodiments. The modifications and simple changes made by those skilled in the art do not deviate from the technical idea and scope of the present invention, and all belong to the protection scope of the technical solution of the present invention.

Claims

1. A method for predicting anisotropic reservoir fracture pressure, characterized in that: The following steps are involved: Collect basic parameters required for calculation; Calculate the anisotropic induced stress generated by the difference in anisotropic mechanical parameters of the anisotropic reservoir, superimpose the in situ stress induced stress and the casing cement sheath induced stress, and obtain the total stress distribution parameters of the horizontal wellbore through the principle of stress component superposition. The total stress distribution parameters of the horizontal wellbore include normal stress and shear stress; The three-dimensional displacement discontinuity method is used to solve the additional induced stress caused by the strain dislocation of the surrounding rocks caused by the perforation holes, and then the total stress distribution parameters of the horizontal wellbore and the induced stress of the fracturing fluid percolation are superimposed. The induced stress of the perforation holes is obtained through the stress decomposition and superposition principle; the perforation hole induced stress distribution parameters include radial stress, circumferential stress, axial stress, and tangential stress around the perforation holes; According to the reservoir parameters corresponding to the perforation holes, the radial stress, circumferential stress, axial stress and tangential stress around the perforation holes are calculated; further based on the rock body cracking criterion and the natural fracture cracking criterion, the anisotropic reservoir fracture pressure is calculated; Compare the calculated fracture pressures under different failure criteria and predict the fracture pressure of anisotropic reservoirs; The anisotropic reservoir fracture pressure prediction further includes: Anisotropic tensile strength is calculated using perpendicular-to-bedding and parallel-to-bedding tensile strengths; Based on the rock body fracture initiation criterion and the perforation hole stress relationship, the anisotropic reservoir fracture pressure is calculated; Based on the tensile fracture criterion of natural fractures and the stress relationship of perforation holes, the anisotropic reservoir fracture pressure is calculated. Based on the shear failure criterion of natural fractures and the perforation hole stress relationship, the anisotropic reservoir failure pressure is calculated; The anisotropic reservoir fracture pressures calculated based on three anisotropic failure criteria are compared, and the one with the minimum fracture pressure is used to predict the anisotropic reservoir fracture pressure.

2. The anisotropic reservoir fracture pressure prediction method according to claim 1, characterized in that: The basic parameters required for calculation include reservoir parameters, anisotropic mechanical parameters, fracturing parameters, and completion parameters.

3. The anisotropic reservoir fracture pressure prediction method according to claim 2, characterized in that: The reservoir parameters include original formation pressure, reservoir thickness, reservoir permeability, reservoir porosity, ground stress, comprehensive compression coefficient, and fracture zone parameters; the anisotropic mechanical parameters include Young's modulus parallel to bedding, Young's modulus perpendicular to bedding, Poisson's ratio parallel to bedding, Poisson's ratio perpendicular to bedding, rock tensile strength, weak plane cohesion, formation dip, formation inclination, and internal friction angle parameters; the fracturing parameters include construction displacement, fracturing fluid viscosity, cluster number, perforation depth, hole radius, perforation length, perforation density, and perforation phase angle parameters; and the completion parameters include Young's modulus of casing, Poisson's ratio of casing, outer diameter of casing, inner diameter of casing, and wellbore radius.

4. The anisotropic reservoir fracture pressure prediction method according to claim 1, characterized in that: Also includes: Based on the equilibrium equation, strain-displacement equation, strain compatibility equation, and high-order mixed partial differential characteristic equation method, the stress distribution relation of anisotropic reservoir wellbore is established. Based on anisotropic induced stress, superimposed on in situ stress induced stress and casing cement sheath induced stress, the total stress relationship of horizontal wellbore is established; Based on the total stress of the horizontal wellbore, the stress distribution of the perforation holes is converted through the stress decomposition and superposition principles. The perforation holes are then superimposed to cause the surrounding rocks to produce additional induced stress due to strain dislocation and fracturing fluid infiltration induced stress, and the perforation hole stress relationship is established.

5. An anisotropic reservoir fracture pressure prediction device, comprising: Basic parameter acquisition module, used to collect basic parameters required for calculation; Anisotropic induced stress acquisition module, used to establish anisotropic reservoir wellbore stress distribution model and calculate anisotropic induced stress components through high-order mixed partial differential characteristic equation method; The horizontal wellbore total stress acquisition module is used to obtain the total stress distribution parameters of the horizontal wellbore by superimposing the anisotropic induced stress generated by the difference in anisotropic mechanical parameters and the in-situ stress induced stress and the casing cement sheath induced stress through the principle of stress component superposition; The perforation hole induced stress acquisition module is used to calculate the additional induced stress caused by the strain dislocation of the surrounding rocks caused by the perforation holes, and then superimpose the total stress distribution parameters of the horizontal wellbore and the induced stress of the fracturing fluid percolation to obtain the hole induced stress parameters around the perforation holes; Anisotropic reservoir fracture pressure prediction module, used to calculate radial stress, circumferential stress, axial stress and tangential stress around the perforation holes according to the reservoir parameters corresponding to the perforation holes; Furthermore, based on the rock body cracking criteria and natural fracture initiation criteria, the anisotropic reservoir fracture pressure is calculated; the calculated fracture pressures under different failure criteria are compared to predict the anisotropic reservoir fracture pressure.

6. The anisotropic reservoir fracture pressure prediction device according to claim 5, characterized in that: The basic parameters required for calculation include reservoir parameters, anisotropic mechanical parameters, fracturing parameters, and completion parameters.

7. The anisotropic reservoir fracture pressure prediction device according to claim 6, characterized in that: The anisotropic reservoir fracture pressure prediction further includes: The minimum value of the minimum rupture pressure is calculated based on the anisotropic failure criterion, and the judgment method is: Where: is the anisotropic reservoir fracture pressure calculated based on the rock bulk fracture initiation criterion, MPa; is the anisotropic reservoir failure pressure calculated based on the natural fracture shear failure criterion, MPa; is the anisotropic reservoir failure pressure calculated based on the tensile failure criterion of natural fractures, MPa.

8. The anisotropic reservoir fracture pressure prediction device according to claim 5, characterized in that: Also includes: The three-dimensional displacement discontinuity calculation unit is used to solve the three-dimensional displacement discontinuity of the discrete unit in the perforation hole direction, and then calculate the additional induced stress caused by the strain dislocation of the surrounding rock caused by the perforation hole.

9. The anisotropic reservoir fracture pressure prediction device according to claim 5, characterized in that: Also includes: Fracturing fluid percolation induced stress calculation unit, used to establish the stress distribution relationship of the perforation holes; The poroelastic coefficient calculation unit is used to establish the anisotropic fracture criterion relationship.

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