A method for predicting hydraulic fracturing pressure based on the unified strength theory

Abstract

The present invention discloses a method for predicting hydraulic fracturing pressure based on the unified strength theory, which includes collecting in-situ stress field data, formation fluid pressure and rock mechanics parameters of the target reservoir; calculating the material tensile-compressive ratio parameter and the rock mass tensile strength according to the rock mechanics parameters; determining the relative magnitude order of the three-dimensional effective principal stresses borne by the wellbore during hydraulic fracturing according to the effective stress calculation formula in the poroelastic medium of the rock mass; determining the corresponding stress mode and the calculation coefficients of the three-dimensional effective principal stresses according to the relative magnitude order of the three-dimensional effective principal stresses; establishing a hydraulic fracturing pressure calculation model by using the unified strength theory; calculating the fracture pressure according to the hydraulic fracturing pressure calculation model and the calculation coefficients of the three-dimensional effective principal stresses; and conducting a consistency check of the fracture pressure and the stress mode to determine the fracture pressure of the hydraulically fractured rock mass. The present invention fills the blank of predicting hydraulic fracturing pressure by comprehensively considering the influence of normal stress and shear stress; and improves the accuracy of predicting the fracture pressure of hydraulically fractured rock mass.

Description

Technical Field

[0001] The present invention relates to a method for predicting hydraulic fracturing pressure based on the unified strength theory, belonging to the technical field of hydraulic fracturing stimulation in oil and gas field development. Background Technique

[0002] Hydraulic fracturing of rock mass is the core technology in the field of oil and gas field development. The fracture pressure of the target reservoir rock mass is a key parameter that restricts the reasonable configuration of fracturing equipment, the optimization of construction parameters, and the improvement of the economy of hydraulic fracturing. Currently, the methods for predicting the fracture pressure of hydraulic fractured rock mass are all carried out using the first strength theory or linear elastic fracture mechanics, ignoring the influence of the cooperative effect of rock mass units under shear action, resulting in a significant difference between the obtained prediction results and the field response. To improve the prediction accuracy of hydraulic fracturing fracture pressure and more accurately guide field applications, corrections are usually made using empirical correction coefficients combined with field practice data in characteristic regions, but the objectivity and effectiveness of this correction are poor.

[0003] Research results in rock mechanics have shown that shear stress is the basic factor for rock mass failure, and both the normal stress and shear stress on the shear stress plane affect rock mass fracture. The wellbore wall of the hydraulically fractured formation is subjected to the action of three principal stresses in the vertical direction, the maximum and minimum horizontal directions, and they all contribute to the fractured rock, and their influence should be comprehensively considered. The unified strength theory considers the different action effects of all stress components on the double-shear unit body. When the influence functions of the two larger shear stresses and the normal stress on the acting surface acting on the double-shear unit body reach a certain limit value, the rock mass fails. Wang Jixiu et al. considered the seepage effect and pore water pressure of the rock around the wellbore, and carried out elastoplastic analysis on the rock around the wellbore based on the unified strength theory, and studied the stress distribution of the rock around the wellbore and the elastic and plastic limit loads of wellbore stability. Obviously, the unified strength theory can better characterize the hydraulic fracturing pressure of rock mass, and no relevant research results have been seen in this regard, which is still blank. Summary of the Invention

[0004] In order to overcome the defects existing in the prior art, the present invention aims to provide a method for predicting hydraulic fracturing pressure based on the unified strength theory. This method can comprehensively and objectively reflect the hydraulic fracturing mechanism under the combined action of the two larger shear stresses and the normal stress acting on the double-shear unit body, filling the blank of comprehensively considering the influence of normal stress and shear stress to predict hydraulic fracturing pressure; and improving the accuracy of predicting the fracture pressure of hydraulically fractured rock mass.

[0005] The technical solution provided by the present invention to solve the above technical problems is: a method for predicting hydraulic fracturing pressure based on the unified strength theory, including the following steps:

[0006] A. Collect the in-situ stress field data, reservoir fluid pressure, and rock mechanics parameters of the target reservoir;

[0007] B. Calculate the material tensile-compressive ratio parameter and the rock mass tensile strength based on the rock mechanics parameters;

[0008] C. Determine the relative magnitude order of the three-dimensional effective principal stresses borne by the wellbore during hydraulic fracturing according to the effective stress calculation formula in the poroelastic medium of the rock mass;

[0009] D. Determine the corresponding stress mode and the calculation coefficients of the three-dimensional effective principal stresses according to the relative magnitude order of the three-dimensional effective principal stresses;

[0010] E. Establish a hydraulic fracturing pressure calculation model using the unified strength theory;

[0011] F. Calculate the fracture pressure according to the hydraulic fracturing pressure calculation model and the calculation coefficients of the three-dimensional effective principal stresses;

[0012] G. Conduct a consistency check between the fracture pressure and the stress mode to determine the fracture pressure of the hydraulically fractured rock mass.

[0013] A further technical solution is that the in-situ stress field data includes the maximum horizontal principal stress, the minimum principal stress, and the overburden rock pressure; the rock mechanics parameters include the cohesion, the internal friction angle, the poroelastic constant, the Poisson's ratio, and the material characteristic parameter.

[0014] A further technical solution is that the calculation formulas for the material tensile-compressive ratio parameter and the rock mass tensile strength are:

[0015]

[0016]

[0017] In the formula: C is the cohesion of the rock mass, MPa; φ is the internal friction angle of the rock mass, °; σ ten is the rock mass tensile strength, MPa; a is the material tensile-compressive ratio parameter, dimensionless.

[0018] A further technical solution is that the effective stress calculation formula in the poroelastic medium of the rock mass includes:

[0019]

[0020] σ1 = max(σ t,e , σ r,e , σ z,e )

[0021] σ3 = min(σ t,e , σ r,e , σ z,e )

[0022] σ2 = mid(σ t,e , σr,e , σ z,e )

[0023] Where: σ r,e , σ t,e , σ z,e are respectively the effective total stresses acting on the shaft wall in the radial, circumferential and axial directions, MPa; σ H , σ h are respectively the maximum horizontal principal stress and the minimum horizontal principal stress, MPa; α is the poroelastic constant of the rock mass, dimensionless; p i , p r are respectively the injection pressure into the wellbore and the formation fluid pressure during hydraulic fracturing, MPa; σ1, σ2, σ3 are respectively the maximum, intermediate and minimum effective principal stresses, MPa; t0, r0, z0, t1, r1, z1, k are all intermediate parameters.

[0024] A further technical solution is that in step D, it is divided into the following six stress modes according to the relative magnitude relationship of the three principal stresses, that is,

[0025] σ1 = σ r,e > σ2 = σ z,e > σ3 = σ t,e

[0026] σ1 = σ r,e > σ2 = σ t,e > σ3 = σ z,e

[0027] σ1 = σ z,e > σ2 = σ r,e > σ3 = σ t,e

[0028] σ1 = σ z,e > σ2 = σ t,e > σ3 = σ r,e

[0029] σ1 = σ t,e > σ2 = σ z,e > σ3 = σ r,e

[0030] σ1 = σ t,e > σ2 = σ r,e > σ3 = σ z,e

[0031] And the calculation coefficients of the corresponding σ1, σ2, σ3 are determined according to the six stress modes:

[0032] (max0, max1), (mid0, mid1), (min0, min1)

[0033] In the formula: max0, mid0, and min0 are the coefficients of the maximum, intermediate, and minimum effective principal stresses independent of the injection pressure, dimensionless; max1, mid1, and min1 are the coefficients of the maximum, intermediate, and minimum effective principal stresses related to the injection pressure, dimensionless.

[0034] A further technical solution is that the hydraulic fracturing pressure calculation model includes:

[0035] When ;

[0036]

[0037] When ;

[0038]

[0039] In the formula: max0, mid0, and min0 are the coefficients of the maximum, intermediate, and minimum effective principal stresses independent of the injection pressure, dimensionless; max1, mid1, and min1 are the coefficients of the maximum, intermediate, and minimum effective principal stresses related to the injection pressure, dimensionless; b is the material characteristic parameter, dimensionless; a is the material tensile-compressive ratio parameter, dimensionless; φ is the internal friction angle of the rock mass, °; σ ten is the tensile strength of the rock mass, MPa; σ1, σ2, and σ3 are the maximum, intermediate, and minimum effective principal stresses, MPa; p F is the splitting pressure of the rock mass, MPa.

[0040] A further technical solution is that the specific process of step G is as follows:

[0041] Compare the splitting pressure of the rock mass calculated in step F with the injection pressure in step C. If the splitting pressure of the rock mass is not equal to the injection pressure, repeat steps C - step F until the splitting pressure of the rock mass is equal to the injection pressure, then the splitting pressure of the rock mass is the fracture pressure of the hydraulically fractured rock mass.

[0042] The present invention has the following beneficial effects: It belongs to the technical field of hydraulic fracturing stimulation in oil and gas field development. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a diagram of the relationship between the three-dimensional effective principal stresses and the injection pressure during hydraulic fracturing;

[0044] Figure 2 It is a consistency check diagram of the hydraulic fracturing fracture pressure PF - three-dimensional effective principal stresses under three stress modes;

[0045] Figure 3 It is a consistency check diagram of the hydraulic fracturing fracture pressure PF* - three-dimensional effective principal stresses under three stress modes. Detailed implementation manners

[0046] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] A method for predicting hydraulic fracturing pressure based on the unified strength theory of the present invention includes the following steps:

[0048] A. Collect in-situ stress field data, reservoir fluid pressure, and rock mechanical parameters of the target reservoir;

[0049] A1. The in-situ stress of the hydraulic fracturing rock formation (maximum horizontal principal stress, minimum principal stress, overburden pressure) is obtained by methods such as field stress testing, differential strain or Kaiser effect experimental testing, and logging data interpretation;

[0050] A2. The rock mechanical parameters of the hydraulic fracturing rock formation, including cohesion and internal friction angle, pore elastic constant and Poisson's ratio, and material characteristic parameters, are obtained through core experiments according to national standards;

[0051] A3. The formation pressure of the hydraulic fracturing rock formation is obtained by methods such as logging or pressure build-up.

[0052] B. Calculate the material tension-compression ratio parameter and the tensile strength of the rock mass according to the rock mechanical parameters;

[0053]

[0054] In the formula: C is the cohesion of the rock mass, MPa; φ is the internal friction angle of the rock mass, °; σ ten is the tensile strength of the rock mass, MPa; a is the material tension-compression ratio parameter, dimensionless;

[0055] C. Determine the relative magnitude order of the three-dimensional effective principal stresses borne by the wellbore during hydraulic fracturing according to the effective stress calculation formula in the poroelastic medium of the rock mass;

[0056] Establish a calculation model for the three-dimensional principal stresses on the wellbore wall during hydraulic fracturing; use the method of elastic mechanics to calculate the circumferential (tangential), radial, and axial three-dimensional principal stresses acting on the wellbore wall due to the combined action of in-situ stress, high-pressure injection of fracturing fluid into the wellbore, and seepage effect due to pressure difference.

[0057] The three-dimensional principal stress calculation model using elastic mechanics notation is as follows:[[]]

[0058]

[0059] where: σ r 、σ t 、σ z are the total combined stresses acting on the wellbore in the radial, circumferential, and axial directions, respectively, in MPa; σ H 、σ h are the maximum horizontal principal stress and the minimum horizontal principal stress, respectively, in MPa; p i 、p r are the injection pressure into the wellbore during hydraulic fracturing and the formation fluid pressure, respectively, in MPa; α and ν are the poroelastic constants and Poisson's ratio of the rock mass, dimensionless;

[0060] Let

[0061]

[0062] where: α and ν are the poroelastic constants and Poisson's ratio of the rock mass, dimensionless; t0, r0, z0, t1, r1, z1, and k are all intermediate parameters; σ H 、σ h are the maximum horizontal principal stress and the minimum horizontal principal stress, respectively, in MPa; σ v is the overburden pressure, in MPa;

[0063] According to the principle of effective stress, the calculation formula for the effective stress in a poroelastic medium of rock mass is expressed as:

[0064]

[0065] where: σ r,e 、σ t,e 、σ z,e are the effective total stresses acting on the wellbore in the radial, circumferential, and axial directions, respectively, in MPa;

[0066] After calculating the three-dimensional effective principal stresses of the wellbore, compare their relative magnitudes

[0067]

[0068] where: σ1, σ2, and σ3 are the maximum, intermediate, and minimum effective principal stresses, respectively, in MPa;

[0069] C. Determine the corresponding stress mode and the calculation coefficients of the three-dimensional effective principal stresses according to the relative magnitude order of the three-dimensional effective principal stresses;

[0070] According to the relative magnitude relationship of the three-dimensional principal stresses, it is divided into the following six stress modes, namely,

[0071]

[0072] And determine the corresponding calculation coefficients of σ1, σ2, and σ3 according to the six stress modes:

[0073] (max0, max1), (mid0, mid1), (min0, min1)(10)

[0074] Where: max0, mid0, and min0 are the coefficients corresponding to the maximum, intermediate, and minimum effective principal stresses in Equation (7) that are independent of the injection pressure, dimensionless; max1, mid1, and min1 are the coefficients corresponding to the maximum, intermediate, and minimum effective principal stresses in Equation (7) that are related to the injection pressure, dimensionless;

[0075] D. Establish a calculation model for the hydraulic fracturing pressure using the unified strength theory;

[0076] According to the unified strength theory, the rock mass fracture pressure of hydraulic fracturing is calculated in two categories. When the rock mass fractures under any stress mode, the following calculation model should be satisfied. That is,

[0077] When ;

[0078]

[0079] When ;

[0080]

[0081] Where: max0, mid0, and min0 are the coefficients corresponding to the maximum, intermediate, and minimum effective principal stresses that are independent of the injection pressure, dimensionless; max1, mid1, and min1 are the coefficients corresponding to the maximum, intermediate, and minimum effective principal stresses that are related to the injection pressure, dimensionless; b is the material characteristic parameter, dimensionless; a is the material tensile-compressive ratio parameter, dimensionless; φ is the internal friction angle of the rock mass, °; σ ten is the tensile strength of the rock mass, MPa; σ1, σ2, and σ3 are the maximum, intermediate, and minimum effective principal stresses, MPa; p F is the splitting pressure of the rock mass, MPa;

[0082] F. Calculate the fracture pressure according to the hydraulic fracturing pressure calculation model and the calculation coefficients of the three-dimensional effective principal stresses;

[0083] G. Conduct a consistency check of the fracture pressure and the stress mode to determine the fracture pressure of the hydraulically fractured rock mass;

[0084] In Equation (7), the injection pressure is included. In fact, the injection fluid pressure during rock mass fracture is the formation fracture pressure. Let p F = p i in Equation (7) and solve to obtain the fracture pressure calculation formula.

[0085] Compare the rock mass splitting pressure calculated in step F with the injection pressure in step C. If the rock mass splitting pressure is not equal to the injection pressure, repeat steps C - F until the rock mass splitting pressure is equal to the injection pressure. Then, the rock mass splitting pressure is the fracture pressure of the water - pressure - fractured rock mass.

[0086] Embodiment

[0087] The first embodiment of a method for calculating the fracture pressure of a plastic formation fracturing in the present invention includes the following steps:

[0088] A. Collect the in - situ stress field data, Poisson's ratio of the rock mass, cohesion, internal friction angle, reservoir fluid pressure, and pore - elastic constant of the target reservoir.

[0089] In this example, the horizontal two - dimensional principal stresses are determined by the core Kaiser experiment test. The horizontal maximum principal stress σ H = 102 MPa, the horizontal minimum principal stress σ h = 90 MPa, and the overburden pressure σ v = 96 MPa.

[0090] In this example, it is determined by core experiments. The rock cohesion C = 25 MPa, the internal friction angle φ = 30°, the pore - elastic constant α = 0.7, Poisson's ratio ν = 0.2, and the material characteristic parameter b = 0.5.

[0091] In this example, it is obtained by well - logging interpretation. The reservoir fluid pressure Pr = 75 MPa.

[0092] B. Calculate the material tension - compression ratio parameter and strength parameter.

[0093] The material parameters are calculated according to the following formula:

[0094]

[0095] [[ID=�6]]C. Determine the relative magnitude order of the three - dimensional effective principal stresses borne by the wellbore during water - pressure fracturing

[0096] C1. Calculation model of the three - dimensional effective principal stresses borne by the wellbore during water - pressure fracturing;

[0097]

[0098] Calculate the effective stress of the rock mass;

[0099]

[0100] C2. Given the injection pressure change, the relative magnitudes of the three - dimensional effective principal stresses during water - pressure fracturing can be compared

[0101] For example, when the injection pressure during water - pressure fracturing is 120.23 MPa

[0102]

[0103] Then there is

[0104] σ1 = max(σ t,e , σ r,e , σ z,e ) = max(-12.645, 36.07, 7.04) = 36.07 MPa

[0105] σ3 = min(σ t,e , σ r,e , σ z,e ) = min(-12.645, 36.07, 7.04) = -12.645 MPa

[0106] σ2 = mid(σ t,e , σ r,e , σ z,e ) = mid(-12.645, 36.07, 7.04) = 7.04 MPa

[0107] D. Establish a calculation model for the hydraulic fracturing pressure using the unified strength theory;

[0108] E. Calculate the fracture pressure according to the calculation model for the hydraulic fracturing pressure and the calculation coefficients of the three-dimensional effective principal stresses;

[0109] E1. Divide the stress patterns of the rock mass subjected to hydraulic fracturing;

[0110] Assume that the stress pattern during hydraulic fracturing is the following stress pattern among the six patterns, that is,

[0111] σ1 = σ r,e > σ2 = σ t,e > σ3 = σ z,e

[0112] Determine the corresponding calculation coefficients of σ1, σ2, and σ3 according to the stress pattern:

[0113] max0 = r0 = 0, max1 = r1 = 0.3

[0114] mid0 = t0 = 128.625, mid1 = t1 = -1.175

[0115] min0 = z0 = 91.2, min1 = z1 = -0.7

[0116] E2. Calculation model for the fracture pressure of the rock mass subjected to hydraulic fracturing;

[0117] The injection fluid pressure during rock mass fracture is the formation fracture pressure as the three-dimensional effective pressure borne by the wellbore includes the injection pressure. That is, p F = pi The calculation formula for the fracture pressure is obtained by solving.

[0118] According to the unified strength theory, the rock mass fracture pressure of hydraulic fracturing is calculated in two categories. When the rock mass fractures under any stress mode, it should satisfy the following calculation model. That is

[0119] When

[0120]

[0121] (2) When

[0122]

[0123] Calculate the fracture pressure under each stress mode;

[0124] For each stress mode, calculate the corresponding fracture pressure according to formula (11) and formula (12) respectively.

[0125]

[0126] Take the fracture pressure as the injection pressure to calculate the corresponding triaxial effective principal stress when the rock mass fractures (see the above table). The fracture pressure consistent with the assumed stress mode is the true fracture pressure of the rock mass, as shown by "√" in the above table. That is, the fracture pressure is 129.87 MPa.

[0127] As mentioned above, it is not a restriction on the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in this field can make some changes or modifications within the scope of the technical solution of the present invention to obtain equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of the technical solution of the present invention.

Claims

1. A method for predicting hydraulic fracturing pressure based on unified strength theory, characterized in that: The following steps are involved: A. Collect in-situ stress field data, formation fluid pressure and rock mechanical parameters of the target reservoir; B. Calculate the material tension-compression ratio parameters and rock mass tensile strength based on rock mechanics parameters; C. Determine the relative magnitude order of the three-dimensional effective principal stresses borne by the wellbore wall during hydraulic fracturing based on the calculation formula for effective stress in the pore elastic medium of the rock mass; D. Determine the corresponding stress mode and the calculation coefficient of the three-dimensional effective principal stress according to the relative magnitude order of the three-dimensional effective principal stress; In step D, the stress modes are divided into the following six types according to the relative magnitude relationship of the three principal stresses, namely, σ1=σ r,e >σ2=σ z,e >σ3=σ t,e σ1=σ r,e >σ2=σ t,e >σ3=σ z,e σ1=σ z,e >σ2=σ r,e >σ3=σ t,e σ1=σ z,e >σ2=σ t,e >σ3=σ r,e σ1=σ t,e >σ2=σ z,e >σ3=σ r,e σ1=σ t,e >σ2=σ r,e >σ3=σ z,e And the calculation coefficients of corresponding σ1, σ2, and σ3 are determined according to the six stress modes: (max0,max1), (mid0,mid1), (min0,min1) Where: max0, mid0, min0 are the coefficients of the maximum, intermediate and minimum effective principal stresses that are independent of the injection pressure, respectively, and are dimensionless; max1, mid1, min1 are the coefficients of the maximum, intermediate and minimum effective principal stresses that are related to the injection pressure, respectively, and are dimensionless; σ r,e , σ t,e , σ z,e are the effective total stresses acting on the wellbore wall in radial, circumferential and axial directions, MPa; E. Use unified strength theory to establish a hydraulic fracturing pressure calculation model; The hydraulic fracturing pressure calculation model includes: when hour; when hour; Where: max0, mid0, min0 are the coefficients of the maximum, intermediate and minimum effective principal stresses that are independent of the injection pressure, respectively, and are dimensionless; max1, mid1, min1 are the coefficients of the maximum, intermediate and minimum effective principal stresses that are related to the injection pressure, respectively, and are dimensionless; b is the material characteristic parameter, dimensionless; a is the material tension-compression ratio parameter, dimensionless; φ is the internal friction angle of the rock mass, in degrees; σ ten is the tensile strength of the rock mass, MPa; σ1, σ2, σ3 are the maximum, intermediate and minimum effective principal stresses, MPa respectively; p F is the rock splitting pressure, MPa; F. Calculate the fracture pressure based on the hydraulic fracturing pressure calculation model and the calculation coefficients of the three-dimensional effective principal stress; G. Perform consistency check of fracture pressure and stress pattern to determine the fracture pressure of hydraulically fractured rock mass.

2. The method for predicting hydraulic fracturing pressure based on unified strength theory according to claim 1, characterized in that: The in-situ stress field data include horizontal maximum principal stress and minimum principal stress, and overlying rock pressure; the rock mechanics parameters include cohesion and internal friction angle, poroelastic constant, Poisson's ratio and material characteristic parameters.

3. The method for predicting hydraulic fracturing pressure based on unified strength theory according to claim 1, characterized in that: The calculation formulas for the material tension-compression ratio parameters and rock mass tensile strength are as follows: Where: C is the cohesion of the rock mass, MPa; φ is the internal friction angle of the rock mass, °; σ ten is the tensile strength of rock mass, MPa; a is the material tension-compression ratio parameter, dimensionless.

4. The method for predicting hydraulic fracturing pressure based on unified strength theory according to claim 1, characterized in that: The formula for calculating the effective stress in the rock mass poroelastic medium includes: σ1=max(σ t,e ,s r,e ,s z,e ) σ3=min(σ t,e ,s r,e ,s z,e ) σ2=mid(σ t,e ,s r,e ,s z,e ) Where: σ r,e , σ t,e , σ z,e are the effective total stresses acting on the wellbore wall in radial, circumferential and axial directions, MPa; σ H , σ h are the maximum horizontal principal stress and the minimum horizontal principal stress, MPa; α is the poroelastic constant of the rock mass, dimensionless; p i 、p r are the injection pressure into the wellbore and the formation fluid pressure during hydraulic fracturing, MPa; σ1, σ2, σ3 are the maximum, intermediate and minimum effective principal stresses, MPa; t0, r0, z0, t1, r1, z1, k are all intermediate parameters; σ r , σ t , σ z are the combined total stresses in radial, circumferential and axial directions acting on the well wall, MPa; ν is the Poisson's ratio of the rock mass, dimensionless.

5. The method for predicting hydraulic fracturing pressure based on unified strength theory according to claim 1, characterized in that: The specific process of step G is: Compare the rock splitting pressure calculated in step F with the injection pressure in step C. If the rock splitting pressure is not equal to the injection pressure, repeat steps C-F until the rock splitting pressure is equal to the injection pressure. The rock splitting pressure is the fracture pressure of the hydraulically fractured rock mass.

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