A quantitative prediction method for reservoir fractures based on the principle of minimum energy consumption

Abstract

The present invention discloses a quantitative prediction method for reservoir fractures based on the principle of minimum energy consumption. Based on rock mechanics experiments, classical mechanics theory and the law of conservation of energy, a new theory reflecting the basic development law of nature, the principle of minimum energy consumption, is introduced. The stress-energy consumption coupling concept is applied to analyze the deformation and fracture process of the rock mass, a rock fracture criterion under a unified theoretical framework is constructed, and a fracture parameter characterization model is derived and established. On the basis of three-dimensional finite element stress field simulation, a quantitative prediction of the three-dimensional spatial distribution of fractures in low-permeability sandstone reservoirs is achieved. The present invention solves the problem of accurately obtaining and quantitatively characterizing the complex fracture parameters of low-permeability sandstone reservoirs, and is suitable for any quantitative prediction of fractures dominated by low-permeability sandstone reservoirs; it effectively predicts the occurrence, volume density and linear density of fractures in low-permeability sandstone reservoirs under the action of stress fields, providing a reliable basis for studying the favorable development areas of fractured reservoirs, and reducing the risks and costs of exploration and development.

Description

Technical Field

[0001] The present invention relates to the field of oil exploration, and particularly to a method for quantitatively predicting reservoir fractures based on the principle of minimum energy consumption. Background Art

[0002] With the continuous development of conventional reservoirs, there is an urgent need to find new oil and gas replacement areas in China and even the world to meet the growing energy demand. Therefore, low-permeability sandstone reservoirs have become a hot spot in global oil and gas exploration. It has been proven that low-permeability sandstone reservoirs are widely developed in various oil and gas bearing basins in China, and their resource volume accounts for about 30% of the total national oil resources. In low-permeability sandstone reservoirs, due to strong diagenetic compaction and cementation, the matrix porosity is usually less than 10%, and the permeability is lower than 1×10 -3 μm 2 , making it difficult to form an efficient seepage system. However, such reservoirs often develop a large number of tectonic fractures, and thus tectonic fractures become an important factor in improving reservoir physical properties and increasing oil and gas production capacity. Therefore, how to quantitatively predict tectonic fractures in low-permeability sandstone reservoirs has become a hot research issue at present. However, limited by conditions such as the quality of geophysical data and the number of wells drilled, accurate fracture prediction is a difficult task, and no effective and general research means have been formed yet.

[0003] The stress field, as a necessary condition for the generation of tectonic fractures, is also the most effective way to predict fractures in areas lacking geological data. The key lies in how to build a "bridge" between stress, energy, and fracture parameters. All kinds of natural phenomena prove that no matter how complex the rock structure and mechanical behavior are, they all satisfy the basic laws of natural development, just like the extreme value is the most basic law in the universe. As a general natural law existing in living and non-living systems, linear equilibrium and non-equilibrium mechanical systems, the principle of minimum energy consumption holds that the essence of material or rock failure always occurs in the weakest place in the easiest way to be damaged, that is, the principle of minimum energy consumption rate is satisfied at any moment during the energy consumption process. Therefore, the concept of instantaneous steady state is introduced, and under the conditions of equilibrium or non-equilibrium, for each moment of the entire energy consumption process, the minimum value of all possible energy consumption rates at that time is taken. Further research and exploration are carried out on the mechanical mechanism and evolution law of the rock fracture process from a new perspective, to explore the mapping relationship between fracture parameters, stress field, and energy field, and finally to improve and construct a rock fracture criterion and fracture parameter characterization model under a unified theoretical framework to solve the problems of "quality" (fracture generation and propagation) and "quantity" (fracture scale and quantity) of fractures, and to achieve three-dimensional quantitative prediction of fractures in low-permeability sandstone reservoirs. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for quantitatively predicting reservoir fractures based on the principle of minimum energy consumption to solve the above problems.

[0005] The present invention realizes the above object through the following technical solutions:

[0006] A quantitative prediction method for reservoir fractures based on the principle of minimum energy consumption. Based on rock mechanics experiments, classical mechanics theory and the law of conservation of energy, a new theory reflecting the basic development law of nature - the principle of minimum energy consumption is introduced. The stress-energy coupling concept is applied to analyze the deformation and fracture process of rock masses, a rock fracture criterion under a unified theoretical framework is constructed, and a fracture parameter characterization model is derived and established. Based on the three-dimensional finite element stress field simulation, the quantitative prediction of the three-dimensional spatial distribution of fractures in low-permeability sandstone reservoirs is realized, and the theoretical and method systems for fracture prediction are further improved; it includes the following steps:

[0007] Step 1: Conduct triaxial rock mechanics experiments to obtain mechanical parameters;

[0008] Step 2: Construct a three-dimensional geomechanical model;

[0009] Step 3: Conduct three-dimensional finite element stress field dynamic simulation;

[0010] Step 4: Establish a rock fracture criterion based on the principle of minimum energy consumption; the specific method is as follows:

[0011] (1). During the damage process of low-permeability sandstone, without considering other energy consumption factors, the non-recoverable principal strain ε i , i = 1, 2, 3 is regarded as the only energy consumption mechanism of the rock mass during the failure process. Combining with the generalized Hooke's law containing the damage variable D(t), the energy consumption rate corresponding to the energy consumption process is obtained Expression:

[0012]

[0013] In the formula: D(t) represents the damage variable; represents the time derivative of the loss variable D(t); E and μ are the elastic modulus and Poisson's ratio of the rock mass before failure energy consumption; σ 1 , σ 2 , σ 3 are the three principal stresses, with the unit of MPa;

[0014] (2). Considering the numerical relationship between shear strain energy and volumetric strain energy, and combining with the three-shear energy yield criterion, the constraint condition of rock damage energy consumption under the triaxial stress path is obtained:

[0015]

[0016] In the formula: α and β are material parameters, characterizing the numerical relationship between shear strain energy and volumetric deformation energy; is the internal friction angle of the rock, with the unit of radian; G is the shear modulus, with the unit of MPa, and K is the bulk modulus, with the unit of MPa, and

[0017] (3) During the rock damage evolution process, when the energy dissipation rate takes a stationary value under corresponding conditions, introducing the Lagrange multiplier λ, according to the principle of minimum energy dissipation:

[0018]

[0019] the rock damage equation under the triaxial stress state is obtained:

[0020]

[0021] (4) Considering the threshold effect, introducing the damage threshold strain ε 0 , the expression of the rock damage equation is:

[0022]

[0023] Combining with the generalized Hooke's law, the rock constitutive model is obtained:

[0024]

[0025] In the formula:

[0026] λ, C 0 are constants related to the lithology;

[0027] (5) Identify the model parameters according to the results of the triaxial rock mechanics experiment of intact rock and the strength peak point of the stress-strain curve; assuming that the stress and strain at the peak point of the stress-strain curve of the rock under confining pressure are σ 1s , σ 2s , σ 3s , ε 1s , ε 2s , ε 3s , then at the peak point, there are:

[0028]

[0029] Thus, the values of the constants λ and C 0 are:

[0030]

[0031] (6) Substitute the constants λ and C 0 , and the damage threshold is obtained:

[0032]

[0033] The fracture threshold:

[0034]

[0035] In the formula:

[0036]

[0037] (7) In summary, the new criterion for rock fracture under the principle of minimum energy consumption:

[0038]

[0039] According to the principle of minimum energy consumption or minimum energy consumption rate, when the rock loses its steady state and fractures occur;

[0040] Step Five: Establish a prediction model for the strike and dip angle of fractures under the constraint of the principle of minimum energy consumption;

[0041] Step Six: Establish a prediction model for the fracture volume density and linear density under the constraint of the principle of minimum energy consumption;

[0042] Step Seven: Instantaneous extraction of the dynamic stress field and quantitative prediction of fractures;

[0043] Step Eight: Verify the reliability of the results of quantitative fracture prediction.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] It solves the problem of accurately obtaining complex fracture parameters of low-permeability sandstone reservoirs and quantitatively characterizing them, and is suitable for any quantitative fracture prediction work mainly for low-permeability sandstone reservoirs; it effectively predicts the occurrence, volume density and linear density of fractures in low-permeability sandstone reservoirs under the action of the stress field, provides a reliable basis for studying the favorable development areas of fractured reservoirs, and reduces the risks and costs of exploration and development. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for description in the embodiments or the prior art.

[0047] Figure 1 is a schematic flow chart of a method for quantitatively predicting reservoir fractures based on the principle of minimum energy consumption according to the present invention;

[0048] Figure 2 is the calculation of the fracture rupture angle in the polar coordinate system of a method for quantitatively predicting reservoir fractures based on the principle of minimum energy consumption according to the present invention;

[0049] Figure 3 is a schematic diagram of the conversion between the principal stress coordinate system and the space rectangular coordinate system of a method for quantitatively predicting reservoir fractures based on the principle of minimum energy consumption according to the present invention;

[0050] Figure 4Schematic diagram of fracture plane normal vector characterization of a reservoir fracture quantitative prediction method based on the principle of minimum energy consumption according to the present invention;

[0051] Figure 5 Schematic diagram of fracture strike prediction of a reservoir fracture quantitative prediction method based on the principle of minimum energy consumption according to the present invention;

[0052] Figure 6 Schematic diagram of fracture dip calculation of a reservoir fracture quantitative prediction method based on the principle of minimum energy consumption according to the present invention. Detailed implementation manners

[0053] The present invention will be further described below with reference to the accompanying drawings:

[0054] As Figures 1 - 6 shown, a reservoir fracture quantitative prediction method based on the principle of minimum energy consumption includes the following steps:

[0055] Step 1: Conduct triaxial rock mechanics experiments to obtain mechanical parameters. The specific method is as follows:

[0056] (1). Since it is necessary to analyze the mechanical properties of low-permeability sandstone reservoirs, here, all the cored sections of wells are roughly observed, and the core sections without surface cracks are preferably selected for triaxial rock mechanics experiments. Since 3 rock samples with similar depths and similar lithologies are required as a group for such experiments, the core drilling direction is defined to be perpendicular to the core axis. Referring to the rock mechanics test specification, the size of the rock sample is a cylindrical shape of 50mm×25mm×25mm, the height-diameter ratio is 2:1, the perpendicularity of the end face to the axis of the rock sample is less than 0.25°, and the two end faces are ground flat with the unevenness less than 0.5%;

[0057] (2). For low-permeability sandstone rock samples, the confining pressure levels are set every 5 - 10 MPa. Three core samples in each group are subjected to true triaxial mechanical loading experiments on an MTS true triaxial rock mechanics instrument to test and obtain the triaxial compressive strength, Poisson's ratio, elastic modulus, and internal friction angle of the rock, and at the same time obtain the stress-strain curve of the rock mechanics experiment;

[0058] (3). Select a logging interpretation model to perform logging interpretation on the dynamic rock mechanics parameters such as Young's modulus, Poisson's ratio, and density, and perform dynamic-static correction on the results of the rock mechanics experiment to obtain more realistic formation mechanical strength parameters;

[0059] Step 2: Construct a three-dimensional geomechanics model. The specific method is as follows:

[0060] (1). Analyze the tectonic evolution history. Based on the current three-dimensional geological structure, combined with methods such as the fault-related fold theory, restore the paleotectonic morphology through flexural folding, restoration to the reference plane, and patchwork restoration method to establish a paleotectonic geological model;

[0061] (2) Using the Petrel geological modeling software as a platform, construct the layer model, fault model, and reservoir geological model of the study area. Import the layer and fault data into the AutoCad software for surface model reconstruction, and then export the surface model to the ANSYS software for 3D model construction. After dividing the grid, discretely assign mechanical parameters to each grid of the 3D model according to the "centroid" search method to complete the establishment of the 3D geomechanical model;

[0062] Step 3: Conduct 3D finite element stress field dynamic simulation. The specific method is as follows:

[0063] (1) Conduct acoustic emission test sampling on the drilling cores in the study area. The drilling positions are preferably evenly distributed on the plane of the study area or in a quadrilateral shape. Each group of samples should include at least 4 specimens, with 1 taken from the vertical direction (parallel to the wellbore axis) and the other 3 taken from 3 directions that are 45° apart in the horizontal plane;

[0064] (2) The equipment used for the acoustic emission test consists of a servo rock rigid testing machine and an acoustic emission testing system. Conduct repeated loading experiments on the processed specimens indoors at a loading rate of 0.1 MPa, measure the change curve of the acoustic emission signal of the rock sample during the loading process, and find the point where the acoustic emission cannot be completely erased on the acoustic emission load change curve during the second loading. Referring to the load value at the point where the acoustic emission cannot be completely erased, determine the Kaiser point on the acoustic emission load curve during the first loading. Take the average value of the Kaiser point and the load at the point where the acoustic emission cannot be completely erased, which is the maximum normal stress suffered by the core underground;

[0065] (3) According to the tectonic trace mechanics method, conduct fracture staging and matching, use rose diagrams to statistically analyze the fracture strike, find the dominant set of conjugate fractures, and use the bisector of the conjugate angle as the direction of the maximum principal stress in the paleo-stress field;

[0066] (4) Based on the 3D geomechanical model established in ANSYS and the paleo-stress test results, conduct finite element 3D stress field simulation, determine the mechanical boundaries of the model, apply forces, set the loading rate to 0.1 MPa / s, and simulate the dynamic evolution process of the 3D tectonic stress field in the time domain;

[0067] Step 4: Establish a rock fracture criterion based on the principle of minimum energy dissipation. The specific method is as follows:

[0068] (1) During the damage process of low-permeability sandstone, without considering other energy dissipation factors, regard the non-recoverable principal strain ε i , i = 1, 2, 3 as the only energy dissipation mechanism during the rock failure process. Combining with the generalized Hooke's law containing the damage variable D(t), obtain the energy dissipation rate expression:

[0069]

[0070] In the formula: D(t) represents the damage variable; represents the time derivative of the loss variable D(t); E and μ are the elastic modulus and Poisson's ratio of the rock mass before energy dissipation due to failure; σ 1 、σ 2 、σ 3 are the three principal stresses, with the unit of MPa;

[0071] (2) Considering the numerical relationship between the shear strain energy and the volumetric strain energy, and combining with the three-shear energy yield criterion, the constraint condition of rock damage energy dissipation under the triaxial stress path is obtained:

[0072]

[0073] In the formula: α and β are material parameters, characterizing the numerical relationship between the shear strain energy and the volumetric deformation energy; is the internal friction angle of the rock, with the unit of radian; G is the shear modulus, with the unit of MPa, and K is the bulk modulus, with the unit of MPa, and

[0074] (3) During the rock damage evolution process, the energy dissipation rate takes a stationary value under the corresponding conditions. Introducing the Lagrange multiplier λ, from the principle of minimum energy dissipation:

[0075]

[0076] The rock damage equation under the triaxial stress state is obtained:

[0077]

[0078] (4) Considering the threshold effect, introducing the damage threshold strain ε 0 , the expression of the rock damage equation is:

[0079]

[0080] Combining with the generalized Hooke's law, the rock constitutive model is obtained:

[0081]

[0082] In the formula:

[0083] λ, C 0 are constants related to the rock properties;

[0084] (5) Identifying the model parameters according to the results of the triaxial rock mechanics experiment of intact rock and the strength peak point of the stress-strain curve; assuming that the stress and strain at the peak point of the stress-strain curve of the rock under confining pressure are σ 1s 、σ2s 、σ 3s 、ε 1s 、ε 2s 、ε 3s , then at the peak point, there is:

[0085]

[0086] Thus, the values of the constants λ and C 0 are:

[0087]

[0088] (6) Substitute the constants λ and C 0 , and the damage threshold is obtained:

[0089]

[0090] Fracture threshold:

[0091]

[0092] In the formula:

[0093]

[0094] (7) To sum up, the new criterion for rock fracture under the principle of minimum energy dissipation:

[0095]

[0096] According to the principle of minimum energy dissipation or minimum energy dissipation rate, when , the rock loses its steady state and fractures;

[0097] Step Five: Establish a prediction model for the fracture strike and dip angle under the constraint of the principle of minimum energy dissipation. The specific method is as follows:

[0098] (1) In the principal stress coordinate system, with the origin of coordinates as the pole and the positive half-axis of the maximum principal stress axis σ 1 as the polar axis, establish a polar coordinate system and determine the stress function of any point on the fracture surface:

[0099] F(r, θ) = r 2 (Acos2θ + Bsin2θ + Cθ + D)

[0100] Substitute to satisfy the compatibility equation;

[0101] In the formula: θ represents the angle between the fracture surface and the maximum principal stress, that is, the fracture angle, in radians; A, B, C, and D are arbitrary constants;

[0102] (2) Consider the boundary conditions:

[0103] When θ = 0°, When θ = 90°, The stress function expression is obtained:

[0104]

[0105] (3) Combining the energy dissipation rate expression constrained by the principle of minimum energy dissipation, the crack rupture angle calculation formula is:

[0106]

[0107] In the formula: D is the damage variable, and

[0108] is the time derivative of the damage variable, and

[0109] (4) The X-axis of the spatial rectangular coordinate system coincides with the X-axis (east) of the geodetic coordinate system, the positive direction of the Z-axis coincides with the negative direction of the Y-axis (south), and the Y-axis and the Z-axis coincide. Therefore, project the crack surface normal vector onto the xOz plane, and the crack strike predicted by the principle of minimum energy dissipation is:

[0110]

[0111] In the formula:

[0112] θ is the rupture angle, in radians, and

[0113] (5) In the geodetic coordinate system, the crack dip angle is the angle between the crack surface and the xOz plane, that is, the angle α between the plane lx + my + nz = 0 and the plane y = 0 dip (0° ≤ α dip ≤ 90°), so the crack dip angle calculation formula predicted by the principle of minimum energy dissipation is:

[0114]

[0115] In the formula:

[0116] θ is the rupture angle, in radians, and

[0117] Step 6: Establish a prediction model for the crack body and line density under the constraint of the principle of minimum energy dissipation. The specific method is as follows:

[0118] (1) When the fracture strength of low-permeability sandstone is reached, the rock fractures to generate macroscopic fractures and releases energy. Combining with the energy dissipation rate expression under the principle of minimum energy consumption, the dissipated energy during the fracture generation process is obtained (assuming that the energy consumption at time t = 0 is 0):

[0119]

[0120] (2) Further combining with the law of conservation of energy, the fracture volume density model under the constraint of the minimum energy consumption theory is:

[0121]

[0122] Where: D v is the fracture density in the unit volume, with the unit of m 2 / m 3 ; ω is the strain energy released by the newly added fractures, with the unit of J; ω s is the strain energy density of the newly added fracture surface area, with the unit of J / m 3 ; V is the volume representing the unit volume, with the unit of m 3 ; S is the newly added fracture surface area, with the unit of m 2 ; J is the energy required to generate a unit area of fractures, that is, the fracture surface energy, with the unit of J / m 2 ;

[0123] (3) Therefore, the fracture line density parameter model under the principle of minimum energy consumption is:

[0124]

[0125] Where: D l is the fracture line density, with the unit of number of fractures / m; L 1 , L 3 are the lengths in the σ 1 , σ 3 directions, with the unit of m, and the values are related to the specific research problem; D v is the fracture volume density, with the unit of m 2 / m 3 ; θ is the fracture angle, with the unit of radian, and

[0126] Step 7: Instantaneous extraction of the dynamic stress field and quantitative prediction of fractures. The specific method is as follows:

[0127] (1) Based on the rock mechanics parameters and dynamic stress field simulation obtained in Steps 1 to 3, set the time step, extract the parameter values of the maximum principal stress, minimum principal stress, intermediate principal stress, maximum principal strain, minimum principal strain, intermediate principal strain, etc. of each node instantaneously, and store them in txt format;

[0128] (2) Write the rock fracture criterion, fracture occurrence, and density mechanical model obtained in steps four to six into an executable Python program, read the txt file exported from the finite element platform, and automatically calculate the energy dissipation rate and determine the rock fracture state by the program to obtain the fracture strike, dip angle, and density value;

[0129] (3) Output the calculation results of the Python program as an Excel table and import it back to the finite element platform for display to obtain the three-dimensional distribution of the fracture state and fracture prediction results;

[0130] Step eight: Verify the reliability of the quantitative fracture prediction results. The specific method is as follows:

[0131] For the above-obtained rock fracture state and three-dimensional distribution results of fracture prediction, conduct accuracy verification through single-well core statistics, imaging logging interpretation, and CT scan fracture results. If the coincidence degree between the simulation results and the actual data is greater than, it is considered that the calculation simulation results are reliable; otherwise, re-analyze and correct the rock mechanics parameters and stress test results, adjust the boundary conditions, and re-simulate the three-dimensional dynamic stress field to finally complete the three-dimensional quantitative prediction of structural fractures in low-permeability sandstone reservoirs.

Claims

1. A quantitative prediction method for reservoir fractures based on the minimum energy consumption principle, characterized by: The following steps are involved: Step 1: Conduct triaxial rock mechanics experiments to obtain mechanical parameters; Step 2: Construct a three-dimensional geomechanical model; Step 3: Conduct three-dimensional finite element stress field dynamic simulation; Step 4: Establish rock fracture criteria based on the minimum energy consumption principle; the specific method is as follows: (1) In the process of low permeability sandstone damage, without considering other energy consumption factors, the irreversible principal strain ε generated by the load is i , i = 1, 2, 3 is regarded as the only energy dissipation mechanism of rock mass in the process of destruction. Combined with the generalized Hooke's law including the damage variable D(t), the energy dissipation rate corresponding to the energy dissipation process is obtained. expression: Where: D(t) represents the damage variable; represents the time derivative of the loss variable D(t); E and μ are the elastic modulus and Poisson's ratio of the rock mass before it is damaged and consumes energy; σ1, σ2, and σ3 are the three principal stresses, in MPa; (2) Considering the numerical relationship between shear strain energy and volumetric strain energy and combining the three-shear energy yield criterion, the constraint condition of rock damage energy dissipation under triaxial stress path is obtained: Where: α and β are material parameters, representing the numerical relationship between shear strain energy and volume deformation energy; is the internal friction angle of the rock, in radians; G is the shear modulus, in MPa, and K is the bulk modulus in MPa, and (3) During the evolution of rock damage, the energy consumption rate takes a stationary value under the corresponding conditions. The Lagrange multiplier λ is introduced, and according to the minimum energy consumption principle: The rock damage equation under triaxial stress state is obtained: (4) Considering the threshold effect, the damage threshold strain ε0 is introduced, and the rock damage equation is expressed as: Combined with the generalized Hooke's law, the rock constitutive model is obtained: Where: λ, C0 is a constant related to lithology; (5) Identify the model parameters based on the triaxial rock mechanics test results of intact rock and the strength peak point of the stress-strain curve; assume that the stress and strain at the peak point of the stress-strain curve of the rock under confining pressure are σ 1s , σ 2s , σ 3s , σ 1s , σ 2s , σ 3s , then at the peak point, we have: So the values ​​of constants λ and C0 are: (6) Substituting constants λ and C0, we get the damage threshold: Rupture threshold: Where: (7) In summary, the new criterion for rock fracture under the principle of minimum energy consumption is: According to the principle of minimum energy consumption or minimum energy consumption rate, when When the rock loses its stability, it breaks; Step 5: Establish a crack direction and inclination prediction model under the constraint of the minimum energy consumption principle; Step 6: Establish a prediction model of crack volume and line density under the constraint of minimum energy consumption principle; Step 7: Instantaneous extraction of dynamic stress field and quantitative prediction of cracks; Step 8: Verify the reliability of the crack quantitative prediction results.

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