A method for calculating rock fatigue damage with constant amplitude and rising average stress
By establishing a nonlinear fatigue damage evolution model with a constant amplitude and linearly increasing average stress, the problem of lack of models in existing technologies is solved, and the effect of accurately predicting the fatigue damage characteristics of rocks in variable load hydraulic fracturing technology is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA NAT OFFSHORE OIL CORP
- Filing Date
- 2023-06-26
- Publication Date
- 2026-05-26
AI Technical Summary
Existing technologies lack models for calculating the evolution of fatigue damage variables in rocks under linearly increasing mean stress of constant amplitude, thus failing to effectively describe and predict the fatigue damage characteristics of rocks under such loads.
A nonlinear fatigue damage evolution model for rocks under cyclic loading with linearly increasing average stress of constant amplitude was established. By designing loading parameters and conducting experiments, the model coefficients were fitted to predict the fatigue damage evolution characteristics of rocks.
It can accurately predict the evolution of fatigue damage variables in similar rocks with a small number of experiments, reduce experimental costs, and is applicable to fracture network simulation in variable load hydraulic fracturing technology.
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Figure CN116858708B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rock fatigue damage technology, specifically to a method for calculating fatigue damage variables under a constant amplitude linearly increasing mean stress. Background Technology
[0002] The evolution of fatigue damage variables in rocks under cyclic loading is a crucial basis for understanding and describing the mechanical characteristics of rock fatigue damage, and also an important basis for determining rock fatigue life. The form of load applied to the rock determines the law of rock fatigue damage, the form of rock fatigue failure, and the morphological characteristics of the rock after fatigue failure. Cyclic loading with a constant amplitude and linearly increasing average stress is rare in engineering fields, but it is very important in variable-load hydraulic fracturing technology. Variable-load hydraulic fracturing technology is a novel fracturing technology proposed in recent years. It involves circulating fracturing fluid during fracturing to generate continuously changing loads. Under these constantly changing loads, the rock undergoes fatigue failure, forming a complex fracture network in the reservoir rock. Variable-load hydraulic fracturing technology can form more complex fracture networks at lower fracturing pressures.
[0003] In variable-load hydraulic fracturing technology, fracturing fluid can be pumped in pulsed flow rate and pulsed pressure. When the fracturing fluid is pumped in pulsed flow rate, the load applied to the rock is a cyclic load with a constant amplitude and linearly increasing mean stress. Under this cyclic load with a constant amplitude and linearly increasing mean stress, the internal damage of the reservoir rock gradually evolves and accumulates until fatigue failure, resulting in a complex hydraulic fracture network.
[0004] In the existing technology, there have been many studies on the calculation models of the evolution of fatigue damage variables of rocks under constant amplitude and constant average stress cyclic loading. However, no model has been found for calculating the evolution of fatigue damage variables of rocks under constant amplitude and linearly increasing average stress cyclic loading.
[0005] Therefore, there is an urgent need for a method to calculate rock fatigue damage with constant amplitude and rising average stress. Summary of the Invention
[0006] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention provides a method for calculating rock fatigue damage with constant amplitude increasing average stress. This method establishes a fatigue damage evolution model of rock under cyclic loading with linearly increasing average stress at a constant amplitude. Using this model, without conducting cyclic loading fatigue experiments, the fatigue damage evolution characteristics of rocks of the same lithology under other loading parameters can be predicted.
[0007] To achieve the above objectives, the present invention adopts the following technical solution:
[0008] Firstly, a method for calculating rock fatigue damage based on constant amplitude average stress includes the following steps:
[0009] The amplitude, average stress increase rate and loading rate are designed, and a constant amplitude linearly increasing average stress cyclic load fatigue test is carried out on the target rock to obtain the rock fatigue stress-strain hysteresis curve and calculate the rock fatigue damage variable defined by residual strain.
[0010] A nonlinear fatigue damage evolution model is established for constant amplitude and continuously increasing average stress;
[0011] The data on the variation of rock fatigue damage variables defined by residual strain under different cyclic loading parameters with the number of cycles were fitted with the nonlinear fatigue damage evolution model to obtain the coefficients in the nonlinear fatigue damage evolution model under different cyclic loading parameters.
[0012] By fitting each coefficient to the amplitude, the average stress increase rate, and the loading rate, the relationship between each coefficient and the loading parameter is obtained.
[0013] Substituting the relationships between the coefficients and the loading parameters into the nonlinear fatigue damage evolution model, a fatigue damage evolution model of lithological rocks under a constant amplitude linearly increasing average stress cyclic load is obtained. Based on the fatigue damage evolution model, the fatigue damage of rocks under a constant amplitude increasing average stress is calculated, and the fatigue damage evolution characteristics of rocks are predicted.
[0014] The method for calculating rock fatigue damage under constant amplitude and average stress is preferably used to calculate the rock fatigue damage variable defined by residual strain using the following formula (1):
[0015]
[0016] in,
[0017] D represents the rock fatigue damage variable;
[0018] The residual strain after n cycles;
[0019] This represents the final residual strain upon fatigue failure.
[0020] The method for calculating rock fatigue damage with constant amplitude and increasing average stress is preferably defined by the following formula (2):
[0021]
[0022] in,
[0023] α, τ, λ, μ, ∈, β are all coefficients related to rock properties and cyclic loading conditions;
[0024] n is the number of iterations;
[0025] Nf represents fatigue life.
[0026] The method for calculating rock fatigue damage with constant amplitude and increasing average stress is preferably defined in the following formulas (3) to (8):
[0027] α=α(σ a ,Δσ,υ) (3)
[0028] τ=τ(σ a ,Δσ,υ) (4)
[0029] λ=λ(σ a ,Δσ,υ) (5)
[0030] μ=μ(σ a ,Δσ,υ) (6)
[0031] ∈=∈(σ a ,Δσ,υ) (7)
[0032] β=β(σ a ,Δσ,υ) (8)
[0033] in,
[0034] σ a The amplitude;
[0035] Δσ is the average rate of increase in stress;
[0036] υ represents the loading rate.
[0037] The method for calculating rock fatigue damage under constant amplitude and increasing average stress is preferably defined as follows: the fatigue damage evolution model of the lithology under cyclic loading with linearly increasing average stress at a constant amplitude is Equation (9):
[0038]
[0039] Secondly, a rock fatigue damage calculation device with constant amplitude rising average stress includes:
[0040] The first processing unit designs the amplitude, average stress increase rate and loading rate, and conducts a constant amplitude linearly increasing average stress cyclic load fatigue test on the target lithology rock to obtain the rock fatigue stress-strain hysteresis curve and calculate the rock fatigue damage variable defined by residual strain.
[0041] The second processing unit establishes a nonlinear fatigue damage evolution model for a constant amplitude and an ever-increasing average stress.
[0042] The third processing unit fits the data of residual strain damage variables changing with the number of cycles under different cyclic load loading parameters using the nonlinear fatigue damage evolution model to obtain the coefficients in the nonlinear fatigue damage evolution model under different cyclic load loading parameters.
[0043] The fourth processing unit fits each coefficient in the nonlinear fatigue damage evolution model with the amplitude, the rate of increase of average stress, and the loading rate, respectively, to obtain the relationship between the amplitude, the rate of increase of average stress, and the loading rate and the loading parameters.
[0044] The fifth processing unit substitutes the relationship of the loading parameters into the nonlinear fatigue damage evolution model to obtain the fatigue damage evolution model of lithological rocks under cyclic loading of linearly increasing average stress with constant amplitude. Based on the fatigue damage evolution model, the fatigue damage of rocks with constant amplitude increasing average stress is calculated, and the fatigue damage evolution characteristics of rocks are predicted.
[0045] Thirdly, a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method for calculating rock fatigue damage with constant amplitude rising average stress.
[0046] Fourthly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method for calculating rock fatigue damage with constant amplitude rising average stress.
[0047] The present invention has the following advantages due to the adoption of the above technical solutions:
[0048] To address the lack of a model for the evolution of rock fatigue damage variables under cyclic loading with a constant amplitude and linearly increasing mean stress, this paper proposes a model for calculating the evolution of rock fatigue damage variables under cyclic loading with a constant amplitude and linearly increasing mean stress, based on the theory of damage mechanics and combined with rock fatigue experiments on target lithology under cyclic loading with a constant amplitude and linearly increasing mean stress.
[0049] The model in this invention for calculating the evolution of fatigue damage variables in rocks under cyclic loading with a constant amplitude and linearly increasing average stress can establish an accurate model for predicting the evolution of fatigue damage variables in similar lithologies with only a small number of experiments, reducing the number of cyclic loading experiments and costs. The model accurately describes the evolution of rock damage variables; these rock property parameters are key input parameters in rock deformation simulation. It can be used to simulate crack propagation during pulsed flow control of fracturing fluid injection in variable-load hydraulic fracturing technology, and also in numerical simulations of rock deformation and crack propagation under such cyclic loading. Attached Figure Description
[0050] Figure 1 The stress-strain hysteresis curve of rock under cyclic loading with a constant amplitude and linearly increasing average stress.
[0051] Figure 2 The relationship between the damage variable defined for residual strain in rock and the number of cycles. Detailed Implementation
[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.
[0053] This invention provides a method for calculating rock fatigue damage under constant amplitude and increasing average stress, comprising the following steps: designing the amplitude, average stress increase rate, and loading rate; conducting a constant amplitude linearly increasing average stress cyclic loading fatigue experiment on the target lithology to obtain the rock fatigue stress-strain hysteresis curve; calculating the rock fatigue damage variable defined by residual strain; establishing a nonlinear fatigue damage evolution model for constant amplitude and continuously increasing average stress; fitting the residual strain damage variable under different cyclic loading parameters with the nonlinear fatigue damage evolution model to obtain the coefficients in the nonlinear fatigue damage evolution model under different cyclic loading parameters; fitting each coefficient with the amplitude, average stress increase rate, and loading rate respectively to obtain the relationship between each coefficient and the loading parameters; substituting the relationship between each coefficient and the loading parameters into the nonlinear fatigue damage evolution model to obtain the fatigue damage evolution model of the lithology under constant amplitude linearly increasing average stress cyclic loading.
[0054] This invention utilizes this model to predict the evolution characteristics of rock fatigue damage under other loading parameters when cyclic loading fatigue experiments are not conducted under other loading parameters.
[0055] The following section uses shale as an example to explain the entire technical process in detail.
[0056] Example 1
[0057] This embodiment provides a method for calculating rock fatigue damage based on constant amplitude average stress, including the following steps:
[0058] S1: As shown in Table 1, different cyclic loading parameters were designed, specifically amplitude, mean stress increase rate, and loading rate. A constant amplitude linearly increasing mean stress cyclic loading fatigue test was conducted on the target lithology to obtain the rock stress-strain hysteresis curves under different cyclic loading parameters (e.g., ...). Figure 1 (As shown), calculate the rock fatigue damage variable defined by residual strain;
[0059] Table 1. Parameter amplitude, average stress increase rate, and loading rate
[0060]
[0061] In Table 1, UCS represents the uniaxial compressive strength of the shale sample.
[0062] The damage variables defined by the residual strain of rock under different cyclic loading parameters are obtained according to formula (1), such as... Figure 2 The diagram shows the relationship between the damage variable defined by the residual strain of the rock and the number of cycles under different cyclic loading parameters.
[0063] Formula (1) is as follows:
[0064]
[0065] In the formula,
[0066] D represents the rock fatigue damage variable;
[0067] The residual strain after n cycles;
[0068] This represents the final residual strain upon fatigue failure.
[0069] S2: Based on the theory of rock fatigue damage mechanics, a nonlinear fatigue damage evolution model is established for constant amplitude and continuously increasing average stress.
[0070] The specific method is as follows:
[0071] S21: Measurement results obtained from the changes in damage mechanical response indicate that the form of the cyclic loading fatigue damage rate equation is:
[0072]
[0073]
[0074] In the formula,
[0075] D * Damage variables related to continuous damage mechanics;
[0076] D represents the damage variable;
[0077] δ is a coefficient;
[0078] σ M This is the maximum load of the cyclic load;
[0079] The average load;
[0080] It is a function related to the mean stress;
[0081] N is the number of iterations.
[0082] S22: D and D * The relationship is:
[0083] D = 1 - (1 - D) * ) δ+1 (12)
[0084] S23: Integrate equation (4), D and D * The boundaries are all [0,1], corresponding to N=0 and N=Nf respectively, where Nf is the fatigue life. After sorting the coefficients, a nonlinear fatigue damage evolution model considering constant amplitude and continuously increasing average stress under fatigue cyclic loading is obtained, as shown below:
[0085]
[0086] In the formula,
[0087] D represents the rock fatigue damage variable;
[0088] α, τ, λ, μ, ∈, β are all coefficients related to rock properties and cyclic loading conditions;
[0089] n is the number of iterations;
[0090] Nf represents fatigue life.
[0091] S3: The residual strain damage variable data obtained from the experiment in S1 under different cyclic load loading parameters are fitted with formula (2) to obtain the coefficients in formula (2) under different cyclic load loading parameters;
[0092] S4: Compare each coefficient with the loading parameter (amplitude σ) aBy fitting the mean stress increase rate Δσ and the loading rate υ, the relationship between each coefficient and the loading parameters is obtained:
[0093] τ=0.785Δσ 0.421 υ -0.534 σ a 0.0018 (4)
[0094] λ=1.241Δσ 0.232 v -0.279 σ a 0.0024 (5)
[0095] μ=4.162Δσ 0.843 v -0.751 σ a 0.0147 (6)
[0096] ∈=0.578Δσ 0.542 υ -0.824 σ a 0.0003 (7)
[0097] β=1.227Δσ 0.098 υ -0.091 σ a 0.0011 (8)
[0098] S5: Substitute the relationship of the loading parameters into the nonlinear fatigue damage evolution model to obtain the fatigue damage evolution model of lithological rocks under the action of constant amplitude linearly increasing average stress cyclic load, as shown in formula (9).
[0099]
[0100] in,
[0101] α = 2.315Δσ 0.133 υ -0.279 σ a 0.0024 ;
[0102] τ=0.785Δσ 0.421 υ -0.534 σ a 0.0018 ;
[0103] λ=1.241Δσ 0.232 υ -0.279 σ a 0.0024 ;
[0104] μ=4.162Δσ 0.843 υ-0.751 σ a 0.0147 ;
[0105] ∈=0.578Δσ 0.542 υ -0.824 σ a 0.0003 ;
[0106] β=1.227Δσ 0.098 υ -0.091 σ a 0.0011 .
[0107] Example 2
[0108] The fatigue damage evolution model of shale under a constant amplitude linearly increasing average stress cyclic load obtained in Example 1 above can predict the fatigue damage evolution characteristics of shale under other loading parameters without conducting cyclic loading fatigue experiments.
[0109] Example 3
[0110] The above-described embodiment 1 provides a method for calculating rock fatigue damage under a constant amplitude increasing average stress. Correspondingly, this embodiment provides a device for calculating fatigue damage variables under a constant amplitude linearly increasing average stress. The device for calculating fatigue damage variables under a constant amplitude linearly increasing average stress provided in this embodiment can implement the rock fatigue damage calculation method of embodiment 1. This calculation system can be implemented through software, hardware, or a combination of both. For example, the calculation system may include integrated or separate functional modules or units to execute the corresponding steps in the methods of embodiment 1. Since the device for calculating fatigue damage variables under a constant amplitude linearly increasing average stress in this embodiment is basically similar to the method embodiment, the description process of this embodiment is relatively simple. Relevant details can be found in the description of embodiment 1. The device for calculating fatigue damage variables under a constant amplitude linearly increasing average stress in this embodiment is merely illustrative.
[0111] The first processing unit designs the amplitude, average stress increase rate and loading rate, and conducts a constant amplitude linearly increasing average stress cyclic load fatigue test on the target lithology rock to obtain the rock fatigue stress-strain hysteresis curve and calculate the rock fatigue damage variable defined by residual strain.
[0112] The second processing unit establishes a nonlinear fatigue damage evolution model for a constant amplitude and an ever-increasing average stress.
[0113] The third processing unit fits the data of residual strain damage variables changing with the number of cycles under different cyclic load loading parameters using the nonlinear fatigue damage evolution model to obtain the coefficients in the nonlinear fatigue damage evolution model under different cyclic load loading parameters.
[0114] The fourth processing unit fits each coefficient in the nonlinear fatigue damage evolution model with the amplitude, the rate of increase of average stress, and the loading rate, respectively, to obtain the relationship between the amplitude, the rate of increase of average stress, and the loading rate and the loading parameters.
[0115] The fifth processing unit substitutes the relationship of the loading parameters into the nonlinear fatigue damage evolution model to obtain the fatigue damage evolution model of lithological rocks under cyclic loading of linearly increasing average stress with constant amplitude. Based on the fatigue damage evolution model, the fatigue damage of rocks with constant amplitude increasing average stress is calculated, and the fatigue damage evolution characteristics of rocks are predicted.
[0116] Example 4
[0117] The rock fatigue damage calculation method with constant amplitude rising average stress in Embodiment 1 can be specifically implemented as a computer program product. The computer program product may include a computer-readable storage medium loaded with computer-readable program instructions for executing the calculation method described in Embodiment 1.
[0118] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.
[0119] Example 5
[0120] This embodiment provides a processing device for implementing the constant amplitude rise average stress rock fatigue damage calculation method provided in Embodiment 1. The processing device can be a client-side processing device, such as a mobile phone, laptop, tablet computer, desktop computer, etc., to execute the calculation method of Embodiment 1.
[0121] The processing device includes a processor, a memory, a communication interface, and a bus. The processor, memory, and communication interface are connected via the bus to enable communication between them. The memory stores a computer program that can run on the processor. When the processor runs the computer program, it executes the three-dimensional characterization method for deltaic distributary channel sand bodies provided in Embodiment 1.
[0122] Preferably, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.
[0123] Preferably, the processor can be any type of general-purpose processor such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation herein.
[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for calculating rock fatigue damage under constant amplitude average stress, characterized in that, Includes the following steps: The amplitude, average stress increase rate and loading rate are designed, and a constant amplitude linearly increasing average stress cyclic load fatigue test is carried out on the target rock to obtain the rock fatigue stress-strain hysteresis curve and calculate the rock fatigue damage variable defined by residual strain. A nonlinear fatigue damage evolution model is established for constant amplitude and continuously increasing average stress; The data on the variation of rock fatigue damage variables defined by residual strain under different cyclic loading parameters with the number of cycles were fitted with the nonlinear fatigue damage evolution model to obtain the coefficients in the nonlinear fatigue damage evolution model under different cyclic loading parameters. By fitting each coefficient to the amplitude, the average stress increase rate, and the loading rate, the relationship between each coefficient and the loading parameter is obtained. Substituting the relationships between the coefficients and the loading parameters into the nonlinear fatigue damage evolution model, a fatigue damage evolution model of lithological rocks under a constant amplitude linearly increasing average stress cyclic load is obtained. Based on the fatigue damage evolution model, the fatigue damage of rocks under a constant amplitude increasing average stress is calculated, and the fatigue damage evolution characteristics of rocks are predicted. The rock fatigue damage variable defined by residual strain is calculated using the following equation (1): （1） in, D represents the rock fatigue damage variable; The residual strain after n cycles; This represents the final residual strain upon fatigue failure. The nonlinear fatigue damage evolution model with constant amplitude and continuously increasing average stress is specifically as follows (2): （2） in, ， ， ， ， ， All of these are coefficients related to rock properties and cyclic loading conditions; n is the number of iterations; Nf represents fatigue life; The relationships between the amplitude, the rate of increase of average stress, the loading rate, and the coefficients are given by formulas (3) to (8): （3） （4） （5） （6） （7） （8） in, The amplitude; The rate of increase of average stress; For loading rate; The fatigue damage evolution model of the lithological rock under a constant amplitude linearly increasing mean stress cyclic load is given by equation (9). （9）。 2. A rock fatigue damage calculation device with constant amplitude rising average stress, characterized in that, The apparatus is used to implement the calculation method according to claim 1, and the apparatus includes: The first processing unit designs the amplitude, average stress increase rate and loading rate, and conducts a constant amplitude linearly increasing average stress cyclic load fatigue test on the target lithology rock to obtain the rock fatigue stress-strain hysteresis curve and calculate the rock fatigue damage variable defined by residual strain. The second processing unit establishes a nonlinear fatigue damage evolution model for a constant amplitude and an ever-increasing average stress. The third processing unit fits the data of residual strain damage variables changing with the number of cycles under different cyclic load loading parameters using the nonlinear fatigue damage evolution model to obtain the coefficients in the nonlinear fatigue damage evolution model under different cyclic load loading parameters. The fourth processing unit fits each coefficient in the nonlinear fatigue damage evolution model with the amplitude, the rate of increase of average stress, and the loading rate, respectively, to obtain the relationship between the amplitude, the rate of increase of average stress, and the loading rate and the loading parameters. The fifth processing unit substitutes the relationship of the loading parameters into the nonlinear fatigue damage evolution model to obtain the fatigue damage evolution model of lithological rocks under cyclic loading of linearly increasing average stress with constant amplitude. Based on the fatigue damage evolution model, the fatigue damage of rocks with constant amplitude increasing average stress is calculated, and the fatigue damage evolution characteristics of rocks are predicted.
3. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the rock fatigue damage calculation method with constant amplitude rising average stress as described in claim 1.
4. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the rock fatigue damage calculation method with constant amplitude rising average stress as described in claim 1.