A fracturing fracture inversion method integrating optical fiber strain monitoring and fracture propagation simulation

Abstract

The invention discloses a fracturing crack dynamic inversion method integrating optical fiber strain monitoring and crack extension simulation, belonging to the technical field of oil and gas field exploitation. The method comprises establishing a state control equation based on a state variable, and predicting the crack width distribution of the next time step according to the established state control equation; calculating the covariance matrix of the prediction error of the next time step of the state control equation according to the covariance matrix of the system error of the crack extension model; establishing an observation equation of distributed optical fiber strain, and calculating the optical fiber strain corresponding to the state variable of the next time step; establishing a state update equation for the crack width distribution according to the monitored optical fiber strain data and the optical fiber strain corresponding to the state variable of the next time step calculated; updating the crack unit state, and entering into the prediction of the crack width distribution of the next time step again after the update, until the set end time is reached, so as to fuse the physical mechanism and the observed strain data.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field exploitation, and in particular to a fracturing crack inversion method integrating optical fiber strain monitoring and crack extension simulation. Background Art

[0002] Distributed fiber optic strain sensing has the advantages of long-distance, high-precision, and high-spatial-resolution monitoring, and plays an important role in monitoring hydraulic fracturing crack morphology. Usually, the fiber optic strain monitoring well is an adjacent well to the fracturing well. The fiber optic cable is installed in the casing of the monitoring well or fixed in the cement ring. The fiber optic cable, which is well coupled with the casing or formation, senses the formation deformation strain induced by the cracks in the fracturing process and performs dynamic diagnosis of crack expansion. Some domestic oil fields have carried out on-site applications of fracturing crack diagnosis and monitoring using fiber optic strain in adjacent wells, and have gained important insights into the dynamics of fracturing crack expansion.

[0003] At present, the dynamics of crack extension are mainly explained based on forward modeling. Through forward modeling, the strain pattern of the fracturing crack extension process can be obtained, and the crack extension process can be analyzed based on the strain pattern observed in the field. The fiber optic strain inversion study of crack induced is mainly based on static crack induced strain, and the crack parameters are obtained by optimization method. However, the physical mechanisms satisfied by crack extension, such as fluid-solid coupling process and time series relationship of fracture process, have not been considered in the inversion.

[0004] The above contents are only used to assist in understanding the technical solution of the present invention and do not constitute an admission that the above contents are prior art. Summary of the invention

[0005] The main purpose of the present invention is to provide a fracturing crack inversion method integrating optical fiber strain monitoring and crack extension simulation, aiming to solve or partially solve the above problems.

[0006] To achieve the above object, the present invention provides a fracturing crack dynamic inversion method integrating optical fiber strain monitoring and crack extension simulation, wherein the fracturing crack dynamic inversion method integrating optical fiber strain monitoring and crack extension simulation comprises:

[0007] Establish a state control equation based on state variables, and predict the crack width distribution in the next time step according to the established state control equation;

[0008] Calculating the covariance matrix of the prediction error of the next time step of the state control equation according to the covariance matrix of the system error of the crack propagation model;

[0009] Establish the observation equation of distributed optical fiber strain and calculate the optical fiber strain corresponding to the state variable in the next time step;

[0010] According to the monitored optical fiber strain data and the calculated optical fiber strain corresponding to the state variable of the next time step, a state update equation for the seam width distribution is established;

[0011] The state of the fracture unit is updated, and after the update, the prediction of the fracture width distribution of the next time step is entered again until the set end time is reached.

[0012] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, in the step of establishing a state control equation based on state variables and predicting the fracture width distribution at the next time step according to the established state control equation,

[0013] The formula for predicting the crack width distribution in the next time step is:

[0014] ;

[0015] in, is the estimated value of the crack width at time n+1, that is, the crack width distribution of the next time step predicted based on the result at time n;

[0016] is the estimated value of the slit width at time n;

[0017] Φ is a nonlinear equation, and its Jacobian matrix is ​​J w , the numerical method can be used to calculate J w ;

[0018] f is the state control equation based on the state variables.

[0019] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, the state control equation based on the state variable is established, and the state control equation is predicted according to the established state control equation in the step of the fracture width distribution in the next time step.

[0020] ;

[0021] in,

[0022] ∆t is the time step;

[0023] ∆x is the spatial step length;

[0024] μ is the fracturing fluid viscosity;

[0025] w i+0.5 is the width at the interface between units i and i+1, where w i+0.5 =0.5(w i +w i+1 );

[0026] W i-0.5is the width at the interface between the i and i-1 units, where w i-0.5 =0.5(w i +w i-1 );

[0027] p i , p i-1 , p i+1 are the pressures at the center points of units i, i-1, and i+1 respectively.

[0028] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, in the step of calculating the covariance matrix of the next time step prediction error of the state control equation according to the covariance matrix of the system error of the fracture extension model, the calculation formula of the covariance matrix of the next time step prediction error is:

[0029] ;

[0030] Among them, P n+1,n is the error covariance matrix P at time n n,n The error covariance matrix of the predicted n+1 time;

[0031] P n,n is the error covariance matrix at time n;

[0032] is the covariance matrix of the systematic error of the crack propagation model;

[0033] J is the Jacobian matrix; the calculation formula of the Jacobian matrix is:

[0034] ;

[0035] Where, f is the state control equation;

[0036] I is the identity matrix;

[0037] w is the slit width.

[0038] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and crack extension simulation, in the step of establishing the observation equation of distributed optical fiber strain and calculating the optical fiber strain corresponding to the state variable of the next time step, the observation equation of distributed optical fiber strain is:

[0039] ;

[0040] Where, u is the fiber displacement;

[0041] y is the axial coordinate of the optical fiber;

[0042] L is the fiber scale;

[0043] A is the coefficient matrix of the three-dimensional displacement discontinuous boundary element;

[0044] H is the coefficient matrix of the observation equation.

[0045] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, the formula for calculating the optical fiber strain corresponding to the state variable of the next time step is:

[0046] ;

[0047] Among them, H n+1 is the coefficient matrix of the observation equation at time n+1;

[0048] is the state variable for the next time step The corresponding fiber strain.

[0049] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, the state update equation for the fracture width distribution is established based on the monitored optical fiber strain data and the calculated optical fiber strain corresponding to the state variable of the next time step, including:

[0050] Establish the state update equation:

[0051] ;

[0052] Among them, Z n+1 is the optical fiber strain data monitored at time n+1;

[0053] is the estimated value of the seam width at time n+1 predicted in step S300;

[0054] is the estimated value of the crack width at the updated time n+1, that is, the estimated value of the crack width at the time n+1 calculated by the state update equation;

[0055] K n+1 is the Kalman gain matrix at time n+1, and the calculation formula is as follows:

[0056] ;

[0057] Among them, H n+1 is the coefficient matrix of the observation equation at time n+1;

[0058] is the covariance matrix of the strain measurement error;

[0059] According to the calculated covariance matrix of the prediction error of the next time step of the state control equation, the covariance matrix of the prediction error of the next time step of the state update equation is updated. The calculation formula is:

[0060] ;

[0061] Among them, P n+1,n is the error covariance matrix P at time n n,n The error covariance matrix of the predicted n+1 time;

[0062] P n+1,n+1 is the error covariance matrix at the updated n+1 moment.

[0063] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, the fracture unit state is updated, and after the update, the step of predicting the fracture width distribution of the next time step is entered again until the set end time is reached, and the fracture unit state is updated according to the updated fracture width estimation value of the next time step;

[0064] Among them, when the seam tip reaches the expansion condition, it is updated to a new tip.

[0065] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, before the step of establishing a state control equation based on state variables and predicting the fracture width distribution at the next time step according to the established state control equation, the method further includes:

[0066] Initialize the state variable parameters and use the slit width w as the state variable parameter.

[0067] Preferably, in the fracturing fracture dynamic inversion method integrating optical fiber strain monitoring and fracture extension simulation, before the step of establishing a state control equation based on state variables and predicting the fracture width distribution at the next time step according to the established state control equation, the method further includes:

[0068] Initial crack morphology, covariance matrix of initial errors of state variables, covariance matrix of model system errors, and covariance matrix of measurement errors.

[0069] The present invention has at least the following beneficial effects:

[0070] The present invention provides a fracturing crack dynamic inversion method that integrates optical fiber strain monitoring and crack extension simulation, establishes a state control equation based on state variables, and predicts the crack width distribution of the next time step according to the established state control equation; calculates the covariance matrix of the prediction error of the state control equation for the next time step according to the covariance matrix of the system error of the crack extension model; establishes an observation equation for distributed optical fiber strain, and calculates the optical fiber strain corresponding to the state variable of the next time step; establishes a state update equation for the crack width distribution according to the monitored optical fiber strain data and the optical fiber strain corresponding to the state variable of the next time step calculated; updates the crack unit state, and after the update, enters the prediction of the crack width distribution of the next time step again until the set end time is reached, so that by integrating the physical mechanism and the observed strain data, the dynamic parameters of crack extension can be explained more reasonably, rigorously and fully, and the crack extension information contained in the optical fiber strain monitoring data can be deeply excavated;

[0071] Furthermore, the present invention uses crack length and crack width distribution as inversion target variables, adopts nonlinear Kalman filtering for data fusion, the state space equation is a two-dimensional crack extension model, the observation equation is a displacement discontinuity model, and the nonlinear mapping relationship of the covariance matrix time series is processed by linear approximation. The calculation is efficient and can be used for real-time interpretation of optical fiber strain monitoring data, with strong engineering practicality. The basic logic of the method can be extended to the dynamic inversion of optical fiber strain crack parameters based on unscented Kalman filtering, ensemble Kalman filtering and other methods.

[0072] Furthermore, the present invention makes full use of the rich data information of the "time-continuous and spatially distributed" monitoring of distributed optical fiber strain, combines it with the physical equation of crack extension, and adopts the nonlinear Kalman filtering method to minimize the strain measurement error and the mathematical model error. On the one hand, it supplements the physical information of the measurement data (a regularization method), and on the other hand, it corrects the crack extension simulation and realizes the dynamic inversion of the crack extension morphology based on distributed optical fiber strain.

[0073] Furthermore, the present invention makes full use of the time series correlation of the fracture extension process, overcomes the deficiency of performing parameter inversion only through static fractures, and can invert fracture dynamic parameters more comprehensively and reasonably. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A flow chart of a method for dynamic inversion of a fracturing crack integrating optical fiber strain monitoring and crack extension simulation according to the present invention;

[0075] Figure 2 A schematic diagram of a model of an example of the present invention;

[0076] Figure 3 is the fracture width inversion result of the example of the present invention;

[0077] Figure 4 This is the fracture length inversion result of the example of the present invention.

[0078] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0079] In the embodiments of the present invention, the term "and / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent three situations: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the associated objects before and after are in an "or" relationship.

[0080] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0081] In the embodiments of the present invention, the term "plurality" refers to two or more than two, and other quantifiers are similar.

[0082] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. However, it can be understood by those skilled in the art that in the embodiments of the present invention, many technical details are proposed in order to enable the reader to better understand the present invention. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed in the present invention can also be implemented. The division of the following embodiments is for the convenience of description and should not constitute any limitation on the specific implementation of the present invention. The various embodiments can be combined and referenced with each other under the premise of no contradiction.

[0083] The present invention provides a fracturing crack dynamic inversion method integrating optical fiber strain monitoring and crack extension simulation. Figure 1 The flowchart of the method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation of the present invention is shown. Figure 1 shown.

[0084] At step S100, the state variable parameters are initialized. The state variable parameters include formation parameters and fluid parameters. Taking formation parameters as an example, the formation parameters include elastic modulus E, Poisson's ratio v, critical stress intensity factor, and minimum horizontal principal stress. Taking fluid parameters as an example, the fluid parameters include fracturing fluid viscosity and injection flow rate.

[0085] Initialize the state variable parameters, such as elastic modulus E is 35GPa, Poisson's ratio v is 0.2, critical stress intensity factor K c 0.5 MPa·m 0.5, minimum horizontal principal stress σ h is 50MPa, the viscosity of the fracturing fluid is 10mPa.s, and the injection flow rate is Q t 3m 3 / min.

[0086] More specifically, the crack extension is regarded as a nonlinear moving boundary problem, and the crack length and crack width are taken as state variables. When the crack unit width is not opened, it is 0, and the crack length is implicit in the width distribution. Therefore, the state variables of the system can be uniformly expressed by the crack width w. That is, the crack width w is used as the state variable for the crack parameter inversion.

[0087] At step S200, the initial crack morphology, the covariance matrix of the initial error of the state variable, the covariance matrix of the model system error, and the covariance matrix of the measurement error.

[0088] (1) Initial crack morphology

[0089] The PKN model can be used, with the initial fracture height preset to 100 m, the fracture extension as a nonlinear moving boundary problem, and the state quantity as the fracture length and width distribution. The width of the closed fracture unit is 0.

[0090] As mentioned above, the state variables of the system can be uniformly represented by the slit width w. Therefore, it can also be considered as initializing the slit width w.

[0091] (2) Covariance matrix P of the initial error of the state variable n，n

[0092] ;

[0093] Among them, the dimension n of the covariance matrix of the initial error of the state variable is equal to the total number of slit width opening units.

[0094] (3) Covariance matrix of the systematic error of the crack propagation model

[0095] ;

[0096] in, Defined as (10 -6 ) 2 ;

[0097] γ is an adjustment factor, reflecting the overall weight of system noise. In this embodiment, it is set to 0.2;

[0098] I is the identity matrix;

[0099] H is the coefficient matrix of the observation equation, and its specific form is as follows:

[0100] ;

[0101] y is the axial coordinate of the optical fiber;

[0102] L is the fiber scale;

[0103] represents the contribution of the right monitoring point and Represents the contribution of the left monitoring point, the specific form is as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] Where a is the half-width of the crack unit dx / 2;

[0108] b is the half height of the crack unit h / 2;

[0109] G 3 (x 1 , x 3 , h, a) is the geometric correction function;

[0110] J 1 (a, b, x 1 , x 2 , x 3 ) and J 2 (a, b, x 1 , x 2 , x 3 ) is the kernel function.

[0111] (4) Covariance matrix of measurement error

[0112] .

[0113] In step S300, a state control equation based on the state variable is established, and the crack width distribution of the next time step is predicted according to the established state control equation. The formula for predicting the crack width distribution of the next time step is:

[0114] ;

[0115] in, is the estimated value of the crack width at time n+1, that is, the crack width distribution of the next time step predicted based on the result at time n;

[0116] is the estimated value of the slit width at time n;

[0117] Φ is a nonlinear equation, and its Jacobian matrix is ​​J w , the numerical method can be used to calculate Jw .

[0118] Furthermore, the 2D crack propagation model can be used as the state control equation of the state variable w. Specifically, the finite difference method is used to discretize the equation to obtain the component expressions of f, the state control equation f, as follows:

[0119] ;

[0120] in,

[0121] ∆t is the time step;

[0122] ∆x is the spatial step length;

[0123] μ is the fracturing fluid viscosity;

[0124] w i+0.5 is the width at the interface between units i and i+1, where w i+0.5 =0.5(w i +w i+1 );

[0125] W i-0.5 is the width at the interface between the i and i-1 units, where w i-0.5 =0.5(w i +w i-1 );

[0126] p i , p i-1 , p i+1 are the pressures at the center points of units i, i-1, and i+1 respectively.

[0127] At step S400, the covariance matrix of the prediction error of the next time step of the state control equation is calculated according to the covariance matrix of the system error of the crack propagation model. The calculation formula is:

[0128] ;

[0129] Among them, P n+1,n is the error covariance matrix P at time n n,n The error covariance matrix of the predicted n+1 time;

[0130] P n,n is the error covariance matrix at time n;

[0131] is the covariance matrix of the systematic error of the crack propagation model;

[0132] J is the Jacobian matrix; the calculation formula of the Jacobian matrix is:

[0133] ;

[0134] Where, f is the state control equation;

[0135] I is the identity matrix;

[0136] w is the seam width;

[0137] In step S500, an observation equation of distributed optical fiber strain is established to calculate the optical fiber strain corresponding to the state variable of the next time step.

[0138] The monitored quantity is the optical fiber strain, and the inverted quantity is the crack width distribution. The two are connected through the observation equation. The optical fiber calculates the strain through the displacement distribution. According to the displacement of adjacent measuring points, the calculation formula of the optical fiber strain induced by the crack (that is, the observation equation of the distributed optical fiber strain) is:

[0139] ;

[0140] Where, u is the fiber displacement;

[0141] y is the axial coordinate of the optical fiber;

[0142] L is the fiber scale;

[0143] A is the coefficient matrix of the three-dimensional displacement discontinuous boundary element;

[0144] H is the coefficient matrix of the observation equation.

[0145] According to the observation equation of the distributed optical fiber strain above, the optical fiber strain corresponding to the state variable of the next time step is calculated. The calculation formula is:

[0146] ;

[0147] Among them, H n+1 is the coefficient matrix of the observation equation at time n+1;

[0148] is the state variable for the next time step The corresponding fiber strain.

[0149] At step S600, a state update equation for the slot width distribution is established based on the monitored optical fiber strain data and the calculated optical fiber strain corresponding to the state variable of the next time step.

[0150] It should be noted that the state update equation for the crack width distribution at this time is the distribution of the state variable (crack width) that integrates the crack extension model and the monitored optical fiber strain data.

[0151] Among them, the state update equation is:

[0152] ;

[0153] Among them, Z n+1 is the optical fiber strain data monitored at time n+1;

[0154] is the estimated value of the seam width at time n+1 predicted in step S300;

[0155] is the estimated value of the crack width at the updated time n+1, that is, the estimated value of the crack width at the time n+1 calculated by the state update equation;

[0156] K n+1 is the Kalman gain matrix at time n+1, and the calculation formula is as follows:

[0157] ;

[0158] Among them, H n+1 is the coefficient matrix of the observation equation at time n+1;

[0159] is the covariance matrix of the strain measurement error.

[0160] According to the calculated covariance matrix of the prediction error of the next time step of the state control equation, the covariance matrix of the prediction error of the next time step of the state update equation is updated. The calculation formula is:

[0161] ;

[0162] Among them, P n+1,n is the error covariance matrix P at time n n,n The error covariance matrix of the predicted n+1 time;

[0163] P n+1,n+1 is the error covariance matrix at the updated n+1 moment.

[0164] At step S700, the crack unit state is updated. , update the crack unit state. When the crack tip reaches the expansion condition, it is updated to a new tip. After the update is completed, enter step S300 to step S700 again until the set end time is reached.

[0165] At each time step, the optimal estimate of the state parameter (crack width) is obtained by minimizing the model error and the measurement error. Finally, the width distribution of each time step is obtained, which is the time series distribution of the crack parameter inversion.

[0166] Example 1

[0167] like Figure 2The fiber optic monitoring well is 200m away from the fracturing well. A fiber optic monitoring point is arranged every meter on the monitoring well to record the observation data. The monitoring range is 200m. This example uses the dynamic inversion of fracture parameters of a single cluster and a single fracture as an example.

[0168] S1, initialize state parameters.

[0169] Main formation parameters: elastic modulus E is 35 GPa, Poisson's ratio v is 0.2, and critical stress intensity factor Kc is 0.5 MPa·m 0.5 , minimum horizontal principal stress σ h It is 50MPa.

[0170] Main fluid parameters, fracturing fluid viscosity It is 10mPa.s and the injection flow rate Qt is 3m3 / min.

[0171] The PKN model is used, the initial fracture height is preset to 100m, the fracture extension is a nonlinear moving boundary problem, and the state variables are the fracture length and width distribution. The width of the unopened fracture unit is 0, so the fracture length is implicit in the width distribution, and the state variables of the system can be uniformly expressed by the fracture width w.

[0172] S2 to S7 refer to the above-mentioned steps S200 to S700.

[0173] Figure 3 and Figure 4 The inversion results are shown in Fig. Figure 3 and Figure 4 It can be seen that the inverted crack length and width results are basically consistent with the true values.

[0174] Obviously, the embodiments described above are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, ordinary technicians in this field can make other different forms of changes or modifications without creative work, which should fall within the scope of protection of the present invention.

Claims

1. A method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation, characterized in that: include: Establish a state control equation based on state variables, and predict the crack width distribution in the next time step according to the established state control equation; Calculating the covariance matrix of the prediction error of the next time step of the state control equation according to the covariance matrix of the system error of the crack propagation model; Establish the observation equation of distributed optical fiber strain and calculate the optical fiber strain corresponding to the state variable in the next time step; According to the monitored optical fiber strain data and the optical fiber strain corresponding to the calculated state variable of the next time step, a state update equation for the slot width distribution is established, wherein the state update equation is: ； Among them, Z n+1 is the optical fiber strain data monitored at time n+1; The estimated value of the seam width at time n+1 predicted in the step of establishing a state control equation based on the state variable and predicting the seam width distribution of the next time step according to the established state control equation; is the estimated value of the crack width at the updated time n+1, that is, the estimated value of the crack width at the time n+1 calculated by the state update equation; K n+1 is the Kalman gain matrix at time n+1; H n+1 is the coefficient matrix of the observation equation at time n+1; The state of the crack unit is updated, and after the update, the prediction of the crack width distribution of the next time step is entered again until the set end time is reached, including updating the state of the crack unit according to the estimated value of the crack width of the next time step after the update; wherein, when the crack tip reaches the expansion condition, it is updated to the new tip; Wherein, in the step of establishing a state control equation based on the state variable and predicting the crack width distribution at the next time step according to the established state control equation, The formula for predicting the crack width distribution in the next time step is: ； in, is the estimated value of the crack width at time n+1, that is, the crack width distribution of the next time step predicted based on the result at time n; is the estimated value of the slit width at time n; Φ is a nonlinear equation, and its Jacobian matrix is ​​Jw, which can be calculated by numerical methods; f is the state control equation based on the state variables.

2. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: In the step of establishing a state control equation based on the state variable and predicting the crack width distribution in the next time step according to the established state control equation, the state control equation is: ； in, ∆t is the time step; ∆x is the spatial step length; μ is the fracturing fluid viscosity; w i+0.5 is the width at the interface between units i and i+1, where w i+0.5 =0.5(w i +w i+1 ); W i-0.5 is the width at the interface between the i and i-1 units, where w i-0.5 =0.5(w i +w i-1 ); p i , p i-1 , p i+1 are the pressures at the center points of units i, i-1, and i+1 respectively.

3. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: In the step of calculating the covariance matrix of the prediction error of the next time step of the state control equation according to the covariance matrix of the system error of the crack propagation model, the calculation formula of the covariance matrix of the prediction error of the next time step is: ； Among them, P n+1,n is the error covariance matrix P at time n n,n The error covariance matrix of the predicted n+1 time; P n,n is the error covariance matrix at time n; is the covariance matrix of the systematic error of the crack propagation model; J is the Jacobian matrix; the calculation formula of the Jacobian matrix is: ； Where, f is the state control equation; I is the identity matrix; w is the slit width.

4. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: In the step of establishing the observation equation of the distributed optical fiber strain and calculating the optical fiber strain corresponding to the state variable of the next time step, the observation equation of the distributed optical fiber strain is: ； Where, u is the fiber displacement; y is the axial coordinate of the optical fiber; L is the fiber scale; A is the coefficient matrix of the three-dimensional displacement discontinuous boundary element; H is the coefficient matrix of the observation equation.

5. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: The formula for calculating the fiber strain corresponding to the state variable in the next time step is: ； in, is the state variable for the next time step The corresponding fiber strain.

6. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: In the step of establishing a state update equation for the seam width distribution based on the monitored optical fiber strain data and the optical fiber strain corresponding to the calculated state variable of the next time step, K n+1 The calculation formula is as follows: ； Among them, H n+1 is the coefficient matrix of the observation equation at time n+1; is the covariance matrix of the strain measurement error; According to the calculated covariance matrix of the prediction error of the next time step of the state control equation, the covariance matrix of the prediction error of the next time step of the state update equation is updated. The calculation formula is: ; Among them, P n+1,n is the error covariance matrix P at time n n,n The error covariance matrix of the predicted n+1 time; P n+1,n+1 is the error covariance matrix at the updated n+1 moment.

7. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: Before the step of establishing a state control equation based on the state variable and predicting the crack width distribution at the next time step according to the established state control equation, the method further includes: Initialize the state variable parameters and use the slit width w as the state variable parameters.

8. The method for dynamic inversion of fracturing cracks integrating optical fiber strain monitoring and crack extension simulation according to claim 1, characterized in that: Before the step of establishing a state control equation based on the state variable and predicting the crack width distribution at the next time step according to the established state control equation, the method further includes: Initial crack morphology, covariance matrix of initial errors of state variables, covariance matrix of model system errors, and covariance matrix of measurement errors.

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