A method and system for predicting casing deformation during volume fracturing based on energy theory

Abstract

The application provides a casing deformation prediction method and system for volume fracturing process based on energy theory. According to the energy conservation and material balance principle, the total energy injected into the stratum in the volume fracturing process is considered to be converted into pressure energy of fluid in the fracture, kinetic energy of fluid in the fracture, elastic deformation energy and surface energy of rock, friction energy consumed by fluid flow in the fracture, pressure energy consumed by fluid filtration in the fracture, deformation energy of cement sheath and casing deformation energy, and then the extreme work principle is used to solve key parameters such as casing deformation load and displacement, so that the prediction accuracy of the casing deformation degree is improved, and basic basis is provided for the optimization of fracturing design, casing damage prevention and treatment.

Description

Technical Field

[0001] This invention belongs to the field of petroleum drilling and production engineering technology, and relates to a method and system for predicting casing deformation in volumetric fracturing process based on energy theory. Background Technology

[0002] Hydraulic fracturing technology is widely used to intensify low-permeability, unconventional, and shale reservoirs to improve oil and gas recovery. It involves injecting high-pressure fluid into the formation through fracturing wells to induce hydraulic fractures, connecting the surface and deep formations and forming a complex fracture network that significantly increases the overall permeability of the reservoir. my country's large-scale exploration and development of shale gas resources relies on two core engineering technologies: horizontal wells and volumetric fracturing. The casing string of unconventional and shale gas wells constitutes the medium transport channel during fracturing and production stimulation; its integrity is fundamental to completing the reservoir stimulation process and achieving production targets. Taking shale gas development in southwestern my country as an example, the casing service conditions of fracturing and production stimulation wells are characterized by long horizontal sections, large doglegs, staged volumetric fracturing, and long-term production stimulation after completion, placing high demands on the integrity of the casing string. To ensure the reservoir stimulation effect of fracturing projects, fracturing conditions are continuously optimized, mainly manifested in: longer horizontal well sections (average length exceeding 2000 meters), more fracturing segments (around 30 segments), shorter segment lengths (30-60 meters), and greater proppant addition intensity (up to 3 tons of proppant per meter). High-intensity horizontal well volumetric fracturing drives formation slippage through natural fractures or weak bedding planes, exacerbating casing deformation problems primarily caused by shear and non-uniform external pressure. Casing deformation control during volumetric fracturing is a global challenge, not only troubling shale gas development in my country (in 2019, the casing deformation rate of shale gas wells in a certain block exceeded 20%), but also prevalent in shale gas development abroad.

[0003] According to research, the casing deformation rate in shale gas wells in Argentina's Neuquén Basin is 25%, while in Canada's Duvernay shale gas wells it reaches 47%. The causes of casing deformation are complex, involving a combination of geological, engineering, and pipe material factors, and are influenced by a combination of factors including in-situ stress, reservoir thickness, fracturing conditions, cementing quality, and pipe material resistance. Implementing a physical simulation test method for casing deformation based on integrated geological and engineering principles is very difficult. Loading modes and test loads are often unclear and difficult to achieve, and the few existing simulation test methods are insufficient to answer the complex deformation problems of casing downhole.

[0004] Currently, casing deformation prediction mainly involves nonlinear mechanical calculations considering multiple physical fields of geology, cement sheath, and casing string. This involves various materials such as soil, cement, and steel, as well as multiple nonlinear factors such as large displacement and large strain geometric conditions and complex boundary conditions at multiple interfaces. Among these, the load or displacement boundary conditions of casing deformation are difficult to obtain quantitatively, making the solution very difficult. A large number of simplifications and approximations must be adopted, which inevitably sacrifices the accuracy of deformation prediction. As a result, the casing deformation mechanism has not yet been explored, making it impossible to accurately predict casing deformation. The limited understanding of the casing deformation mechanism seriously affects the prevention and control of casing deformation. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method and system for predicting casing deformation during volumetric fracturing based on energy theory. The propagation of hydraulic fractures and wellbore deformation during volumetric fracturing can be regarded as a quasi-static process. By considering various energy dissipations, including the pressure energy of the fluid within the fracture, the kinetic energy of the fluid within the fracture, the elastic deformation energy and surface energy of the rock, the frictional energy consumed by the fluid flow within the fracture, the pressure energy consumed by the fluid filtration within the fracture, the deformation energy of the cement sheath, and the deformation energy of the casing, the total effective energy injected during the fracturing process can be calculated in the process of generating casing deformation. Then, by applying the principle of extreme work in the metal deformation process, the degree of deformation under different possible deformation modes of the casing can be calculated.

[0006] This invention is achieved through the following technical solution:

[0007] A method for predicting casing deformation during volumetric fracturing based on energy theory, comprising:

[0008] S1. Obtain fracturing operating parameters, geological parameters, cement sheath parameters, and casing parameters;

[0009] S2. Based on the geological parameters, cement ring parameters and casing parameters in S1, predict the initial strain field of casing deformation, calculate the nonlinear stress of casing deformation, and thus establish the energy consumption functional of casing deformation.

[0010] S3. Based on the fracturing parameters in S1, calculate the input energy and energy consumption during the volumetric fracturing process, and establish a nonlinear equilibrium equation;

[0011] S4. Set the casing deformation boundary constraints based on the initial strain field in S2;

[0012] S5. Based on the nonlinear equilibrium equation in S3 and the casing deformation boundary constraints in S4, the NR iterative solution is used to predict the casing deformation.

[0013] Preferably, the energy functional consumed by the deformation of the sleeve in S2 is calculated as follows:

[0014]

[0015] in, For the work term of plastic deformation, ∫ V (ε V ) 2 dV is the penalty function term; V is the volume of the deformed casing. For the equivalent stress of casing deformation and The equivalent strain is the casing deformation; α is the penalty factor; ε V For volumetric strain.

[0016] Preferably, the input energy in S3 includes the pressure energy of the fluid inside the fracture and the kinetic energy of the fluid inside the fracture.

[0017] Preferably, the energy consumed in S3 includes the elastic deformation energy of the rock, the surface energy of the rock deformation, the frictional energy consumed by the fluid flow in the fracture, the pressure energy consumed by the fluid loss in the fracture, and the deformation energy of the cement sheath.

[0018] Preferably, the specific method for calculating the input energy and energy consumption during the volumetric fracturing process based on the fracturing condition parameters in S4 is as follows:

[0019] Calculate the total energy injected during volumetric fracturing based on the fracturing operating parameters, and calculate the input energy and consumed energy based on the total energy injected during fracturing.

[0020] Preferably, the total energy injected during volumetric fracturing is calculated based on the fracturing operating parameters. The specific calculation method is as follows:

[0021] E in =p in q in t

[0022] Among them, E in The total energy injected into the formation for fracturing; p in To inject pressure; q in t represents the injection displacement; t represents the injection time.

[0023] Preferably, in S3, the input energy and energy consumption during the volumetric fracturing process are calculated based on the fracturing operating parameters, and a nonlinear equilibrium equation is established. The specific method is as follows:

[0024] Based on the input energy and consumed energy obtained and the consumed energy of casing deformation obtained in S2, the overall energy function of the volumetric fracturing process is established; based on the overall energy function of the volumetric fracturing process, a nonlinear equilibrium equation is established.

[0025] Preferably, the overall energy function of the volumetric fracturing process in S4 is calculated using the following method:

[0026] L=E p +Ek -E s -E f -E1-E c -π

[0027] Where L is the total energy function of the volumetric fracturing process, and E p E represents the pressure energy of the fluid within the fracture. k E represents the kinetic energy of the fluid within the fracture. e E represents the elastic deformation energy of rock. s Surface energy from rock deformation; pressure energy lost due to fluid filtration within the fracture (E1); E c Cementing sheath deformation energy, where π is the energy functional consumed by casing deformation.

[0028] Preferably, in S8, the NR iterative solution is used to predict the casing deformation. The specific method is as follows:

[0029] The casing deformation value is obtained by NR iterative calculation. A convergence criterion is established, and the casing deformation value is iteratively converged for each time. The casing deformation strain field is output to realize the prediction of casing deformation.

[0030] A casing deformation prediction system based on energy theory in volumetric fracturing process includes:

[0031] The information acquisition module is used to acquire fracturing operating parameters, geological parameters, cement sheath parameters, and casing parameters;

[0032] A module is established to predict the initial strain field of casing deformation based on geological parameters, cement sheath parameters, and casing parameters, calculate the nonlinear stress of casing deformation, thereby establishing the energy consumption functional of casing deformation and calculating the input and consumption energy in the volumetric fracturing process based on fracturing condition parameters, and establishing nonlinear equilibrium equations.

[0033] The condition setting module is used to set the casing deformation boundary constraints based on the initial strain field.

[0034] The calculation module is used to predict the deformation of the casing by applying NR iteration to solve the nonlinear equilibrium equation and the casing deformation boundary constraints.

[0035] Compared with the prior art, the present invention has the following beneficial technical effects:

[0036] This invention employs a casing deformation prediction method based on energy theory. It attributes the total energy input by high-pressure, high-volume fracturing fluid to the energy dissipation of the formation, cement sheath, and casing, respectively. It integrates the complex multiphysics field into an energy balance system, avoiding complex boundary condition handling at multiple interfaces. Parameters such as fracturing volume, fracture network conductivity, and fracture density are typically used to evaluate the effectiveness of volumetric fracturing projects and are important assessment criteria for oil and gas production establishment and enhancement. In this invention, these parameters are used to calculate the energy dissipation of the formation system during fracturing. Cement cementing quality and deformation resistance are typically used to assess wellbore integrity. In this invention, the evolution of cement sheath fracture failure under pre-set and iterative boundary conditions is used to calculate the energy absorbed by the cement sheath during compression deformation. Within the framework of global system energy conservation, the true strain value is calculated based on the plastic work of casing deformation, yielding the casing deformation resistance and the final casing deformation configuration. This invention improves the prediction accuracy of casing deformation through a novel approach, providing a fundamental basis for optimizing fracturing design and preventing and managing casing damage. Attached Figure Description

[0037] The accompanying drawings are provided to further illustrate the invention and form part of this application. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation thereof.

[0038] Figure 1 This is a schematic diagram illustrating the implementation process of the present invention;

[0039] Figure 2 This is a schematic diagram of the shear deformation of the sleeve in the embodiment;

[0040] Figure 3 This is a schematic diagram of the non-uniform external pressure deformation of the sleeve in the embodiment;

[0041] Figure 4 This is a diagram showing the calculation results of non-uniform external pressure deformation in the embodiment;

[0042] Figure 5 The figure shows the calculation results of the sleeve shear deformation in the embodiment. Detailed Implementation

[0043] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0044] Casing deformation is caused by formation pressure. When the external extrusion pressure on the casing exceeds the internal pressure, it can cause casing deformation and damage, such as one or more instances of diameter reduction, flattening, or bending. This type of casing deformation and damage is called casing deformation. Casing deformation includes: casing diameter reduction, casing flattening, and casing bending.

[0045] This invention proposes a method and system for predicting casing deformation during volumetric fracturing based on energy theory. According to the principles of energy conservation and mass balance, the method considers the conversion of the total energy injected into the formation during volumetric fracturing into the pressure energy of the fluid within the fracture, the kinetic energy of the fluid within the fracture, the elastic deformation energy and surface energy of the rock, the frictional energy consumed by the fluid flow within the fracture, the pressure energy consumed by the fluid filtration within the fracture, the deformation energy of the cement sheath, and the deformation energy of the casing. Furthermore, the principle of extreme work is used to solve for key parameters such as casing deformation load and displacement. This method is expected to improve the accuracy of predicting the degree of casing deformation through a new approach, providing a fundamental basis for optimizing fracturing design and preventing and managing casing damage.

[0046] A method for predicting casing deformation during volumetric fracturing based on energy theory includes the following steps.

[0047] S1. Obtain fracturing operating parameters, geological parameters, cement sheath parameters, and casing parameters;

[0048] S2. Based on the geological parameters, cement sheath parameters and casing parameters in S1, predict the initial strain solution of the casing deformation and calculate the nonlinear stress of the casing deformation;

[0049] S3. Establish the energy consumption functional of casing deformation based on the nonlinear stress of casing deformation in S2;

[0050] S4. Calculate the input energy and energy consumption during the volumetric fracturing process based on the fracturing conditions parameters in S1;

[0051] S5. Based on the input energy and energy consumption obtained in S4 and the energy consumption function of casing deformation obtained in S3, establish the overall energy function of the volumetric fracturing process;

[0052] S6. Establish a nonlinear equilibrium equation based on the overall energy function of the volumetric fracturing process in S5;

[0053] S7. Set the casing deformation boundary constraints based on the initial strain solution in S1;

[0054] S8. Based on the nonlinear equilibrium equation in S6 and the casing deformation boundary constraints in S7, the NR iterative solution is used to predict the casing deformation.

[0055] The casing deformation manifests as a metal plastic deformation process under the action of external forces from the formation and cement sheath. Based on the constrained variational principle, an energy functional is used to represent the change in plastic potential energy of the system under quasi-static equilibrium. A penalty function is introduced to introduce the incompressibility condition of the deformation volume. A functional is established for the energy consumed by the casing deformation. The energy consumption functional of the casing deformation in S3 is calculated as follows:

[0056]

[0057] The first term is the work term for plastic deformation, the second term is the penalty function term, and V is the volume of the deformed casing. For the equivalent stress of casing deformation and The equivalent strain is the casing deformation; α is the penalty factor; ε V For volumetric strain.

[0058] The fracturing operating parameters include fracturing stage, injection pressure, and injection flow rate.

[0059] The input energy includes the pressure energy and kinetic energy of the fluid within the fracture; the consumed energy includes the elastic deformation energy of the rock, the surface energy of the rock deformation, the frictional energy consumed by the fluid flow within the fracture, the pressure energy consumed by the fluid filtration within the fracture, and the deformation energy of the cement sheath.

[0060] The specific method for calculating the input energy and energy consumption during volumetric fracturing based on fracturing operating parameters in S4 is as follows:

[0061] Calculate the total energy injected during volumetric fracturing based on fracturing operating parameters, and calculate the input energy and consumed energy based on the total energy injected during fracturing.

[0062] The total energy injected during volumetric fracturing is calculated based on the fracturing operating parameters. The specific calculation method is as follows:

[0063] E in =p in q in t

[0064] Among them, E in The total energy injected into the formation for fracturing; p in To inject pressure; q in t represents the injection displacement; t represents the injection time.

[0065] The energy injected into the formation during volumetric fracturing is

[0066] E in =p in q in t

[0067] In the formula, E in The total energy injected into the formation for fracturing, kJ; p in Injection pressure, MPa; q in t represents the injection displacement, in mm / s; t represents the injection time, in seconds.

[0068] The total energy injected into the formation during volumetric fracturing is converted into the following components: pressure energy of the fluid within the fracture, kinetic energy of the fluid within the fracture, elastic deformation energy and surface energy of the rock, frictional energy consumed by fluid flow within the fracture, pressure energy consumed by fluid filtration within the fracture, and deformation energy of the cement sheath and casing. Among these:

[0069] The pressure energy of the fluid inside the fracture is

[0070] E p =pnwhx

[0071] In the formula, E p denoted as ρ, where ρ is the pressure energy of the fluid within the fracture, in kJ; p is the average pressure within the fracture, in MPa; n is the equivalent number of fractures; and w, h, and x are the average fracture width, fracture height, and fracture length, respectively, in m.

[0072] The kinetic energy of the fluid within the fracture is

[0073]

[0074] In the formula, E k ν is the kinetic energy of the fluid inside the fracture, kJ; m is the mass of the fluid inside the fracture, tons; v is the velocity of the fluid inside the fracture, mm / s.

[0075] The elastic deformation energy of rock is

[0076]

[0077] In the formula, E e σ is the elastic deformation energy, kJ; σ and ε are the stress (MPa) and strain, respectively; V is the volume of rock deformation, mm. 3 .

[0078] The surface energy of rock deformation is

[0079] E s =2e s nhx

[0080] In the formula, E s For surface energy, kJ; e s Specific surface energy, kJ / mm 2 .

[0081] The frictional energy consumed by fluid flow within the crack is

[0082]

[0083] In the formula, E f Friction energy consumed by fluid flow, kJ; f is the friction coefficient; n is the equivalent number of cracks; ρ is the fluid density, t / mm³. 3 .

[0084] The pressure energy consumed by fluid filtration within the crack is

[0085] E1=pV1

[0086] In the formula, p is the average pressure inside the fracture, MPa; V1 is the volume of fracturing fluid lost.

[0087] The deformation of the cement sheath manifests as fracture failure under compressive stress conditions. This primarily considers the propagation of minute internal damage to the cement sheath under normal tensile stress under high confining pressure until fracture. According to the principle of virtual work, the energy consumed is...

[0088]

[0089] In the formula, the first term on the right is the thermodynamic internal energy of the cement ring medium, and the second term is the surface energy; d is the thickness of the cement ring, σ is the uniform compressive stress, u is the normal displacement of the damaged surface, x1 is the spatial coordinate, and γ is the unit surface free energy.

[0090] Based on Hamilton's principle, the specific calculation method for the overall energy function of the volumetric fracturing process based on the Lagrange method is as follows:

[0091] L=E p +E k -E s -E f -E1-E c -π

[0092] Where L is the total energy function of the volumetric fracturing process, and E p E represents the pressure energy of the fluid within the fracture. k E represents the kinetic energy of the fluid within the fracture. e E represents the elastic deformation energy of rock. s Surface energy from rock deformation; pressure energy lost due to fluid filtration within the fracture (E1); E c Cementing sheath deformation energy, where π is the energy functional consumed by casing deformation.

[0093] The transformation of fracturing pressure energy and fluid kinetic energy into rock deformation energy, surface energy, fluid friction energy, fluid filtration dissipation energy, cement sheath failure deformation energy, and casing deformation energy follows the principle of extreme work. Thus, in all permissible casing deformation displacement fields that satisfy casing deformation geometry, volume incompressibility, and boundary conditions, the actual displacement field should make the casing deformation energy closer to the total energy dissipation of the formation-cement sheath and casing string after the total energy injected by fracturing. The nonlinear equilibrium equation is established by minimizing the system energy functional and solved iteratively using the Newton-Raphson (NR) method.

[0094] The process of calculating and solving for the casing deformation follows these steps (see...) Figure 1(1) First, select the initial strain field to characterize the casing deformation; (2) Calculate the fracturing working conditions at the deformation time according to the strain field, calculate the input energy and the dissipated energy of each part, including the plastic deformation work of the casing; (3) Assemble the nonlinear equilibrium equation according to the principle of extreme work principle of system energy functional minimization; (4) Apply displacement boundary conditions according to the preset initial state; (5) Solve by continuous NR iteration, and after each iteration, repeat steps (1)-(4) according to the iteration convergence criterion until the calculation is completed, and output the casing deformation strain field.

[0095] Among them, establishing a suitable convergence criterion can balance the accuracy and efficiency of the solution. The following convergence criterion is adopted:

[0096] When the functional variation is zero, the true strain solution of the casing deformation state is obtained. When the calculated value is close to the true strain field, the first-order variation of the functional approaches zero.

[0097] The method of using NR iterative solution to predict sleeve deformation is as follows:

[0098] The casing deformation value is obtained by NR iterative calculation; the established convergence criterion is used to iteratively converge the casing deformation value obtained each time, and the casing deformation strain field is output.

[0099] The convergence criteria include,

[0100] When the first variation of the energy functional consumed by the casing deformation is zero, the true solution of the casing deformation strain is obtained.

[0101] When the first variation of the energy-consuming functional of the casing deformation approaches zero, the calculated value of the casing deformation is close to the true strain field, and the strain solution of the casing deformation is obtained.

[0102]

[0103] Where ε is the casing deformation strain, L is the total energy function of the volumetric fracturing process, e is the first variational value of the energy functional consumed by casing deformation, and δ is 10. -5 .

[0104] The casing deformation prediction method proposed in this invention adopts the principle of energy conservation and directly predicts the degree of deformation through the casing deformation energy. Different possible deformation modes can be considered and calculated separately. The solution is developed based on fracturing, geological and tubing mechanical parameters, without involving nonlinear mechanical calculations of multiple physical fields such as surrounding soil and rock, oil and gas reservoir, hydraulic fracture, cementing cement, and casing material. The load or displacement boundary conditions of casing deformation are obtained indirectly, and a quantitative prediction result of the degree of casing deformation is obtained.

[0105] A casing deformation prediction system based on energy theory in volumetric fracturing process includes:

[0106] Information acquisition module, the information acquisition module is used to acquire fracturing condition parameters, geological parameters, cement sheath parameters and casing parameters;

[0107] A module is established to predict the initial strain field of casing deformation based on geological parameters, cement sheath parameters, and casing parameters, calculate the nonlinear stress of casing deformation, thereby establishing the energy consumption functional of casing deformation and calculating the input energy and energy consumption during volumetric fracturing based on fracturing condition parameters, and establishing nonlinear equilibrium equations.

[0108] The condition setting module is used to set the casing deformation boundary constraint conditions according to the initial strain field.

[0109] The calculation module is used to predict the deformation of the casing by applying NR iteration to solve the nonlinear equilibrium equation and the casing deformation boundary constraints.

[0110] like Figure 1 As shown, the casing deformation prediction method for volumetric fracturing based on energy theory of the present invention performs iterative calculations based on fluid-structure interaction (FSI) in the initial intra-fracture pressure field and geometric space according to the fracturing injection rate. Specifically, within each iteration step, based on the intra-fracture pressure field and geometric space converged in the previous iteration, the fracturing fluid flow rate and energy distribution are calculated. The fracture propagation energy criterion is used to determine the fracture propagation amount, and a new fracture size and pressure distribution are formed after convergence. During the fracturing fracture propagation process, on the one hand, the intra-fracture pressure leads to the evolution of the fracture size, and on the other hand, the updated fracture geometry affects the change in intra-fracture pressure distribution. Thus, the propagation morphology of the fracturing fracture is obtained through iterative calculations using FSI.

[0111] The number, spacing, and size of fractures are calculated based on fracturing conditions (including well depth, horizontal section length, fracturing stage, injection pressure, fluid injection rate, and proppant volume), and verified using post-fracturing evaluation data. Based on this, the overall energy of the fracturing process is calculated. The casing deformation energy is obtained from the total energy of the injected fracturing fluid, the energy dissipation during fracture propagation, the energy consumption due to rock deformation, and the energy consumption due to cement sheath deformation.

[0112] Based on the constrained variational principle, a plastic potential energy functional of the system under quasi-static equilibrium state of casing deformation is established, and a penalty function is introduced to introduce the volumetric incompressibility condition of metal plastic deformation. In all permissible displacement fields satisfying the geometric, volumetric incompressibility, and boundary conditions, the actual displacement field minimizes the functional. The initial displacement field of casing deformation is predetermined based on the deformation of the formation and cement sheath. Based on the theory of metal plastic deformation, the Ilyushin theory is applied to adapt to the power-law strengthening constitutive relation of metal-hardening materials. The relationship between the deformation displacement field and the strain field is established using linear and nonlinear geometric equations, and iteratively solved using numerical analysis methods. The specific calculation process is as follows (e.g.) Figure 1 Based on the parameters of the fracturing fractures, formation rock, cement sheath, and casing determined by the energy method, the initial displacement field of the casing deformation is inferred. Strain solutions are obtained through geometric equations. The nonlinear stress of the casing is calculated based on the metal constitutive relation. The total plastic deformation work and deformation boundary constraints of the casing are calculated based on the total fracturing input energy and the dissipated work of each component. The nonlinear equilibrium equations established based on the approximate plastic potential of the casing deformation are systematically checked. Iterative calculations are performed using the Newton-Raphson (NR) method. Based on the fact that the first-order variational functional approaches zero, the calculated casing deformation value continuously approaches the true strain field and iteratively converges. Finally, the final configuration, stress / strain, and other results of the deformed casing are output. The calculated results are compared and verified with the results of a full-scale laboratory experiment. Figure 2 and 3 This involves correcting parameters such as the initial displacement field, iteration time increment step size, penalty function factor, and iteration convergence criterion to improve prediction accuracy.

Claims

1. A method for predicting casing deformation during volumetric fracturing based on energy theory, characterized in that, include, S1. Obtain fracturing operating parameters, geological parameters, cement sheath parameters, and casing parameters; S2. Based on the geological parameters, cement ring parameters and casing parameters in S1, predict the initial strain field of casing deformation, calculate the nonlinear stress of casing deformation, and thus establish the energy consumption functional of casing deformation. S3. Based on the fracturing parameters in S1, calculate the input energy and energy consumption during the volumetric fracturing process, and establish a nonlinear equilibrium equation; S4. Set the casing deformation boundary constraints based on the initial strain field in S2; S5. Based on the nonlinear equilibrium equation in S3 and the casing deformation boundary constraint conditions in S4, the NR iterative solution is used to predict the casing deformation. The energy functional consumed by the deformation of the sleeve in S2 is specifically calculated as follows: in, For the work term of plastic deformation, ∫ V (ε V ) 2 dV is the penalty function term; V is the volume of the deformed casing. For the equivalent stress of casing deformation and The equivalent strain is the casing deformation; α is the penalty factor. ε V For volumetric strain; The input energy in S3 includes the pressure energy and kinetic energy of the fluid inside the fracture. The energy consumed in S3 includes the elastic deformation energy of the rock, the surface energy of the rock deformation, the frictional energy consumed by the fluid flow in the fracture, the pressure energy consumed by the fluid loss in the fracture, and the deformation energy of the cement sheath.

2. The method for predicting casing deformation in volumetric fracturing based on energy theory according to claim 1, characterized in that, The specific method for calculating the input and consumption energy during volumetric fracturing based on fracturing operating parameters in S3 is as follows: Calculate the total energy injected during volumetric fracturing based on the fracturing operating parameters, and calculate the input energy and consumed energy based on the total energy injected during fracturing.

3. The method for predicting casing deformation during volumetric fracturing based on energy theory according to claim 1, characterized in that, The total energy injected during volumetric fracturing is calculated based on the fracturing operating parameters. The specific calculation method is as follows: E in =p in q in t Among them, E in The total energy injected into the formation for fracturing; p in To inject pressure; q in t represents the injection displacement; t represents the injection time.

4. The method for predicting casing deformation during volumetric fracturing based on energy theory according to claim 3, characterized in that, In S3, the input and consumption energy during the volumetric fracturing process are calculated based on the fracturing operating parameters, and a nonlinear equilibrium equation is established. The specific method is as follows: Based on the input energy and consumed energy obtained and the consumed energy of casing deformation obtained in S2, the overall energy function of the volumetric fracturing process is established; based on the overall energy function of the volumetric fracturing process, a nonlinear equilibrium equation is established.

5. The method for predicting casing deformation in volumetric fracturing based on energy theory according to claim 4, characterized in that, The overall energy function of the volumetric fracturing process is calculated using the following method: L =E p +E k -AND s -AND f -E1-E c -π Where L is the total energy function of the volumetric fracturing process, and E p E represents the pressure energy of the fluid within the fracture. k E represents the kinetic energy of the fluid within the fracture. e E represents the elastic deformation energy of rock. s Surface energy from rock deformation; pressure energy lost due to fluid filtration within the fracture (E1); E c Cementing sheath deformation energy, where π is the energy functional consumed by casing deformation.

6. The method for predicting casing deformation in volumetric fracturing based on energy theory according to claim 1, characterized in that, In step S5, the NR iterative solution is used to predict the deformation of the casing. The specific method is as follows: The casing deformation value is obtained by NR iterative calculation. A convergence criterion is established, and the casing deformation value is iteratively converged for each time. The casing deformation strain field is output to realize the prediction of casing deformation.

7. A casing deformation prediction system based on energy theory in volumetric fracturing process, characterized in that, include: The information acquisition module is used to acquire fracturing operating parameters, geological parameters, cement sheath parameters, and casing parameters; The energy consumption functional establishment module is used to predict the initial strain field of casing deformation based on geological parameters, cement sheath parameters and casing parameters, calculate the nonlinear stress of casing deformation, and thus establish the energy consumption functional of casing deformation. The nonlinear equilibrium equation establishment module is used to calculate the input energy and energy consumption during the volumetric fracturing process based on the fracturing operating parameters, and to establish nonlinear equilibrium equations. The condition setting module is used to set the casing deformation boundary constraints based on the initial strain field. The calculation module is used to predict the deformation of the casing by applying NR iteration to solve the nonlinear equilibrium equation and the casing deformation boundary constraints. The specific calculation method for the energy consumption functional in the energy consumption functional establishment module is as follows: in, For the work term of plastic deformation, ∫ V (ε V ) 2 dV is the penalty function term; V is the volume of the deformed casing. For the equivalent stress of casing deformation and The equivalent strain is the casing deformation; α is the penalty factor; ε V The volumetric strain is used; the input energy in the nonlinear equilibrium equation establishment module includes the pressure energy and kinetic energy of the fluid within the fracture. The energy consumed in the nonlinear equilibrium equation establishment module includes the elastic deformation energy of rock, the surface energy of rock deformation, the frictional energy consumed by fluid flow in the fracture, the pressure energy consumed by fluid filtration in the fracture, and the deformation energy of cement sheath.

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