A method for predicting the conductivity impairment of hydraulic fractures

Abstract

The application relates to a hydraulic fracturing fracture conductivity attenuation prediction method, which comprises the following steps: obtaining the change of the closure stress of a hydraulic fracturing fracture along the fracture length direction; according to the change of the closure stress of the hydraulic fracturing fracture along the fracture length direction, calculating the fracture width change of the hydraulic fracturing fracture along the fracture length direction based on a pre-constructed spring model, and obtaining the volume change of the hydraulic fracturing fracture according to the fracture width change; calculating the porosity change of the hydraulic fracturing fracture according to the volume change, and calculating the permeability change according to the porosity change; and obtaining the hydraulic fracturing fracture conductivity attenuation prediction according to the permeability change and the fracture width change. The application provides a hydraulic fracturing fracture conductivity attenuation prediction method, which can more accurately calculate the change of the fracture conductivity.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development technology, specifically to a method for predicting the attenuation of the conductivity of hydraulic fracturing fractures. Background Technology

[0002] Low-permeability oil reservoirs are characterized by their tightness, fine pore throats, and low permeability, making fluid flow difficult. To improve the production of low-permeability reservoirs, reservoir stimulation measures such as hydraulic fracturing are often adopted.

[0003] Currently, hydraulic fracturing technology mostly uses proppant injection to maintain fracture size. However, during production, the proppant undergoes compaction and embedding under the closure stress of formation pressure and fluid pressure, leading to fracture closure. After fracture closure, the space between proppant particles within the fracture is compressed, reducing high-velocity seepage channels and increasing the tortuosity of the flow space, resulting in a decrease in permeability.

[0004] For predicting the conductivity of hydraulic fracturing fractures, existing techniques mostly use the method of fitting experimental data to obtain semi-empirical formulas. However, since this method does not analyze the weakening of fracture conductivity from the perspective of mechanisms such as fracture closure, the fitted data may not be accurate.

[0005] Therefore, a method for predicting the attenuation of conductivity is needed, which is derived from the crack closure angle and mechanical mechanism. Summary of the Invention

[0006] To address the above problems, the purpose of this invention is to provide a method for predicting the attenuation of fracture conductivity in hydraulic fracturing, which can more accurately calculate the changes in fracture conductivity.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, this application provides a method for predicting the attenuation of conductivity of hydraulic fracturing fractures, the method comprising: Obtain the change in closure stress along the length of the hydraulic fracturing fracture; Based on the change in closure stress along the length of the hydraulic fracturing fracture, and using a pre-built spring model, the change in fracture width along the length of the hydraulic fracturing fracture is calculated, and the change in volume of the hydraulic fracturing fracture is obtained based on the change in fracture width. The porosity change of the hydraulic fracturing fracture is calculated based on the volume change, and the permeability change is calculated based on the porosity change. Based on the changes in permeability and fracture width, the predicted attenuation of the hydraulic fracturing fracture conductivity is obtained.

[0008] In one implementation of this application, in the pre-constructed spring model, the deformation of the proppant in the hydraulic fracturing fracture is equated to the deformation of the spring; the deformation of the proppant includes elastic deformation, elastoplastic deformation, and plastic deformation.

[0009] In one implementation of this application, during the elastic deformation stage, the stress-strain relationship in the model is expressed as: ,in, Indicates stress, Let d represent the generalized elastic modulus, and d be the strain.

[0010] In one implementation of this application, during the elastoplastic deformation stage, the stress-strain relationship in the model is expressed as: .

[0011] In one implementation of this application, during the plastic deformation stage, the stress-strain relationship in the model is expressed as: .

[0012] In one implementation of this application, calculating the permeability change based on the porosity change includes: The permeability change is calculated based on the porosity change according to the Gauzyni-Kalman equation.

[0013] In one implementation of this application, a correction coefficient is introduced to characterize the influence of the proppant structure during the calculation of permeability changes.

[0014] In one implementation of this application, the step of obtaining the predicted attenuation of the hydraulic fracturing fracture conductivity based on the permeability change and the fracture width change includes: Based on the preset functional relationship between flow capacity, permeability, and slit width, the flow capacity attenuation is predicted.

[0015] In one implementation of this application, the preset functional relationship between the flow-guiding capacity and the permeability and slit width is specifically as follows:

[0016] in, For traffic diversion capability, For seam width, This refers to penetration rate.

[0017] In a second aspect, this application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, controls the device in which the computer-readable storage medium is located to implement the method described in the first aspect.

[0018] The present invention has the following advantages due to the adoption of the above technical solutions: This invention employs a theoretical analysis method, transforming the fracture closure process into the deformation calculation of a supporting spring. The deformation involves three stages: an "elastic stage," an "elastoplastic stage," and a "plastic stage." The elastoplastic stage has a complex mechanical mechanism, and an exponential equation is used. Combining the limits of the "elastic stage" and the starting conditions of the "plastic stage," a stress-strain equation for the elastoplastic stage is constructed. Using a stress-strain model of the "supporting spring," the closure amount of the fracture width under different closure stresses is calculated. Furthermore, the porosity change of the hydraulic fracturing fracture is calculated based on the volume change, and the permeability change is calculated based on the porosity change. Finally, based on the permeability change and the fracture width change, a prediction of the hydraulic fracturing fracture conductivity attenuation is obtained. Therefore, compared to existing technologies, this provides a more accurate method for predicting conductivity attenuation. Attached Figure Description

[0019] Figure 1 This is a deformation diagram of the spring model provided in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the relationship between the calculated closure stress and the seam width in an embodiment of the present invention; Figure 3 This is a schematic diagram of the predicted results of the flow capacity attenuation in an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present 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 the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0021] One embodiment of the present invention provides a method for predicting the attenuation of conductivity of hydraulic fracturing fractures, comprising: S1, obtain the change of closure stress along the length of the hydraulic fracturing fracture; S2, based on the change in the closing stress of the hydraulic fracturing fracture along the fracture length direction, and based on the pre-built spring model, calculate the change in the fracture width of the hydraulic fracturing fracture along the fracture length direction, and obtain the change in the volume of the hydraulic fracturing fracture based on the change in the fracture width; S3, calculate the porosity change of the hydraulic fracturing fracture based on the volume change, and calculate the permeability change based on the porosity change; S4. Based on the changes in permeability and the changes in fracture width, the predicted decrease in the conductivity of the hydraulic fracturing fracture is obtained.

[0022] The following is combined Figures 1 to 3 The above method is further illustrated in a more detailed example in this application.

[0023] The embodiments of this application first construct a spring model.

[0024] During the compression of a spring, the spring undergoes three deformation stages under the application of external force: elastic deformation, elastoplastic deformation, and plastic deformation. Similarly, during the compaction and embedding of a supporting fracture into the formation under closure stress, three deformation processes—elastic deformation, elastoplastic deformation, and plastic deformation—also occur. Both exhibit the same deformation pattern, thus providing a basis for analogy.

[0025] Assuming a slit spring Figure 1 As shown, ① is the supporting spring.

[0026] Elastic deformation stage: After the fracturing reverse flow operation is completed, the proppant is tightly arranged in the formation, but there are still some gaps and compressible spaces between the proppant. At the same time, the edge proppant in contact with the formation also undergoes elastic deformation under the influence of formation stress.

[0027] Therefore, in the initial stage of deformation, due to the compaction of the proppant and the elastic deformation at the contact points, the "prop spring" as a whole is in the elastic deformation stage. Satisfying the generalized Hooke's law, the stress-strain relationship can be expressed as: (1) —Contact stress, GPa —Deformation amount, m in The generalized modulus of elasticity is used to represent the mechanical properties of a supporting spring. (2) —Poisson's ratio of rocks —Propionage Poisson's Ratio —Rock elastic modulus, GPa —Prop elastic modulus, GPa Based on the spring model assumptions and elastic limit calculations, the spring elastic deformation limit value can be expressed as: (3) —The limit of elastic deformation of a spring, m —Prop compressive strength, GPa L – Spring height, m Plastic deformation: When the contact stress reaches the plastic yield limit of the rock, the deformation process is considered to have entered the plastic stage. In the theory of contact elastoplastic deformation, the plastic yield limit of rock is usually defined as the hardness of the rock. Experiments have shown that the plastic yield limit of rock is directly proportional to the yield stress of the material, that is: (4) —Rock plastic yield limit, GPa Based on the elastoplastic deformation mechanism of sphere contact embedding, the contact stress remains constant when entering the fully plastic stage, and the positive correlation coefficient C is 3. Therefore, the contact stress in the plastic stage can be expressed as: (5) —Contact stress, GPa At the end of the elastoplastic stage, when transitioning from elastoplastic deformation to plastic deformation, the critical deformation amount is a multiple of the elastic limit deformation. For solid materials, the deformation amount at the onset of plastic deformation is 82.5 times the elastic limit deformation. Therefore, the critical deformation amount for plastic deformation is: (6) —The limit of elastic deformation of a spring, m Elastic-plastic deformation: when At this point, the deformation is in the elastoplastic stage. The elastoplastic stage is a deformation process between elastic and plastic deformation, and its deformation mechanism is complex. According to the elastoplastic deformation theory, the contact stress is proportional to the logarithm of the deformation. and The two coefficients need to be determined using the elastic deformation limit and the plastic deformation limit.

[0028] (7) —Undetermined coefficients d——deformation amount The stress-strain relationship of the supporting spring can then be expressed as: Elastic phase: (8) Elastic-plastic stage: (9) Plastic stage: (10) By using the stress-strain relationship, the crack closure amount under different closure stresses can be calculated, thereby obtaining the crack width of the support crack under different closure stresses. Figure 2 The meaning is as shown.

[0029] According to the Gauzyni-Kalman equation, permeability is related to porosity, and the average capillary radius of the rock is related to the tortuosity of the pores.

[0030] (11) —Penetration rate, mD Porosity r—average capillary radius, μm τ—Tortuosity, 1~1.4 The rate of change in permeability can then be expressed as: (12) a—Permeability change rate b—Correction coefficient In the process of using the rate of change of permeability to characterize the change of crack permeability, it is also affected by the changes in average capillary radius and tortuosity. At the same time, considering the limitations of the model assumptions that the proppant is not broken and that the proppant is spherical, a correction coefficient b is introduced to characterize the model bias caused by these phenomena.

[0031] The conductivity of a hydraulic fracturing fracture is a commonly used evaluation parameter to characterize the fracturing effect. Fracture conductivity is represented as the product of the hydraulic fracture width and the fracture permeability.

[0032] (13) —Fracture conductivity, D·cm —Seam width, cm —Fracture conductivity, mD Therefore, the predictive calculation of flow capacity can be characterized by changes in permeability and slit width.

[0033] Assuming the proppant does not break, the minimum porosity within the crack is equal to the porosity of the ceramsite, therefore: Porosity within the crack (14) —Propionage volume, m3 —Hydraulic fracture volume, m3 Minimum porosity within the crack (15) —Net volume, m3 —Regarding volume, m3 —Volume density, kg / m3 — Apparent density, kg / m3 In summary, this invention employs a theoretical analysis method to transform the crack closure process into the deformation calculation of a supporting spring. The deformation involves three stages: an "elastic stage," an "elastoplastic stage," and a "plastic stage." The elastoplastic stage has a complex mechanical mechanism, and an exponential equation is used. Combining the limits of the "elastic stage" and the starting conditions of the "plastic stage," a stress-strain equation for the elastoplastic stage is constructed. Furthermore, using a stress-strain model of the "supporting spring," the closure amount of the crack width under different closure stresses is calculated. Further, the porosity change of the hydraulic fracturing crack is calculated based on the volume change, and the permeability change is calculated based on the porosity change. Finally, based on the permeability change and the crack width change, a prediction of the hydraulic fracturing crack conductivity attenuation is obtained. Therefore, compared to existing technologies, this invention provides a more accurate method for predicting conductivity attenuation.

[0034] This application also provides a computer-readable storage medium, which includes a stored program, wherein the program, when running, controls the device where the storage medium is located to execute the above-described method. The specific implementation process will not be repeated here.

[0035] This application also provides an electronic device. The electronic device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the methods described above in the embodiment; to avoid repetition, these will not be elaborated further here. Alternatively, when the computer program is executed by the processor, it implements the functions of each model / unit in the device of the embodiment; to avoid repetition, these will not be elaborated further here.

[0036] Electronic devices can be computing devices such as desktop computers, laptops, handheld computers, servers, and cloud servers. Electronic devices may include, but are not limited to, processors and memory. Those skilled in the art will understand that they may include more or fewer components than illustrated, or combinations of certain components, or different components; for example, electronic devices may also include input / output devices, network access devices, buses, etc.

[0037] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0038] Memory can be an internal storage unit of an electronic device, such as a hard drive or RAM. Memory can also be an external storage device, such as a plug-in hard drive, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, memory can include both internal and external storage units. Memory is used to store computer programs and other programs and data required by the electronic device. Memory can also be used to temporarily store data that has been output or will be output.

[0039] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0040] In the embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between devices or units through some interfaces, and may be electrical, mechanical, or other forms.

[0041] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0042] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the attenuation of conductivity in hydraulic fracturing fractures, characterized in that, The method includes: Obtain the change in closure stress along the length of the hydraulic fracturing fracture; Based on the change in closure stress along the length of the hydraulic fracturing fracture, and using a pre-built spring model, the change in fracture width along the length of the hydraulic fracturing fracture is calculated, and the change in volume of the hydraulic fracturing fracture is obtained based on the change in fracture width. The porosity change of the hydraulic fracturing fracture is calculated based on the volume change, and the permeability change is calculated based on the porosity change. Based on the changes in permeability and fracture width, the predicted attenuation of the hydraulic fracturing fracture conductivity is obtained. In the pre-constructed spring model, the deformation of the proppant in the hydraulic fracturing fracture is equated to the deformation of a spring; the deformation of the proppant includes elastic deformation, elastoplastic deformation, and plastic deformation. During the elastic deformation stage, the stress-strain relationship in the model is expressed as: ,in, This represents stress, expressed in gigabytes (GPa). Represents the generalized modulus of elasticity. In response to the situation; During the elastoplastic deformation stage, the stress-strain relationship in the model is expressed as follows: Where d is the deformation amount. and The two coefficients need to be determined using the elastic deformation limit and the plastic deformation limit; During the plastic deformation stage, the stress-strain relationship in the model is expressed as follows: ;in, The value represents the compressive strength of the proppant, in GPa.

2. The method for predicting the attenuation of conductivity of hydraulic fracturing fractures according to claim 1, characterized in that, The calculation of permeability change based on the porosity change includes: The permeability change is calculated based on the porosity change according to the Gauzyni-Kalman equation.

3. The method for predicting the attenuation of conductivity of hydraulic fracturing fractures according to claim 1, characterized in that, In the process of calculating the change in permeability, a correction coefficient is introduced to characterize the influence of the proppant structure.

4. The method for predicting the attenuation of conductivity of hydraulic fracturing fractures according to claim 3, characterized in that, The step of predicting the attenuation of the conductivity of the hydraulic fracturing fracture based on the changes in permeability and fracture width includes: Based on the preset functional relationship between flow capacity, permeability, and slit width, the flow capacity attenuation is predicted.

5. The method for predicting the attenuation of conductivity of hydraulic fracturing fractures according to claim 4, characterized in that, The preset functional relationship between the flow-conducting capacity and the permeability and slit width is as follows: in, For flow conduction capacity, D·cm; Seam width, in cm; Let mD be the penetration rate.

6. A computer-readable storage medium, characterized in that, The device containing the computer program, when executed by a processor, controls the device containing the computer-readable storage medium to implement the method of any one of claims 1 to 5.

Images