Determination method for critical reflux flow of deep coal bed gas fracturing propping agent

Abstract

The invention belongs to the field of oil and gas field development, and particularly relates to a method for determining the critical reflux flow of a deep coal bed gas fracturing propping agent. A method for determining the critical reflux flow of deep coal bed gas fracturing propping agents is characterized in that in the fracturing flow-back process, on one hand, the propping agents have the reflux phenomenon, the propping agents collide with one another to generate momentum exchange, and the propping agents are subjected to dragging force generated by coal bed gas on the propping agents; proppant driving force is obtained according to the collision momentum exchange force, the collision frequency and the dragging force of the collision; on the other hand, in the migration process of the proppant, the proppant is also subjected to gravity horizontal component force and friction force; a proppant critical reflux velocity calculation model is established through balance conditions of proppant driving force, gravity horizontal component force and friction force in a critical state, and then the proppant critical reflux velocity calculation model is converted into a proppant critical reflux flow calculation model to calculate the proppant critical reflux flow. Reliable technical support can be provided for coal bed gas development.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas field development, and specifically relates to a method for determining the critical reflux flow rate of proppant in deep coalbed methane fracturing. Background Technology

[0002] With the development of unconventional natural gas resources, deep coalbed methane, as an important clean energy source, has received increasing attention for its extraction technology. Hydraulic fracturing is one of the key technologies for improving coalbed methane recovery, and the injection and retention of proppant directly determine the conductivity of the fracture after fracturing. However, in the process of deep coalbed methane fracturing, the problem of proppant backflow is particularly prominent, especially under high pressure, high ground stress, and complex fluid environments. Propant is prone to migration with the flowback fluid, leading to fracture closure, reduced conductivity, and even wellbore blockage and equipment wear, seriously affecting production efficiency and economic benefits.

[0003] Based on extensive research, the publication CN118133693A, titled "An Optimization Method and Device for the Working System of the Propendant Nozzle in a Horizontal Well," established a critical proppant backflow discrimination model based on the calculated critical backflow velocity. The publication CN117744512A, titled "Propendant Backflow Judgment, Fracturing Fluid Flowback Adjustment Method, Device, and Storage Medium," calculated the Reynolds number using the fracturing fluid flowback velocity and formation parameters, determined the corresponding critical backflow velocity calculation method, and, based on the Reynolds number and fracturing parameters, used the corresponding critical backflow velocity calculation method to determine the critical backflow velocity.

[0004] In general, there are many methods for determining the critical backflow rate; however, these methods have their own limitations. Therefore, it is particularly important to study a scientific method for determining the critical backflow rate of proppant in deep coalbed methane fracturing, which can accurately predict the critical backflow rate of proppant during deep coalbed methane fracturing, thereby effectively preventing fracture closure problems caused by proppant backflow. Summary of the Invention

[0005] This invention aims to solve the problem of proppant backflow caused by unreasonable critical backflow flow rate of proppant in deep coalbed methane fracturing, and proposes a method for determining the critical backflow flow rate of proppant in deep coalbed methane fracturing.

[0006] The technical solution of this invention is as follows: A method for determining the critical backflow rate of proppant in deep coalbed methane fracturing is as follows: During the fracturing flowback process, on the one hand, proppant exhibits backflow, with proppant particles colliding and exchanging momentum, and the proppant is subjected to a drag force from the coalbed methane. The proppant driving force is obtained based on the collision momentum exchange force, collision frequency, and drag force. On the other hand, during proppant migration, it is also subjected to the horizontal component of gravity and friction. By establishing the equilibrium condition reached by the proppant driving force, the horizontal component of gravity, and friction under critical conditions, a calculation model for the critical backflow velocity of the proppant is established, which is then converted into a calculation model for the critical backflow rate of the proppant to calculate the critical backflow rate of the proppant.

[0007] A method for determining the critical reflux flow rate of proppant in deep coalbed methane fracturing is proposed, using the following calculation model for the critical reflux flow rate of proppant. The critical reflux flow rate of the proppant was obtained by solving the problem.

[0008] A method for determining the critical reflux flow rate of proppant in deep coalbed methane fracturing is as follows.

[0009] In S100, during the fracturing flowback process, proppant backflow occurs, and proppant particles collide with each other, causing changes in their motion state. A proppant collision momentum exchange mechanism is introduced, using the collision momentum exchange force to describe the momentum transfer between proppant particles. The formula for calculating the collision momentum exchange force is as follows: In the formula: F c The force is the momentum exchange force during the collision, N; D p The particle size of the proppant is in meters (m). e s The density of the proppant is kg / m³. 3 ; v 1 represents the velocity of the proppant before impact, in m / s; v 2 represents the velocity of the proppant after impact, in m / s; t Let be the collision time between proppant elements, in seconds.

[0010] S200, combining collision frequency quantification of the impact of proppant collisions on momentum exchange, shows that the collision frequency between proppants is positively correlated with the number of proppants and changes in proppant velocity. The formula for calculating the collision frequency is: in, f c Let s be the collision frequency. -1 ; n sm is the amount of proppant per unit volume. -3 ; A c For the proppant contact area, m 2 .

[0011] In S300, the proppant in the coal seam not only exchanges momentum through collisions with each other, but also experiences a drag force from the coalbed methane. Introducing the drag force calculation formula, and combining it with the collision momentum exchange force calculation formula and the collision frequency calculation formula, the proppant driving force calculation formula is established as follows: In the formula: F D For the proppant driving force, N; C D The drag force coefficient is dimensionless. e f The density of coalbed methane is expressed in kg / m³. A v For the maximum cross-sectional area of ​​the proppant, m 2 ; v c is the critical reflux velocity of the proppant, in m / s.

[0012] S400, during the actual migration of the proppant, is simultaneously hindered by the horizontal component of gravity and friction. The steps to establish the calculation formulas for the horizontal component of gravity and friction are as follows: S401, the horizontal component of gravity is related to the well inclination angle, proppant density, coalbed methane density, and proppant diameter. The formula for calculating the horizontal component of gravity is: In the formula: F G Let N be the horizontal component of gravity. g The acceleration due to gravity is m / s². 2 ; R The well inclination angle is expressed in degrees. S402, the frictional force is generated by the vertical component of gravity and the closed stress. The formula for calculating the frictional force is: In the formula: F f Friction force, N; u f The coefficient of friction is dimensionless. P n The stress is the closing stress, Pa.

[0013] S500, under critical conditions, the proppant reaches force equilibrium, where the proppant driving force equals the sum of the horizontal component of gravity and the frictional force. Based on the equilibrium conditions of the proppant driving force, the horizontal component of gravity, and the frictional force, a calculation model for the critical backflow velocity of the proppant is established, specifically: .

[0014] S600 converts the critical reflux velocity of the proppant into the critical reflux flow rate of the proppant, and establishes a calculation model for the critical reflux flow rate of the proppant, specifically as follows: in, Q c For the critical reflux flow rate of the proppant, m 3 / s; A t Let m be the cross-sectional area of ​​the transport channel. 2 .

[0015] Wherein, the number of proppant per unit volume n s The specific calculation process is as follows: In the formula: C The concentration of the sand used for laying is kg / m³. 3 .

[0016] Wherein, the contact area of ​​the proppant A c The specific calculation process is as follows: : in, a is the contact coefficient, a dimensionless quantity.

[0017] The technical effects of this invention are as follows: This invention can accurately predict the critical backflow rate of proppant during deep coalbed methane fracturing, thereby effectively preventing fracture closure caused by proppant backflow. Compared with the prior art, this invention has the following advantages: (1) simple operation process, strong applicability, and reduced engineering implementation difficulty; (2) multi-factor dynamic coupling analysis to optimize fracturing backflow control; (3) significantly improved calculation accuracy and efficiency, and high work efficiency. Attached Figure Description

[0018] Figure 1 This is the overall technical roadmap of the present invention. Detailed Implementation

[0019] Example 1 A method for determining the critical backflow rate of proppant in deep coalbed methane fracturing is as follows: During the fracturing flowback process, on the one hand, proppant exhibits backflow, with proppant particles colliding and exchanging momentum, and the proppant is subjected to a drag force from the coalbed methane. The proppant driving force is obtained based on the collision momentum exchange force, collision frequency, and drag force. On the other hand, during proppant migration, it is also subjected to the horizontal component of gravity and friction. By establishing the equilibrium condition reached by the proppant driving force, the horizontal component of gravity, and friction under critical conditions, a calculation model for the critical backflow velocity of the proppant is established, which is then converted into a calculation model for the critical backflow rate of the proppant to calculate the critical backflow rate of the proppant.

[0020] Example 2 A method for determining the critical reflux flow rate of proppant in deep coalbed methane fracturing is proposed, using the following calculation model for the critical reflux flow rate of proppant. The critical reflux flow rate of the proppant is obtained by solving the problem; in, ; ; ; ; .

[0021] Example 3 A method for determining the critical reflux flow rate of proppant in deep coalbed methane fracturing is as follows: In S100, during the fracturing flowback process, proppant backflow occurs, and proppant particles collide with each other, causing changes in their motion state. A proppant collision momentum exchange mechanism is introduced, using the collision momentum exchange force to describe the momentum transfer between proppant particles. The formula for calculating the collision momentum exchange force is as follows: ; S200, combining collision frequency quantification of the impact of proppant collisions on momentum exchange, shows that the collision frequency between proppants is positively correlated with the number of proppants and changes in proppant velocity. The formula for calculating the collision frequency is: ; In S300, the proppant in the coal seam not only exchanges momentum through collisions with each other, but also experiences a drag force from the coalbed methane. Introducing the drag force calculation formula, and combining it with the collision momentum exchange force calculation formula and the collision frequency calculation formula, the proppant driving force calculation formula is established as follows: ; S400, during the actual migration of the proppant, is simultaneously hindered by the horizontal component of gravity and friction. The steps to establish the calculation formulas for the horizontal component of gravity and friction are as follows: S401, the horizontal component of gravity is related to the well inclination angle, proppant density, coalbed methane density, and proppant diameter. The formula for calculating the horizontal component of gravity is: ; S402, the frictional force is generated by the vertical component of gravity and the closed stress. The formula for calculating the frictional force is: ; S500, under critical conditions, the proppant reaches force equilibrium, where the proppant driving force equals the sum of the horizontal component of gravity and the frictional force. Based on the equilibrium conditions of the proppant driving force, the horizontal component of gravity, and the frictional force, a calculation model for the critical backflow velocity of the proppant is established, specifically: ; S600 converts the critical reflux velocity of the proppant into the critical reflux flow rate of the proppant, and establishes a calculation model for the critical reflux flow rate of the proppant, specifically as follows: ; Wherein, the number of proppant per unit volume n s The specific calculation process is as follows: Wherein, the contact area of ​​the proppant A c The specific calculation process is as follows: .

[0022] Specific experimental cases Taking a deep coalbed methane well as an example, the fracturing horizontal well uses density e s 2950kg / m 3 and particle size D p It is 6.46×10 -4 Using m-sized quartz sand as a proppant, the sand concentration... C 1kg / m 3 The closing pressure of the coal seam P n The density of coalbed methane is 15,000,000 Pa. e f It is 0.717 kg / m 3 The inclination angle of a horizontal well R The angle is 90°, and the cross-sectional area of ​​the transport channel is... A t It is 1.45m2 The acceleration due to gravity g is 9.80 m / s². 2 The calculated parameters obtained through proppant reflux experiments are shown in Table 1.

[0023] Table 1 Calculation parameters The frictional force and the horizontal component of gravity were calculated. These parameters were then substituted into the critical backflow rate calculation model for the proppant to obtain the critical backflow rate. The calculation results are shown in Table 2. The critical backflow rate of the proppant is 0.3181 m³ / s. 3 / s, converted to on-site production, the critical reflux flow rate of the proppant can be determined to be 27483.84m³. 3 / d.

[0024] Table 2 Calculation results of critical backflow rate of proppant To verify the accuracy of the calculation model for the critical reflux flow rate of the proppant, numerical simulation was used for verification and comparison. The specific results are shown in Table 3, with an average deviation of 0.395%.

[0025] Table 3 Comparison of Critical Reflux Flow Rates for Proppants The comparison shows that the calculation model for the critical reflux flow rate of the proppant has high accuracy and the calculation results are accurate.

[0026] This invention can accurately predict the critical backflow rate of proppant during deep coalbed methane fracturing, thereby effectively preventing fracture closure caused by proppant backflow. Compared with the prior art, this invention has the following advantages: (1) simple operation process, strong applicability, and reduced engineering implementation difficulty; (2) multi-factor dynamic coupling analysis to optimize fracturing backflow control; (3) significantly improved calculation accuracy and efficiency, and high work efficiency.

[0027] Finally, it should be noted that the above embodiments are only used to illustrate and not limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention without departing from the spirit and scope of the present invention. Any modifications or partial substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for determining the critical reflux flow rate of proppant in deep coalbed methane fracturing, characterized in that, During fracturing and flowback, on the one hand, proppant exhibits backflow, with proppant particles colliding and exchanging momentum. Furthermore, the proppant is subjected to a drag force from the coalbed methane. The proppant driving force is derived from the momentum exchange force, collision frequency, and drag force. On the other hand, during proppant migration, it is also subjected to the horizontal component of gravity and friction. By establishing the equilibrium condition reached by the proppant driving force, the horizontal component of gravity, and friction under critical conditions, a calculation model for the critical proppant backflow velocity is established, which is then converted into a calculation model for the critical proppant backflow rate to calculate the critical proppant backflow rate.

2. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 1, characterized in that, The specific calculation model for the critical reflux flow rate of the proppant is as follows: In the formula: Q c For the critical reflux flow rate of the proppant, m 3 / s; A t Let m be the cross-sectional area of ​​the transport channel. 2 ; F G Let N be the horizontal component of gravity. t The collision time between proppants is in seconds. n s m is the amount of proppant per unit volume. -3 ; A c For the proppant contact area, m 2 ; F f Friction force, N; D p The particle size of the proppant is in meters (m). e s The density of the proppant is kg / m³. 3 ; f c Let s be the collision frequency. -1 ; C D The drag force coefficient is dimensionless. e f The density of coalbed methane is expressed in kg / m³. A v For the maximum cross-sectional area of ​​the proppant, m 2 .

3. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 1, characterized in that, The specific calculation model for the critical reflux velocity of the proppant is as follows: In the formula: v c is the critical reflux velocity of the proppant, in m / s.

4. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 2, characterized in that, The specific solution process for the collision momentum exchange force is as follows: In the formula: F c N is the momentum exchange force during the collision.

5. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 4, characterized in that, The collision frequency f c The specific calculation process is as follows: In the formula: v 2 represents the velocity of the proppant after impact, in m / s; v 1 represents the velocity of the proppant before impact, in m / s.

6. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 5, characterized in that, The specific calculation process for the proppant driving force is as follows: In the formula: F D N is the proppant driving force.

7. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 2, characterized in that, The horizontal component of gravity F G The specific calculation process is as follows: In the formula: g The acceleration due to gravity is m / s². 2 ; R The inclination angle is °.

8. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 2, characterized in that, The friction force F f The specific calculation process is as follows: In the formula: u f The coefficient of friction is dimensionless. P n The stress is the closing stress, Pa.

9. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 2, characterized in that, The number of proppant per unit volume n s The specific calculation process is as follows: In the formula: C The concentration of the sand used for laying is kg / m³. 3 .

10. The method for determining the critical reflux flow rate of the proppant in deep coalbed methane fracturing according to claim 2, characterized in that, The contact area of ​​the proppant A c The specific calculation process is as follows: In the formula: a is the contact coefficient, which is dimensionless.

Images