A method for simulating and quantitatively evaluating intra-fragment multi-cluster crack propagation considering hole erosion

Abstract

The application discloses a kind of segmental multi-cluster fracture propagation simulation and quantitative evaluation method considering hole erosion, comprising the following steps: (1) collecting geological and engineering parameters;(2) establish rock deformation model;(3) establish hole erosion diameter expansion correction equation;(4) establish wellbore and fracture fluid flow equation set;(5) establish fracture propagation criterion;(6) comprehensive step (2)-(5) establish segmental multi-cluster fracture propagation model considering hole erosion;(7) the flow difference and fracture length difference coefficient quantitative evaluation each cluster fracture flow distribution balance degree and multi-cluster fracture propagation uniformity;(8) the parameters of step (1) are substituted into step (6) to simulate the extension trajectory of fracture propagation under different perforation and fracturing parameters, and are quantitatively evaluated by step (7).The application fully considers the influence law of hole erosion on multi-cluster fracture propagation, establishes segmental multi-cluster fracture propagation model, analyzes the influence of different construction parameters on fracture propagation, and provides theoretical guidance for horizontal well fracturing construction parameter optimization design and efficient development.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field production enhancement and renovation, specifically to a method for simulating and quantitatively evaluating the propagation of multiple clusters of fractures within a section, taking into account porosimetry erosion. Background Technology

[0002] In order to implement the energy security strategy and continuously increase the exploration and development of unconventional oil and gas fields, the main way to increase production in unconventional oil and gas fields is through hydraulic fracturing.

[0003] Horizontal well volumetric fracturing has become an important production enhancement technology for developing tight sandstone gas, shale gas, and tight oil. Through field practice and theoretical research, horizontal well volumetric fracturing has become the main development method for the Mahu conglomerate reservoir in Xinjiang. During staged multi-cluster fracturing, the proppant-carrying fluid experiences throttling at the perforation orifice, causing erosion and increasing the orifice's geometric parameters or creating cracks. This reduces perforation friction, leading to temporary plugging failure or weakened orifice flow restriction capacity, which in turn significantly impacts flow distribution and multi-cluster fracture propagation. Currently, there is a lack of a multi-cluster fracture propagation model and quantitative evaluation method to correct for orifice erosion and enlargement, making it difficult to optimize fracturing operation parameters. Summary of the Invention

[0004] To address the shortcomings of current technologies, this invention proposes a method for simulating and quantitatively evaluating the propagation of multiple clusters of cracks within a segment, taking into account porosimetry erosion. This method overcomes the deficiencies of existing technologies and enables the simulation of the propagation of multiple clusters of cracks within a segment, taking into account porosimetry erosion, as well as the quantitative determination of whether the flow rate is evenly distributed and whether the multiple clusters of cracks propagate uniformly.

[0005] The technical solution provided by this invention to solve the above-mentioned technical problems is: a method for simulating and quantitatively evaluating the propagation of multiple clusters of cracks within a segment considering porosity erosion, comprising the following steps:

[0006] Step 1: Collect geological and engineering parameters;

[0007] Step 2: Establish a rock deformation model;

[0008] Step 3: Establish the correction equation for borehole erosion and diameter expansion;

[0009] Step 4: Establish the fluid flow equations in the wellbore and the fluid flow equations within the fracture;

[0010] Step 5: Establish crack propagation criteria;

[0011] Step 6: Combine steps 2-5 to establish an intra-segment multi-cluster crack propagation model that considers pore erosion;

[0012] Step 7: Quantitatively evaluate the degree of flow distribution balance and the uniformity of multi-cluster fracture propagation by using the flow difference coefficient and fracture length difference coefficient;

[0013] Step 8: Substitute the parameters from Step 1 into Step 6 to simulate the extension trajectory of the fracture under different perforation parameters and fracturing parameters, and then perform quantitative evaluation through Step 7.

[0014] A further technical solution is that the geological and engineering parameters in step 1 include: reservoir thickness, Poisson's ratio, Young's modulus, minimum horizontal principal stress, fracturing fluid viscosity, number of fracture clusters, number of boreholes, construction flow rate, proppant concentration, total pumping time, fracturing fluid density, fracture spacing, borehole diameter, initial borehole flow coefficient, maximum borehole flow coefficient, and proppant-carrying fluid injection time.

[0015] A further technical solution is that the rock deformation model in step 2 is:

[0016]

[0017] In the formula: σ n,i ,σ s,i denoted as the normal stress and tangential stress respectively experienced by crack element i, in MPa; N represents the total number of crack elements; C represents the boundary strain influence coefficient matrix; D s,j D represents the tangential displacement discontinuity at crack element j, in meters. n,j The value m represents the discontinuity of the normal displacement at crack element j.

[0018] A further technical solution is that, in step 3, the orifice erosion and diameter expansion correction equation is derived by statistically analyzing the total amount of proppant injected into a portion of the fracturing section and the change in orifice diameter before and after fracturing based on field data, and calculating the average single-cluster proppant injection amount and the average single-orifice diameter expansion amount. A linear fit is then performed between the average single-cluster proppant injection amount and the average single-orifice diameter expansion amount for each section, resulting in the orifice diameter calculation expression as follows:

[0019]

[0020] In the formula: d 0,i Let ε be the initial diameter of the i-th cluster of fracture holes (mm), and ε be the slope of the fitting formula for hole enlargement under different numbers of perforations (mm / m). 3 ;ρ p The density of the proppant is kg / m³. 3 ;q i Let m be the flow rate of the i-th cluster of fractures. 3 / min; t is the injection time of the sand-carrying fluid, in seconds.

[0021] A further technical solution is that the wellbore fluid flow equations in step 4 are as follows:

[0022]

[0023] P0 = Pwf,i +P pf,i +P cf,i (4)

[0024]

[0025]

[0026] In the formula: Q all m is the total injection volume. 3 / min; P0 is the wellbore root pressure, MPa; P wf,i P is the inlet pressure of the i-th cluster of fractures, in MPa; pf,i The frictional resistance of the i-th cluster of fractures at the perforation point is given in MPa; P cf,i ρ is the wellbore friction from the i-th fracture cluster to the wellbore root, MPa; ρ is the fracturing fluid density, kg / m³. 3 ;n p,i d represents the number of perforations in the i-th cluster of fractures; p,i Let K be the diameter of the perforation in the i-th cluster of fractures, in meters; d is the orifice flow rate coefficient, dimensionless; n is the power-law exponent of the fracturing fluid, dimensionless; K is the consistency coefficient of the fracturing fluid, mPa·s; D w Q is the diameter of the wellbore, in meters; w,j Let m be the flow rate between the j-th fracture cluster and the (j-1)-th fracture cluster. 3 / min; L w,j Let be the distance between the j-th cluster of cracks and the (j-1)-th cluster of cracks, in meters.

[0027] The fluid flow equations within the slit are as follows:

[0028]

[0029]

[0030]

[0031] In the formula: q(s,t) is the flow rate at section s at the current time, m 3 / min; q t (s,t) represents the fracturing fluid loss rate per unit fracture length at the current time s, m 2 / min; A(s,t) is the cross-sectional area of ​​the crack at the current time s, in m³. 2 t represents the fracturing operation time, in minutes; p represents the fluid friction in the hydraulic fracture; n represents the power law exponent of the water fluid; k represents the fluid viscosity index; h represents the reservoir thickness, in meters; w represents the hydraulic fracture width, in meters; C t The fracturing fluid loss coefficient is given in m / min. 0.5 t0 is the crack opening time, in minutes.

[0032] A further technical solution is that the crack propagation criterion in step 5 is:

[0033] The seam length extension criterion is:

[0034]

[0035] K I sinθ+K II (3cosθ-1)=0 (11)

[0036]

[0037]

[0038]

[0039] Where: K IC_R The fracture toughness of the rock matrix, MPa·m 0.5 ;K I The stress intensity factor for type I cracks is MPa·m. 0.5 ;K II The stress intensity factor for type II cracks is MPa·m. 0.5 θ is the crack deflection angle, °; d ri Let m be the expansion step size of crack element i; ξ is an empirical coefficient.

[0040] The criterion for suture height extension is:

[0041]

[0042]

[0043]

[0044]

[0045] In the formula: Let m be the step length for the crack tip extension at the top of the i-th longitudinal section; Let m be the step length for the crack tip expansion at the lower part of the i-th longitudinal section; The maximum equivalent stress intensity factor at the tips of all cracks in the longitudinal section, in MPa·m 0.5 h ui,t Let h be the seam height at the current i-th longitudinal section, in meters (m); li,t The current seam height at the i-th longitudinal section is m; h li,0 K represents the original lower seam height of the i-th longitudinal section, in meters. I,top The stress intensity factor at the crack tip on the longitudinal section is the Type I stress intensity factor, in MPa·m. 0.5 ;r hThe half-length of the crack tip element in the longitudinal section is m; w top_tip K represents the crack width at the center of the upper crack element in the longitudinal section, in meters. I,low The stress intensity factor at the crack tip in the longitudinal section is the Type I stress intensity factor, in MPa·m. 0.5 ;w top_tip Let be the width of the crack at the center of the lower crack unit in the longitudinal section, in meters (m).

[0046] A further technical solution is that, in step 6, the rock deformation in the segment multi-cluster crack propagation model considering pore erosion is discretized using the displacement discontinuity method, the fluid flow is discretized using the finite volume method, and then a fluid-structure interaction equation set is constructed and solved using Newton iteration.

[0047] A further technical solution is that, in step 7, the flow rate difference coefficient and the slit length difference coefficient are respectively:

[0048]

[0049]

[0050] In the formula: Let m be the average volume of n clusters of cracks. 3 V i Let m be the volume of the i-th cluster of cracks. 3 ; Let L be the average length of n clusters of cracks, in meters. i Let m be the length of the i-th cluster of cracks.

[0051] The beneficial effects of this invention are as follows: Based on the pseudo-three-dimensional displacement discontinuity method, this invention proposes a multi-cluster crack propagation model and quantitative evaluation method to correct the hole erosion and diameter expansion, which improves the accuracy of predicting crack morphology, optimizes the design of fracturing construction parameters, and makes the results more in line with the actual needs of engineering. Attached Figure Description

[0052] Figure 1 A fitting graph showing the relationship between the average perforation diameter and the average proppant injection amount per cluster for different numbers of perforations.

[0053] Figure 2 A bar chart comparing the enlargement of the orifice for different numbers of perforations.

[0054] Figure 3 Comparison of fracture propagation morphology with different numbers of perforations

[0055] Figure 4 Curves showing the difference coefficients of slot length and flow rate for different numbers of perforations. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings, but this does not constitute any limitation on the invention. The described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] Step 1: Collect geological and engineering parameters;

[0058] The geological and engineering parameters include: reservoir thickness, Poisson's ratio, Young's modulus, minimum horizontal principal stress, fracturing fluid viscosity, number of fracture clusters, number of boreholes, construction flow rate, proppant concentration, total pumping time, fracturing fluid density, fracture spacing, borehole diameter, initial borehole flow coefficient, maximum borehole flow coefficient, and proppant injection time.

[0059] Step 2: Establish a rock deformation model;

[0060] The rock deformation model is as follows:

[0061]

[0062] In the formula: σ n,i ,σ s,i denoted as the normal stress and tangential stress respectively experienced by crack element i, in MPa; N represents the total number of crack elements; C represents the boundary strain influence coefficient matrix; D s,j D represents the tangential displacement discontinuity at crack element j, in meters. n,j The value m represents the discontinuity of the normal displacement at crack element j.

[0063] Step 3: Establish the correction equation for borehole erosion and diameter expansion;

[0064] The orifice erosion enlargement correction equation is derived from field data, which statistically analyzes the total amount of proppant injected into the fracturing section and the change in orifice diameter before and after fracturing. The average proppant injection amount per cluster and the average orifice enlargement amount are then calculated. A linear fit is performed between the average proppant injection amount per cluster and the average orifice enlargement amount for each section to obtain the orifice diameter calculation expression:

[0065]

[0066] In the formula: d 0,i Let ε be the initial diameter of the i-th cluster of fracture holes (mm), and ε be the slope of the fitting formula for hole enlargement under different numbers of perforations (mm / m). 3 ;ρ p The density of the proppant is kg / m³. 3 ;q i Let m be the flow rate of the i-th cluster of fractures. 3 / min; t is the injection time of the sand-carrying fluid, in seconds.

[0067] Step 4: Establish the fluid flow equations in the wellbore and the fluid flow equations within the fracture;

[0068] The fluid flow equations are as follows:

[0069]

[0070] P0 = P wf,i +P pf,i +P cf,i (4)

[0071]

[0072]

[0073] In the formula: Q all m is the total injection volume. 3 / min; P0 is the wellbore root pressure, MPa; P wf,i P is the inlet pressure of the i-th cluster of fractures, in MPa; pf,i The frictional resistance of the i-th cluster of fractures at the perforation point is given in MPa; P cf,i ρ is the wellbore friction from the i-th fracture cluster to the wellbore root, MPa; ρ is the fracturing fluid density, kg / m³. 3 ;n p,i d represents the number of perforations in the i-th cluster of fractures; p,i Let K be the diameter of the perforation in the i-th cluster of fractures, in meters; d is the orifice flow rate coefficient, dimensionless; n is the power-law exponent of the fracturing fluid, dimensionless; K is the consistency coefficient of the fracturing fluid, mPa·s; D w Q is the diameter of the wellbore, in meters; w,j Let m be the flow rate between the j-th fracture cluster and the (j-1)-th fracture cluster. 3 / min; L w,j Let be the distance between the j-th cluster of cracks and the (j-1)-th cluster of cracks, in meters.

[0074] The fluid flow equations within the slit are as follows:

[0075]

[0076]

[0077]

[0078] In the formula: q(s,t) is the flow rate at section s at the current time, m 3 / min; q t (s,t) represents the fracturing fluid loss rate per unit fracture length at the current time s, m 2 / min; A(s,t) is the cross-sectional area of ​​the crack at the current time s, in m³.2 t represents the fracturing operation time, in minutes; p represents the fluid friction in the hydraulic fracture; n represents the power law exponent of the water fluid; k represents the fluid viscosity index; h represents the reservoir thickness, in meters; w represents the hydraulic fracture width, in meters; C t The fracturing fluid loss coefficient is given in m / min. 0.5 t0 is the crack opening time, in minutes.

[0079] Step 5: Establish crack propagation criteria;

[0080] The seam length extension criterion is:

[0081]

[0082] K I sinθ+K II (3cosθ-1)=0 (11)

[0083]

[0084]

[0085]

[0086] Where: K IC_R The fracture toughness of the rock matrix, MPa·m 0.5 ;K I The stress intensity factor for type I cracks is MPa·m. 0.5 ;K II The stress intensity factor for type II cracks is MPa·m. 0.5 θ is the crack deflection angle, °; d ri Let m be the expansion step size of crack element i; ξ is an empirical coefficient.

[0087] The criterion for suture height extension is:

[0088]

[0089]

[0090]

[0091]

[0092] In the formula: Let m be the step length for the crack tip extension at the top of the i-th longitudinal section; Let m be the step length for the crack tip expansion at the lower part of the i-th longitudinal section; The maximum equivalent stress intensity factor at the tips of all cracks in the longitudinal section, in MPa·m 0.5 h ui,tLet h be the seam height at the current i-th longitudinal section, in meters (m); li,t The current seam height at the i-th longitudinal section is m; h li,0 K represents the original lower seam height of the i-th longitudinal section, in meters. I,top The stress intensity factor at the crack tip on the longitudinal section is the Type I stress intensity factor, in MPa·m. 0.5 ;r h The half-length of the crack tip element in the longitudinal section is m; w top_tip K represents the crack width at the center of the upper crack element in the longitudinal section, in meters. I,low The stress intensity factor at the crack tip in the longitudinal section is the Type I stress intensity factor, in MPa·m. 0.5 ;w top_tip Let be the width of the crack at the center of the lower crack unit in the longitudinal section, in meters (m).

[0093] Step 6: Combine steps 2-5 to establish an intra-segment multi-cluster crack propagation model that considers pore erosion;

[0094] In the segmental multi-crack propagation model considering pore erosion, rock deformation is discretized using the displacement discontinuity method, and fluid flow is discretized using the finite volume method. Then, a fluid-structure interaction equation set is constructed and solved using Newton iteration.

[0095] Step 7: Quantitatively evaluate the degree of flow distribution balance and the uniformity of multi-cluster fracture propagation by using the flow difference coefficient and fracture length difference coefficient;

[0096] The flow rate difference coefficient and the seam length difference coefficient are respectively:

[0097]

[0098]

[0099] In the formula: Let m be the average volume of n clusters of cracks. 3 V i Let m be the volume of the i-th cluster of cracks. 3 ; Let L be the average length of n clusters of cracks, in meters. i Let m be the length of the i-th cluster of cracks.

[0100] By setting the standard line for the flow difference coefficient as a and the standard line for the crack length difference coefficient as b, we can quantitatively evaluate the degree of flow distribution balance among crack clusters and the degree of uniformity of crack expansion.

[0101] Step 8: Substitute the parameters from Step 1 into Step 6 to simulate the extension trajectory of the fracture under different perforation parameters and fracturing parameters, and then perform quantitative evaluation through Step 7.

[0102] The geological and engineering parameters from step 1 are then incorporated into the multi-cluster fracture propagation model within the segment considering perforation erosion in step 5. This allows for the quantitative evaluation of the flow distribution balance and fracture length uniformity of each cluster of fractures under different perforation and fracturing parameters, including fracture trajectory, perforation diameter, flow distribution ratio, flow difference coefficient, and fracture length difference coefficient.

[0103] Example:

[0104] Step 1: Obtain geological and engineering parameters, as shown in Table 1.

[0105] Table 1 Basic Input Parameters

[0106]

[0107]

[0108] Step 2: Based on field data, the total amount of proppant injected into some fracturing sections and the change in orifice diameter before and after fracturing were statistically analyzed. The average proppant injection amount per cluster and the average orifice enlargement were calculated. Assuming that the total orifice erosion area is equal under the same proppant injection amount, the average orifice enlargement was calculated under different perforation numbers and a linear fit was performed. Figure 1 As shown in the figure. Simultaneously, the average orifice diameter expansion per unit proppant injection volume under different perforation numbers was statistically analyzed. This led to the derive of the orifice diameter calculation expression.

[0109] Step 3: Substitute the parameters in Table 1 into the segment multi-cluster crack propagation model considering perforation erosion established in this invention to simulate the multi-cluster crack propagation morphology under perforation numbers of 3, 8, 12 and 16 holes.

[0110] Step 4: In this embodiment, the standard line for the flow rate difference coefficient is set at 20%. A flow rate difference coefficient greater than the standard line indicates that the flow rate distribution among the crack clusters is uneven. At the same time, the standard line for the crack length difference coefficient is set at 15%. A crack length difference coefficient greater than the standard line indicates that the expansion of multiple crack clusters is uneven.

[0111] Step 5: Simulate different numbers of perforations and the amount of orifice enlargement, such as... Figure 2 As shown, with the increase of the number of perforations, the increase in the perforation diameter expansion becomes more gradual; the simulated multi-cluster crack propagation morphology for different perforation diameters is as follows: Figure 3 As shown, the degree of uneven propagation of multi-cluster fractures increases with the increase of the number of perforations; further, the difference coefficients of flow rate and fracture length for different numbers of perforations are obtained as follows: Figure 4 As shown, with the increase of the number of perforations, the degree of non-uniform fluid inflow in each cluster of fractures and the degree of non-equilibrium expansion of multiple clusters of fractures increase. The flow rate difference coefficient increases from 2.18% to 37.15%, and the fracture length difference coefficient increases from 5.52% to 24.70%.

[0112] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for simulating and quantitatively evaluating the propagation of multiple clusters of cracks within a section, considering porosity erosion, characterized in that, Includes the following steps: Step 1: Collect geological and engineering parameters; Step 2: Establish a rock deformation model; Step 3: Establish the correction equation for borehole erosion and diameter expansion; Step 4: Establish the fluid flow equations in the wellbore and the fluid flow equations within the fracture; Step 5: Establish crack propagation criteria; Step 6: Combine steps 2-5 to establish an intra-segment multi-cluster crack propagation model that considers pore erosion; Step 7: Quantitatively evaluate the degree of flow distribution balance and the uniformity of multi-cluster fracture propagation by using the flow difference coefficient and fracture length difference coefficient; Step 8: Substitute the parameters from Step 1 into Step 6 to simulate the extension trajectory of the fracture under different perforation parameters and fracturing parameters, and then perform quantitative evaluation through Step 7. The orifice erosion and diameter expansion correction equation in step 3 is obtained through statistical analysis of the total proppant injection volume and the change in orifice diameter before and after fracturing in some fracturing sections based on field data. Specifically, by calculating the average single-cluster proppant injection volume and the average single-orifice diameter expansion volume in each fracturing section, and performing linear fitting on the correlation between the two, the orifice diameter calculation expression is obtained as follows: In the formula: For the first i Initial diameter of cluster crack opening, mm The slope of the fitting formula for orifice enlargement under different numbers of perforations, in mm / m 3 ; The density of the proppant is kg / m³. 3 ; For the first i Cluster crack flow rate, m 3 / min; t The injection time of the sand-carrying fluid is in seconds.

2. The method for simulating and quantitatively evaluating the propagation of multiple clusters of cracks within a segment considering porosity erosion, as described in claim 1, is characterized in that... In step 7, the flow rate difference coefficient and the seam length difference coefficient are respectively: In the formula: Let m be the average volume of n clusters of cracks. 3 ; For the first i Volume of cluster cracks, m 3 ; Let n be the average length of the crack clusters, in meters. For the first i The length of the cluster crack, in meters.

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