A method for simulating and quantitatively characterizing multi-cluster fracturing fracture propagation and proppant transport

Abstract

The application discloses a kind of multi-cluster fracturing fracture and proppant transport coupling simulation and quantitative characterization method, comprising the following steps: (1) collecting geological and engineering parameters;(2) establishing fluid flow equation;(3) establishing fracture constitutive equation;(4) establishing proppant transport equation group;(5) comprehensive step (2)-(4) establishes the coupling model of multi-cluster fracturing fracture and proppant transport;(6) by the quantitative characterization of the uniformity of multi-cluster fracturing fracture propagation and the uniformity of proppant placement in fracture through the uniformity index of multi-cluster fracturing fracture propagation;(7) the parameters of step (1) are substituted into step (5) to simulate the propagation morphology of multi-cluster fracturing fracture and the proppant placement morphology in fracture under different engineering parameters, and quantitatively characterized by step (6).The application is based on three-dimensional block discrete element method, establishes the coupling model of multi-cluster fracturing fracture propagation and proppant transport considering the influence of barrier and weak plane, analyzes the influence of different engineering parameters on fracturing fracture propagation and proppant transport, and provides theoretical guidance for predicting and optimizing the propagation morphology of multi-cluster fracturing fracture and the proppant placement morphology in fracture in complex reservoir.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of oil and gas field stimulation and reconstruction, and particularly relates to a method for simulating and quantitatively characterizing the coupling of multi-cluster fracturing fracture propagation and proppant transport. BACKGROUND

[0002] Unconventional oil and gas resources such as shale oil and gas are replacing conventional oil and gas resources to become a new field of oil and gas exploration and development and sustainable increase in reserves and production, and hydraulic fracturing is a key technology for realizing the large-scale and efficient development of unconventional oil and gas resources, which mainly consists of two parts of fracturing fracture propagation and proppant transport.

[0003] Most of the researches on proppant transport are based on the pre-defined static fracture model, without considering the dynamic changes of the fracture, which is not consistent with the actual fracturing process. Therefore, coupling the fracturing fracture propagation and the proppant transport to explore the proppant transport law in the dynamic fracture is one of the difficulties faced by the current numerical simulation technology of hydraulic fracturing. Previous studies have made preliminary exploration on this difficulty, but the fracture models used in the existing researches are simple, mostly single fracture and do not consider the weak planes such as interlayer and natural fracture. At present, there is still a lack of a multi-cluster fracturing fracture propagation and proppant transport coupling model and quantitative characterization method considering the influence of interlayer and weak plane, which makes it difficult to explain the actual engineering problems faced by the current complex reservoir. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a method for simulating and quantitatively characterizing the coupling of multi-cluster fracturing fracture propagation and proppant transport, which overcomes the deficiencies of the prior art and can realize the simulation of the coupling of multi-cluster fracturing fracture propagation and proppant transport considering the influence of interlayer and weak plane, and quantitatively characterize the uniformity of multi-cluster fracturing fracture propagation and the uniformity of proppant placement in the fracture.

[0005] The technical solution provided by the present application to solve the above technical problems is: a method for simulating and quantitatively characterizing the coupling of multi-cluster fracturing fracture propagation and proppant transport, comprising the following steps:

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

[0007] Step 2: establishing a fluid flow equation;

[0008] Step 3: establishing a fracture constitutive equation;

[0009] Step 4: establishing a proppant transport equation set;

[0010] Step 5: establishing a multi-cluster fracturing fracture propagation and proppant transport coupling model by integrating steps 2-4;

[0011] Step 6: quantitatively characterizing the uniformity of multi-cluster fracturing fracture propagation and the uniformity of proppant placement in the fracture by a multi-cluster fracturing fracture propagation uniformity index and a placement efficiency.

[0012] Step 7: Substitute the parameters in step 1 into step 5 to simulate the fracture propagation pattern and proppant placement pattern under different engineering parameters, and quantitatively characterize by step 6.

[0013] Further technical solutions are that the geological and engineering parameters in step 1 include reservoir separation layer thickness, Poisson's ratio, Young's modulus, maximum horizontal principal stress, minimum horizontal principal stress, vertical stress, bedding tensile strength, bedding cohesion, bedding internal friction angle, natural fracture tensile strength, natural fracture cohesion, natural fracture internal friction angle, fracturing fluid viscosity, fracturing fluid density, fracture cluster number, cluster spacing, construction displacement, proppant particle size, proppant density, proppant volume fraction, total pumping time, and sand slurry injection time.

[0014] Further technical solutions are that the fluid flow equation in step 2 is:

[0015]

[0016] In the formula, p is the fluid pressure, Pa; t is the time, s; u is the fracture width, m; K w is the fluid bulk modulus, Pa; and μ is the fracturing fluid viscosity, Pa·s.

[0017] Further technical solutions are that the fracture constitutive equation in step 3 is characterized by using a continuous yield model. When the crack element does not produce sliding, the shear strength is the maximum value; when the crack element shear stress exceeds the maximum shear strength, the shear strength evolves nonlinearly. The relationship expression between crack shear stress and plastic slip is:

[0018]

[0019] In the formula, τ s is the shear stress, Pa; is the shear stress peak value, Pa; c peak is the maximum cohesion value, Pa; σ n is the normal stress, Pa; is the maximum internal friction angle, °; is the shear stress residual value, Pa; D c is the critical slip distance, m; and β is the shear strength attenuation index, dimensionless. is the plastic slip, m; c residual is the cohesion residual value, Pa; is the internal friction angle residual value, °.

[0020] Further technical solutions are that the proppant transport equation set in step 4 is:

[0021]

[0022] V proppant =V+(1-e)V s (4)

[0023] V s =f(e)V stokes (5)

[0024] f(e) = (1-e) 4.65 (6)

[0025]

[0026]

[0027]

[0028] In the formula: e is the volume fraction of the proppant, %; V proppant V is the proppant transport velocity, m / s; V is the mixing fluid velocity, m / s; V s V is the gravitational settling velocity, in m / s; stokes ρ is the Stokes settling velocity, m / s; f(e) is the correction factor, dimensionless; proppant The density of the proppant is kg / m³. 3 ;ρ fluid The density of the fracturing fluid is kg / m³. 3 ;d proppant ρ is the proppant particle size, m; g is the gravitational acceleration, m / s². 2 ρ is the density of the sand-mixing solution, kg / m³ 3 μ slurry The viscosity of the sand-mixing solution is expressed in Pa·s; e max The maximum volume fraction of the proppant is %.

[0029] A further technical solution is that, in step 5, the fluid flow equation, fracture constitutive equation, and proppant transport equation set in the multi-cluster fracturing fracture propagation and proppant transport coupling model are solved using the three-dimensional block discrete element method, and then the fluid-solid coupling equation set is constructed and calculated using the finite difference method.

[0030] A further technical solution is that, in step 6, the uniformity index of multi-cluster fracturing fracture propagation and the layup efficiency are respectively:

[0031]

[0032]

[0033] In the formula: U a The uniformity index of multi-cluster fracturing fracture propagation, %; A i Let m be the expansion area of ​​the i-th cluster of cracks.2 ; The mean area of ​​the multi-crack propagation is m. 2 η is the layup efficiency, %; A proppant For the area of ​​proppant application, m 2 A total For the total area of ​​the crack expansion, m 2 .

[0034] The beneficial effects of this invention are as follows: Based on the three-dimensional block discrete element method, this invention proposes a coupling model for the propagation of multi-cluster fracturing fractures and proppant transport that considers the influence of interlayers and weak surfaces. This improves the accuracy of predicting the morphology of multi-cluster fracturing fractures and proppant placement in complex reservoirs, making the results more consistent with engineering practice. Attached Figure Description

[0035] Figure 1 Comparison of multi-cluster fracturing fracture propagation morphology under different cluster spacings

[0036] Figure 2 Comparison of proppant distribution within cracks under different cluster spacings

[0037] Figure 3 Line graphs showing the uniformity index and layup efficiency of multi-cluster fracturing fractures with different cluster spacing. Detailed Implementation

[0038] 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.

[0039] Step 1: Collect geological and engineering parameters;

[0040] The geological and engineering parameters include: reservoir thickness, Poisson's ratio, Young's modulus, maximum horizontal principal stress, minimum horizontal principal stress, vertical stress, tensile strength of bedding, cohesion of bedding, internal friction angle of bedding, tensile strength of natural fractures, cohesion of natural fractures, internal friction angle of natural fractures, fracturing fluid viscosity, fracturing fluid density, number of fracture clusters, cluster spacing, construction flow rate, proppant particle size, proppant density, proppant volume fraction, total pumping time, and injection time of mixed sand fluid.

[0041] Step 2: Establish the fluid flow equations;

[0042] The fluid flow equation is:

[0043]

[0044] where p is fluid pressure, Pa; t is time, s; u is fracture width, m; K w is fluid bulk modulus, Pa; μ is fracturing fluid viscosity, Pa-s.

[0045] Step 3: Establishing the fracture constitutive equation;

[0046] The fracture constitutive equation is characterized by using the continuous yield model. When the crack element does not produce sliding, the shear strength is the maximum value; when the crack element shear stress exceeds the maximum shear strength, the shear strength evolves nonlinearly. The expression of the relationship between crack shear stress and plastic slip is:

[0047]

[0048] where τ s is shear stress, Pa; is shear stress peak value, Pa; c peak is maximum cohesion, Pa; σ n is normal stress, Pa; is maximum internal friction angle, °; is shear stress residual value, Pa; D c is critical slip distance, m; β is shear strength attenuation index, dimensionless; is plastic slip, m; c residual is cohesion residual value, Pa; is internal friction angle residual value, °.

[0049] Step 4: Establishing the proppant transport equation group;

[0050] The proppant transport equation group is:

[0051]

[0052] V proppant = V + (1 - e) V s (4)

[0053] V s = f(e) V stokes (5)

[0054] f(e) = (1 - e) 4.65 (6)

[0055]

[0056]

[0057]

[0058] where e is the proppant volume fraction, %; Vproppant V is the proppant transport velocity, m / s; V is the sand slurry velocity, m / s; V s V is the gravity settling velocity, m / s; V stokes V is the Stokes settling velocity, m / s; f(e) is the correction factor, dimensionless; p proppant V is the proppant density, kg / m 3 ; p fluid V is the fracturing fluid density, kg / m 3 ; d proppant V is the proppant particle size, m; g is the gravitational acceleration, m / s 2 ; p is the sand slurry density, kg / m 3 ; m slurry V is the sand slurry viscosity, Pa·s; e max V is the maximum volume fraction of proppant, %.

[0059] Step 5: Establish a multi-cluster fracturing fracture propagation and proppant transport coupling model by integrating steps 2-4;

[0060] Among them, the fluid flow equation, fracture constitutive equation and proppant transport equation group in the multi-cluster fracturing fracture propagation and proppant transport coupling model are solved by three-dimensional block discrete element method, and then the flow-solid coupling equation group is calculated by finite difference method.

[0061] Step 6: Quantitatively characterize the uniformity of multi-cluster fracturing fracture propagation and the uniformity of proppant placement in the fracture by multi-cluster fracturing fracture propagation uniformity index and placement efficiency;

[0062] Among them, the multi-cluster fracturing fracture propagation uniformity index and the placement efficiency are respectively:

[0063]

[0064]

[0065] In the formula: U a V is the multi-cluster fracturing fracture propagation uniformity index, %; A i V is the propagation area of the i-th cluster fracture, m 2 ; V is the average of the multi-cluster fracture propagation area, m 2 ; n is the placement efficiency, %; A proppant V is the proppant placement area, m 2 ; A total V is the total fracture propagation area, m 2 .

[0066] Step 7: Substitute the parameters of step 1 into step 5 to simulate the multi-cluster fracturing fracture propagation pattern and the proppant placement pattern in the fracture under different engineering parameters, and quantitatively characterize by step 6.

[0067] wherein the geological parameters and engineering parameters of step 1 are brought into the multi-cluster fracturing fracture propagation and proppant transport coupling model in step 5 to obtain the multi-cluster fracturing fracture propagation morphology, the multi-cluster fracturing fracture propagation uniformity index, the proppant placement morphology and the placement efficiency in the fracture to quantitatively characterize the uniformity of the multi-cluster fracturing fracture propagation and the uniformity of the proppant placement in the fracture.

[0068] Embodiment

[0069] First step: obtain the geological parameters and engineering parameters, as shown in Tables 1-3.

[0070] Table 1: Thickness and rock mechanics parameters of each layer of the model

[0071] Position Thickness / m Young's modulus / GPa Poisson's ratio Top layer 24 32 0.32 1 sublayer 18 26 0.25 Upper barrier 2 30 0.31 2 sublayer 10 28 0.26 Lower barrier 6 34 0.33 3 sublayer 20 25 0.25 Bottom layer 20 35 0.34

[0072] Table 2: Stress parameters of each layer of the model

[0073] Position Maximum horizontal principal stress / MPa Minimum horizontal principal stress / MPa Vertical stress / MPa Top layer 80 69 75 1 sublayer 75 64 68 Upper barrier 78 67 73 2 sublayer 76 63 70 Lower barrier 79 68 72 3 sublayer 74 62 69 Bottom layer 80 70 75

[0074] Table 3: Other input parameters of the model

[0075] Other parameters Value Unit Fracturing fluid viscosity 5 mPa·s Fracturing fluid density 1000 kg / m 3 ]]> Number of fracture clusters 5 - Cluster spacing 10 m Operation displacement 15 m 3 / min]]> Proppant particle size 275 μm Proppant density 2600 kg / m 3 ]]> Proppant volume fraction 15 ％ Bedding tensile strength 4.71 MPa Bedding cohesion 0.5 MPa Bedding internal friction angle 20 ° Natural fracture tensile strength 2.58 MPa Natural fracture cohesion 0.05 MPa Natural fracture internal friction angle 20 ° Total pumping time 10 min Sand slurry injection time 10 min

[0076] Second step: bring the parameters in Tables 1-3 into the multi-cluster fracturing fracture propagation and proppant transport coupling model established by the present application to simulate the multi-cluster fracturing fracture propagation morphology and the proppant placement morphology in the fracture under the conditions of cluster spacing of 6m, 10m, 14m and 18m.

[0077] Third step: according to the simulation results of the present embodiment, draw the multi-cluster fracturing fracture propagation morphology comparison chart under different cluster spacings ( Figure 1 ) and the proppant distribution comparison chart in the fracture ( Figure 2 ); and respectively count the hydraulic fracture propagation area of each cluster, the total fracture propagation area and the proppant placement area, calculate the multi-cluster fracturing fracture propagation uniformity index and the placement efficiency, and draw the multi-cluster fracturing fracture propagation uniformity index and the placement efficiency line chart under different cluster spacings ( Figure 3 ).

[0078] Fourth step: from Figure 1 It can be seen that the cluster spacing has a significant effect on the multi-cluster fracturing fracture morphology. The smaller the cluster spacing, the greater the competition between the multi-cluster fracturing fractures. When the cluster spacing is 6m, the middle 3 clusters of fractures are most severely inhibited, and the two wing fractures are most fully expanded, and the SRA is about 5 times that of the adjacent fractures. With the increase of the cluster spacing, the competition between the multi-cluster fracturing fractures gradually weakens, and the 5 clusters of fractures are relatively uniform. At the same time, the larger the cluster spacing, the smaller the overall fracturing fracture width, and the greater the influence on the proppant transport in the fracture, which is easy to cause blockage. From Figure 2It can be seen that, due to the accumulation of proppant near the fracture front position, the flow of fracturing fluid is limited, resulting in the emergence of proppant-free area in the front of multi-cluster hydraulic fracture, for example, in the first cluster of hydraulic fracture with 18m cluster spacing, there is a significant proppant-free area in the fracture front; the barrier effect of the barrier will significantly affect the transport of proppant, for example, the proppant in the fourth cluster of hydraulic fracture is distributed above the lower barrier; when the cluster spacing is 6m and 10m, the fifth cluster of hydraulic fracture expands more fully, and the proppant breaks through the constraint of the lower barrier; when the cluster spacing is 14m and 18m, the fifth cluster of hydraulic fracture expands relatively weakly, and the proppant is blocked by the lower barrier. From Figure 3 It can be seen that, as the cluster spacing increases from 6m to 18m, the uniformity index of multi-cluster hydraulic fracture propagation increases from 19.2% to 81.3%, indicating that the smaller the cluster spacing, the more serious the stress interference between fractures, and the more obvious the competition of multi-cluster hydraulic fracture propagation; the placement efficiency decreases from 86.9% to 58.6%, indicating that the proppant placement in the fracture is more uniform under small cluster spacing.

[0079] The above is not any form of limitation on the present application, although the present application has been disclosed by the above examples, however, not used to limit the present application, any skilled person in the art, without departing from the scope of the technical scheme of the present application, can use the above disclosed technical content to make some changes or modifications as equivalent examples of equivalent changes, but as long as it does not deviate from the content of the technical scheme of the present application, according to the technical essence of the present application, any simple modification, equivalent change and modification of the above examples, still belongs to the scope of the technical scheme of the present application.

Claims

1. A method for multi-cluster fracture propagation and proppant transport coupling simulation and quantitative characterization, characterized in that, Comprising the following steps: Step 1: Collecting geological and engineering parameters; Step 2: Establishing fluid flow equation; Step 3: Establishing fracture constitutive equation; Step 4: Establishing proppant transport equation set; Step 5: Integrating steps 2-4 to establish a multi-cluster fracturing fracture propagation and proppant transport coupling model; Step 6: Quantitatively characterizing the uniformity of multi-cluster fracturing fracture propagation and the uniformity of proppant placement in the fracture by a multi-cluster fracturing fracture propagation uniformity index and a placement efficiency, wherein the multi-cluster fracturing fracture propagation uniformity index and the placement efficiency are respectively defined as: （1） （2） In the formula: is the uniformity index of the multi-cluster fracture propagation; is the propagation area of the i-th cluster fracture, m 2 ; is the average of the multi-cluster fracture propagation area, m 2 ; η is the placement efficiency; is the proppant placement area, m 2 ; is the total fracture propagation area, m 2 ; Step 7: Substituting the parameters of step 1 into step 5 to simulate the multi-cluster fracturing fracture propagation pattern and the proppant placement pattern in the fracture under different engineering parameters, and quantitatively characterizing by step 6.

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