An unconventional reservoir multi-fracture propagation efficient simulation method

Abstract

The application provides an unconventional reservoir multi-fracture propagation efficient simulation method, and the simulation method comprises the following steps: S1, establishing a horizontal well multi-fracture propagation geometric model; S2, establishing an energy conservation based hydraulic fracturing multi-fracture propagation mathematical model; S3, setting fracturing parameters for the energy conservation based hydraulic fracturing multi-fracture propagation mathematical model; and S4, simulating multi-fracture propagation to obtain a multi-fracture propagation mode and a fracture state parameter. The application provides more powerful guidance for unconventional reservoir fracturing design.

Description

Technical Field

[0001] This invention relates to the field of oil and gas extraction technology, and in particular to an efficient simulation method for multi-fracture propagation in unconventional reservoirs. Background Technology

[0002] Unconventional reservoirs face varying degrees of problems such as low porosity and permeability, and poor flow capacity, necessitating staged fracturing of horizontal wells for efficient development. Currently, the length of horizontal sections and the number of fracturing stages are gradually increasing, making it more challenging to efficiently simulate multi-fracture propagation.

[0003] For the problem of fracture propagation in staged fracturing of unconventional reservoirs, various numerical simulation methods have been employed to conduct extensive research on the mechanisms involved, including multi-fracture competitive propagation, hydraulic-natural fracture interaction, and hydraulic fracture cross-layer propagation. However, these studies often sacrifice computational efficiency to reveal the complex laws governing hydraulic fracture propagation. This makes it difficult to provide real-time and effective guidance for fracturing design schemes in practical engineering applications. Furthermore, while some commonly used commercial fracturing simulation software can achieve efficient calculations of fracture propagation, the models involved in these software programs involve numerous assumptions, making it difficult to accurately reflect the true morphology of fractures in the reservoir. Some software programs can only simulate the propagation of a single fracture, offering limited guidance for multi-fracture propagation in staged fracturing. Summary of the Invention

[0004] In view of the above problems, the present invention is proposed to provide an efficient simulation method for multi-fracture propagation in unconventional reservoirs that overcomes or at least partially solves the above problems.

[0005] According to one aspect of the present invention, an efficient simulation method for multi-fracture propagation in unconventional reservoirs is provided, the simulation method comprising:

[0006] Step S1: Establish a geometric model of multi-fracture propagation in a horizontal well;

[0007] Step S2: Establish a mathematical model for multi-fracture propagation in hydraulic fracturing based on energy conservation;

[0008] Step S3: Set the fracturing parameters for the energy-conservation-based hydraulic fracturing multi-fracture propagation mathematical model;

[0009] Step S4: Simulate the propagation of multiple cracks to obtain the propagation morphology and crack state parameters of the multiple cracks.

[0010] Optionally, step S1: establishing a geometric model of multi-fracture propagation in a horizontal well specifically includes:

[0011] Collect various parameters of fractured wells and establish a geometric model of multi-fracture propagation in horizontal wells.

[0012] Optionally, the various parameters specifically include: geological parameters, segmentation and clustering, and perforation parameters.

[0013] Optionally, the geological parameters include reservoir depth, thickness, permeability, and triaxial principal stress; the segmentation and clustering parameters include fracturing segment length, number of clusters, and cluster spacing; and the perforation parameters include perforation diameter and number of perforations.

[0014] Optionally, step S2: establishing a mathematical model for multi-fracture propagation in hydraulic fracturing based on energy conservation specifically includes:

[0015] Establish mathematical models for fluid flow within fractures and matrix, fracture elastic deformation, inter-fracture interaction forces, and fracture propagation criteria.

[0016] Based on global energy conservation, the mathematical models of fluid flow within the fracture-matrix, elastic deformation of the fracture, and interaction forces between fractures are coupled to establish a hydraulic fracturing multi-fracture propagation mathematical model based on energy conservation.

[0017] Optionally, the fluid-matrix flow mathematical model within the fracture uses Cattell's law and Poiseuille's equation to describe fluid loss into the formation and fluid flow within the fracture, respectively. The fluid mass balance equation is:

[0018]

[0019] Among them, C L The filtration coefficient is m·s -1 / 2 k is the rock permeability, mD; c r Pa is the reservoir compressibility factor. -1 φ is the rock porosity, %; μ is the hydrodynamic viscosity, Pa·s; σ o For the minimum horizontal principal stress, Pa; p o t0 represents the reservoir pore pressure, in Pa; t0 represents the moment, in seconds, when filtration occurs at a certain point in the hydraulic fracture.

[0020] Optionally, the mathematical model for the elastic deformation of the crack is derived by coupling the crack width with the traction force to obtain the crack elastic equation:

[0021]

[0022] Where x and s are both distances from a point inside the crack to the center of the crack, in meters; E' is a rock characteristic parameter under the plane strain assumption.

[0023] Optionally, the mathematical model of the interaction forces between fractures utilizes the pressure distribution within each hydraulic fracture and, based on the superposition principle, calculates the sum of stresses exerted on any fracture i by the other fractures:

[0024]

[0025] Where, σ i σ is the total interaction force exerted by crack i on other cracks; j,i Let J be the interaction force between crack j and crack i.

[0026] Optionally, the fracture propagation criterion is expressed as:

[0027]

[0028] Among them, K I K represents the type I stress intensity factor of the rock, in MPa·m1 / 2. IC R(t) is the fracture toughness of the rock, MPa·m1 / 2; R(t) is the radial crack radius, m; T(ρ,t) is the tensile force on the crack, MPa; σ is the crack interaction force, MPa; σ o ρ is the far-field stress, MPa; ρ is the ratio of the distance from any point in the radial crack to the crack center to the crack radius, dimensionless.

[0029] Optionally, step S3: setting fracturing parameters for the energy-conservation-based hydraulic fracturing multi-fracture propagation mathematical model specifically includes:

[0030] Based on the fracturing construction plan of the block where the fracturing well is located, fracturing parameters are set for the hydraulic fracturing multi-fracture propagation mathematical model based on energy conservation, including total construction time, construction flow rate and fracturing fluid viscosity.

[0031] Optionally, step S4: simulating the propagation of multiple cracks to obtain the propagation morphology and crack state parameters specifically includes:

[0032] By combining the established geometric model and the mathematical model of multi-crack propagation based on energy conservation, multi-crack propagation simulation was carried out until the total construction time was reached, and the multi-crack propagation morphology and crack state parameters were obtained.

[0033] Optionally, the crack state parameters specifically include: crack radius, flow rate within the crack, crack opening width, and total crack area.

[0034] This invention provides an efficient simulation method for multi-fracture propagation in unconventional reservoirs. The simulation method includes: Step S1: establishing a geometric model of multi-fracture propagation in a horizontal well; Step S2: establishing a mathematical model of multi-fracture propagation in hydraulic fracturing based on energy conservation; Step S3: setting fracturing parameters for the mathematical model of multi-fracture propagation in hydraulic fracturing based on energy conservation; Step S4: simulating multi-fracture propagation to obtain the propagation morphology and fracture state parameters of the multi-fractures. This provides stronger guidance for fracturing design in unconventional reservoirs.

[0035] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 A flowchart illustrating an efficient simulation method for multi-fracture propagation in unconventional reservoirs based on energy conservation, provided in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of a geometric model of multi-crack propagation;

[0039] Figure 3 This is a schematic diagram of the propagation morphology of multiple fractures within a single fracturing segment;

[0040] Figure 4 It is a graph showing the changes in crack radius, flow rate within the crack, crack width, and total crack area over time.

[0041] Figure 5 This is a schematic diagram of the fracture propagation morphology throughout the entire horizontal well section; Figure 6 This is a schematic diagram showing the length and width of cracks in each segment and cluster; Figure 7 This is a schematic diagram showing the simulation results of fracture propagation in all sections of the four wells. Detailed Implementation

[0042] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0043] The terms "comprising" and "having," and any variations thereof, in the specification, embodiments, claims, and drawings of this invention are intended to cover non-exclusive inclusion, such as including a series of steps or units.

[0044] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0045] Figure 1 This invention provides a flowchart of an efficient simulation method for multi-fracture propagation in unconventional reservoirs based on energy conservation. The method includes:

[0046] Step 1: Collect geological parameters, segmentation / clustering, and perforation parameters of the fractured well. Geological parameters include reservoir depth, thickness, permeability, and triaxial principal stress. Segmentation / clustering parameters include fracture segment length, cluster number, and cluster spacing. Perforation parameters include perforation diameter and number of perforations. Then, based on these parameters, establish a multi-fracture propagation geometric model of the horizontal well, such as... Figure 2 As shown.

[0047] Step 2: Establish mathematical models for fluid flow within the fracture and matrix, fracture elastic deformation, inter-fracture interaction forces, and fracture propagation criteria; couple these models based on global energy conservation to establish a hydraulic fracturing multi-fracture propagation mathematical model based on energy conservation.

[0048] Specifically, the fluid-matrix flow mathematical model within the fracture uses Cattell's law and Poiseuille's equation to describe fluid loss into the formation and fluid flow within the fracture, respectively. The fluid mass balance equation is as follows:

[0049]

[0050] Among them, C L The filtration coefficient is m·s -1 / 2 k is the rock permeability, mD; c r Pa is the reservoir compressibility factor. -1 φ is the rock porosity, %; μ is the hydrodynamic viscosity, Pa·s; σ o For the minimum horizontal principal stress, Pa; p o t0 represents the reservoir pore pressure, in Pa; t0 represents the moment, in seconds, when filtration occurs at a certain point in the hydraulic fracture.

[0051] The mathematical model for the elastic deformation of the crack derives the crack elastic equation by coupling the crack width with the traction force:

[0052]

[0053] Where x and s are both distances from a point inside the crack to the center of the crack, in meters; E' is a rock characteristic parameter under the plane strain assumption.

[0054] The mathematical model of inter-fracture interaction forces utilizes the pressure distribution within each hydraulic fracture and, based on the superposition principle, calculates the sum of stresses exerted on any fracture i by the other fractures:

[0055]

[0056] Where, σi σ is the total interaction force exerted by crack i on other cracks; j,i Let J be the interaction force between crack j and crack i.

[0057] According to the linear elastic fracture mechanics principle, the fracture propagation criterion for radial cracks is expressed as:

[0058]

[0059] Among them, K I The stress intensity factor of the rock is the type I stress intensity factor, in MPa·m. 1 / 2 ;K IC For rock fracture toughness, MPa·m 1 / 2 R(t) is the radial crack radius, m; T(ρ,t) is the traction force on the crack, MPa; σ is the crack interaction force, MPa; σ o ρ is the far-field stress, MPa; ρ is the ratio of the distance from any point in the radial crack to the crack center to the crack radius, dimensionless.

[0060] By using uniform pressure within a space to replace non-uniform pressure, approximate forms of pressure distribution, crack toughness, and inter-crack interaction forces can be obtained.

[0061]

[0062] Where, μ c denoted as "composite viscosity," a physical quantity reflecting the additional energy loss related to filtration and toughness; Π(ρ,t) is a dimensionless pressure distribution function; ψ(t) is spatially uniform pressure, related to toughness; A, B, and ω are coefficients, taken as 0.3581, 0.09269, and 2.479 respectively under the assumptions of constant construction discharge and infinitely uniform elastic rock.

[0063] The above physical processes are coupled based on the global energy conservation principle:

[0064]

[0065] Where, p f (R w Q(t) represents the energy input of the crack.

[0066] D c The dissipation rate associated with rock fracturing is calculated using the following formula:

[0067]

[0068] D f The dissipation rate associated with viscous fluid flow is calculated using the following formula:

[0069]

[0070] D L The fluid loss rate related to filtration loss is calculated using the following formula:

[0071]

[0072] U is the increase in strain energy caused by rock deformation, calculated using the following formula:

[0073]

[0074] The work done by the compressive stress of adjacent cracks in each crack is calculated using the following formula:

[0075]

[0076] The work done by the in-situ stress on the crack is calculated using the following formula:

[0077]

[0078] P perf The power loss through the seam is calculated using the following formula:

[0079]

[0080] Step 3: Based on the fracturing construction plan for the block where the fracturing well is located, set the fracturing parameters for the hydraulic fracturing multi-fracture propagation mathematical model based on energy conservation, including the total construction time, construction flow rate, and fracturing fluid viscosity.

[0081] Step 4: Combine the established geometric model and the multi-crack propagation mathematical model based on energy conservation to carry out multi-crack propagation simulation until the total construction time is reached, and obtain the multi-crack propagation morphology, crack radius, flow rate within the crack, crack opening width and total crack area.

[0082] Example 1:

[0083] Example 1 includes one fracturing section with five perforation clusters spaced 20m apart, and a flow rate of 0.1m³ / min. 3 / s, fracturing fluid viscosity 1 Pa·s. Formation Young's modulus 9.5 GPa, Poisson's ratio 0.2, in-situ stress 70 MPa, wellbore diameter 0.2 m. Multiple fracture propagation morphology as follows: Figure 3 As shown, the curves depicting the changes in crack radius, flow rate within the crack, crack width, and total crack area over time are as follows: Figure 4 As shown.

[0084] In addition, the computational efficiency of this embodiment was compared with that of the implicit level set algorithm for planar three-dimensional crack propagation, and the comparison results are shown in Table 1 below.

[0085] Table 1 Comparison of computational efficiency results

[0086]

[0087]

[0088] Example 2:

[0089] Example 2 includes one fractured horizontal well A, which comprises a total of 31 fractured sections. The parameters such as section spacing, cluster spacing, and cluster number during the simulation of fracture propagation throughout the well were set according to the actual segmentation and clustering scheme of the well, as shown in Table 2 (only data for a portion of the well are listed for illustration). Furthermore, the Young's modulus and Poisson's ratio of this well were set based on the well logging data.

[0090] Table 2. Partial data of horizontal well A segment cluster in Example 2.

[0091]

[0092]

[0093] Multi-fracture propagation morphology throughout the entire horizontal well section, such as Figure 5 As shown, the length and width of the cracks in each segment and cluster are as follows: Figure 6 As shown.

[0094] Example 3:

[0095] Example 3, based on Example 2, focuses on the well group containing horizontal well A from Example 2. This well group comprises four horizontal wells, and a zipper-style fracturing simulation was conducted on all four wells. The segmentation, clustering, and pumping procedures for each well were set according to actual conditions. The simulation results of fracture propagation in all segments of the four wells are as follows: Figure 7 As shown.

[0096] The method provided in this application can simulate multi-fracture propagation for a single fracturing section, all fracturing sections of a fracturing well, or even multiple wells. It can obtain the multi-fracture propagation morphology, fracture radius, flow rate within the fracture, fracture opening width, and total fracture area over time. At the same time, the method has extremely high computational efficiency and can optimize the fracturing parameters of each fracturing section in a short time according to different fracturing parameters, providing strong guidance for unconventional reservoir fracturing design and is suitable for large-scale application.

[0097] Beneficial effects: This method obtains approximate forms of the physical quantities involved in fracture propagation and performs coupled solutions based on energy conservation, resulting in extremely high simulation efficiency. It can quickly optimize perforation and fracturing process parameters, providing more powerful guidance for unconventional reservoir fracturing design.

[0098] The above specific embodiments further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above are merely specific embodiments of the present invention and are not intended to limit the scope of protection of 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 highly efficient simulation method for multi-fracture propagation in unconventional reservoirs, characterized in that, The simulation method includes: Step S1: Establish a geometric model of multi-fracture propagation in a horizontal well; Step S2: Establish a mathematical model for multi-fracture propagation in hydraulic fracturing based on energy conservation; Step S3: Set the fracturing parameters for the energy-conservation-based hydraulic fracturing multi-fracture propagation mathematical model; Step S4: Simulate the propagation of multiple cracks to obtain the propagation morphology and crack state parameters of the multiple cracks.

2. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 1, characterized in that, Step S1: Establishing a geometric model for multi-fracture propagation in a horizontal well specifically includes: Collect various parameters of fractured wells and establish a geometric model of multi-fracture propagation in horizontal wells.

3. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 2, characterized in that, The various parameters specifically include: geological parameters, segmentation and clustering, and perforation parameters.

4. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 3, characterized in that, The geological parameters include reservoir depth, thickness, permeability, and triaxial principal stress; the segmentation and clustering parameters include fracturing segment length, number of clusters, and cluster spacing; the perforation parameters include perforation diameter and number of perforations.

5. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 1, characterized in that, Step S2: Establishing a mathematical model for multi-fracture propagation in hydraulic fracturing based on energy conservation specifically includes: Establish mathematical models for fluid flow within fractures and matrix, fracture elastic deformation, inter-fracture interaction forces, and fracture propagation criteria. Based on global energy conservation, the mathematical models of fluid flow within the fracture-matrix, elastic deformation of the fracture, and interaction forces between fractures are coupled to establish a hydraulic fracturing multi-fracture propagation mathematical model based on energy conservation.

6. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 5, characterized in that, The fluid-matrix flow mathematical model within the fracture uses Cattell's law and Poiseuille's equation to describe fluid loss into the formation and fluid flow within the fracture, respectively. The fluid mass balance equation is as follows: Among them, C L The filtration coefficient is m·s -1 / 2 k is the rock permeability, mD; c r Pa is the reservoir compressibility factor. -1 φ is the rock porosity, %; μ is the hydrodynamic viscosity, Pa·s; σ o For the minimum horizontal principal stress, Pa; p o t0 represents the reservoir pore pressure, in Pa; t0 represents the moment, in seconds, when filtration occurs at a certain point in the hydraulic fracture.

7. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 5, characterized in that, The mathematical model for the elastic deformation of the crack derives the crack elastic equation by coupling the crack width with the traction force: Where x and s are both distances from a point inside the crack to the center of the crack, in meters; E' is a rock characteristic parameter under the plane strain assumption.

8. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 5, characterized in that, The mathematical model of inter-fracture interaction forces utilizes the pressure distribution within each hydraulic fracture and, based on the superposition principle, calculates the sum of stresses exerted on any fracture i by the other fractures: Where, σ i σ is the total interaction force exerted by crack i on other cracks; j,i Let J be the interaction force between crack j and crack i.

9. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 5, characterized in that, The fracture propagation criterion is expressed as follows: Among them, K I K represents the type I stress intensity factor of the rock, in MPa·m1 / 2. IC R(t) is the fracture toughness of the rock, MPa·m1 / 2; R(t) is the radial crack radius, m; T(ρ,t) is the tensile force on the crack, MPa; σ is the crack interaction force, MPa; σ o ρ is the far-field stress, MPa; ρ is the ratio of the distance from any point in the radial crack to the crack center to the crack radius, dimensionless.

10. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 1, characterized in that, Step S3: Setting fracturing parameters for the energy-conservation-based hydraulic fracturing multi-fracture propagation mathematical model specifically includes: Based on the fracturing construction plan of the block where the fracturing well is located, fracturing parameters are set for the hydraulic fracturing multi-fracture propagation mathematical model based on energy conservation, including total construction time, construction flow rate and fracturing fluid viscosity.

11. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 1, characterized in that, Step S4: Simulating the propagation of multiple cracks to obtain the propagation morphology and crack state parameters specifically includes: By combining the established geometric model and the mathematical model of multi-crack propagation based on energy conservation, multi-crack propagation simulation was carried out until the total construction time was reached, and the multi-crack propagation morphology and crack state parameters were obtained.

12. The efficient simulation method for multi-fracture propagation in unconventional reservoirs according to claim 11, characterized in that, The specific crack state parameters include: crack radius, flow rate within the crack, crack opening width, and total crack area.

Images