Multi-cluster crack competition and propagation discrete element simulation method and quantitative evaluation method

Abstract

The application discloses a kind of multi-cluster fracture competition expansion discrete element simulation method and quantitative evaluation method, it is related to oil and gas reservoir exploitation technical field, the method includes: obtaining the geological parameters of target reservoir, rock mechanics parameters, wellbore parameter of target well, engineering parameter in fracturing reconstruction, fluid parameter of using fluid;Establish wellbore friction calculation model;Establish perforation hole erosion correction model;Establish dynamic wellbore flow distribution model;Dynamic wellbore flow distribution model is simulated to discrete element, and iterative calculation is carried out to obtain hole diameter, flow coefficient, final flow variation curve, obtains variation coefficient.The application can more accurately simulate the flow distribution and fracture propagation process under complex reservoir conditions, improve the scientificity and field applicability of hydraulic fracturing design.

Description

Technical Field

[0001] This invention relates to the field of oil and gas reservoir development technology, and in particular to a discrete element simulation method and quantitative evaluation method for competitive propagation of multi-cluster fractures based on dynamic flow distribution. Background Technology

[0002] my country's unconventional oil and gas resources are widely distributed, characterized by complex sedimentary environments, strong reservoir heterogeneity, well-developed horizontal bedding and natural fractures, and complex stress fields. Traditional development simulation methods, such as the finite element method (FEM) and boundary element method (BEM), struggle to effectively handle heterogeneous media, especially when coupled with numerous randomly distributed natural fractures. Therefore, research based on the discrete element method (DEM) offers significant advantages in applications involving weak surfaces and discontinuous media such as shale and carbonate rocks. The DEM can more realistically reflect the mechanical response behavior of rocks under complex conditions, making it an ideal tool for simulating hydraulic fracturing.

[0003] However, current applications of the Discrete Element Method (DEM) for coupled simulation of flow distribution are still limited. Existing patents and papers typically consider only a few influencing factors, neglecting the multiple coupling effects of wellbore friction, perforation erosion, and fracture closure pressure, leading to significant deviations between simulation results and actual field conditions. Especially during the propagation of multiple fracture clusters, the flow competition among fractures significantly impacts the final fracture morphology and fracturing effect. Coupled simulation of flow distribution using the DEM can more realistically reflect the synchronous propagation process of multiple fracture clusters in complex reservoirs, quantitatively assess fracture propagation uniformity and flow distribution patterns, and thus optimize hydraulic fracturing strategies. Summary of the Invention

[0004] To address the aforementioned issues, this invention aims to provide a discrete element method for simulating and quantitatively evaluating the competitive propagation of multi-cluster fractures based on dynamic flow distribution. This method uses the discrete element method to perform coupled simulation and quantitative evaluation of the competitive propagation of multi-cluster fractures and flow distribution. It considers the wellbore friction caused by commonly used slickwater fracturing fluid in construction sites, perforation erosion, and the flow distribution caused by the closure pressure within the fracture, and quantitatively judges the uniformity of fracture propagation. This method can more realistically reflect the synchronous propagation process of multi-cluster fractures in complex reservoirs, quantitatively evaluate the uniformity of fracture propagation and the flow distribution law, and thus optimize hydraulic fracturing schemes.

[0005] The technical solution provided by this invention to solve the above-mentioned technical problems is: a discrete element simulation method for multi-cluster crack competition propagation based on dynamic flow allocation, comprising the following steps:

[0006] Obtain geological parameters, rock mechanics parameters, wellbore parameters of the target well, engineering parameters during fracturing, and fluid parameters of the fluids used in the fracturing process;

[0007] The rheological properties of the power-law fluid are obtained based on the fluid parameters; a wellbore friction calculation model is established based on the rheological properties of the power-law fluid, wellbore parameters, and engineering parameters.

[0008] Based on fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were conducted to establish a perforation hole erosion correction model.

[0009] Based on the geological and rock mechanics parameters of the target reservoir, a reservoir geological model is established, and the hydraulic fracture closure pressure is obtained from the reservoir geological model. Based on Kirchhoff's law, a dynamic wellbore flow distribution model is established according to the wellbore friction calculation model, the perforation erosion correction model, and the hydraulic fracture closure pressure.

[0010] Discrete element simulation was performed on the dynamic wellbore flow distribution model, and the orifice diameter, flow coefficient, and final flow change curve were obtained through iterative calculation to obtain the coefficient of variation.

[0011] Furthermore, in some embodiments of this application, the coefficient of variation CV is:

[0012]

[0013] In the formula, k is the number of crack clusters; n i Let x be the number of flow rate changes in crack cluster i. ij Let represent the flow rate of crack cluster i at different times, and j be the index of the flow rate change.

[0014] Furthermore, in some embodiments of this application, the geological parameters include: reservoir thickness, interlayer thickness, and bedding density; the rock mechanical parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, and vertical stress.

[0015] The engineering parameters include: number of clusters, cluster spacing, number of perforations, orifice diameter, initial orifice flow coefficient, maximum orifice flow coefficient, and discharge rate;

[0016] The fluid parameters include: concentration, viscosity, density, bulk modulus, and shear rate;

[0017] The wellbore parameters include: wellbore diameter.

[0018] Furthermore, in some embodiments of this application, the rheological properties of the power-law fluid include a flow pattern coefficient and a consistency coefficient, which are obtained by fitting the shear rate and viscosity.

[0019] The fitting equations for shear rate and viscosity are as follows:

[0020] η=K·γ n-1 (2)

[0021] In the formula: η is the viscosity, Pa·s; K is the consistency coefficient, Pa·s n γ is the shear rate, s -1 ; n is the manifold coefficient.

[0022] Furthermore, in some embodiments of this application, the wellbore friction calculation model is as follows:

[0023]

[0024] In the formula: Δp pp ρ is the flow friction in the wellbore, Pa; ρ is the fluid density, kg / m³. 3 v is the flow velocity inside the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s is the pipe friction coefficient; f is the friction factor; A and B are the calculation parameters for the friction factor; K is the consistency coefficient, Pa·s. n ; n is the manifold coefficient.

[0025] Furthermore, in some embodiments of this application, the perforation hole abrasion correction model is as follows:

[0026]

[0027] In the formula: Δp pf For the frictional resistance of the orifice, Pa; Q i Let m be the displacement corresponding to crack cluster i. 3 / s; N is the number of perforations, and i is the cluster number of the cracks.

[0028] Furthermore, in some embodiments of this application, indoor simulation experiments are conducted based on fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters to establish a perforation erosion correction model, including the following steps:

[0029] Based on the above proppant concentration and reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were conducted. The concentration, injection rate, and time of the injected proppant were adjusted to simulate the effects of proppant concentration, injection rate, and time on the perforation erosion degree. Data on different proppant injection rates and times and their corresponding perforation diameters were obtained. Linear relationship fitting was performed to obtain the perforation erosion parameters. The fitting relationship is shown in (5):

[0030]

[0031] In the formula: d t+Δt With d t α and β are the perforation diameters at times t+Δt and t, respectively, in meters; α and β are empirical coefficients obtained from linear fitting, in meters. 2(m·s) / kg and (m·s) / kg; v p The velocity of the fluid inside the orifice is given in m / s; Cd t+Δt Cd t with cd max These represent the flow coefficients at time t+Δt, time t, and the maximum flow rate, respectively; C is the proppant concentration, kg / m³. 3 ;

[0032] The equation for real-time perforation friction obtained from (5) is the perforation hole erosion correction model.

[0033] Furthermore, in some embodiments of this application, the dynamic wellbore flow distribution model is as follows:

[0034]

[0035] In the formula: p cp,i Let be the closing pressure of crack cluster i, in Pa.

[0036] Furthermore, in some embodiments of this application, the dynamic wellbore flow distribution model is established as follows:

[0037] Let Δp be the total flow equivalent pressure drop of the i-th fracture cluster. i for:

[0038]

[0039] In the formula: Δp f,i For the perforation pressure drop of fracture cluster i, Pa; Δp pp,i Let be the pressure drop along the wellbore for fracture cluster i, k be the total number of fracture clusters, and i be the number of the fracture cluster, which takes a value in the range of 1 to k.

[0040] Δp is calculated based on the above formula. i Substitute these equations (8) and (9) into the following formulas:

[0041] r i =Δp i / q i (8)

[0042]

[0043] In the formula: q i Let m be the flow rate of crack cluster i. 3 / s;r t For equivalent friction, Pa;

[0044] The flow rate q of crack cluster i can then be obtained. i The calculation formula is the dynamic wellbore flow distribution model.

[0045] This application also provides a quantitative evaluation method for engineering parameters in hydraulic fracturing. The method uses the above-mentioned discrete element simulation method for competitive propagation of multi-cluster fractures to obtain the propagation morphology and flow distribution of multi-cluster fractures under different engineering parameter conditions, and evaluates the corresponding engineering parameters based on the obtained propagation morphology and flow distribution of multi-cluster fractures.

[0046] A further technical solution is to perform real-time calculation of the single-cluster closure pressure and monitoring of the degree of orifice erosion and the change in single-cluster flow rate in step 7, and to quantitatively evaluate the final results using the coefficient of variation.

[0047] The single-cluster closure pressure is calculated in real time, and the flow plane area and sub-contacts are recorded in real time. The hydraulic fracture closure pressure is calculated through the sub-contact reaction force and returned to the flow distribution model in real time to participate in the flow distribution calculation iteration.

[0048] Record the orifice diameter, flow coefficient, and stable flow rate after iteration. Input the required parameters back into the model to calculate the next time step, until the pumping time of this stage.

[0049] By deriving the orifice diameter, flow coefficient, and final flow rate variation curves, the coefficient of variation under different parameters is calculated using the following formula:

[0050]

[0051] In the formula, k is the number of crack clusters; n i Let x be the number of flow rate changes in crack cluster i. ij The flow rate values ​​of crack cluster i at different times are given.

[0052] The uniformity of flow distribution among different clusters under different geological and engineering parameters is evaluated by comparing the coefficient of variation (CV) of flow under different geological and engineering parameters.

[0053] The beneficial effects of this invention are as follows: Based on the discrete element method, this invention proposes a multi-cluster fracture propagation model and quantitative evaluation method that comprehensively considers pore erosion, power-law fluid wellbore friction, and intra-fracture closure pressure. This model is more suitable for discontinuous media such as shale reservoirs with a large number of discrete fractures, improves the accuracy of multi-cluster fracture morphology prediction, and can be used for hydraulic fracturing simulation and optimization of engineering parameters under various conditions, which is more in line with actual engineering needs. Attached Figure Description

[0054] Figure 1 A schematic diagram of the multi-cluster flow distribution process throughout the hydraulic fracturing process;

[0055] Figure 2 The figure shows the results of an indoor test of power-law fluids, using polyacrylamide as an example.

[0056] Figure 3 A graph showing the real-time changes in the diameter of each cluster of apertures;

[0057] Figure 4 A graph showing the real-time changes in flow rate for each cluster;

[0058] Figure 5 Flow rate difference coefficient diagram under different parameters;

[0059] Figure 6 The images show the propagation morphology of multiple fracture clusters under different parameters. (a) shows the propagation morphology of multiple fracture clusters with an upper septum, (b) shows the propagation morphology of multiple fracture clusters with an lower septum, and (c) shows the propagation morphology of multiple fracture clusters with both upper and lower septa. Detailed Implementation

[0060] The technical solutions of this application will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] This application provides a method for simulating the competitive expansion of multi-cluster cracks using discrete element method, including:

[0062] Obtain geological parameters, rock mechanics parameters, wellbore parameters of the target well, engineering parameters during fracturing, and fluid parameters of the fluids used in the fracturing process;

[0063] The rheological properties of the power-law fluid are obtained based on the fluid parameters; a wellbore friction calculation model is established based on the rheological properties of the power-law fluid, wellbore parameters, and engineering parameters.

[0064] Based on fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were conducted to establish a perforation hole erosion correction model.

[0065] Based on the geological parameters and rock mechanics parameters of the target reservoir, a reservoir geological model is established. Based on the reservoir geological model and Kirchhoff's laws, a dynamic wellbore flow distribution model is established based on the wellbore friction calculation model, the perforation erosion correction model, and the hydraulic fracture closure pressure.

[0066] Discrete element simulation was performed on the dynamic wellbore flow distribution model, and the orifice diameter, flow coefficient, and final flow change curve were obtained through iterative calculation to obtain the coefficient of variation.

[0067] Kirchhoff's laws are the fundamental laws governing voltage and current in a circuit. Here, voltage drop is analogous to voltage, and flow rate is analogous to current to establish a flow distribution model.

[0068] The formula for calculating the coefficient of variation (CV) is as follows:

[0069]

[0070] In the formula, k is the number of crack clusters; n i Let x be the number of flow rate changes in crack cluster i. ij Let i represent the flow rate of fracture cluster i at different times, where i is the number of the fracture cluster and j is the index of the flow rate change.

[0071] By calculating the overall coefficient of variation under different conditions, the differences in flow distribution under different engineering or geological parameters are evaluated. A large coefficient of variation indicates that some fracture clusters have not been effectively extended. For example, when the coefficient of variation is ≥10%, it indicates that some fractures in the reservoir have not been effectively extended; when the coefficient of variation is ≤10%, the fractures in the surface reservoir have been fully extended, the corresponding engineering parameters are better, and the flow distribution is more balanced.

[0072] The geological parameters include: reservoir thickness, interlayer thickness, and bedding density; the rock mechanical parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, and vertical stress.

[0073] The engineering parameters include: number of clusters, cluster spacing, number of perforations, orifice diameter, initial orifice flow coefficient, maximum orifice flow coefficient, and discharge rate;

[0074] The fluid parameters include: concentration, viscosity, density, bulk modulus, and shear rate;

[0075] The wellbore parameters include: wellbore diameter.

[0076] Among them, geological parameters and rock mechanics parameters can be obtained through well logging data or laboratory experiments on core samples, such as core sample displacement experiments; engineering parameters can be obtained through engineering data; fluid parameters can be obtained through laboratory experiments, such as fluid viscosity and rheological property measurement experiments; and wellbore parameters can be obtained through engineering data.

[0077] The reservoir geological model is a hydraulic fracturing model based on the discrete element method. This model is not a mathematical model, but a simulation model. All parameters are obtained from experiments or well logging, and can reflect the in-situ geomechanical characteristics of the reservoir under real conditions, for use in hydraulic fracturing simulation. The method of its establishment is existing technology and can be referenced from the reservoir geological model establishment method described in (Huang T, Zhong Y, Mou Q, et al. Discrete element method simulation of competitive fracture propagation in staged multi-cluster fracturing in shale oil reservoirs[J]. Bulletin of Engineering Geology and the Environment,2024,83(10):1-13.).

[0078] Furthermore, fracture propagation morphologies include single fractures, complex fractures, natural fracture opening fractures, complex fracture networks, and directional fractures, which are classified based on fracturing modes and propagation paths. In this application, the reservoir geological model is also used to determine the fracture propagation morphology after reservoir fracturing. The specific determination method is as follows: using a discrete element model, analyzing sub-contact failure modes, quantifying the proportion of failure types, and directly observing the overall fracture morphology. Power-law fluids refer to fluids that conform to the rheological law τ=K*γ^n.

[0079] Where τ is the shear stress.

[0080] K -- Consistency coefficient, also known as the power-law coefficient, unit: Pa·sn

[0081] n -- Flow index, also known as the power law index, has no unit.

[0082] K-value is a measure of viscosity, but it is not equal to the viscosity value. The higher the viscosity, the higher the K-value.

[0083] Within a certain range of shear rates, the value of n can be treated as a constant.

[0084] The n-value is a measure of non-Newtonianness. The lower or higher the n-value, the more curved the curve and the stronger the non-Newtonianness. Generally, an n-value below 0.5 is better for mud.

[0085] In the process of oil and gas development, slickwater used for fracturing is a power-law fluid, so its consistency coefficient and flow index (flow pattern coefficient) can also be obtained by the above calculation formula.

[0086] Specifically, the flow pattern coefficient and consistency coefficient of the slickwater are obtained by fitting the shear rate and viscosity.

[0087] The fitting equations for shear rate and viscosity are as follows:

[0088] η=K·γ n-1 (2)

[0089] In the formula: η is the viscosity, Pa·s; K is the consistency coefficient, Pa·s n γ is the shear rate, s -1 ; n is the manifold coefficient.

[0090] Based on the above parameters, a wellbore friction calculation model is established considering the flow characteristics of power-law fluid in the wellbore. The wellbore friction calculation model is as follows:

[0091]

[0092] In the formula: Δp pp ρ is the flow friction in the wellbore, Pa; ρ is the fluid density, kg / m³. 3 v is the flow velocity inside the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s is the pipe friction coefficient; f is the friction factor; A and B are the calculation parameters for the friction factor; K is the consistency coefficient, Pa·s. n ; n is the manifold coefficient.

[0093] Then, based on fluid parameters, reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were conducted to establish a perforation erosion correction model, including the following steps:

[0094] Based on the above proppant concentration and reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were conducted. The concentration, injection rate, and time of the injected proppant were adjusted to simulate the effects of proppant concentration, injection rate, and time on the perforation erosion degree. Data on different proppant injection rates and times and their corresponding perforation diameters were obtained. Linear relationship fitting was performed to obtain the perforation erosion parameters. The fitting relationship is shown in (5):

[0095]

[0096] In the formula: d t+Δt With d t α and β are the perforation diameters at times t+Δt and t, respectively, in meters; α and β are empirical coefficients obtained from linear fitting, in meters. 2 (m·s) / kg and (m·s) / kg; v p The velocity of the fluid inside the orifice is given in m / s; Cd t+Δt Cd t with cd max These represent the flow coefficients at time t+Δt, time t, and the maximum flow rate, respectively; C is the proppant concentration, kg / m³.3 .

[0097] The equation for real-time perforation friction obtained from (5) is the perforation hole erosion correction model, which is as follows:

[0098]

[0099] In the formula: Δp pf For the frictional resistance of the orifice, Pa; Q i Let m be the displacement corresponding to crack cluster i. 3 / s; N is the number of perforations, and i is the number of the crack cluster.

[0100] Discrete element simulation of the reservoir geological model updates the model's state in real time as the fracturing process progresses. The reaction force of hydraulic fracturing on the wall surface is calculated by traversing all grid nodes in the model and divided by the fracture area to obtain the hydraulic fracture closure pressure. Based on Kirchhoff's laws, this hydraulic fracture closure pressure is coupled into the perforation erosion correction model to establish a dynamic wellbore flow distribution model. The process is as follows:

[0101] Let Δp be the total flow equivalent pressure drop of the i-th fracture cluster. i for:

[0102]

[0103] In the formula: Δp f,i For the perforation pressure drop of fracture cluster i, Pa; Δp pp,i Let be the pressure drop along the wellbore for fracture cluster i, where i is the number of the fracture cluster, and its value is in the range of 1 to k.

[0104] Δp is calculated based on the above formula. i Substitute these equations (8) and (9) into the following formulas:

[0105] r i =Δp i / q i (8)

[0106]

[0107] In the formula: q i Let m be the flow rate of crack cluster i. 3 / s;r t For equivalent friction, Pa;

[0108] The flow rate q of crack cluster i can then be obtained. i The calculation formula is the dynamic wellbore flow distribution model. The dynamic wellbore flow distribution model is:

[0109]

[0110] In the formula: p cp,i Let be the closing pressure of crack cluster i, in Pa.

[0111] After obtaining the dynamic wellbore flow distribution model described above, the closure pressure of each fracture cluster is obtained through real-time detection. The process is iterated until the flow of each cluster converges, and the flow rate q of fracture cluster i is simulated and calculated. i Until the sand-carrying fluid stage is reached, the orifice diameter, flow coefficient, and final flow rate change curves are derived. The coefficient of variation can then be calculated, and hydraulic fracturing simulation and engineering parameter optimization can be performed based on the coefficient of variation to make it more in line with actual engineering needs.

[0112] This application also provides a quantitative evaluation method for engineering parameters in hydraulic fracturing. The method uses the above-mentioned discrete element simulation method for competitive propagation of multi-cluster fractures to obtain the propagation morphology and flow distribution of multi-cluster fractures under different engineering parameter conditions, and evaluates the corresponding engineering parameters based on the obtained propagation morphology and flow distribution of multi-cluster fractures.

[0113] The following uses the Jimsar shale oil reservoir as an example to illustrate the discrete element simulation method and quantitative evaluation method for multi-cluster fracture competitive propagation based on dynamic flow distribution provided in this application. (See reference...) Figure 1 Specifically, it is as follows:

[0114] Step 1: Obtain the geological parameters, rock mechanics parameters, wellbore parameters, engineering parameters for fracturing stimulation, and fluid parameters of the fluids used in the target reservoir;

[0115] The geological parameters mentioned include: reservoir thickness, interlayer thickness, and bedding density; the rock mechanical parameters include: Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress, and vertical stress.

[0116] The engineering parameters include: number of clusters, cluster spacing, number of perforations, orifice diameter, initial orifice flow coefficient, maximum orifice flow coefficient, and discharge rate;

[0117] The fluid parameters include: proppant concentration, fracturing fluid viscosity, fracturing fluid density, and fracturing fluid bulk modulus;

[0118] The wellbore parameters include: wellbore diameter.

[0119] The obtained parameters are shown in Table 1.

[0120] Table 1 Simulation Parameters

[0121]

[0122]

[0123] To obtain the rheological properties of power-law fluids such as slickwater, such as shear rate and viscosity, the flow pattern coefficient and consistency coefficient of the power-law fluid are obtained by fitting according to equation (1):

[0124] η=K·γ n-1 (2)

[0125] In the formula: η is the viscosity, Pa·s; K is the consistency coefficient, Pa·s n γ is the shear rate, s -1 ; n is the manifold coefficient.

[0126] Based on the above parameters, a wellbore friction calculation model is established considering the flow characteristics of power-law fluid in the wellbore. The established wellbore module calculation model is shown in (2):

[0127]

[0128] In the formula: Δp pp ρ is the flow friction in the wellbore, Pa; ρ is the fluid density, kg / m³. 3 v is the flow velocity inside the wellbore, m / s; D is the wellbore diameter, m; L is the cluster spacing, m; K s The coefficient of friction of the pipeline.

[0129] Based on the above proppant concentration and reservoir parameters, wellbore parameters, and engineering parameters, indoor simulation experiments were conducted, and the concentration, injection rate, and time of the injected proppant were adjusted to simulate the effects of proppant concentration, injection rate, and time on the degree of perforation erosion. Data on different proppant injection rates and times and their corresponding perforation diameters were obtained, and linear relationship fitting was performed to obtain the perforation erosion parameters. The fitting relationship is shown in (3):

[0130]

[0131] In the formula: d t+Δt With d t α and β are the perforation diameters at times t+Δt and t, respectively, in meters; α and β are empirical coefficients obtained from linear fitting, in meters. 2 (m·s) / kg and (m·s) / kg; v p The velocity of the fluid inside the orifice is given in m / s; Cd t+Δt Cd t with cd max These represent the maximum flow coefficient at time t+Δt, time t, and time t, respectively.

[0132] From the above formula, the real-time perforation friction is:

[0133]

[0134] In the formula: Δppf For the frictional resistance of the orifice, Pa; Q i m is the displacement of crack cluster i. 3 / s; N is the number of perforations.

[0135] Discrete element simulation of the reservoir geological model updates the model's state in real time as the fracturing process progresses. The reaction force of hydraulic fracturing on the wall surface is calculated by traversing the grid nodes of the reservoir geological model and divided by the fracture opening area to obtain the hydraulic fracture closure pressure. Based on Kirchhoff's laws, a dynamic wellbore flow distribution model is established by coupling the hydraulic fracture closure pressure. The specific establishment process is as follows:

[0136] Taking the heel end as crack cluster 1 and the toe end as crack cluster 5 as an example, the overall flow equivalent pressure drop Δp of the i-th cluster is... i for:

[0137]

[0138] In the formula: Δp f,i For the perforation pressure drop of fracture cluster i, Pa; Δp pp,i Let be the pressure drop along the wellbore for fracture cluster i, k be the total number of fracture clusters, and i be the number of the fracture cluster, which takes a value in the range of 1 to k.

[0139] Δp is calculated based on the above formula. i Substituting these equations into equations (6) and (7), the formulas for equations (6) and (7) are:

[0140] r i =Δp i / q i (7)

[0141]

[0142] In the formula: q i Let m be the flow rate of crack cluster i. 3 / s;r t Pa is the equivalent frictional resistance.

[0143] The flow rate q of crack cluster i can then be obtained. i The calculation formula is shown in equation (8), which is the dynamic wellbore flow distribution model:

[0144]

[0145] In the formula: p cp,i Let be the closing pressure of crack cluster i, in Pa.

[0146] The step is solved iteratively using the Newton-Raphson iterative algorithm until the equation converges and a stable converged flow rate is obtained. The above model is then fully coupled and analyzed using discrete element hydraulic fracturing simulation. The closure pressure of a single cluster and the model status are monitored in real time. The degree of perforation erosion and the change of flow rate of a single cluster are quantitatively compared. The uniformity of flow distribution and the expansion morphology of multiple cluster fractures are also quantitatively evaluated using the coefficient of variation.

[0147] The specific steps are as follows: Select the constitutive model required for discrete element simulation, taking the Mohr-Coulomb strength criterion as an example:

[0148]

[0149] In the formula: T f For tensile strength, Pa; S f σ is the peak shear strength, Pa; c is the cohesion, Pa; σ n Normal stress, Pa; θ is the internal friction angle, °.

[0150] The fluid-structure interaction model in the discrete element method is as follows:

[0151]

[0152] In the formula: u h0 Let m be the initial aperture; Δu m is the change in opening, m; f is the correction factor; Q is the flow velocity, m 3 / s;u m ρ is the boundary distance, in meters; ρ is the fluid density, in kilograms per cubic meter of water. 3 g is the acceleration due to gravity, m / s² 2 μ is the fluid viscosity in Pa·s; K H The water head is measured in meters (m).

[0153] The detailed process of the discrete element method simulation of competitive propagation of multiple crack clusters is as follows: the flow rate of each cluster is preset to 3.2 m³ / s. 3 At a time step of [min], perform fluid-structure interaction (FSI) calculations to verify if the time has reached the sand-carrying fluid stage. If not, calculate the frictional resistance along the path and read the closing pressure of the open cracks. Substitute this into the flow distribution equation based on Kirchhoff's laws and iterate until the flow rates of each cluster converge. Update the flow parameters and perform FSI calculations for the next time step. Repeat the above steps until the sand-carrying fluid stage is reached. After reaching the sand-carrying fluid stage, update the orifice diameter and flow coefficient according to the previous time step, calculate the perforation friction and frictional resistance along the path, read the closing pressure, calculate the combined frictional resistance, substitute this into the flow distribution equation based on Kirchhoff's laws, iterate until the flow rates of each cluster converge, update the flow parameters, perform FSI calculations, and repeat the above steps until the simulation time is reached.

[0154] The simulation results are used to derive curves for orifice diameter, flow coefficient, and final flow rate variation. The coefficient of variation under different parameters is calculated using the following formula:

[0155]

[0156] In the formula, k is the number of crack clusters; n i Let x be the number of flow rate changes in crack cluster i. ij The flow rate values ​​of crack cluster i at different times are given.

[0157] By changing parameters, the flow distribution and fracture propagation morphology under different conditions are calculated for hydraulic fracturing simulation and optimization of engineering parameters, making them more consistent with actual engineering needs. (See reference...) Figures 2-6 As can be seen from the figure: the perforation radius increases non-linearly; in the pre-fracturing stage, as the fracturing process proceeds, the flow rate of each cluster tends to be evenly distributed; in the sand-carrying fluid stage, the fractures in each cluster change rapidly, and the dominant fractures become apparent; as the number of interlayers increases, the flow rate variation coefficient decreases significantly, and the fractures in each cluster tend to develop evenly.

Claims

1. A multi-cluster crack competition and propagation discrete element simulation method based on dynamic flow distribution, characterized in that, The method comprises the following steps: obtaining geological parameters of a target reservoir, rock mechanics parameters, wellbore parameters of a target well, engineering parameters in fracturing reconstruction, and fluid parameters of a fluid used; obtaining rheological characteristics of a power-law fluid according to the fluid parameters; and establishing a wellbore friction calculation model according to the rheological characteristics of the power-law fluid and the wellbore parameters and the engineering parameters; performing indoor simulation experiments according to the fluid parameters, the reservoir parameters, the wellbore parameters and the engineering parameters, and establishing a perforation hole erosion correction model; establishing a reservoir geological model according to the geological parameters of the target reservoir and the rock mechanics parameters; and establishing a dynamic wellbore flow distribution model according to the reservoir geological model and the Kirchhoff law, the wellbore friction calculation model, the perforation hole erosion correction model and the hydraulic fracture closure pressure; performing discrete element simulation on the dynamic wellbore flow distribution model to iteratively calculate hole diameter, flow coefficient and final flow variation curve, and obtain a variation coefficient. The wellbore friction calculation model is as follows: (3) where: Δp pp is the wellbore flow friction, Pa; p is the fluid density, kg / m 3 ; v is the flow velocity in the wellbore, m / s; D is the wellbore diameter, m; L is the spacing between clusters, m; K s is the pipe friction factor; f is the Darcy friction factor; A, B are the Darcy friction factor calculation parameters; K is the consistency factor, Pa-s n ; n is the flow regime factor; The perforation hole erosion correction model is as follows: (4) where: Δp pf is the perforation friction, Pa; Q i is the displacement corresponding to fracture cluster i, m 3 / s; N is the number of perforation holes, i is the number of fracture cluster; d t is the perforation hole diameter at time t, m; Cd t is the flow coefficient at time t; The dynamic wellbore flow distribution model is as follows: (6) where: p cp,i is the closure pressure of fracture cluster i, Pa; q i is the flow rate of fracture cluster i, m 3 / s; r t is the equivalent friction, Pa; k is the total number of fracture clusters; i is the number of fracture cluster, which is in the range of 1~k.

2. A multi-cluster crack competition and propagation discrete element method based on dynamic flow distribution according to claim 1, characterized in that, The variation coefficient CV is as follows: (1) where k is the number of fracture clusters; n i is the number of flow rate changes for fracture cluster i, x ij is the flow rate value for fracture cluster i at different times; j is the index of flow rate change.

3. The method of claim 1, wherein, The geological parameters include reservoir thickness, barrier thickness and bedding seam density; and the rock mechanics parameters include Poisson's ratio, Young's modulus, tangential stiffness, normal stiffness, cohesion, internal friction angle, tensile strength, maximum horizontal principal stress, minimum horizontal principal stress and vertical stress. The engineering parameters include cluster number, cluster spacing, perforation number, hole diameter, initial hole flow coefficient, maximum hole flow coefficient and displacement. The fluid parameters include concentration, viscosity, density, bulk modulus and shear rate. The wellbore parameters include wellbore diameter.

4. The method of claim 3, wherein, The rheological characteristics of the power-law fluid include flow pattern coefficient and consistency coefficient, which are obtained by fitting shear rate and viscosity. The shear rate and viscosity fitting equation is as follows: (2) wherein: η is the viscosity, Pa-s; K is the consistency coefficient, Pa-s n ; γ is the shear rate, s -1 ; n is the flow behavior index.

5. The method of claim 4, wherein, The indoor simulation experiments are performed according to the fluid parameters, the reservoir parameters, the wellbore parameters and the engineering parameters to establish the perforation hole erosion correction model, which comprises the following steps: The indoor simulation experiments are performed according to the concentration of the proppant and the reservoir parameters, the wellbore parameters and the engineering parameters, and the concentration and injection speed and time of the injected proppant are adjusted to simulate the influence of the concentration, injection speed and time of the proppant on the degree of hole erosion, so as to obtain data of different proppant injection speeds and times and corresponding perforation hole diameters, perform linear relationship fitting, and obtain perforation erosion parameters, and the fitting relationship is as shown in equation (5): (5) wherein: d t+Δt and d t are the perforation hole diameters at time t+Δt and time t, respectively, in meters; and α and β are empirical coefficients obtained from linear fitting, (m 2 (m·s) / kg and (m·s) / kg; v p is the flow rate of the fluid in the hole, in meters per second; and Cd t+Δt , Cd t , and Cd max are the flow coefficients at time t+Δt, time t, and the maximum flow coefficient, respectively; and C is the proppant concentration, in kilograms per meter 3 ; The equation of real-time perforation friction obtained according to equation (5) is the perforation hole erosion correction model.

6. The method of claim 5, wherein, The dynamic wellbore flow distribution model is established as follows: Let Δp be the total flow equivalent pressure drop of the i-th cluster of fractures i is: (7) where: Δp f,i is the perforation pressure drop for fracture cluster i, Pa; Δp pp,i is the wellbore along the pressure drop for fracture cluster i, k is the total number of fracture clusters, i is the number of fracture cluster, which is in the range of 1 ~ k. Δp calculated according to the above formula i and the following equations (8) and (9) are obtained: （8） （9） where: q i is the flow rate of the fracture cluster i, m 3 / s; r t is the equivalent friction, Pa; The fracture cluster i flow rate q is obtained i The calculation formula of the fracture cluster i flow rate q is as follows, that is, a dynamic wellbore flow rate distribution model.

7. A method for quantitative evaluation of engineering parameters for hydraulic fracturing, characterized by The multi-cluster fracture competition and expansion discrete element simulation method according to any one of claims 1-6 is used to obtain the expansion morphology and flow distribution of the multi-cluster fractures under different engineering parameter conditions, and the corresponding engineering parameters are evaluated according to the obtained expansion morphology and flow distribution of the multi-cluster fractures.

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