Method for regulating and controlling laying form of multi-cluster crack proppant

Abstract

The invention discloses a method for regulating and controlling the laying form of a multi-cluster crack proppant. The method comprises the steps that basic parameters needed by calculation are collected; a double-layer model is used as a research basis, and a competitive crack initiation expansion process of multiple clusters of cracks is simulated based on a displacement discontinuity method; obtaining intermediate data based on simulation, and calculating propping agent migration and a sand embankment profile by using the intermediate data to obtain crack propagation and propping agent laying conditions of each cluster of cracks; and adjusting construction parameters or material parameters, and optimizing the paving condition of the proppant. According to the method, the migration of the proppant and the profile of the sand bank are calculated by utilizing intermediate data such as dynamic fracture geometric parameters and sand transportation time, and the fracture propagation and proppant laying conditions are obtained. According to the method for regulating and controlling the laying form of the multi-cluster fracture proppant, the distribution of the proppant in the fracture can be optimized, and the fracturing yield increasing effect is improved.

Description

Technical Field

[0001] The invention relates to the field of petroleum and natural gas engineering, and in particular to a method for regulating the paving morphology of multi-cluster fracture proppants. Background Art

[0002] Unconventional oil and gas reservoirs have poor rock properties and fluidity, strong geological heterogeneity, and many layers, making it difficult for conventional production stimulation measures to achieve ideal results. In order to achieve economical and effective development, the industry generally adopts segmented multi-cluster fracturing transformation methods to effectively reduce seepage resistance and increase transformation volume, thereby maximizing the potential of the reservoir.

[0003] The purpose of staged multi-cluster fracturing is to create multiple stable sand-filled flow channels with high conductivity. However, microseismic and fiber optic monitoring results reveal the heterogeneity of the multi-cluster perforation process, which leads to "over-reformation" of some perforation clusters and "under-reformation" of others. This heterogeneity results in the inadequately sanded oil and gas clusters contributing little to the production capacity, severely limiting the degree of oil and gas production in the geological sweet spot area, and significantly affecting the overall effect of fracturing. Therefore, in-depth research on the proppant migration mechanism under complex fracture propagation conditions is crucial to optimize the transportation and placement of proppant in multi-cluster fractures.

[0004] The researchers studied the placement morphology of proppants in fractures through experiments and numerical simulations. Sand-laying experiments can truly reflect the morphology of sand banks, but existing experimental research methods are usually based on pre-set fracture dimensions and fail to fully consider the impact of the dynamic expansion process of fractures on proppant migration and placement. In addition, the scale limitations and size effects of indoor experiments also limit their ability to reflect the morphology of fractures and sand banks in real formation environments.

[0005] The existing fracture propagation model mainly simulates the fracture propagation behavior in the pre-fluid stage, but the sand-carrying fluid stage may account for more than 75% of the entire construction time. The impact of sand bank accumulation on the flow profile in the fracture during this stage cannot be ignored. The EL method can accurately simulate and track the movement mechanism of particle micro-elements in the fluid, which is more in line with the actual situation of solid-liquid flow, but its high computational cost limits its application in large-scale field conditions. In contrast, the EE method has a lower computational cost and is more flexible when coupled with the fracture model, but this method ignores the interaction between particles and does not consider the bed formation mechanism of proppant sedimentation and accumulation, which may lead to deviations in prediction results in practical applications. Summary of the invention

[0006] The present invention provides a method for regulating the paving morphology of multiple clusters of fracture proppants, characterized in that it comprises the following steps:

[0007] Collect basic parameters required for calculation;

[0008] Based on the double-layer model, the competitive initiation and propagation process of multiple clusters of cracks is simulated based on the displacement discontinuity method.

[0009] Based on the simulation, intermediate data are obtained, and the proppant migration and sand bank profile are calculated using the intermediate data to obtain the crack extension and proppant placement of each cluster of cracks;

[0010] Adjust construction parameters or material parameters to optimize proppant placement.

[0011] Furthermore, the basic parameters include geological parameters, construction parameters, and material parameters.

[0012] Furthermore, based on the double-layer model, the competitive initiation and propagation process of multiple clusters of cracks is simulated based on the displacement discontinuity method, which also includes:

[0013] The displacement discontinuity method is used to calculate the induced stress component at any point in the formation, and the fracture extension stress field is obtained by superimposing it with the ground stress field and the friction pressure. According to Kirchhoff's law, the dynamic distribution of flow in the process of initiation and extension of multiple fracture clusters, the extension of the first fracture initiation perforation cluster and the fracture induced stress are coupled to obtain the flow and pressure distribution of each fracture cluster. Combined with the fracture extension criterion, the fracture width and length variation equation, the fracture extension stress field and the flow pressure distribution, simulation is carried out to obtain the expansion of each fracture cluster in the pre-fluid stage.

[0014] Furthermore, the intermediate data include dynamic fracture geometry parameters, sand transport time and flow distribution data.

[0015] Furthermore, the intermediate data is used to calculate proppant migration and sand bank profiles to obtain the fracture propagation and proppant placement of each cluster of fractures, including:

[0016] The fracture parameters formed in the pre-fluid stage are embedded, and the horizontal flow velocity of the fracture is derived using the principle of material balance. Based on the double-layer model of proppant laying, the sand transport boundary conditions are set, the proppant volume concentration diffusion equation is solved, and calculations are carried out for the proppant concentration, bed accumulation rate, scouring rate, and bed accumulation volume in the grid. The height of the sand bank in the grid is updated in real time to maintain dynamic balance.

[0017] The present invention has the following advantages: The present invention provides a method for regulating the proppant paving morphology of multiple clusters of fractures. The method uses a double-layer model as a research basis, simulates the competitive cracking and expansion process of multiple clusters of fractures based on the displacement discontinuity method, and uses intermediate data such as dynamic fracture geometric parameters, sand delivery time and flow distribution to calculate proppant migration and sand bank profiles, thereby obtaining the crack expansion and proppant paving conditions of each cluster of fractures. The method for regulating the proppant paving morphology of multiple clusters of fractures provided by the present invention can optimize the proppant distribution in the fractures and improve the fracturing production increase effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of crack boundary discretization and coordinate transformation in an embodiment of the present invention.

[0019] Figure 2 It is a schematic diagram of the formation of a sand bank profile in a variable seam width environment in an embodiment of the present invention.

[0020] Figure 3 Schematic diagram of the length and width of each cluster of cracks at different crack spacings in the embodiment of the present invention.

[0021] Figure 4 The cross-sectional morphology of each cluster of sandbanks at different crack spacings in the embodiment of the present invention.

[0022] Figure 5 Schematic diagram of the length and width of each cluster of seams at different displacements in the embodiment of the present invention.

[0023] Figure 6 The cross-sectional morphology of each cluster of sand banks at different displacements in the embodiment of the present invention.

[0024] Figure 7 1 and 2 show the length and width of each cluster of slits at different viscosities in the embodiment of the present invention.

[0025] Figure 8 The cross-sectional morphology of each cluster of sand banks at different viscosities in the embodiment of the present invention. DETAILED DESCRIPTION

[0026] The details of the present invention can be more clearly understood by combining the accompanying drawings and the description of the specific embodiments of the present invention. However, the specific embodiments of the present invention described herein are only used for the purpose of explaining the present invention and cannot be construed as limiting the present invention in any way. Under the guidance of the present invention, technicians can conceive of any possible variations based on the present invention, which should all be considered to belong to the scope of the present invention.

[0027] The present invention proposes a method for regulating the paving morphology of multiple clusters of fracture proppants, the method comprising the following steps:

[0028] 1. Collect the basic parameters required for calculation, including geological parameters, construction parameters, and material parameters.

[0029] 2. Based on the double-layer model, the competitive initiation and propagation process of multiple clusters of cracks is simulated based on the displacement discontinuity method:

[0030] Figure 1-2 The diagrams are respectively the schematic diagram of the fracture boundary discretization and coordinate transformation and the schematic diagram of the sand bank profile formation in the variable fracture width environment. The net pressure inside the fracture is Effects, such as Figure 2As shown in the figure, the crack is discretized into N boundary units, and each unit is approximately replaced by a straight line segment instead of a curved boundary. Then the known boundary condition of any unit i can be written as:

[0031]

[0032] The shear stress and normal stress at the midpoint of element i can be calculated from the displacement discontinuity of element j:

[0033]

[0034] Where:

[0035] ——Factors affecting stress boundary, among which Respectively represent the unit tangential constant displacement discontinuity on element j The corresponding shear force and normal force at the midpoint of element i;

[0036] ——discontinuity with the unit normal constant displacement on element j The corresponding shear force and normal force at the midpoint of element i.

[0037] Combining the local and global relationships, the stress component expression is transformed into the local coordinate system of element i, and the expression of the stress boundary influence coefficient can be obtained as follows:

[0038]

[0039] Where:

[0040] v——Poisson’s ratio, dimensionless;

[0041] G——shear modulus, MPa;

[0042] f(x,y)——Simulation function related only to unit coordinates. The subscript f represents its derivatives with respect to x and y, and a represents the half-length of the crack unit.

[0043] When the cracks extend in a non-planar manner, the crack extension is affected by both type I and type II failure of the rock mass. The maximum circumferential stress criterion is:

[0044]

[0045] Where:

[0046] K IC - fracture toughness of rock,

[0047] K Ⅰ and K Ⅱ It can be obtained based on the normal and tangential displacement discontinuities at the crack end:

[0048]

[0049] The circumferential stress refers to the force that closes the crack during the crack extension process, that is, the superposition of the original stress and the induced stress. According to the rectangular coordinate system established previously, the stress component in the y direction at a point i around the artificial crack can be converted into:

[0050]

[0051]

[0052] Where:

[0053] G ij ——three-dimensional correction factor, dimensionless;

[0054] d ij ——the distance between crack units i and j, mm;

[0055] H f，ji ——crack height, mm;

[0056] H bed ——Height of proppant sand bank bed, m;

[0057] ε, η——empirical coefficients, usually ε=1, η=2.3;

[0058] σ h ——minimum horizontal principal stress, MPa;

[0059] ν——Poisson’s ratio of reservoir rock, dimensionless;

[0060] α——Biot poroelastic coefficient, dimensionless;

[0061] p p ——Current formation pressure, MPa;

[0062] p e ——Original formation pressure, MPa.

[0063] The extended length equation is:

[0064]

[0065] The expansion width equation is:

[0066]

[0067] Where:

[0068] E——elastic modulus of rock, MPa;

[0069] m——intermediate variable, dimensionless.

[0070] Based on Kirchoff's first law, the volume of injected liquid is equal to the sum of the volumes of the liquids in each cluster:

[0071]

[0072] Based on Kirchoff's second law, the crack mouth pressure is equal to the sum of the pressure loss in each cluster of extended cracks and the circumferential stress at the crack tip:

[0073]

[0074] Where:

[0075] p O ——Fluid pressure at the main fracture end, MPa;

[0076] Δp f,ji ——The crack pressure drop at the jth stage when the crack expands to the i-th stage, MPa;

[0077] σ β,i ——Circumferential stress when the new crack expands to the i-th section, MPa.

[0078] The friction pressure drop formula is:

[0079]

[0080]

[0081] Where:

[0082] n——Fracturing fluid flow index, dimensionless, generally taken as 0.5;

[0083] ΔL f,ji ——The length of the jth section when the straight seam is extended to the ith section, m;

[0084] w f,ji ——The average crack width of the jth section when the straight crack expands to the ith section, m;

[0085] H f ——straight seam height, m;

[0086] K f ——Power-law fracturing fluid viscosity coefficient of fluid in fracture, Pa·s n ;

[0087] K——Fracturing fluid viscosity coefficient measured in the laboratory, Pa·s n , generally taken as 0.7.

[0088] 3. Use the intermediate data to calculate the proppant migration and sand bank profile to obtain the crack extension and proppant placement of each cluster of cracks. The intermediate data includes dynamic crack geometry parameters, sand transport time and flow distribution:

[0089] In order to calculate the movement of proppant particles, the flow field parameters need to be determined. The fracture extension results are embedded as the input and modeling parameters for proppant migration simulation, without considering the effects of fracture trajectory, wall roughness, etc. on proppant migration. Based on the material balance principle, the horizontal flow velocity of the sand-carrying fluid is obtained as:

[0090]

[0091] Where:

[0092] μ——liquid viscosity, Pa·s;

[0093] P——fluid pressure in the crack, MPa;

[0094] Based on the Stokes equation, the settling velocity of the proppant in the fluid is obtained as:

[0095]

[0096] Where:

[0097] v ps ——proppant settling velocity, m / s;

[0098] ρ p ——Proppant density, kg / m 3 ;

[0099] ρ f ——Fluid density, kg / m 3 ;

[0100] D——proppant diameter, m;

[0101] g——acceleration due to gravity, m / s 2 ;

[0102] C is the proppant volume concentration, dimensionless;

[0103] Assuming that the fracture sand injection is linear sand injection, the sand is evenly spread in the width direction, the horizontal diffusion velocity is replaced by the liquid flow rate, and the single-phase internal force and the sudden change of the flow field in the fracture are ignored, the proppant volume concentration diffusion equation is:

[0104]

[0105] Where:

[0106] v p ——Particle velocity, m / s.

[0107] A dimensionality reduction strategy is adopted, and meshing is performed only in the horizontal direction based on the boundary element fracture propagation simulation results. According to the double-layer model bed accumulation theory, the bed volume change in the grid at time t is determined by the fracture geometry parameters, accumulation rate, and scouring rate of the previous time step. The specific calculation process is as follows:

[0108]

[0109] Where: dH b / dt is the bed accumulation rate, dH w / dt is the bed flushing rate, and the calculation formula is as follows:

[0110]

[0111]

[0112] Where: K 1 is the comprehensive experimental factor, dimensionless;

[0113] f——friction coefficient, dimensionless;

[0114] ρ upper ——Density of the upper fluid, kg / m 3 ;

[0115] v upper ——Velocity of the upper fluid, m / s.

[0116] The friction coefficient f can be obtained by the following formula:

[0117]

[0118] Where:

[0119] Re is the upper layer Reynolds number, dimensionless;

[0120] D h is the hydraulic diameter of the upper layer, m.

[0121] In this paper, the hydraulic diameter D h It can be obtained through the following methods:

[0122]

[0123] In addition, the density of the upper fluid ρ upper The calculation formula of Reynolds number Re is as follows:

[0124]

[0125] Since the proppant will continue the bed state after settling to form a sand bank, considering the proppant mass balance, the upper proppant concentration needs to be updated at each time step. The calculation method is as follows:

[0126]

[0127] At the same time, the current bed height is also updated to:

[0128]

[0129] 4. Adjust construction parameters or material parameters to optimize proppant placement.

[0130] By adjusting construction parameters, such as displacement and other parameters, and adjusting material parameters, such as proppant and fracturing fluid parameters, the above method can be used to obtain the proppant laying conditions under different working conditions, thereby optimizing and obtaining relevant parameters that can promote the fracturing effect.

[0131] Computational Examples and Analysis

[0132] (1) Basic parameters

[0133] Table 1 Calculation basic parameters

[0134]

[0135] (2) Calculation results of working conditions

[0136] The calculation was performed according to the basic parameters in Table 1. The calculation results are as follows Figure 3-Figure 8 shown.

[0137] like Figure 3 , Figure 4 As shown in the figure, when the fracture spacing is 6m, the fracture competition expansion is obvious, and the unevenness of sand bank accumulation is aggravated. The fracture lengths of the 2nd and 5th clusters and the 3rd and 4th clusters are 86.05m and 37.45m respectively, and the positions of the sand bank crests are 17.21m and 3.02m respectively. The difference in the length of the expansion fracture is 48.6m, and the difference in the position of the crest is 14.19m. As the fracture spacing increases to 25m, the difference in the length of the expansion fracture between the 2nd and 5th clusters and the 3rd and 4th clusters is only 6.09m, and the difference in the crest distance is also shortened to 3.55m. The liquid inflow of each cluster of fractures is different under the three fracture spacings. The middle cluster is disturbed by stress, and the distribution flow is small. The ability of the sand bank to migrate deep into the fracture is weakened, and the crest position is closer to the fracture mouth. However, the laying height of the sand bank of each cluster of fractures is not much different, indicating that the fracture spacing has limited influence on the sedimentation of proppant particles. When the stress interference caused by the fracture spacing is large, the unevenness of the sand bank laying will be aggravated.

[0138] like Figure 5 , Figure 6 As shown, when the displacement is 12m 3 / min, the extension length of the second and fifth clusters of cracks reached 68.48m, the maximum crack width was 1.73mm, the maximum sand transport distance was 44.4m, and the position of the sand bank crest was 6.54m; when the displacement increased to 20m 3 / min, the extension length of the 2nd and 5th clusters of cracks increased to 86.71m, the maximum crack width became 2.41mm, the maximum sand transport distance could reach 58.82m, and the farthest position of the sand bank crest reached 19.16m. As the displacement gradually increased, the flow rate allocated to each cluster increased, and the net pressure in the cracks continued to increase, which increased the length and width of the reformed cracks. At the same time, the horizontal force on the single particle became stronger, and the proppant particles were further carried to the depth of the cracks and settled. The settled sand bank was also more susceptible to shearing and was more likely to migrate to the depth of the cracks as a whole.

[0139] like Figure 7 , Figure 8 As shown in the figure, when the viscosity is 3mPa·s, the extension length of the second and fifth clusters of cracks reaches 82.96m, the maximum crack width is 2.18mm, the sand transport distance is up to 58.82m, and the position of the sand bank crest is 12.2m; when the viscosity increases to 10mPa·s, the extension length of the second and fifth clusters of cracks increases to 86.48m, the maximum crack width becomes 3.03mm, the sand transport distance is up to 84.92m, and the position of the sand bank crest is up to 69.03m. As the viscosity gradually increases, the filtration volume decreases, and the energy used to support the expansion of the cracks is more sufficient, so that the extension length of each cluster of hydraulic fractures is longer and the width is wider. Viscosity has a great influence on the sand-carrying performance of fracturing fluid. In the movement of proppant particle suspension, particles in low-viscosity fluid settle quickly and have a short transportation distance, while particles in high-viscosity fluid settle slowly and have a long transportation distance. As a result, when the viscosity is low, sand dams are easily accumulated at the crack mouth, and the distal cracks have no support. When the viscosity is further increased, most of the particles are suspended in the fracturing fluid, the sedimentation volume of the sand dam is reduced, and the extended cracks are almost fully supported. In the movement of sand dam bedload, high-viscosity fluids exert greater shear force than low-viscosity fluids, and the sand dam as a whole is more easily carried to the depths of the crack, with the wave crest position further away from the crack mouth.

[0140] The present invention is specifically described above through the embodiments. It is necessary to point out that the embodiments are only preferred embodiments of the present invention, and do not limit the present invention in any way, nor are they limited to the forms disclosed herein, and should not be regarded as excluding other embodiments. The modifications and simple changes made by those skilled in the art do not deviate from the technical idea and scope of the present invention, and all belong to the protection scope of the technical solution of the present invention.

Claims

1. A method for regulating the paving morphology of multi-cluster fracture proppants, characterized in that: The following steps are involved: Collect basic parameters required for calculation; Based on the double-layer model, the competitive initiation and propagation process of multiple clusters of cracks is simulated based on the displacement discontinuity method. Based on the simulation, intermediate data are obtained, and the proppant migration and sand bank profile are calculated using the intermediate data to obtain the crack extension and proppant placement of each cluster of cracks; Adjust construction parameters or material parameters to optimize proppant placement.

2. The method for controlling the paving morphology of multi-cluster fracture proppants according to claim 1, characterized in that: Furthermore, the basic parameters include geological parameters, construction parameters, and material parameters.

3. The method for controlling the paving morphology of multi-cluster fracture proppants according to claim 1, characterized in that: Based on the double-layer model, the competitive initiation and propagation process of multiple clusters of cracks is simulated based on the displacement discontinuity method, which also includes: The displacement discontinuity method is used to calculate the induced stress component at any point in the formation, and the fracture extension stress field is obtained by superimposing it with the ground stress field and the friction pressure. According to Kirchhoff's law, the dynamic distribution of flow in the process of initiation and extension of multiple fracture clusters, the extension of the first fracture initiation perforation cluster and the fracture induced stress are coupled to obtain the flow and pressure distribution of each fracture cluster. Combined with the fracture extension criterion, the fracture width and length variation equation, the fracture extension stress field and the flow pressure distribution, simulation is carried out to obtain the expansion of each fracture cluster in the pre-fluid stage.

4. The method for controlling the placement morphology of multi-cluster fracture proppants according to claim 1, characterized in that: The intermediate data include dynamic fracture geometry parameters, sand transport time and flow distribution data.

5. The method for controlling the placement morphology of multi-cluster fracture proppants according to claim 1, characterized in that: The intermediate data is used to calculate proppant migration and sand bank profiles, and the fracture propagation and proppant placement of each fracture cluster are obtained, including: The fracture parameters formed in the pre-fluid stage are embedded, and the horizontal flow velocity of the fracture is derived using the principle of material balance. Based on the double-layer model of proppant laying, the sand transport boundary conditions are set, the proppant volume concentration diffusion equation is solved, and calculations are carried out for the proppant concentration, bed accumulation rate, scouring rate, and bed accumulation volume in the grid. The height of the sand bank in the grid is updated in real time to maintain dynamic balance.

Images