A method for judging the in-seam migration similarity of a proppant

Abstract

The application discloses a support agent seam internal migration similarity judgment method, comprising the following steps: obtaining a plane similarity ratio according to the length and height of an actual flow field fracture and the fracture length and fracture height of a simulation flow field fracture; calculating a support agent single particle settling velocity, a concentration correction coefficient and a wall correction coefficient; obtaining particle settling velocities of the actual flow field and the simulation flow field; calculating particle moving velocities and horizontal moving velocities of the actual flow field and the simulation flow field; obtaining a settling velocity similarity ratio; obtaining migration similarity ratios, fluid Reynolds number similarity ratios, particle Reynolds number similarity ratios and particle Froude number similarity ratios of the actual flow field and the simulation flow field; judging whether the plane similarity ratio, the settling velocity similarity ratio, the migration similarity ratio, the fluid Reynolds number similarity ratio, the particle Reynolds number similarity ratio and the particle Froude number similarity ratio of the actual flow field and the simulation flow field are located between 0.9 and 1.1, and if yes, the actual flow field and the simulation flow field are completely similar.

Description

Technical Field

[0001] This application relates to the field of proppant sedimentation and transport technology, and in particular to a method for judging the similarity of proppant intra-slit transport. Background Technology

[0002] Hydraulic fracturing is a crucial technology for unconventional resource extraction. It involves rapidly injecting pre-fracturing fluid into the wellbore, creating high pressure at the bottom. When this pressure exceeds the formation fracturing pressure, the formation is forced open, forming a symmetrical fracture. Subsequent pumping of proppant-laden fluid closes the fracture on the proppant, creating a highly conductive channel for oil and gas flow. Finally, displacement fluid is pumped in, forcing the proppant-laden fluid into the formation. However, the underground conditions are invisible and intangible; accurately understanding how the proppant migrates within the fractured surface and the shape of the resulting sand embankment is difficult.

[0003] The similarity criterion is the only key point that combines physical model experiments with on-site construction conditions. By using the similarity criterion, on-site construction parameters are converted into physical model experimental parameters, allowing the experimental results to directly reflect the on-site construction effects. The on-site construction effects are then evaluated and optimized, and the optimized physical model experimental parameters are converted back into on-site construction parameters using the similarity criterion to guide subsequent fracturing operations.

[0004] However, most scholars skipped the similarity part when conducting proppant sedimentation and transport experiments and went directly to the subsequent experiments. Although the experimental results had some guiding significance for the field, the supporting evidence was insufficient. Or, some scholars considered this aspect but only made a simple point of it without implementing it in practice.

[0005] To address this issue, this patent proposes a novel similarity criterion and a specific similarity method. The similarity criterion proposed in this patent is simple and easy to implement, and can effectively combine physical model experiments with on-site construction results. Summary of the Invention

[0006] This application provides a method for judging the similarity of proppant migration within joints, in order to address the weakness in the study of the similarity between proppant settlement and migration model experiments and field construction effects.

[0007] The technical solution adopted in this application is as follows:

[0008] This invention discloses a method for determining the similarity of proppant intra-slit transport, comprising:

[0009] The surface similarity ratio is obtained by comparing the length and height of the crack in the actual flow field with the crack length and height in the simulated flow field.

[0010] Calculate the settling velocity of a single proppant particle, the concentration correction factor, and the wall correction factor;

[0011] The particle settling velocities of the actual and simulated flow fields are obtained based on the single particle settling velocity, concentration correction factor, and wall correction factor.

[0012] Calculate the particle moving velocity and horizontal moving velocity in the actual flow field and the simulated flow field;

[0013] Based on the particle moving velocity, particle settling velocity, and horizontal moving velocity of the actual flow field and the simulated flow field, obtain the similarity ratio of settling velocity;

[0014] Obtain the transport similarity ratio, fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number similarity ratio of the actual flow field and the simulated flow field;

[0015] Determine whether the surface similarity ratio, settling velocity similarity ratio, transport similarity ratio, fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number similarity ratio of the actual flow field and the simulated flow field are between 0.9 and 1.1. If they are, then the actual flow field and the simulated flow field are completely similar.

[0016] Furthermore, surface similarity refers to the fact that the length and height of the cracks in the actual flow field and the simulated flow field are proportional, and the proportionality coefficient is the same. The formula for calculating the surface similarity ratio is:

[0017]

[0018] Wherein, L1 and H1 are the length and height of the actual flow field crack, in meters; L2 and H2 are the length and height of the simulated flow field crack, in meters.

[0019] Furthermore, the formula for calculating the concentration correction factor is as follows:

[0020]

[0021] Where: C is the sand ratio, %;

[0022] The proppant ratio, also known as the surface proppant ratio, refers to the ratio of the volume of proppant to the volume of fracturing fluid.

[0023] The formula for calculating the wall correction coefficient is:

[0024]

[0025] Where: d p is the proppant particle size, m; w is the crack width, m;

[0026] The formula for calculating the settling velocity of a single particle is:

[0027] When N Re When ≤2:

[0028]

[0029] When 2≤N Re <500 hours:

[0030]

[0031] When N Re When ≥500:

[0032]

[0033] Where, N Re ρ is the particle Reynolds number. p ρ l These are the proppant density and fracturing fluid density, respectively, in kg / m³. 3 d is the proppant particle size, in meters; μ is the fracturing fluid viscosity, in Pa·s; g is the gravitational acceleration, in m / s². 2 ;

[0034] The formula for calculating the particle Reynolds number is as follows:

[0035]

[0036] Where: V is the particle velocity, m / s, V L This represents the horizontal velocity of the particle.

[0037] Furthermore, the settling velocity of particles in the actual flow field crack is calculated using the same method as that in the simulated flow field. The formula for calculating the settling velocity of particles in the actual flow field crack is as follows:

[0038] V zs1 =V s1 ·f C1 ·h w1

[0039] Where: V s1 The velocity of a single particle in the actual flow field crack is denoted as m / s.

[0040] Furthermore, the calculation method for the particle velocity in the actual flow field crack is the same as that for the particle velocity in the simulated flow field crack. The formula for calculating the particle velocity in the actual flow field crack is as follows:

[0041]

[0042] Among them, V L1 V represents the horizontal velocity of the particles in the crack of the actual flow field. zs1 This represents the settling velocity of particles in the crack within the actual flow field.

[0043] Furthermore, the horizontal movement velocity V of particles in the actual flow field crack L1 Equal to the horizontal speed of the fluid;

[0044] The horizontal velocity V of particles in the simulated flow field L2 It equals the horizontal speed of the fluid.

[0045] Furthermore, the formula for calculating the similarity ratio of settlement velocities is:

[0046]

[0047] Among them: V1, V zs1 V L1 V2, V3 represent the moving velocity, settling velocity, and horizontal moving velocity of particles in the actual flow field crack, in m / s; zs2 V L2 To simulate the moving velocity, settling velocity, and horizontal moving velocity of particles in the flow field crack, m / s.

[0048] Furthermore, transport similarity refers to the fact that in both actual and simulated flow fields, the ratio of the time required for a particle to move one unit distance horizontally to the time required to move one unit distance vertically is equal. The formula for calculating transport similarity is:

[0049]

[0050] Among them, T L1 T s1 These represent the horizontal transport time and settling time of particles in the cracks of the actual flow field, in seconds; T L2 T s2 L1 and H1 represent the horizontal transport and settling times of particles in the simulated flow field crack, respectively, in seconds; L1 and H1 represent the length and height of the actual flow field crack, respectively, in meters; L2 and H2 represent the length and height of the actual flow field crack, respectively, in meters; V zs1 V L1 These represent the actual settling velocity and horizontal movement velocity of particles in the crack of the actual flow field, respectively, in m / s; V zs2 V L2 These represent the actual settling velocity and horizontal movement velocity of particles in the simulated flow field crack, respectively, in m / s;

[0051] The equality of fluid Reynolds numbers refers to the fact that the Reynolds numbers generated by the horizontal movement of fluids in two flow fields are equal. The formula for calculating the equality of fluid Reynolds numbers is as follows:

[0052]

[0053] Where ρ1 and ρ2 are the fracturing fluid densities in the actual and simulated flow fields, respectively, in kg / m³. 3 V L1 V L2μ1 and μ2 are the horizontal fluid transport velocities in the actual and simulated flow fields, respectively, in m / s; μ1 and μ2 are the fracturing fluid viscosities in the actual and simulated flow fields, respectively, in Pa·s.

[0054] The equality of particle Reynolds numbers refers to the fact that the Reynolds numbers generated by particles under the traction of the fluid in two flow fields are equal. The formula for calculating the equality of particle Reynolds numbers is as follows:

[0055]

[0056] Where V1 and V2 are the particle velocities in the actual and simulated flow fields, respectively, in m / s; d1 and d2 are the proppant particle diameters in the actual and simulated flow fields, respectively, in m.

[0057] The equality of particle Froude numbers refers to the fact that the Froude numbers generated by particles under the influence of gravity in two flow fields are equal. The formula for calculating the equality of particle Froude numbers is as follows:

[0058]

[0059] Where g is the acceleration due to gravity, m / s² 2 V1 is the velocity of the particles moving in the crack in the actual flow field, m / s; V2 is the velocity of the particles moving in the crack in the simulated flow field, m / s.

[0060] Furthermore, the formulas relating the particle movement velocity, settling velocity, and horizontal movement velocity in the cracks of both the actual and simulated flow fields to the crack width ratio are as follows:

[0061]

[0062]

[0063]

[0064] Where 'a' represents the ratio of the crack width in the actual flow field to the crack width in the simulated flow field.

[0065] Furthermore, if not, the experimental parameters of the simulated flow field are fine-tuned based on the known construction parameters of the actual flow field, or the construction parameters of the actual flow field are fine-tuned based on the known experimental parameters of the simulated flow field, until the ratio of each parameter in the similarity result is between 0.9 and 1.1.

[0066] The construction parameters include: crack length and height, sand ratio, crack width, single particle settling velocity, particle horizontal movement velocity, particle settling velocity, fracturing fluid density, fluid horizontal migration velocity, proppant particle size, and gravitational acceleration.

[0067] The beneficial effects of adopting the technical solution of this application are as follows:

[0068] This invention provides a method for determining the similarity of proppant transport within joints, linking geometric similarity, kinematic similarity, and dynamic similarity. These are no longer isolated entities but rather a novel whole encompassing the similarity between proppant model experiments and on-site construction. Furthermore, this invention introduces concentration correction coefficients and wall surface correction coefficients, making the similarity results more accurate and reliable.

[0069] This invention provides a complete procedure for determining flow field similarity in the future, which is of great significance for subsequent proppant transport experiments. Detailed Implementation

[0070] The embodiments will now be described in detail. The implementations described in the following embodiments do not represent all implementations consistent with this application. They are merely examples of systems and methods consistent with some aspects of this application as detailed in the claims.

[0071] To address the weakness in research on the similarity between proppant settlement and transport model experiments and field construction results, this invention proposes a proppant settlement and transport similarity criterion applicable to all situations, along with specific methods for ensuring similarity between model experiments and field conditions. Details are as follows:

[0072] This application provides a method for determining the similarity of proppant intra-suture transport, including:

[0073] S01: Obtain the surface similarity ratio based on the length and height of the crack in the actual flow field and the crack length and height in the simulated flow field.

[0074] Surface similarity refers to the fact that the length and height of the cracks in the actual flow field and the simulated flow field are proportional, and the proportionality coefficient is the same. The formula for calculating the surface similarity ratio is:

[0075]

[0076] Wherein, L1 and H1 are the length and height of the actual flow field crack, in meters; L2 and H2 are the length and height of the simulated flow field crack, in meters.

[0077] S02: Calculate the settling velocity of a single proppant particle, the concentration correction factor, and the wall correction factor.

[0078] The formula for calculating the concentration correction factor is:

[0079]

[0080] Where: C is the sand ratio, %;

[0081] The proppant ratio, also known as the surface proppant ratio, refers to the ratio of the volume of proppant to the volume of fracturing fluid.

[0082] The formula for calculating the wall correction coefficient is:

[0083]

[0084] Where: d p is the proppant particle size, m; w is the crack width, m;

[0085] The formula for calculating the settling velocity of a single particle is as follows: Assuming a particle Reynolds number range, calculate the settling velocity of a single particle using the fracturing fluid viscosity, gravitational acceleration, proppant density, and fracturing fluid density. Calculate the particle migration velocity using the particle movement velocity and the horizontal movement velocity of particles in the fracture. Calculate the particle Reynolds number. If the particle Reynolds number is within the assumed particle Reynolds number range, the calculated particle settling velocity is true; otherwise, repeat the above steps until the above conditions are met.

[0086] The revised particle settling velocity (Novoteni settling) is as follows:

[0087] When N Re When ≤2:

[0088]

[0089] When 2 < N Re <500 hours:

[0090]

[0091] When N Re When ≥500:

[0092]

[0093] Where, N Re ρ is the particle Reynolds number. p ρ l These are the proppant density and fracturing fluid density, respectively, in kg / m³. 3 d is the proppant particle size, in meters; μ is the fracturing fluid viscosity, in Pa·s; g is the gravitational acceleration, in m / s². 2 ;

[0094] The formula for calculating the particle Reynolds number is as follows:

[0095]

[0096] Where: V is the particle velocity, m / s, V L This represents the horizontal velocity of the particle.

[0097] S03: Obtain the particle settling velocity of the actual flow field and the simulated flow field based on the single particle settling velocity, concentration correction factor and wall correction factor.

[0098] The settling velocity of particles in the actual flow field crack is calculated using the same method as that in the simulated flow field. Here, the particle settling velocity refers to the actual particle settling velocity after introducing concentration correction and wall correction factors. It is obtained by multiplying the settling velocity of a single particle in an infinitely large plane by the concentration correction factor and the wall correction factor. The formula for calculating the settling velocity of particles in the actual flow field crack is as follows:

[0099] V zs1 =V s1 ·f C1 ·h w1

[0100] Where: V s1 The velocity of a single particle in the actual flow field crack is denoted as m / s.

[0101] S04: Calculate the particle moving velocity and horizontal moving velocity in the actual flow field and the simulated flow field.

[0102] The calculation method for the particle velocity in the actual flow field crack is the same as that for the particle velocity in the simulated flow field crack. The formula for calculating the particle velocity in the actual flow field crack is as follows:

[0103]

[0104] Among them, V L1 V represents the horizontal velocity of the particles in the crack of the actual flow field. zs1 This represents the settling velocity of particles in the crack within the actual flow field.

[0105] Furthermore, the horizontal movement velocity V of particles in the actual flow field crack L1 Equal to the horizontal velocity of the fluid; the horizontal velocity V of particles in the simulated flow field. L2 It equals the horizontal speed of the fluid.

[0106] S05: Obtain the similarity ratio of settling velocities based on the particle moving velocity, particle settling velocity, and horizontal moving velocity in the actual flow field and the simulated flow field.

[0107] The formula for calculating the similarity ratio of settlement velocities is:

[0108]

[0109] Among them: V1, V zs1 V L1 V2, V3 represent the moving velocity, settling velocity, and horizontal moving velocity of particles in the actual flow field crack, in m / s; zs2 V L2 To simulate the moving velocity, settling velocity, and horizontal moving velocity of particles in the flow field crack, m / s.

[0110] S06: Obtain the transport similarity ratio, fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number similarity ratio of the actual flow field and the simulated flow field.

[0111] Transport similarity refers to the ratio of the time required for a particle to move one unit distance horizontally to the time required to move one unit distance vertically in both actual and simulated flow fields. The formula for calculating transport similarity is:

[0112]

[0113] Among them, T L1 T s1 These represent the horizontal transport time and settling time of particles in the cracks of the actual flow field, in seconds; T L2 T s2 L1 and H1 represent the horizontal transport and settling times of particles in the simulated flow field crack, respectively, in seconds; L1 and H1 represent the length and height of the actual flow field crack, respectively, in meters; L2 and H2 represent the length and height of the actual flow field crack, respectively, in meters; V zs1 V L1 These represent the actual settling velocity and horizontal movement velocity of particles in the crack of the actual flow field, respectively, in m / s; V zs2 V L2 These represent the actual settling velocity and horizontal movement velocity of particles in the simulated flow field crack, respectively, in m / s;

[0114] The equality of fluid Reynolds numbers refers to the fact that the Reynolds numbers generated by the horizontal movement of fluids in two flow fields are equal. The formula for calculating the equality of fluid Reynolds numbers is as follows:

[0115]

[0116] Where ρ1 and ρ2 are the fracturing fluid densities in the actual and simulated flow fields, respectively, in kg / m³. 3 V L1 V L2 μ1 and μ2 are the horizontal fluid transport velocities in the actual and simulated flow fields, respectively, in m / s; μ1 and μ2 are the fracturing fluid viscosities in the actual and simulated flow fields, respectively, in Pa·s.

[0117] The equality of particle Reynolds numbers refers to the fact that the Reynolds numbers generated by particles under the traction of the fluid in two flow fields are equal. The formula for calculating the equality of particle Reynolds numbers is as follows:

[0118]

[0119] Where V1 and V2 are the particle velocities in the actual and simulated flow fields, respectively, in m / s; d1 and d2 are the proppant particle diameters in the actual and simulated flow fields, respectively, in m.

[0120] The equality of particle Froude numbers refers to the fact that the Froude numbers generated by particles under the influence of gravity in two flow fields are equal. The formula for calculating the equality of particle Froude numbers is as follows:

[0121]

[0122] Where g is the acceleration due to gravity, m / s² 2 V1 is the velocity of the particles moving in the crack in the actual flow field, and V2 is the velocity of the particles moving in the crack in the simulated flow field.

[0123] S07: Determine whether the surface similarity ratio, settling velocity similarity ratio, transport similarity ratio, fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number similarity ratio of the actual flow field and the simulated flow field are between 0.9 and 1.1. If they are, then the actual flow field and the simulated flow field are completely similar.

[0124] S08: If not, then fine-tune the experimental parameters of the simulated flow field according to the known construction parameters of the actual flow field, or fine-tune the construction parameters of the actual flow field according to the known experimental parameters of the simulated flow field, until the ratio of each parameter in the similarity result is between 0.9 and 1.1; the construction parameters include: the length and height of the fracture, the sand ratio, the fracture width, the settling velocity of a single particle, the horizontal movement velocity of the particle, the settling velocity of the particle, the fracturing fluid density, the horizontal migration velocity of the fluid, the particle size of the proppant, and the gravitational acceleration.

[0125] Furthermore, the formulas relating the particle movement velocity, settling velocity, and horizontal movement velocity in the cracks of both the actual and simulated flow fields to the crack width ratio are as follows:

[0126]

[0127]

[0128]

[0129] Where 'a' represents the ratio of the crack width in the actual flow field to the crack width in the simulated flow field.

[0130] It is understandable that the similarity score range is between 0.9 and 1.1, including 0.9 and 1.1.

[0131] The ratio results are rounded, meaning the range of values ​​is ≥0.845 and ≤1.144.

[0132] The ratio of similarity results should be ≥0.845 and ≤1.144;

[0133] The ratio of similar settlement velocity results should be ≥0.845 and ≤1.144;

[0134] The ratio of transport similarity results should be ≥0.845 and ≤1.144;

[0135] The ratio of fluid Reynolds numbers should be ≥0.845 and ≤1.144;

[0136] The ratio of particle Reynolds numbers should be ≥0.845 and ≤1.144;

[0137] The ratio of particle Froude numbers should be ≥0.845 and ≤1.144.

[0138] This invention provides a method for determining the similarity of proppant transport within joints, linking geometric similarity, kinematic similarity, and dynamic similarity. These are no longer isolated entities but rather a novel whole encompassing the similarity between proppant model experiments and on-site construction. Furthermore, this invention introduces concentration correction coefficients and wall surface correction coefficients, making the similarity results more accurate and reliable.

[0139] Among them, the surface similarity ratio corresponds to geometric similarity, the settling velocity similarity ratio corresponds to kinematic similarity, the transport similarity ratio includes both geometric and kinematic similarity, and the fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number all correspond to dynamic similarity.

[0140] This invention provides a complete procedure for determining flow field similarity in the future, which is of great significance for subsequent proppant transport experiments.

[0141] Example 1

[0142] (1) Given that the actual flow field fracture length, width, and height are 240m, 50m, and 0.008m respectively, and 0.45% slickwater fracturing fluid (viscosity 0.013Pa·s) is used on-site at a depth of 4.5m... 3 A flow rate of 20 / 40 mesh single-grain quartz sand with a sand ratio of 15% is pumped into the fracture. The calculated horizontal flow velocity of the fluid inside the fracture is 0.1875 m / s. The proppant particle size is found to be 0.00056 μm from a table. The length, width, and height of the fracture in the simulated flow field are known to be 2.5 m, 0.5 m, and 0.004 m, respectively.

[0143] (2) Geometric similarity is obtained:

[0144]

[0145] The crack width ratio was obtained as follows:

[0146]

[0147] (3) The velocity ratio, proppant particle size ratio, and fluid viscosity ratio are obtained by solving the three equations together: the fluid Reynolds number equality formula, the particle Reynolds number equality formula, and the particle Froude number equality formula.

[0148]

[0149]

[0150]

[0151] The simulated flow field yielded the fluid velocity, proppant particle size, and fracturing fluid viscosity within the fracture.

[0152]

[0153]

[0154]

[0155] (5) Substitute the obtained experimental parameters into the Novotny particle settling correction form and inversely calculate the settling velocity of the proppant particles in an infinitely large container.

[0156] The actual flow field crack proppant particle settling velocity was obtained as follows:

[0157] V s1 =0.0695

[0158] The settling velocity of the proppant particles in the simulated flow field crack is obtained as follows:

[0159] V s2 =0.0389

[0160] (6) The concentration correction factor in the actual flow field crack is calculated as follows:

[0161]

[0162] Assuming the sand ratio in the simulated flow field is 11%, the concentration correction factor within the cracks in the simulated flow field is calculated as follows:

[0163]

[0164] (7) The actual flow field crack inner wall correction factor is calculated as follows:

[0165]

[0166] The calculated correction factor for the inner wall of the crack in the simulated flow field is as follows:

[0167]

[0168] (8) The actual settling velocity of the proppant particles in the crack in the actual flow field was calculated as follows:

[0169] V zs1 =V s1 ·hw1 ·f C1 =0.0695 × 0.893 × 0.453 = 0.0281

[0170] The calculated actual settling velocities of proppant particles within the simulated flow field cracks are as follows:

[0171] V zs2 =V s2 ·h w2 ·f c2 =0.0389 × 0.893 × 0.561 = 0.0195

[0172] (9) Proof by contradiction that motions are similar:

[0173]

[0174] Established.

[0175] (10) The actual particle velocity within the crack in the actual flow field is calculated as follows:

[0176]

[0177] The calculated actual particle velocity within the crack in the simulated flow field is as follows:

[0178]

[0179] The geometric similarity results are obtained:

[0180]

[0181] The following motion similarity results were obtained:

[0182]

[0183] The results of the settlement velocity comparison were obtained:

[0184]

[0185] The results of the fluid Reynolds number comparison were obtained:

[0186]

[0187] The particle Reynolds number comparison results are obtained as follows:

[0188]

[0189] The results of the particle Froude number comparison were obtained:

[0190]

[0191] (11) Verification of geometric similarity, motion similarity, settling velocity comparison, fluid Reynolds number comparison, particle Reynolds number comparison, and particle Froude number comparison results all show values ​​between 0.9 and 1.1. Therefore, the two flow fields are completely similar.

[0192] The simulated flow field, using 4.6 mPa·s slickwater fracturing fluid at a velocity of 0.133 m / s, can be used to pump 11% quartz sand with a single particle size of 0.00028 m. This allows for the assessment of the following field operation conditions: using 0.45% slickwater fracturing fluid (viscosity 0.013 Pa·s) at a velocity of 4.5 m... 3 20 / 40 mesh single quartz sand is pumped into the crack at a flow rate of / min, with a sand ratio of 15%.

[0193] Example 2

[0194] (1) Given that the actual flow field fracture length, width, and height are 200m, 40m, and 0.01m respectively, and 0.4% guar gum fracturing fluid (viscosity 0.017 Pa·s) is used on-site at a depth of 4.5m... 3 A flow rate of 20 / 40 mesh single-layer ceramic aggregate is pumped into the fracture at a rate of 15% per minute. The calculated horizontal flow velocity of the fluid inside the fracture is 0.1875 m / s. The proppant particle size is found to be 0.00056 μm from a table. The simulated flow field fracture length, width, and height are known to be 2.5 m, 0.5 m, and 0.004 m, respectively.

[0195] (2) Geometric similarity is obtained:

[0196]

[0197] The crack width ratio was obtained as follows:

[0198]

[0199] (3) The velocity ratio, proppant particle size ratio, and fluid viscosity ratio are obtained by solving the three equations together: the fluid Reynolds number equality formula, the particle Reynolds number equality formula, and the particle Froude number equality formula.

[0200]

[0201]

[0202]

[0203] The simulated flow field yielded the fluid velocity, proppant particle size, and fracturing fluid viscosity within the fracture.

[0204]

[0205]

[0206]

[0207] (5) Substitute the obtained experimental parameters into the Novotny particle settling correction form and inversely calculate the settling velocity of the proppant particles in an infinitely large container.

[0208] The actual flow field crack proppant particle settling velocity was obtained as follows:

[0209] V s1 =0.0665

[0210] The settling velocity of the proppant particles in the simulated flow field crack is obtained as follows:

[0211] V s2 =0.0308

[0212] (6) The concentration correction factor in the actual flow field crack is calculated as follows:

[0213]

[0214] Assuming the sand ratio in the simulated flow field is 5%, the concentration correction factor within the cracks in the simulated flow field is calculated as follows:

[0215]

[0216] (7) The actual flow field crack inner wall correction factor is calculated as follows:

[0217]

[0218] The calculated correction factor for the inner wall of the crack in the simulated flow field is as follows:

[0219]

[0220] (8) The actual settling velocity of the proppant particles in the crack in the actual flow field was calculated as follows:

[0221] V zs1 =V s1 ·h w1 ·f C1 =0.0665 × 0.914 × 0.453 = 0.0276

[0222] The calculated actual settling velocities of proppant particles within the simulated flow field cracks are as follows:

[0223] V zs2 =V s2 ·h W2 ·f C2 =0.0308 × 0.914 × 0.77 = 0.0217

[0224] (9) Proof by contradiction that motions are similar:

[0225]

[0226] This is invalid because it exceeds the range of 0.9 to 1.1.

[0227] (10) The sand ratio in the simulated flow field was re-set to 10%, and the concentration correction factor in the crack of the simulated flow field was calculated as follows:

[0228]

[0229] (11) The actual settling velocity of proppant particles in the crack of the actual flow field was recalculated as follows:

[0230] V zs1 =V s1 ·h w1 ·f C1 =0.0665 × 0.914 × 0.453 = 0.0276

[0231] The recalculated actual settling velocities of proppant particles within the simulated flow field cracks are as follows:

[0232] V zs2 =V s2 ·h W2 ·f C2 =0.0308 × 0.914 × 0.592 = 0.0166

[0233] (12) Proof by contradiction that motions are similar:

[0234]

[0235] Established.

[0236] (13) The actual particle velocity within the crack in the actual flow field is calculated as follows:

[0237]

[0238] The calculated actual particle velocity within the crack in the simulated flow field is as follows:

[0239]

[0240] The geometric similarity results are obtained:

[0241]

[0242] The following motion similarity results were obtained:

[0243]

[0244] The results of the settlement velocity comparison were obtained:

[0245]

[0246] The results of the fluid Reynolds number comparison were obtained:

[0247]

[0248] The particle Reynolds number comparison results are obtained as follows:

[0249]

[0250] The results of the particle Froude number comparison were obtained:

[0251]

[0252] (11) Verification of geometric similarity, motion similarity, settling velocity comparison, fluid Reynolds number comparison, particle Reynolds number comparison, and particle Froude number comparison results all show values ​​between 0.9 and 1.1. Therefore, the two flow fields are completely similar.

[0253] The simulated flow field, using guar gum fracturing fluid at 4.3 mPa·s and pumping single-particle-size ceramsite with a sand ratio of 10% and a particle size of 0.000224 μm at a velocity of 0.119 m / s, can be used to assess the following field construction conditions: using 0.4% guar gum fracturing fluid (viscosity 0.017 Pa·s) at a velocity of 4.5 m... 3 20 / 40 mesh single ceramsite is pumped into the crack at a flow rate of / min, with a sand ratio of 15%.

[0254] Similar parts between the embodiments provided in this application can be referred to mutually. The specific implementation methods provided above are only a few examples under the overall concept of this application and do not constitute a limitation on the scope of protection of this application. For those skilled in the art, any other implementation methods extended from the solution of this application without creative effort shall fall within the scope of protection of this application.

Claims

1. A method for judging the similarity of proppant intra-slit transport, characterized in that, include: The surface similarity ratio is obtained by comparing the length and height of the crack in the actual flow field with the crack length and height in the simulated flow field. Calculate the settling velocity of a single proppant particle, the concentration correction factor, and the wall correction factor; The particle settling velocities of the actual and simulated flow fields are obtained based on the single particle settling velocity, concentration correction factor, and wall correction factor. Calculate the particle moving velocity and horizontal moving velocity in the actual flow field and the simulated flow field; Based on the particle moving velocity, particle settling velocity, and horizontal moving velocity of the actual flow field and the simulated flow field, obtain the similarity ratio of settling velocity; Obtain the transport similarity ratio, fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number similarity ratio of the actual flow field and the simulated flow field; Determine whether the surface similarity ratio, settling velocity similarity ratio, transport similarity ratio, fluid Reynolds number similarity ratio, particle Reynolds number similarity ratio, and particle Froude number similarity ratio of the actual flow field and the simulated flow field are between 0.9 and 1.

1. If they are, then the actual flow field and the simulated flow field are completely similar.

2. The method for determining the similarity of proppant intra-slit migration according to claim 1, characterized in that, Surface similarity refers to the fact that the length and height of the cracks in the actual flow field and the simulated flow field are proportional, and the proportionality coefficient is the same. The formula for calculating the surface similarity ratio is: Among them, namely , Let be the length and height of the crack in the actual flow field, in meters (m). , The length and height of the crack in the simulated flow field are given in meters (m).

3. The method for determining the similarity of proppant intra-slit migration according to claim 1, characterized in that, The formula for calculating the concentration correction factor is: Where: C is the sand ratio, % The proppant ratio, also known as the surface proppant ratio, refers to the ratio of the volume of proppant to the volume of fracturing fluid. The formula for calculating the wall correction factor is: in: is the proppant particle size, m; w is the crack width, m; The formula for calculating the settling velocity of a single particle is: when hour: when hour: when hour: in, The particle Reynolds number, , These are the proppant density and fracturing fluid density, respectively. ; The particle size of the proppant is in meters (m). This refers to the viscosity of the fracturing fluid. g is the acceleration due to gravity. ; The formula for calculating the particle Reynolds number is as follows: in: The particle's moving speed, , This represents the horizontal velocity of the particle.

4. The method for judging the similarity of proppant intra-slit migration according to claim 3, characterized in that, The settling velocity of particles in the actual flow field crack is calculated using the same method as that in the simulated flow field. The formula for calculating the settling velocity of particles in the actual flow field crack is as follows: in: This represents the settling velocity of a single particle in the actual flow field crack. .

5. The method for determining the similarity of proppant intra-slit migration according to claim 1, characterized in that, The calculation method for the particle velocity in the actual flow field crack is the same as that for the particle velocity in the simulated flow field crack. The formula for calculating the particle velocity in the actual flow field crack is as follows: in, This represents the horizontal velocity of the particles within the crack in the actual flow field. This represents the settling velocity of particles in the cracks of the actual flow field.

6. The method for determining the similarity of proppant intra-slit migration according to claim 5, characterized in that, Horizontal movement velocity of particles in actual flow field cracks Equal to the horizontal speed of the fluid; Horizontal movement velocity of particles in simulated flow field It equals the horizontal speed of the fluid.

7. The method for determining the similarity of proppant intra-slit migration according to claim 6, characterized in that, The formula for calculating the similarity ratio of settlement velocities is: in: , , The values ​​represent the moving velocity, settling velocity, and horizontal moving velocity of particles in the actual flow field crack. ; , , To simulate the moving velocity, settling velocity, and horizontal movement velocity of particles in the flow field cracks, .

8. The method for determining the similarity of proppant intra-slit migration according to claim 1, characterized in that, Transport similarity refers to the ratio of the time required for a particle to move one unit distance horizontally to the time required to move one unit distance vertically in both actual and simulated flow fields. The formula for calculating transport similarity is: in, , , respectively, represent the horizontal transport time and settling time of particles in the crack of the actual flow field, in seconds; , , respectively, represent the horizontal transport time and settling time of particles in the simulated flow field crack, in seconds; , , respectively, represent the length and height of the crack in the actual flow field, in meters (m); , These are the length and height of the crack in the simulated flow field, respectively, in meters (m). , These represent the actual settling velocity and horizontal movement velocity of particles in the cracks of the actual flow field, respectively. ; , These represent the actual settling velocity and horizontal movement velocity of particles in a simulated flow field crack, respectively. ; The equality of fluid Reynolds numbers refers to the fact that the Reynolds numbers generated by the horizontal movement of fluids in two flow fields are equal. The formula for calculating the equality of fluid Reynolds numbers is as follows: in, , The fracturing fluid density is used for both the actual and simulated flow fields. ; , The horizontal transport velocity of the fluid in the actual flow field and the simulated flow field. ; , The fracturing fluid viscosity is used for both the actual and simulated flow fields. ; The equality of particle Reynolds numbers refers to the fact that the Reynolds numbers generated by particles under the traction of the fluid in two flow fields are equal. The formula for calculating the equality of particle Reynolds numbers is as follows: in, , The velocity of particles in the actual flow field and the simulated flow field. ; , Here, represents the particle size of the proppant in the actual and simulated flow fields, in meters (m). The equality of particle Froude numbers refers to the fact that the Froude numbers generated by particles under the influence of gravity in two flow fields are equal. The formula for calculating the equality of particle Froude numbers is as follows: Where g is the acceleration due to gravity. , Let be the velocity of the particles moving within the crack in the actual flow field. ; To simulate the particle movement velocity in the crack of the flow field, .

9. The method for determining the similarity of proppant intra-slit migration according to claim 1, characterized in that, The formulas relating the particle's moving velocity, settling velocity, and horizontal moving velocity in the crack to the crack width ratio in both actual and simulated flow fields are as follows: Where 'a' represents the ratio of the crack width in the actual flow field to the crack width in the simulated flow field.

10. The method for determining the similarity of proppant intra-slit migration according to claim 1, characterized in that, If not, then fine-tune the experimental parameters of the simulated flow field based on the known construction parameters of the actual flow field, or fine-tune the construction parameters of the actual flow field based on the known experimental parameters of the simulated flow field, until the ratio of each parameter in the similarity result is between 0.9 and 1.

1. The construction parameters include: crack length and height, sand ratio, crack width, single particle settling velocity, particle horizontal movement velocity, particle settling velocity, fracturing fluid density, fluid horizontal migration velocity, proppant particle size, and gravitational acceleration.

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