Method for measuring embedding degree of tight reservoir fracturing propping agent

By using double-stone slabs and three-dimensional laser scanning technology in dense reservoirs, the degree of embedding of fracturing proppants is accurately measured, which solves the problem of inaccurate measurement in the prior art, and improves the oil layer diversion capacity and oil well production.

CN120042579APending Publication Date: 2025-05-27PETROCHINA CO LTD
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Patent Information

Application Number
CN202311581009.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2023-11-24
Publication Date
2025-05-27

AI Technical Summary

Technical Problem

The prior art is difficult to accurately measure the degree of embeddedness of the dense reservoir fracturing proppant, resulting in a decrease in the oil layer's diversion capacity and affecting the oil well production.

Method used

Double-stone slabs are processed using target layer rocks or ground rock outcrops, and three-dimensional laser scanning technology is used to measure the depth of proppant embedding under the conditions of stratigraphic closed stress to simulate the immersion process of fracturing fluid on formation rocks.

Benefits of technology

It realizes accurate measurement of the degree of proppant embedding, accurate test data, high measurement accuracy, and can provide a theoretical basis for proppant optimization and fracturing scheme optimization.

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Abstract

The invention discloses a tight reservoir fracturing propping agent embedding degree measuring method, which comprises the following steps of: processing two rock plates by using target layer rock or ground rock outcrop, clamping a propping agent by using the two rock plates, and performing three-dimensional laser scanning measurement on three-dimensional coordinates of the rock plates before and after the propping agent is embedded into the rock plates under the condition of stratum closed stress. And obtaining the embedding depth of the proppant on the surfaces of the two rock plates. According to the invention, accurate measurement of the embedding degree of the proppant is realized, and the problem of evaluation of the embedding degree of the proppant is effectively solved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of fracturing proppant evaluation, and relates to a method for measuring the embedding degree of fracturing proppants in tight reservoirs. Background Art

[0002] Low-permeability reservoirs such as tight oil have low permeability, and hydraulic fracturing is the main measure to increase the production of oil and gas wells. In order to keep the fracturing cracks open for a long time, it is necessary to squeeze a sand-carrying fluid with proppants into the oil layer during fracturing so that the fractured cracks do not close. However, the formation closure pressure will cause the proppants to embed in the crack wall. To a certain extent, the embedding of proppants will reduce the crack width, resulting in a decrease in the fracture conductivity of the oil layer and a reduction in the production of oil wells. Therefore, it is necessary to conduct research on the embedding degree of proppants to provide a theoretical basis for the optimization of proppant selection and fracturing design.

[0003] Currently, the methods of related theoretical research mainly focus on laboratory experiments and theoretical calculation models. Among them, the setting conditions of the theoretical model calculation method are too ideal, and the reliability of the evaluation results is poor; the conventional laboratory test method mainly uses the method of clamping proppants with a rock plate and a steel plate for testing. Since the steel plate cannot be embedded, the embedding degree of a single rock plate is usually used for conversion, making it difficult to evaluate the embedding degree of proppants under formation conditions. There is a gap between the experimental results and the actual embedding depth of proppants. Therefore, there is no perfect experimental method in the related technology to accurately measure the embedding degree of proppants. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for measuring the embedding degree of fracturing proppants in tight reservoirs, which realizes the accurate measurement of the embedding degree of proppants and effectively solves the problem of evaluating the embedding degree of proppants.

[0005] The technical solution adopted by the present invention is a method for measuring the embedding degree of fracturing proppants in tight reservoirs. Two rock plates are processed from the target layer rock or surface rock outcrop. The proppants are embedded in the rock plates by clamping the proppants with two rock plates. Under the formation closure stress condition, the three-dimensional coordinates of the rock plates before and after the proppants are embedded in the rock plates are measured by three-dimensional laser scanning to obtain the embedding depth of the proppants on the surfaces of the two rock plates.

[0006] The characteristics of the present invention also lie in that

[0007] Specifically, it is implemented according to the following steps:

[0008] Step 1, rock plate production: According to the shape and size requirements of the test samples for the flow conductivity tester, two rock plates are processed from the target layer rock or surface rock outcrop, namely rock plate A and rock plate B; the surfaces of rock plate A and rock plate B that do not contact the proppants are placed flat, and glue is applied around the flat bottoms of rock plate A and rock plate B;

[0009] Step 2, simulate the soaking process of the fracturing fluid on the fracture wall surface and the rock after fracturing;

[0010] Step 3, scan the surfaces of Slab A and Slab B that will contact the proppant respectively, and obtain the three-dimensional coordinate data of the contact surfaces between Slab A, Slab B and the proppant;

[0011] Step 4, place the surface of one of Slab A and Slab B that is glued as the bottom into the API flow conductivity cell. According to the test purpose, lay the required proppant and sand concentration between the two slabs;

[0012] Step 5, set the working pressure of the flow conductivity tester according to the closure stress of the test reservoir formation, and conduct the proppant embedment degree test;

[0013] Step 6, take out Slab A and Slab B from the propped fracture flow conductivity tester, and remove the proppant on the surfaces of Slab A and Slab B. Scan the surfaces of Slab A and Slab B where proppant embedment occurs respectively, and obtain the three-dimensional coordinate data of the proppant embedment surfaces of Slab A and Slab B;

[0014] Step 7, calculate the coordinate difference of the three-dimensional coordinate data obtained for Slab A in Step 3 and Step 6, and calculate the embedment depth of Slab A;

[0015] Calculate the coordinate difference of the three-dimensional coordinate data obtained for Slab B in Step 3 and Step 6, and calculate the embedment depth of Slab B;

[0016] Step 8, add the embedment depth of Slab A to the embedment depth of Slab B, which is the proppant embedment depth of the double slabs.

[0017] In Step 1, place the surfaces of Slab A and Slab B that do not contact the proppant flat on an A4 paper, and use a hot melt gun to glue around the bottoms of Slab A and Slab B.

[0018] In Step 2, soak Slab A and Slab B with formation water or fracturing fluid to simulate the soaking process of the fracturing fluid on the fracture wall surface and the rock after fracturing.

[0019] The three-dimensional coordinate data obtained by scanning are all scanned using a three-dimensional laser scanner.

[0020] The three-dimensional coordinate data of the contact surface between Slab A and the proppant before proppant embedment obtained in Step 3 is AX in the X direction 1 、AX 2 、AX 3 ...AX N ; In the Y direction, AY 1 、AY 2 、AY 3 ...AY N; The three-dimensional coordinate data of the contact surface between the rock slab B and the proppant before proppant embedding, in the X direction is BX 1 、BX 2 、BX 3 ...BX N ; In the Y direction, BY 1 、BY 2 、BY 3 ...BY N ;

[0021] The three-dimensional coordinate data of the contact surface between the rock slab A and the proppant after proppant embedding obtained in step 6, in the X direction is Ax 1 、Ax 2 、Ax 3 ...Ax N ; In the Y direction is Ay 1 、Ay 2 、Ay 3 ...Ay N ; The three-dimensional coordinate data of the contact surface between the rock slab B and the proppant after proppant embedding, in the X direction is Bx 1 、Bx 2 、Bx 3 ...Bx N ; In the Y direction, By 1 、By 2 、By 3 ...By N 。

[0022] Step 7 calculates that the embedding depth of the proppant in the rock slab A is AY 1 -Ay 1 、AY 2 -Ay 2 、AY 3 -Ay 3 ...AY N -Ay N ; The embedding depth of the proppant in the rock slab B is BY 1 -By 1 、BY 2 -By 2 、BY 3 -By 3 ...BY N -By N 。

[0023] The beneficial effects of the present invention are:

[0024] 1) The method for measuring the embedding degree of proppants in a tight reservoir of the present invention uses formation rocks or surface outcrops of the target layer to make double rock plates, soaks the rock plates with formation water or fracturing fluid, and considers the influence of the mechanical property changes caused by the soaking of the fracturing fluid on the formation rocks on the proppant embedding during the embedding degree test, realizing that the experimental conditions for the indoor embedding degree test are basically the same as the formation conditions.

[0025] 2) Through three-dimensional laser scanning of the three-dimensional coordinates of the rock plates before and after the proppant embedding degree test, the embedding degree on the surface of the rock plates is accurately obtained. Compared with the prior art, the test data of this technology is accurate and the measurement accuracy is relatively high.

[0026] 3) Through the embedding degree test and three-dimensional laser scanning under the condition of double rock plates, accurate tests of the embedding degrees of different proppant types, different sand laying concentrations, different proppant combinations, etc. can be realized, providing technical support for proppant optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a schematic flow chart of the method for measuring the embedding degree of proppants in a tight reservoir of the present invention;

[0028] Figure 2 is a schematic diagram of the proppant embedding degree test in Example 3;

[0029] Figure 3 is a three-dimensional laser scanning imaging diagram of the proppant embedding degree in Example 3.

[0030] In the figure, 1. Rock plate A, 2. Rock plate B, 3. Proppant. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] The present invention will be described in detail below in conjunction with the drawings and specific embodiments.

[0032] Example 1

[0033] This example provides a method for measuring the embedding degree of proppants in a tight reservoir. Two rock plates are processed using formation rocks or surface rock outcrops of the target layer. The proppant is embedded in the rock plates by clamping the proppant with two rock plates. Under the formation closure stress condition, three-dimensional laser scanning measurement of the three-dimensional coordinates of the rock plates before and after the proppant is embedded in the rock plates is carried out to obtain the embedding depth of the proppant on the surfaces of the two rock plates.

[0034] Example 2

[0035] This example provides a method for measuring the embedding degree of proppants in a tight reservoir. On the basis of Example 1, as Figure 1 shown, it is specifically implemented according to the following steps:

[0036] Step 1, Slab production: According to the shape and size requirements of the test sample for the flow conductivity tester, use the rock from the target layer or the outcrop of surface rock to process two slabs, namely slab A1 and slab B2; Place the surfaces of slab A1 and slab B2 that do not contact the proppant 3 flat on A4 paper, and use a hot melt gun to apply glue around the bottom of slab A1 and slab B2;

[0037] Step 2, Immerse slab A1 and slab B2 in formation water or fracturing fluid to simulate the immersion process of the fracturing fluid on the fracture wall and the rock after fracturing;

[0038] Step 3, Scan the surfaces of slab A1 and slab B2 that contact the proppant 3 respectively to obtain the three-dimensional coordinate data of the contact surfaces of slab A1 and slab B2 with the proppant 3;

[0039] Step 4, Place the slab with the glued surface of slab A1 or slab B2 as the bottom into the API flow cell. According to the test purpose, lay the required proppant 3 to be tested and the sand concentration between the two slabs;

[0040] Step 5, Set the working pressure of the flow conductivity tester according to the closure stress of the test reservoir formation to conduct the proppant 3 embedment degree test;

[0041] Step 6, Take out slab A1 and slab B2 from the propped fracture flow conductivity tester, and remove the proppant 3 on the surfaces of slab A1 and slab B2. Scan the surfaces of slab A1 and slab B2 where the proppant 3 is embedded respectively to obtain the three-dimensional coordinate data of the surfaces of slab A1 and slab B2 where the proppant 3 is embedded;

[0042] Step 7, Calculate the coordinate difference of the three-dimensional coordinate data obtained for slab A1 in Step 3 and Step 6 to calculate the embedment depth of slab A1;

[0043] Calculate the coordinate difference of the three-dimensional coordinate data obtained for slab B2 in Step 3 and Step 6 to calculate the embedment depth of slab B2;

[0044] Step 8, Add the embedment depth of slab A1 to the embedment depth of slab B2, which is the embedment depth of the proppant 3 for the double slabs.

[0045] Example 3

[0046] This example provides a method for measuring the embedment degree of proppants in a tight reservoir. For the embedment degree test of 20 / 40 mesh quartz sand proppant 3 in Block X of shale oil, with the closure stress of P MPa in this block, on the basis of Examples 1 - 2, it is specifically implemented according to the following steps:

[0047] Step 1, slate production: According to the shape and size requirements of the test sample by the flow conductivity tester, two slates are processed using the target layer rock or the outcrop of the surface rock, namely slate A1 and slate B2; Place the surfaces of slate A1 and slate B2 that do not contact the proppant 3 flat on A4 paper, and use a hot melt gun to apply glue around the bottom of slate A1 and slate B2;

[0048] Step 2, soak slate A1 and slate B2 with formation water or fracturing fluid to simulate the soaking process of the fracturing fluid on the fracture wall and the rock after fracturing;

[0049] Step 3, use a 3D laser scanner to scan the surfaces of slate A1 and slate B2 that will contact the proppant 3 respectively, and obtain the 3D coordinate data of the contact surfaces of slate A1 and slate B2 with the proppant 3. The 3D coordinate data of the contact surface of slate A1 with the proppant 3 in the X direction before the proppant 3 is embedded is AX 1 、AX 2 、AX 3 ...AX N ; In the Y direction, AY 1 、AY 2 、AY 3 ...AY N ; The 3D coordinate data of the contact surface of slate B2 with the proppant 3 in the X direction before the proppant 3 is embedded is BX 1 、BX 2 、BX 3 ...BX N ; In the Y direction, BY 1 、BY 2 、BY 3 ...BY N ;

[0050] Step 4, place one of the glued surfaces of slate A1 and slate B2 as the bottom into the API flow cell. According to the test purpose, lay 20 / 40 mesh quartz sand between the two slates, and set different sand laying concentrations K for multiple groups of experiments 1 、K 1 、K 1 ...K N ;

[0051] Step 5, set the working pressure of the flow conductivity tester according to the formation closure stress of the test reservoir, and conduct the proppant 3 embedding degree test. As Figure 2 shown, it is a schematic diagram of the proppant 3 embedding degree test;

[0052] Step 6: Take out the rock slabs A1 and B2 from the proppant fracture conductivity tester, and remove the proppant 3 on the surfaces of the rock slabs A1 and B2. Use a 3D laser scanner to scan the surfaces of the rock slabs A1 and B2 where the proppant 3 is embedded respectively, and obtain the 3D coordinate data of the surfaces of the rock slabs A1 and B2 where the proppant 3 is embedded. As Figure 3 shown in the 3D laser scanning imaging diagram of the embedding degree of the proppant 3 in the rock slab A1, where the gray points are the size of the embedded proppant 3. The 3D coordinate data of the contact surface between the rock slab A1 and the proppant 3 in the X direction after the proppant 3 is embedded is Ax 1 、Ax 2 、Ax 3 ...Ax N ; The 3D coordinate data of the contact surface between the rock slab B2 and the proppant 3 in the Y direction after the proppant 3 is embedded is Ay 1 、Ay 2 、Ay 3 ...Ay N ; The 3D coordinate data of the contact surface between the rock slab B2 and the proppant 3 in the X direction after the proppant 3 is embedded is Bx 1 、Bx 2 、Bx 3 ...Bx N ; In the Y direction, By 1 、By 2 、By 3 ...By N ;

[0053] Step 7: Calculate the coordinate differences of the 3D coordinate data obtained for the rock slab A1 in Steps 3 and 6, and calculate the embedding depth h of the rock slab A1 A That is, AY 1 -Ay 1 、AY 2 -Ay 2 、AY 3 -Ay 3 ...AY N -Ay N ;

[0054] Calculate the coordinate differences of the 3D coordinate data obtained for the rock slab B2 in Steps 3 and 6, and calculate the embedding depth h of the rock slab B2 B That is, BY 1 -By 1 、BY 2 -By 2 、BY 3 -By 3 ...BY N -By N ;

[0055] Step 8: Add the embedding depth of the rock slab A1 to the embedding depth of the rock slab B2, which is the embedding depth of the proppant 3 in the double rock slabs.

[0056] Example 4

[0057] This example provides a method for measuring the embedding degree of proppants in a tight reservoir. The embedding degree of 20 / 40 mesh ceramic proppants 3 in Block X of shale oil is tested. The closure stress P in this block is in MPa. On the basis of Examples 1-2, it is specifically implemented according to the following steps:

[0058] Step 1, rock plate production: According to the shape and size requirements of the test samples by the conductivity tester, two rock plates are processed using the rock from the target layer or the outcrop of surface rock, namely, rock plate A1 and rock plate B2 are obtained; the surfaces of rock plate A1 and rock plate B2 that do not contact the proppants 3 are placed flat on A4 paper, and a hot melt gun is used to apply glue around the bottom of rock plate A1 and rock plate B2;

[0059] Step 2, soak rock plate A1 and rock plate B2 with formation water or fracturing fluid to simulate the soaking process of the fracturing fluid on the fracture wall and the rock after fracturing;

[0060] Step 3, use a three-dimensional laser scanner to scan the surfaces of rock plate A1 and rock plate B2 that will contact the proppants 3 respectively, and obtain the three-dimensional coordinate data of the contact surfaces of rock plate A1 and rock plate B2 with the proppants 3. The three-dimensional coordinate data of the contact surface of rock plate A1 with the proppants 3 in the X direction before the proppants 3 are embedded is AX 1 、AX 2 、AX 3 ...AX N ; In the Y direction, AY 1 、AY 2 、AY 3 ...AY N ; The three-dimensional coordinate data of the contact surface of rock plate B2 with the proppants 3 in the X direction before the proppants 3 are embedded is BX 1 、BX 2 、BX 3 ...BX N ; In the Y direction, BY 1 、BY 2 、BY 3 ...BY N ;

[0061] Step 4, place one of the glued surfaces of rock plate A1 and rock plate B2 as the bottom into the API flow conductivity cell. According to the test purpose, lay 20 / 40 mesh ceramic proppants between the two rock plates, and set different sand laying concentrations K 1 、K 1 、K 1 ...K N ;

[0062] Step 5: Set the working pressure of the conductivity tester according to the formation closure stress of the test reservoir, and conduct the embedment degree test of the proppant 3.

[0063] Step 6: Take out the rock slabs A1 and B2 from the propped fracture conductivity tester, and remove the proppant 3 on the surfaces of the rock slabs A1 and B2. Use a three-dimensional laser scanner to scan the surfaces of the rock slabs A1 and B2 where the proppant 3 is embedded respectively, and obtain the three-dimensional coordinate data of the surfaces of the rock slabs A1 and B2 where the proppant 3 is embedded. The three-dimensional coordinate data of the contact surface between the rock slab A1 and the proppant 3 in the X direction is Ax 1 、Ax 2 、Ax 3 ...Ax N ; The three-dimensional coordinate data of the contact surface between the rock slab A1 and the proppant 3 in the Y direction is Ay 1 、Ay 2 、Ay 3 ...Ay N ; The three-dimensional coordinate data of the contact surface between the rock slab B2 and the proppant 3 in the X direction is Bx 1 、Bx 2 、Bx 3 ...Bx N ; In the Y direction, By 1 、By 2 、By 3 ...By N ;

[0064] Step 7: Calculate the coordinate differences of the three-dimensional coordinate data obtained for the rock slab A1 in Steps 3 and 6, and calculate the embedment depth h of the rock slab A1 A That is, AY 1 -Ay 1 、AY 2 -Ay 2 、AY 3 -Ay 3 ...AY N -Ay N ;

[0065] Calculate the coordinate differences of the three-dimensional coordinate data obtained for the rock slab B2 in Steps 3 and 6, and calculate the embedment depth h of the rock slab B2 B That is, BY 1 -By 1 、BY 2 -By 2 、BY 3 -By 3 ...BY N -By N ;

[0066] Step 8: Add the embedding depth of slate A1 to the embedding depth of slate B2, which is the embedding depth of the proppant 3 for the double slates.

[0067] For the method for measuring the embedding degree of the proppant in the tight reservoir of the present invention, the measurement of the embedding degree of the proppant 3 with different particle sizes such as 20 / 40 mesh and 40 / 70 mesh, their combined particle sizes, and different sand laying concentrations can also be carried out. Only the type and parameters of the proppant 3 laid in the two slates need to be changed in Examples 2-4 above, and the remaining steps are the same as those in Examples 2-4.

[0068] According to the above content, it can be seen that the method for measuring the embedding degree of the proppant in the tight reservoir of the present invention can accurately measure the embedding degree of the proppant 3, effectively solve the problem of evaluating the embedding degree of the proppant, and provide technical support for the optimization of proppant parameters.

Claims

1. Method for measuring the embedding degree of proppants in tight reservoirs, characterized in that, two rock slabs are processed from the target formation rock or surface rock outcrop. For the proppant embedding in the rock slabs, a method of clamping the proppant between two rock slabs is adopted. Under the formation closure stress condition, three-dimensional laser scanning measurement of the three-dimensional coordinates of the rock slabs before and after the proppant is embedded in the rock slabs is carried out to obtain the embedding depth of the proppant on the surfaces of the two rock slabs.

2. The method for measuring the embedding degree of proppants in tight reservoirs according to claim 1, characterized in that, it is specifically implemented according to the following steps: Step 1, rock slab production: According to the shape and size requirements of the test samples for the conductivity tester, two rock slabs are processed from the target formation rock or surface rock outcrop, namely rock slab A and rock slab B; the surfaces of rock slab A and rock slab B that do not contact the proppant are placed flat, and glue is applied around the bottom of the flat rock slab A and rock slab B; Step 2, simulate the soaking process of the fracturing fluid on the fracture wall surface and the rock after fracturing; Step 3, respectively scan the surfaces of rock slab A and rock slab B that will contact the proppant to obtain the three-dimensional coordinate data of the contact surfaces of rock slab A and rock slab B with the proppant; Step 4, place the surface of one of the rock slabs A and B with glue applied as the bottom into the API conductivity chamber, and lay the proppant and sand concentration to be tested between the two rock slabs according to the test purpose; Step 5, set the working pressure of the conductivity tester according to the formation closure stress of the test reservoir to conduct the test on the embedding degree of the proppant; Step 6, take out rock slab A and rock slab B from the proppant fracture conductivity tester, and remove the proppant on the surfaces of rock slab A and rock slab B. Respectively scan the surfaces of rock slab A and rock slab B where the proppant is embedded to obtain the three-dimensional coordinate data of the proppant-embedded surfaces of rock slab A and rock slab B; Step 7, calculate the coordinate difference for the three-dimensional coordinate data obtained for rock slab A in Step 3 and Step 6 to calculate the embedding depth of rock slab A; calculate the coordinate difference for the three-dimensional coordinate data obtained for rock slab B in Step 3 and Step 6 to calculate the embedding depth of rock slab B; Step 8, add the embedding depth of rock slab A to the embedding depth of rock slab B, which is the embedding depth of the proppant for the double rock slabs.

3. The method for measuring the embedding degree of proppants in tight reservoirs according to claim 2, characterized in that, in Step 1, the surfaces of rock slab A and rock slab B that do not contact the proppant are placed flat on A4 paper, and a hot melt gun is used to apply glue around the bottom of rock slab A and rock slab B.

4. The method for measuring the embedding degree of proppants in tight reservoirs according to claim 2, characterized in that, in Step 2, formation water or fracturing fluid is used to soak rock slab A and rock slab B to simulate the soaking process of the fracturing fluid on the fracture wall surface and the rock after fracturing.

5. The method for measuring the embedding degree of proppants in tight reservoirs according to claim 2, characterized in that, the three-dimensional coordinate data is obtained by scanning using a three-dimensional laser scanner.

6. The method for measuring the embedding degree of proppants in tight reservoirs according to claim 2, characterized in that, The three-dimensional coordinate data of the contact surface between the proppant-embedded pre-slate A and the proppant obtained in step 3 has the X direction as AX 1 , AX 2 , AX 3 ... AX N ; in the Y direction, AY 1 , AY 2 , AY 3 ... AY N ; the three-dimensional coordinate data of the contact surface between the proppant-embedded pre-slate B and the proppant has the X direction as BX 1 , BX 2 , BX 3 ... BX N ; in the Y direction, BY 1 , BY 2 , BY 3 ... BY N ; The X-direction three-dimensional coordinate data of the contact surface between the proppant-embedded rock slab A and the proppant obtained in step 6 is Ax 1 、Ax 2 、Ax 3 ...Ax N ; The Y-direction is Ay 1 、Ay 2 、Ay 3 ...Ay N ; The X-direction three-dimensional coordinate data of the contact surface between the proppant-embedded rock slab B and the proppant is Bx 1 、Bx 2 、Bx 3 ...Bx N ; In the Y-direction, By 1 、By 2 、By 3 ...By N 。 7. The method for measuring the embedding degree of proppants in tight reservoirs according to claim 2, characterized in that, The embedding depth of the proppant in Slab A calculated in Step 7 is AY 1 -Ay 1 、AY 2 -Ay 2 、AY 3 -Ay 3 ...AY N -Ay N ; The embedding depth of the proppant in Slab B is BY 1 -By 1 、BY 2 -By 2 、BY 3 -By 3 ...BY N -By N 。