A fractal-based method for evaluating the fracability of rock based on the mass fractal of broken rock pieces

Abstract

The present invention discloses a method for evaluating the fracturability based on the mass fractal of rock fragmentation blocks. This method obtains the rock mechanical parameters of the core through triaxial core experiments; secondly, by using the fragmented core blocks after fracturing and introducing the mass fractal theory, the fracturability of the reservoir is characterized by the mass fractal dimension; finally, combining the rock mechanical parameters obtained from the experiments, the relationship between the rock mechanical parameters and the mass fractal dimension is fitted through multiple regression analysis. Then, by using data such as drilling, logging, and mud logging, the rock mechanical parameter profile along the wellbore is obtained, and the continuous fractal dimension along the wellbore is calculated through the fitted relationship for comprehensive fracturability evaluation. The fracturability evaluation method provided by the present invention combines the advantages of experimental evaluation and comprehensive evaluation, and can provide theoretical guidance for the selection of sweet spots in exploration and development projects.

Description

Technical Field

[0001] The present invention relates to the field of oil and gas engineering, and particularly to a fracturing evaluation method based on the mass fractal of rock fragments. Background Art

[0002] Tight, low-porosity, and low-permeability are typical characteristics of shale reservoirs. Multi-cluster volume fracturing in horizontal wells is an important means for shale gas development, and fracturability evaluation is an important means for selecting sweet spots in the volume fracturing project of shale gas reservoirs, which is of great significance for identifying engineering sweet spots and forming large-scale complex fractures during fracturing.

[0003] Fracturability is generally defined as the ability of a reservoir to form large-scale complex fractures during fracturing, which is related to parameters such as the brittleness index, fracture toughness, and reservoir stress of reservoir rocks. To characterize the fracturability of a reservoir, there are mainly two methods in the prior art: experimental evaluation and comprehensive evaluation. Among them, experimental evaluation judges the fracturability of the reservoir by directly observing whether a complex hydraulic fracture network is formed in the core sample through physical simulation experiments of hydraulic fracturing in the laboratory. The comprehensive evaluation method gradually deepens the definition of fracturability, and then considers factors such as the brittleness of reservoir rocks, fracture toughness, reservoir in-situ stress, and the development of natural fractures, and uses various comprehensive evaluation methods, such as the product method, entropy weight method, and analytic hierarchy process and other comprehensive weighting methods to establish a fracturability evaluation model. The experimental evaluation method is a direct method with high accuracy, but the evaluation process is cumbersome and complex; the comprehensive evaluation method obtains reservoir information through indirect means such as drilling, logging, and mud logging and then conducts evaluation, and the evaluation process is simple but the accuracy is low. At present, the experimental-based fracturability evaluation method is relatively single, and there are few methods in the prior art that couple experimental and comprehensive evaluations. Summary of the Invention

[0004] In view of this, the purpose of the embodiments of the present invention is to provide a fracturability evaluation method based on the mass fractal of rock fragments.

[0005] To achieve the above technical objectives, the present invention provides the following technical solutions.

[0006] A fracturability evaluation method based on the mass fractal of rock fragments, characterized by comprising the following steps:

[0007] Obtain the core of the target formation, and obtain the rock mechanical parameters of the core through indoor experiments.

[0008] Conduct a triaxial mechanical compression experiment on the core, count the mass and particle size distribution of the core before and after failure, and apply the mass fractal theory to obtain the mass fractal dimension of the fractured core.

[0009] Fitting the mathematical relationship between the fractal dimension of fitting quality and rock mechanical parameters to obtain the first relational expression between the fractal dimension of fitting quality and rock mechanical parameters;

[0010] Obtaining the rock mechanical parameters distributed along the wellbore profile of the well to be evaluated;

[0011] Substituting the rock mechanical parameters distributed along the wellbore profile of the well to be evaluated into the first relational expression to obtain the fractal dimension distributed along the wellbore profile of the well to be evaluated, and using the fractal dimension for the compressibility evaluation.

[0012] Furthermore, the rock mechanical parameters include mineral brittleness index, Young's modulus, Poisson's ratio, and compressive strength.

[0013] Furthermore, the method for obtaining the mineral brittleness index is as follows:

[0014]

[0015] In the formula: MBI is the mineral brittleness index, dimensionless; W 石英 is the quartz mineral content, %; W 白云石 is the dolomite mineral content, %; W 总 is the total mineral content, %.

[0016] Furthermore, the step of applying the mass fractal theory to obtain the mass fractal dimension of the broken core includes:

[0017] Statistical cumulative mass M(R) of fragments with diameter less than R, measure the total mass M of the core, and obtain the fractal dimension D through the relational expression M(R) / M = 1 - exp[-(R / δ) b ;

[0018] D = 3 - b

[0019] where δ is the average size of the rock sample fragments; b is the slope.

[0020] Furthermore, it also includes the step: drawing the double logarithmic coordinate lgR - lg(M(R) / M) curve. If there is a straight line segment on the curve, it indicates that the fragment distribution of the rock sample has a fractal structure; if there are also straight line segments with different slopes on the curve, it indicates that the fragment distribution has statistical self-similarity at multiple scales. According to the particle size range where each straight line segment is located and its slope b, the fractal dimension D can be obtained.

[0021] Furthermore, the first relational expression is:

[0022] D = aMBI + bE + cv + dC t + e

[0023] In the formula: v is the Poisson's ratio; E is the Young's modulus, C tis the compressive strength, and the coefficients a, b, c, d, and e are fitting parameters.

[0024] Furthermore, rock mechanical parameters distributed along the wellbore profile are obtained through drilling, logging, and mud logging data.

[0025] The present invention provides a fractal-based method for evaluating the fracturability of rocks based on the mass fractal of rock fragments. The method obtains the rock mechanical parameters of the core through core triaxial experiments; secondly, the crushed core fragments after fracturing are used to introduce the mass fractal theory, and the fracturability of the reservoir is characterized by the mass fractal dimension; finally, combined with the rock mechanical parameters obtained from the experiments, the relationship between the rock mechanical parameters and the mass fractal dimension is fitted through multiple regression analysis, and then the rock mechanical parameter profile along the wellbore is obtained through data such as drilling, logging, and mud logging, and the continuous fractal dimension along the wellbore is calculated through the fitted relationship for comprehensive fracturability evaluation, providing an index for the selection of sweet spots in shale gas exploration and development projects. Description of the Drawings

[0026] Figure 1 This is the fragmentation situation of the No. 1 rock sample before testing in the embodiment of the present invention.

[0027] Figure 2 This is the fragmentation situation of the No. 1 rock sample after testing in the embodiment of the present invention.

[0028] Figure 3 This is the double logarithmic relationship diagram of the cumulative mass and particle size of the No. 2 rock sample in the embodiment of the present invention.

[0029] Figure 4 This is the correlation between the area and the fractal dimension in the embodiment of the present invention.

[0030] Figure 5 This is the distribution diagram of the rock mechanical parameters and the fracturability profile in the embodiment of the present invention. Detailed Embodiments

[0031] Combined with the description of the drawings and the specific embodiments of the present invention, the details of the present invention can be more clearly understood. However, the specific embodiments of the present invention described herein are only for the purpose of explaining the present invention and cannot be construed in any way as a limitation of the present invention. Under the teaching of the present invention, those skilled in the art can conceive any possible variations based on the present invention, and these should all be regarded as belonging to the scope of the present invention.

[0032] A fractal-based method for evaluating the fracturability of rocks based on the mass fractal of rock fragments is proposed in the present invention, and the method includes the following steps:

[0033] (1) Obtain the core of the target formation, and obtain the rock mechanical parameters of the core through indoor experimental tests;

[0034] The rock samples obtained from downhole coring are relatively large in volume. After processing, the cores need to meet the international experimental standards. Using a coring machine and a core cutter, the cores are processed into cylinders with a length of about 5.0 cm and a diameter of about 2.5 cm, and the two ends are cut and polished into planes perpendicular to the axis of the cylinder. According to the above regulations on length and diameter, the volume of the processed rock specimens can be limited to 15 cm 3 or more. If the value is lower than this, the comparative analysis effect of the experimental results will be weakened, and then the qualified specimens need to be numbered one by one.

[0035] After numbering, measure the length and diameter of the core. Put the core into a drying oven and bake it at a temperature below 60 °C for 48 hours to ensure that the pore structure of the core is not damaged while ensuring that all the moisture has evaporated. Then, take out the sample and put it into a drying dish (with moisture-absorbing silica gel at the bottom) to cool. Dry the measurement room where the electronic balance is located to make the air dryness reach about 40%, and weigh the baked core with the electronic balance.

[0036] Put a special plastic sleeve that can resist oil and pressure for a long time on the processed core, and then conduct uniaxial and triaxial experiments on the rock specimen to measure the rock mechanical parameters such as the elastic modulus, Poisson's ratio, and triaxial compressive strength of the rock sample as shown in Table 1-2.

[0037] Table 1 Rock mechanical parameters of rock samples

[0038]

[0039] Analyze the mineral content of the core, and the results are shown in Table 2. At the same time, take quartz minerals and dolomite minerals as brittle minerals, and calculate the mineral brittleness index of the rock sample.

[0040]

[0041] In the formula: MBI is the mineral brittleness index, dimensionless; W 石英 is the quartz mineral content, %; W 白云石 is the dolomite mineral content, %; W 总 is the total mineral content, %.

[0042] Table 2 Core mineral content and mineral brittleness index

[0043]

[0044] (2) Conduct triaxial mechanical compression experiments on the core, count the mass and particle size distribution of the core before and after failure, and use the mass fractal theory to obtain the mass fractal dimension of the broken core;

[0045] After the core is compressed, the larger the inner surface area of the broken core, the better the transformation effect and the stronger the fracturability. Therefore, counting the surface area of the broken pieces of each core can reflect the level of fracturability. The area statistical steps are as follows:

[0046] After the rock sample is experimented, take a photo of the broken rock sample, use Image-Pro Plus 6.0 software to process the photo of the broken rock sample, calculate the area after breaking. Taking the No. 1 rock sample as an example, the processing process is as follows:

[0047] (a) Convert the picture of the broken No. 1 rock sample into JPG format, and adjust the pixels within an appropriate range so that the picture size should be less than 10M, and import the processed picture into the software;

[0048] (b) Set a scale for the imported picture. The specific scale needs to be reset for different pictures, based on the diameter (25mm) of the rock sample in the picture, to determine the area range of the rock sample in the picture;

[0049] (c) Select the color separation tool to calibrate the broken area of the rock sample; considering the concavity and convexity and irregularity of the broken rock sample, manual color separation is used to complete the definition of the irregular area;

[0050] (d) Referring to the automatic color separation method, color the measured area by adjusting the threshold. Therefore, adjust the smoothing operator for manual color separation to 3.07 to optimize the area of the concave and convex areas;

[0051] (e) After depicting all the test areas, convert the determined areas and calculate the area to obtain the area distribution, and accumulate it to get the total broken area of the No. 1 rock sample; export the picture to get the result.

[0052] Figure 1-2 The area distribution before and after the break of the No. 1 rock sample is shown, and the area distribution of each rock sample is shown in Table 3.

[0053] Table 3 Broken areas of 9 rock samples

[0054] Core Label Core Sample Size (mm) Number of Broken Core Pieces <![CDATA[Total area of fractures in broken pieces (mm 2 )]]> No. 1 D (25mm) × Length (50mm) 6 3695.2 No. 2 D (25mm) × Length (50mm) 4 2069.5 No. 3 D (25mm) × Length (50mm) 3 1238.9 No. 4 D (25mm) × Length (50mm) 6 2020.8 No. 5 D (25mm) × Length (50mm) 4 881.7 No. 6 D (25mm) × Length (50mm) 7 801.6 No. 7 D (25mm) × Length (50mm) 5 3518.6 No. 8 D (25mm) × Length (50mm) 4 1282.9 No. 9 D (25mm) × Length (50mm) 3 918.3

[0055] Let M(R) be the cumulative mass of the fragments with a diameter less than R, and M be the total mass of the rock sample. If the mass of the fragments follows the Weibull distribution, we can get:

[0056] M(R) / M = 1 - exp[-(R / δ) b

[0057] In the formula: δ is the average size of the rock sample fragments. When (R / δ) b << 1, Equation (1) is: ​

[0058] M(R) / M = (R / δ) b

[0059] According to R b-1 dR ∝ R 3 R -D-1 The fractal dimension can be obtained from dR as follows:

[0060] D = 3 - b

[0061] According to the calculation method of the fractal dimension D, the rock fragments of the marble specimen after loading failure can be weighed by the sieving method, and the percentage content M(R) / M of the fragments smaller than the particle size R in the total mass of the rock sample can be obtained. A curve can be plotted on the double logarithmic coordinates lgR - lg(M(R) / M). As long as there is a straight line segment on this curve, it indicates that the fragment distribution of the rock sample has a fractal structure; if there are also straight line segments with different slopes on the curve, it indicates that the fragment distribution has statistical self-similarity at multiple scales. According to the particle size range and slope b of each straight line segment, the scale-free interval and the corresponding fractal dimension D of the fractal distribution of the rock fragments can be obtained from the above mathematical relationship.

[0062] (3) Fit the mathematical relationship between the mass fractal dimension and the rock mechanical parameters to obtain the first relationship between the mass fractal dimension and the rock mechanical parameters;

[0063] Based on the rock samples broken in the triaxial mechanical compression experiment, the mass and particle size distribution of the rock samples after failure are statistically analyzed. Applying the mass fractal theory, the mass fractal dimension of the broken rock samples can be obtained through fitting analysis. Since there are many rock samples, the second rock sample is taken as an example for specific analysis here.

[0064] The relationship table of the mass and particle size distribution of the rock sample after fragmentation is obtained by the sieving method, as shown in Table 4. Furthermore, the data of M(R) / M and logR are obtained, and the relationship diagram between the two is made, as Figure 3 shown. The fractal dimension can be obtained according to the slope of the fitted straight line, and the fracturability of the second rock sample can be characterized.

[0065] Similarly, according to the above calculation and analysis process, the fractal dimensions of 9 rock samples can be obtained, and the results are shown in Table 5.

[0066] Table 4 Mass and Particle Size Distribution Table of the Second Rock Sample

[0067]

[0068]

[0069] Table 5 Mass Fractal Dimensions of 9 Rock Samples after Crushing

[0070] Core Sample Number Core Sample Type Fractal Dimension 1 Fluorescent Argillaceous Dolomite 1.702 2 Oil-Stained Argillaceous Dolomite 1.577 3 Fluorescent Argillaceous Limestone 1.268 4 Dark Gray Dolomitic Mudstone 1.028 5 Fluorescent Argillaceous Dolomite 0.610 6 Dark Gray Mudstone (Medium-Strong Calcareous) 0.528 7 Dark Gray Mudstone 1.900 8 Gray Oil-Stained Fine Sandstone 1.267 9 Gray Fluorescent Fine Sandstone 0.949

[0071] The fractal dimension characterizes the degree of fragmentation of the core after the triaxial compression experiment, and the area of the fragmented blocks is directly related to the quality of the stimulation effect. Therefore, we conducted a correlation analysis between the area of the fragmented rock samples obtained statistically and the fractal dimension, and the results are as Figure 4 shown. It can be seen from this that there is a good correlation between the two, indicating that both can better characterize the fracturability of the reservoir. Therefore, in subsequent studies, we used the fractal dimension as the fracturability index, analyzed its correlation with core minerals and mechanical parameters, and established a relationship through multiple regression fitting.

[0072] The mass fractal dimension characterizes the degree of fragmentation of the rock sample after pressing. The larger its value, the more fragmented and dispersed the crushed blocks of the rock sample, and the larger the area of the formed fracture cracks, indicating the stronger the fracturability of the rock sample. The fracturability is related to parameters such as the brittle mineral content, elastic modulus, Poisson's ratio, and compressive strength of the reservoir rock. Therefore, the above factors affecting fracturability are used as independent variables, and the fractal dimension is used as the dependent variable for multiple regression fitting analysis to obtain the relationship formula for calculating and analyzing the dimension through mineral content and rock mechanical parameters, as shown below.

[0073] Frac=D=aMBI+bE+cv+dC t +e

[0074] (4) Obtain the rock mechanical parameters distributed along the wellbore profile of the well to be evaluated;

[0075] When conducting fracturability evaluation in actual engineering, it is often necessary to obtain the fracturability index distributed along the wellbore profile, which can be achieved through the continuity of logging data. The brittle mineral content distributed along the well profile can be obtained through lithological mineral scanning logging, and then the mineral brittleness index MBI can be calculated. The elastic modulus E, Poisson's ratio v, and triaxial compressive strength C t can also be obtained through logging data such as acoustic wave, density, and natural gamma ray, and the obtaining methods are as follows.

[0076]

[0077]

[0078] C t =0.0045E(1-V cl )+0.008V c1 E

[0079]

[0080]

[0081] In the formula: v is Poisson's ratio, dimensionless; V pis the longitudinal wave velocity, m / s; V s is the shear wave velocity, m / s; E is the Young's modulus, Pa; ρ is the rock density, kg / m 3 . C t is the compressive strength, MPa; V cl is the shale content; GR is the natural gamma log value, API; GCUR is the Hilchie index, related to the geological age. Generally, 3.7 is taken for new formations and 2 for old formations; I GR is the shale content index.

[0082] (5) Substitute the rock mechanical parameters distributed along the wellbore profile of the well to be evaluated into the first relational expression to obtain the fractal dimension distributed along the wellbore profile of the well to be evaluated, and use the fractal dimension to evaluate the compressibility.

[0083] Based on the mineral brittleness, rock mechanical parameters, and fractal dimension obtained from the experiments on 9 rock samples in the embodiments of the present application, the coefficients a, b, c, d, and e in the formula are obtained by multiple regression fitting as 2.5967, 6.8655×10 -6 , -1.2129, -6.5415×10 -4 , 0.4013 respectively, that is, the calculation relational expression of the fractal dimension fracturability is:

[0084] Frac = D = 2.5967×MBI + 6.8655×10 -6 ×E - 1.2129×v - 6.5415×10 -4 ×C t + 0.4013

[0085] Taking a section of the cored well as an example, combining the lithology scan and conventional logging data of the cored well, as shown in Table 6, the continuous mineral brittleness index MBI, elastic modulus E, Poisson's ratio v, and compressive strength C are calculated t , and the results are shown in Table 7. Further, a continuous fracturability profile can be obtained, as Figure 5 shown, thereby providing a basis for optimizing the perforation selection of horizontal well staged fracturing.

[0086] Table 6 Partial logging data and mineral content of the cored well

[0087]

[0088] Table 7 Calculation results of fracturability

[0089]

[0090] The present invention has been specifically described above through embodiments. It is necessary to point out here that these embodiments are only the preferred embodiments of the present invention, and do not impose any limitations on the present invention, nor are they limited to the forms disclosed herein. They should not be regarded as excluding other embodiments. Any modifications and simple changes made by those skilled in the art without departing from the technical idea and scope of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A fractal-based method for evaluating the fracability of rocks based on the mass fractal of broken rock blocks, characterized in that, It includes the following steps: Obtain the core of the target formation, and obtain the rock mechanical parameters of the core through indoor experimental tests; Conduct a triaxial mechanical compression experiment on the core, statistically analyze the mass and particle size distribution of the core before and after failure, and apply the mass fractal theory to obtain the mass fractal dimension of the broken core; Fit the mathematical relationship between the mass fractal dimension and the rock mechanical parameters to obtain the first relationship between the fitted mass fractal dimension and the rock mechanical parameters; The first relationship is: ； In the formula: v is the Poisson's ratio; E is the Young's modulus, C t is the compressive strength, and the coefficients a , b , c , d , e are fitting parameters; The rock mechanical parameters include the mineral brittleness index, Young's modulus, Poisson's ratio, and compressive strength. The method for obtaining the mineral brittleness index is: ； In the formula: MBI is the mineral brittleness index, dimensionless; W 石英 is the quartz mineral content, %; W 白云石 is the dolomite mineral content, %; W 总 is the total mineral content, %; Obtain the rock mechanical parameters distributed along the wellbore profile of the well to be evaluated; Substitute the rock mechanical parameters distributed along the wellbore profile of the well to be evaluated into the first relationship, obtain the fractal dimension distributed along the wellbore profile of the well to be evaluated, and use the fractal dimension for the compressibility evaluation.

2. The fractal-based method for evaluating the fracability according to claim 1, wherein The step of applying the mass fractal theory to obtain the mass fractal dimension of the broken core includes: Cumulative mass of fragments with diameters less than R is measured, and the total mass M of the core is obtained. The fractal dimension D is obtained through the relationship M ( R ), and the fractal dimension D is obtained through the relationship : ； where δ is the average size of the rock sample fragments; b is the slope.

3. The fractal-based method for evaluating the fracability based on the mass fractal of rock fragments according to claim 1, wherein, It further includes the step of plotting a double logarithmic coordinate curve. If there are straight line segments on the curve, it indicates that the fragment distribution of the rock sample has a fractal structure; if there are also straight line segments with different slopes on the curve, it indicates that the distribution of the fragments has statistical self-similarity at multiple scales. According to the particle size range and slope b of each straight line segment, the fractal dimension can be obtained D .

4. The fractal dimension-based method for evaluating the fracability according to claim 1, wherein Obtain the rock mechanical parameters distributed along the wellbore profile through drilling, logging, and mud logging data.

5. The fractal-based method for evaluating the fracability according to claim 1, wherein It also includes the step of calculating the area after the rock sample is broken. The calculation process is as follows: (a)Convert the picture of the broken rock sample into JPG format, adjust the pixels so that the picture size should be less than 10M, and import the processed picture into the software; (b)Set a scale for the imported picture. The scale needs to be reset for different pictures, with the diameter of the rock sample in the picture being 25mm as the standard, and determine the area range of the rock sample in the picture; (c)Select the color separation tool to calibrate the broken area of the rock sample; use hand-drawn color separation to complete the definition of irregular areas; (d)Refer to the automatic color separation method, adjust the threshold to achieve the coloring of the measured area, and realize the optimization of the area of concave and convex areas; (e)After depicting all the test areas, convert the determined areas and perform area calculation to obtain the area distribution, and accumulate them to obtain the total broken area of the rock sample; Export the picture to obtain the result.

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