CN114813303A - Method for calculating rock brittleness index of tight sandstone reservoir - Google Patents
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Abstract
The invention discloses a method for calculating a rock brittleness index of a tight sandstone reservoir, relates to the field of unconventional oil and gas exploration and development, relates to a method for calculating a brittleness index of a stratum rock, and particularly relates to a method for calculating a rock brittleness index of a tight sandstone reservoir, which comprises the following steps of: 1) preparing a compact sandstone sample required by a stress-strain experiment; 2) carrying out a stress-strain experiment until the rock sample is damaged; 3) processing the damaged rock sample to prepare a casting slice; 4) analyzing crack distribution characteristics in the cast body sheet, and calculating a fractional dimensionality; 5) analyzing the fractional dimensionality data, estimating a rock brittleness index, and 6) correcting the rock brittleness index estimated in the step 5 to obtain a tight sandstone reservoir rock brittleness index calculation model; the method effectively improves the calculation precision and reliability of the rock brittleness index of the tight sandstone reservoir and effectively solves the problem that the residual strength surface is not obvious in the brittleness index evaluation method based on elastic strain.
Description
Technical Field
The invention relates to the field of unconventional oil and gas exploration and development, relates to a method for calculating a brittleness index of stratum rocks, and particularly relates to a method for calculating a brittleness index of rocks in a tight sandstone reservoir.
Background
The brittleness index of rock is one of important factors to be considered in the design of compact sandstone oil and gas volume fracturing. It is generally considered that the brittleness index is closely related to rock mineral composition, rock mechanical properties, and the like. The higher the rock brittleness index, the more easily it fractures to form complex fractures.
At present, rock brittleness evaluation methods at home and abroad can be mainly divided into three main categories: an evaluation method based on elastic strain, an evaluation method based on rock elasticity parameters and an evaluation method based on rock mineral composition. For unconventional reservoirs, the difference between brittleness indexes calculated by adopting different brittleness evaluation methods is often large, the existing brittleness index evaluation method is not strong in reliability, and the accuracy needs to be further improved.
The brittleness evaluation method based on elastic strain is one of the main means for researching the brittleness index of the rock in a laboratory. Stress-strain test according to the analysis of the stress-strain test, when the stress is loaded to the peak intensity from a certain initial elastic state, the stress is suddenly changed and rapidly falls to the residual intensity surface (as shown in figure 1). By this feature of rock stress drop, the brittleness index B1 can be expressed as B1= ((B-a) - (c-B))/(B-a). However, in practice, problems of lack of residual strength or insignificant residual strength are often encountered. For this type of stress-strain curve (see fig. 2), the evaluation method based on elastic strain cannot accurately calculate the brittleness index.
Disclosure of Invention
The invention aims to improve the calculation precision and reliability of the rock brittleness index of the tight sandstone reservoir, effectively solve the problem that the residual strength surface is not obvious in the brittleness index evaluation method based on elastic strain, and provide the calculation method of the rock brittleness index of the tight sandstone reservoir, which has the advantages of reasonable design, strong universality and accurate and reliable calculation result.
The invention discloses a method for calculating rock brittleness index of a tight sandstone reservoir, which comprises the following steps:
1) preparing a compact sandstone sample required by a stress-strain experiment;
2) carrying out a stress-strain experiment until the rock sample is damaged;
3) processing the damaged rock sample to prepare a casting slice;
4) analyzing crack distribution characteristics in the cast body sheet, and calculating a fractional dimensionality;
5) analyzing the fractional dimensional data, and estimating the brittleness index of the rock, wherein the estimated model is the brittleness index B = (D-D) min )/(D max -D min ) Wherein D is max For the maximum fractional dimension calculated by step 4), D min The minimum score dimension calculated in the step 4) is obtained, and D is the score dimension of a certain sample;
6) correcting the rock brittleness index estimated in the step 5 to obtain a compact sandstone reservoir rock brittleness index calculation model B 0 =(D-D 0min )/(D 0max -D 0min ) Wherein D is 0min To the corrected minimum fractional dimension, D 0max To be correctedThe maximum score dimension of;
D 0min and D 0max Is calculated as follows:
F(D 0min ，D 0max )=
，
wherein 1 < D 0min ＜D 0max ＜2，B i For the ith rock-like brittleness index calculated from the fractional dimension of the cast sheet, B1 i Is the ith rock-like brittleness index calculated based on elastic strain,
when F (D) 0min ，D 0max ) Taking the minimum value as an objective function to obtain corrected D 0min And D 0max 。
Preferably, the fractional dimension calculation method in step 4): and observing the casting body slice by adopting an optical microscope, shooting the picture, processing the picture to obtain a crack distribution map, and calculating the fractional dimensionality according to the crack distribution map.
Preferably, the step 4) adopts a grid covering method to calculate the fractional dimensionality of the cracks, specifically, a square grid is drawn by taking the center of the cast body slice as a reference point, the length of the cracks is selected as the crack characteristic, and the side length is obtainedRTotal length of cracks in the square gridLFitting ln in log-log coordinatesLIs the same as lnRLinear fitting to obtain
(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture length as a characteristic.
Preferably, the step 4) adopts a grid covering method to calculate the fractional dimensionality of the cracks, specifically, a square grid is drawn by taking the center of the cast body slice as a reference point, the number of the cracks is selected as the crack characteristic, and the number of the cracks in the square grid with the side length of R is obtainedNFitting ln in log-log coordinatesLIs the same as lnNLinear fitting to obtain lnL=c+DlnN(ii) a Wherein c is a proportionality constant, and D is a fracture fraction dimension calculated by taking the number of fractures as a characteristic.
Preferably, the grid coverage method is adopted in the step 4) to calculate the fracture fractional dimensionality, specifically, a square grid is drawn by taking the center of the cast body slice as a reference point, the fracture area is selected as the fracture characteristic, and the fracture area in the square grid with the side length of R is obtainedSFitting ln in log-log coordinatesLIs the same as lnSLinear fitting to obtain lnL=c+DlnS(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture area as a characteristic.
Or preferably, the damaged rock sample is dyed by using blue fluorescent resin in the step 3), the initial form of the crack is marked, and the cast body slice for observation under an optical microscope is formed finally after cutting, grinding and packaging.
Preferably, the stress-strain experiment in the step 2) is a uniaxial compression experiment or a triaxial compression experiment, the sample is loaded into a rubber sleeve and placed in the center of a pressure bearing plate of the press, and the sample is loaded at a loading rate of 0.5MPa/s until the sample is damaged.
Preferably, the stress-strain experiment in step 2) is a tensile experiment or a shear experiment or a cutting experiment.
The method effectively improves the calculation precision and reliability of the rock brittleness index of the tight sandstone reservoir and effectively solves the problem that the residual strength surface is not obvious in the brittleness index evaluation method based on elastic strain.
When the residual strength surface is not obvious, the brittleness evaluation method based on elastic strain fails, and the calculation method based on the fractional dimensionality can still quantitatively evaluate the brittleness.
Drawings
Figure 1 is a stress-strain curve of the residual strength of tight sandstone.
Figure 2 is a stress-strain curve for tight sandstone without residual strength.
FIG. 3 is a broken rock sample.
FIG. 4 is a sheet of cast body obtained by processing a damaged rock sample according to the present invention.
FIG. 5 is a schematic diagram of the method for calculating the fracture fraction dimension by using a grid coverage method.
Fig. 6 is a graph comparing the calculation result of the brittleness index of the present invention with the calculation result of the brittleness index based on the elastic strain.
Detailed Description
The invention discloses a method for calculating rock brittleness index of a tight sandstone reservoir, which comprises the following steps:
1) preparing a compact sandstone sample required by a stress-strain experiment;
2) carrying out a stress-strain experiment until the rock sample is damaged;
3) processing the damaged rock sample to prepare a casting slice;
4) analyzing crack distribution characteristics in the cast body sheet, and calculating a fractional dimensionality;
5) analyzing the fractional dimensional data, and estimating the brittleness index of the rock, wherein the estimated model is the brittleness index B = (D-D) min )/(D max -D min ) Wherein D is max For the maximum fractional dimension calculated by step 4), D min The minimum score dimension calculated in the step 4) is obtained, and D is the score dimension of a certain sample;
6) correcting the rock brittleness index estimated in the step 5 to obtain a compact sandstone reservoir rock brittleness index calculation model B 0 =(D-D 0min )/(D 0max -D 0min ) Wherein D is 0min To the corrected minimum fractional dimension, D 0max Is the corrected maximum score dimension;
D 0min and D 0max Is calculated as follows:
F(D 0min ，D 0max )=
，
wherein 1 < D 0min ＜D 0max ＜2，B i For the ith rock-like brittleness index calculated from the fractional dimension of the cast sheet, B1 i Is the ith rock-like brittleness index calculated based on elastic strain,
when F (D) 0min ，D 0max ) Taking the minimum value as an objective function to obtain corrected D 0min And D 0max 。
The score dimension calculation method in the step 4) comprises the following steps: and observing the casting body slice by adopting an optical microscope, shooting the picture, processing the picture to obtain a crack distribution map, and calculating the fractional dimensionality according to the crack distribution map.
Calculating the fractional dimensionality of the crack by adopting a grid covering method in the step 4), specifically, taking the center of a cast body slice as a reference point, drawing a square grid, selecting the length of the crack as the crack characteristic, and obtaining the side length of the crackRTotal length of cracks in the square gridLFitting ln in log-log coordinatesLIs the same as lnRLinear fitting to obtain
(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture length as a characteristic.
Calculating the fractional dimensionality of the cracks by adopting a grid covering method in the step 4), specifically, taking the center of a cast body slice as a reference point, drawing a square grid, selecting the number of the cracks as crack characteristics, and obtaining the number of the cracks in the square grid with the side length RNFitting ln in log-log coordinatesLIs the same as lnNLinear fitting to obtain lnL=c+DlnN(ii) a Wherein c is a proportionality constant, and D is a fracture fraction dimension calculated by taking the number of fractures as a characteristic.
Calculating the fractional dimensionality of the cracks by adopting a grid covering method in the step 4), specifically, taking the center of a cast body slice as a reference point, drawing a square grid, and selecting the area of the cracks as the crack characteristics to obtain the area of the cracks in the square grid with the side length RSFitting ln in log-log coordinatesLIs the same as lnSLinear fitting to obtain lnL=c+DlnS(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture area as a characteristic.
And 3) dyeing the damaged rock sample by using blue fluorescent resin, marking the initial form of the crack, cutting, polishing and packaging to finally form a casting body slice for observation under an optical microscope.
And 2) loading the sample into a rubber sleeve, placing the rubber sleeve into the center of a pressure bearing plate of a press machine, and loading the sample at a loading rate of 0.5MPa/s until the sample is damaged.
The stress-strain test in step 2) may also be a tensile test or a shear test or a cutting test.
Tensile test: selecting a cylindrical rock sample, and then performing unidirectional stretching on a universal material testing machine until the cylindrical rock sample is broken.
Shearing experiment: selecting a cylindrical rock sample, and then applying a shearing force on a universal material testing machine until the sample is sheared off.
Cutting experiment: cutting experiments were performed on a rock cutting bench. During the experiment, the sample is fixed with rock clamping device, adjusts the cutting tooth height, makes the cutting tooth height be less than the sample top, and the starter motor makes the sample move to the cutting tooth direction, until the sample destruction.
Examples
Selecting a core with a specific depth of a tight sandstone stratum from a core library, drilling a small core by adopting a sleeve drill bit with the diameter of 25mm, and cutting the end face of the small core to obtain a cylindrical sample with the diameter of 25mm and the height of 50 mm;
the rock sample is destroyed in a uniaxial compression experiment mode, the sample is loaded into a rubber sleeve and placed in the center of a pressure bearing plate of a press machine, and the sample is loaded at a loading rate of 0.5MPa/s until the sample is destroyed;
the damaged rock sample was stained with blue fluorescent resin, the initial form of the crack was marked, cut, polished, and encapsulated, and finally a cast sheet sample for observation under an optical microscope was formed, as shown in fig. 4, the crack generated by the compression experiment appeared blue under the optical microscope.
Analyzing crack distribution characteristics in the cast body sheet, drawing a square grid by using the center of the cast body sheet as a reference point by adopting a grid covering method, and obtaining the side length of the square grid by using the length of the crack as the crack characteristicRTotal length of cracks in the square gridLAs shown in FIG. 5, fit ln in log-log coordinatesLIs the same as lnRLinear fitting to obtain
(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture length as a characteristic. The fractional dimensional data set (1.22, 1.29, 1.34, 1.34, 1.35, 1.36, 1.41, 1.42, 1.43, 1.65) is finally obtained.
The maximum score dimension D calculated in the statistical step max (1.65) and minimum indexing dimension D min (1.22), estimating the brittleness index using the formula B = (D-1.22)/(1.65-1.22); the friability index data sets (0, 0.16, 0.27, 0.29, 0.31, 0.32, 0.45, 0.46, 0.50, 1) were estimated.
Correcting the rock brittleness index estimated through the fracture fractional dimensionality in the last step by using a brittleness index data set (0.2, 0.28, 0.32, 0.32, 0.41, 0.41, 0.41, 0.45, 0.51, 0.76) obtained based on elastic strain calculation to obtain a compact sandstone reservoir rock brittleness index calculation model B based on the fracture fractional dimensionality 0 =(D-D 0min )/(D 0max -D 0min ) Wherein D is 0min To the corrected minimum fractional dimension, D 0max Is the corrected maximum score dimension;
D 0min and D 0max Is calculated as follows:
F(D 0min ，D 0max )=
，
wherein 1 < D 0min ＜D 0max ＜2，B i For the ith rock-like brittleness index calculated from the fractional dimension of the cast sheet, B1 i Is the ith rock-like brittleness index calculated based on elastic strain,
when F (D) 0min ，D 0max ) Taking the minimum value as an objective function to obtain corrected D 0min And D 0max ；
In this embodiment by increasing D stepwise max Value and step-wise reduction D min The value is combined, and F (D) is solved 0min ，D 0max ) Maximum fractional dimension D of minimum value max And the minimum score dimension D min At this time, it is maximumFractional dimension D max For the corrected maximum fractional dimension D 0max Minimum fractional dimension D min Is the corrected minimum fractional dimension D 0min And in the solving process, the condition that D is more than 1 is ensured min ＜D max ＜2。
Calibration procedure MATLAB program:
clear, close all, clc
D=[1.22,1.29,1.34,1.34,1.35,1.36,1.41,1.42,1.43,1.65];
B=[0.2, 0.28, 0.32, 0.32, 0.41, 0.41, 0.41, 0.45, 0.51, 0.76];
f=zeros(23,36);
m=0;
for mina=1.22:-0.01:1
m=m+1;
n=0;
for maxa=1.65:0.01:2
n=n+1;
err=0;
for i=1:10
err=err+((((D(i)-mina))/(maxa-mina))-B(i))^2;
end
f(m,n)=err;
end
end
[m, n]=find(f==min(min(f)));
min_real=1.22-(m-1)*0.01
max_real=1.65+(n-1)*0.01)
maximum fractional dimension D obtained after correction in the embodiment 0max Is 1.83, minimum division dimension D 0min At 1.07, the fractal dimension-based brittleness index calculation method B = (D-1.07)/(1.83-1.07) was finally determined;
furthermore, the model can be corrected by using a brittleness index calculated based on rock elasticity parameters or based on rock minerals.
FIG. 6 is a comparison of the brittle index calculation results of the present invention and the brittle index calculation results based on elastic strain. It can be seen that the brittleness index calculated by the present invention is substantially identical to the calculation result of the conventional method, i.e., the calculation of the brittleness index based on the elastic strain. More importantly, by adopting the method, the brittleness index can be quantitatively calculated under the condition of residual strength loss, and a new means is provided for evaluating the compressibility of the sandstone reservoir.
Claims (8)
1. A method for calculating rock brittleness index of a tight sandstone reservoir is characterized by comprising the following steps:
1) preparing a compact sandstone sample required by a stress-strain experiment;
2) carrying out a stress-strain experiment until the rock sample is damaged;
3) processing the damaged rock sample to prepare a casting slice;
4) analyzing crack distribution characteristics in the cast body sheet, and calculating a fractional dimensionality;
5) analyzing the fractional dimensional data, and estimating the brittleness index of the rock, wherein the estimated model is the brittleness index B = (D-D) min )/(D max -D min ) Wherein D is max For the maximum fractional dimension calculated by step 4), D min The minimum score dimension calculated in the step 4) is obtained, and D is the score dimension of a certain sample;
6) correcting the rock brittleness index estimated in the step 5 to obtain a compact sandstone reservoir rock brittleness index calculation model B 0 =(D-D 0min )/(D 0max -D 0min ) Wherein D is 0min To the corrected minimum fractional dimension, D 0max Is the corrected maximum score dimension;
D 0min and D 0max Is calculated as follows:
F(D 0min ，D 0max )=
，
wherein 1 < D 0min ＜D 0max ＜2，B i For the ith rock-like brittleness index calculated from the fractional dimension of the cast sheet, B1 i Is the ith rock-like brittleness index calculated based on elastic strain,
when F (D) 0min ，D 0max ) Taking the minimum value as an objective function to obtain corrected D 0min And D 0max 。
2. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 1, wherein the fractional dimension calculation method in the step 4) comprises the following steps: and observing the casting body slice by adopting an optical microscope, shooting the picture, processing the picture to obtain a crack distribution map, and calculating the fractional dimensionality according to the crack distribution map.
3. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 2, wherein a grid coverage method is adopted in the step 4) to calculate the fracture fraction dimensionality, specifically, a square grid is drawn by taking the center of a cast body slice as a reference point, the fracture length is selected as a fracture characteristic, and the side length is obtainedRTotal length of cracks in the square gridLFitting ln in log-log coordinatesLIs the same as lnRLinear fitting to obtain
(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture length as a characteristic.
4. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 2, wherein the grid coverage method is adopted to calculate the fracture fraction dimension in the step 4), and particularly the casting body slice center is taken as a referencePoint marking, square grid marking, selecting the number of cracks as crack characteristics, and obtaining the number of cracks in the square grid with the side length of RNFitting ln in log-log coordinatesLIs the same as lnNLinear fitting to obtain lnL=c+DlnN(ii) a Wherein c is a proportionality constant, and D is a fracture fraction dimension calculated by taking the number of fractures as a characteristic.
5. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 2, wherein in the step 4), a grid coverage method is adopted to calculate the fracture fractional dimension, specifically, a square grid is drawn by taking the center of a cast body slice as a reference point, the fracture area is selected as the fracture characteristic, and the fracture area in the square grid with the side length of R is obtainedSFitting ln in log-log coordinatesLIs the same as lnSLinear fitting to obtain lnL=c+DlnS(ii) a Wherein c is a proportionality constant, and D is a fracture fractional dimensionality calculated by taking the fracture area as a characteristic.
6. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 3, 4 or 5, wherein the damaged rock sample is dyed by blue fluorescent resin in the step 3), the initial form of the crack is marked, and the cast body slice for observation under an optical microscope is formed by cutting, grinding and packaging.
7. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 6, wherein the stress-strain experiment in the step 2) is a uniaxial compression experiment or a triaxial compression experiment, the sample is loaded into a rubber sleeve and placed in the center of a pressure bearing plate of a press, and the sample is loaded at a loading rate of 0.5MPa/s until the sample is damaged.
8. The method for calculating the rock brittleness index of the tight sandstone reservoir as claimed in claim 6, wherein the stress-strain experiment in the step 2) is a tensile experiment, a shear experiment or a cutting experiment.
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