KR100921569B1 - Geostatistical Method for Calculating Rock Fracture Aperture Using Hydraulic Test Data - Google Patents

Abstract

The present invention relates to a method for estimating rock crack size distribution geological statistics, and more particularly, to a method for estimating the crack crack size distribution of a rock using data collected through hydraulic experiments by drilling a plurality of boreholes in the rock. Set the region of interest to analyze the flow field on the surface, install the measuring equipment by drilling a plurality of boreholes in consideration of the size and the calculation accuracy of the flow field in the region of interest, and then the region of interest as a plurality of blocks And conduct the hydraulic conduction experiment by setting the two boreholes into one pair, and obtain the crack gap value of the rock bottom existing between the two boreholes, and the crack gap value of all the blocks on the straight line connecting the two boreholes. , Repeat the above steps for all repair experiment sets, and assign at least two crack creep values to overlap. The average crack gap value is obtained using weights inversely proportional to the distance between two boreholes in the block, and the unallocated block with no crack gap value assigned using the variation width and the correlation distance and the crack gap value of the surrounding block in the whole area. It is possible to simulate the crack gap size distribution characteristics in the region of interest of the rock, based on the calculation of the crack gap value at, and based on this, it is possible to precisely calculate the groundwater flow field simulation and the movement analysis of pollutants. have.

 Borehole, Rock Crack, Crack Crack, Weight, Hydraulic Conduction

Description

Geostatistical Method for Calculating Rock Fracture Aperture Using Hydraulic Test Data}

The present invention relates to a method for estimating rock crack size distribution geographic statistics, and more particularly, to a method for estimating the rock size distribution by geographic statistical calculation using data collected through hydraulic experiments by drilling a plurality of boreholes in a rock. .

Recently, there has been a growing interest in mediums with very low permeability of groundwater such as underground rocks, due to the construction of oil depots in such underground geology or the disposal of pollutants.

In addition, in Korea, a nuclear transfer model has been developed in underground media to evaluate the disposal safety associated with the construction of a radioactive waste disposal site, and a series of operations are carried out to measure the required parameter values through nuclear transfer experiments. In contaminants flow between rock cracks, it is important to understand the size and distribution of rock cracks.

The crack gap between the crack layer distribution and the top and bottom of the crack is important in describing the movement of groundwater or nuclides in the rock bed. The crack surface is spatially rough and the cracks are undulating.

Rock media are close to impermeable layers, where the permeability is low and virtually no groundwater migration occurs, and these media contain irregular cracks, and groundwater flow occurs mainly through these cracks. Thus, contaminants move with the groundwater in the crack through transport and dispersion, adsorbing to the crack surface in interaction with the underground medium, and diffuse into the rock medium by a concentration gradient, delaying movement compared to groundwater.

 As such, the study of crack cracks in the lower part of the rock occupies an important part in various studies such as the spread of contaminants through groundwater, but it is difficult to measure the distribution of crack cracks in practically accurate manner.

Conventionally, there is an invention (Japanese Laid-Open Patent No. 1998318996, published on Dec. 04, 1998) for measuring the crack extent of a rock using an ultrasonic measuring device, etc., which is a method of measuring the deflection of a ground, rock, concrete structure, etc., local crack range. It is difficult to grasp the crack gap distribution of the cracked rock throughout the flow field, and the ultrasonic scanning borehole logging device (Korea Patent Publication No. 10-2006-0049319, published on May 18, 2006) is an ultrasonic detector. It is only possible to measure the rock crack distribution at a close distance from the borehole, so we cannot know the crack distribution between the borehole and the borehole unless we drill the borehole for all rocks in the region of interest. There is a problem that there is no solution to determine.

The present invention has been devised to solve the above-mentioned problems of the prior art, and does not substitute an arithmetic mean value for a region of interest whose crack gap size is known, and is based on geographic geometry based on known values using borehole repair experiments. Provides the method of calculating the rock crack size distribution geographic statistics using borehole repair experiments that define the crack gap distribution characteristics of the region of interest using correlations and then calculate the crack gap size at each point by geographic statistics method while maintaining the characteristics. It aims to do it.

In order to solve the above problems, the rock crack crack size distribution geographic statistical estimation method using a borehole repair experiment according to the present invention is a first step of setting a region of interest to analyze a flow field on a surface of a cracked rock. Considering the flow field size and calculation accuracy, the second step of installing a plurality of boreholes and measuring equipment, the third step of dividing the region of interest into a plurality of blocks, and setting the two boreholes into one group The fourth step of performing the hydraulic conduction experiment and obtaining the crack gap value of the rock bottom existing between the two boreholes, the fifth step of allocating the crack gap value to all the blocks existing on the straight line connecting the two boreholes, A sixth step of repeating the fourth to fifth steps for the second step; at least two crack gap values The seventh step of obtaining the average crack gap value using weights inversely proportional to the distance between the boreholes and the unassigned unassigned crack gap value using the correlation width and the crack gap value of the surrounding blocks. And an eighth step of obtaining the crack gap value in the block.

Here, the crack gap value in the fourth step is calculated by the following equation.

Here, b _i is the i crude given period crack teumgap, Q _i is the flow rate, Δh _i is the pressure applied between the two boreholes, d _i is two drilling clearances, r _w is the radius of the borehole, ρ is ground water weight, g is Gravitational acceleration.

Further, in the seventh step, the weight is an inverse of the normalized distance calculated by dividing the distance between two repair workers by the length of the entire region of interest.

In the seventh step, the average crack gap value is calculated by the following equation.

Where b is the average crack crack value, ω _i is the weight, δ _l is the normalized distance, X is the horizontal length of the region of interest, Y is the vertical length of the region of interest, d _i is the distance between the two mechanics, and im is i The number of nested values in.

In addition, the eighth step is a first process of obtaining a correlation range λ, which is a value representing a change width σ ² of the crack gap distribution in the entire region of interest and a normal distance of the crack gap measurement density in the entire region of interest, and the change width. And a third step of obtaining a crack gap value of the neighboring block using a correlation distance and a third step of determining the crack gap value of the unassigned block by averaging the crack gap value calculated in the second step using a predetermined weight. It is done by

The first process is calculated by the following equation.

Where b _i is the crack crack value of block i, b _m is the total mean crack crack value, p _i is the ratio of b _i to the total, δ _m is the average distance between hydraulic test tanks, and Δx and Δy are the The horizontal and vertical dimensions, K is the number of repairers, X and Y are the horizontal and vertical dimensions of the entire region of interest, mn is the total number of blocks (m × n), and λ is the correlation distance.

The second process is calculated by the following equation.

Where b _i is the crack gap value calculated from the neighboring block i, σ ² is the change width, λ is the correlation distance, and r _i is the distance from the unassigned block to the neighboring block.

The third process is calculated by the following equation.

Where b _j is the average crack gap value of the unallocated block, im is the number of neighboring blocks, b _i is the crack gap value calculated from the neighboring block i, ωf _i is the weight and is connected to the distance r from the unallocated block to the periphery _Inversely proportional to the average distance d _mi between hydraulic baths.

The rock crack crack size distribution geographic statistical estimation method using the borehole repair experiment according to the present invention configured as described above can simulate the crack gap size distribution characteristics in the region of interest of the rock, and based on the groundwater flow field simulation, contamination There is an effect that can accurately calculate the movement analysis of the material.

Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings.

1 is a flow chart illustrating a method for calculating geographic statistics of rock crack gap size distribution using a borehole repair experiment according to the present invention.

First, a region of interest for analyzing the flow field of groundwater at the rock surface having a crack gap in the lower portion of the rock is set (S10).

The region of interest may be specified in various forms, but in the present invention, the region is set in the form of a rectangle. That is, the size of the horizontal (X) and vertical (Y) of the region of interest is set.

Next, the measurement equipment is installed by drilling a plurality of boreholes in consideration of the size and calculation precision of the flow field in the region of interest (S20).

2 is a view showing the installation of the borehole and the hydraulic conduction test apparatus in the region of interest and region of the cracked rock.

A crack gap (2) exists in the lower part of the rock (1) of the region of interest, and the number of hydraulic test boreholes (K) is determined and drilled in consideration of the size and calculation accuracy of the flow field in the region of interest.

As the number of the boreholes 3 increases, the accuracy is basically higher, but since the flow field through which the groundwater flows increases the degree of perturbation by the boreholes, the overall precision may be lowered. Therefore, it is desirable to determine the number of boreholes 3 at an appropriate level. .

After drilling through the borehole 3, a measuring device 4 capable of measuring the flow rate, flow velocity, pressure, etc. of the groundwater is installed in the borehole 3.

Next, the area of interest is divided into smaller areas (hereinafter referred to as blocks) for subdividing (S30).

That is, the region of interest is divided into M × N blocks. Where M is the number of blocks in the horizontal direction and N is the number of blocks in the vertical direction.

3 is a diagram illustrating an example in which a region of interest is divided into a plurality of blocks.

Next, a hydraulic test tank in which two of the plurality of boreholes become one is set, a hydraulic conduction test is performed for each test bath, and a crack crack value of the lower rock existing between the two boreholes is obtained (S40).

One borehole may be shared among several hydraulic test tanks. That is, except when two boreholes are completely identical, one borehole may be a pair with the other boreholes except him. That is, one borehole does not necessarily belong to only one jaw, but may form a jaw with other boreholes except itself.

3 is a dotted line connected to each borehole, and the connected boreholes become the same pair.

Hydraulic conduction experiments are performed using two boreholes (group i), and the crack gap b _i is obtained using Equation 1 below.

Here, b _i is the i crude given period crack teumgap, Q _i is the flow rate, Δh _i is the pressure applied between the two boreholes, d _i is two drilling clearances, r _w is the radius of the borehole, ρ is ground water weight, g is Gravitational acceleration.

Next, the crack gap values thus obtained are allocated to all the blocks existing on the straight line 5 connecting the two boreholes joined together (S50).

That is, in FIG. 3, when the crack gap value is obtained for the two boreholes at both ends of the dotted line 5, all the crack gap values obtained above are allocated to the block through which the dotted line 5 passes. That is, the blocks primarily have crack gap values calculated by two boreholes.

Repeat this process for all hydraulic tests. If the crack gap values are obtained for all hydraulic test units, and the crack gap values are assigned to the blocks existing on the straight line distance between the two repair workers, the block may be assigned one or more crack gap values. There may be blocks that do not have one.

That is, some values may be overlapped in a partial region, and some regions may have an area to which no value is assigned, such as A (x, y). In areas where values overlap, average values should be obtained, and in areas without values, values should be inferred from the periphery.

For example, in FIG. 3, the A block does not have any crack gap value, and the B block has three crack gap values because three dotted lines pass through the crack gap value.

In this case, the crack gap value in the A block and the crack gap value in the B block should be summarized. Block A has not been assigned a crack gap, because that does not mean that there are no cracks below the rock.

In addition, the B block also has three crack gaps, but in reality, only one crack gap exists.

In other words, it is necessary to determine what value the crack gap value should be set in a block to which multiple crack gap values are assigned.

Therefore, in the next step, the average crack gap value is obtained using a weight that is inversely proportional to the distance between two boreholes in a block in which at least two crack gap values are overlapped and allocated (S70).

The reason that the weight is inversely proportional to the distance is that the closer the borehole distance is, the smaller the crack variance and the higher the probability that the flow field is a straight line.

Specifically, the weight is an inverse of the normalized distance calculated by dividing the distance between two repair workers by the length of the entire region of interest, and the length of the total region of interest is the sum of the horizontal and vertical lengths of the region of interest (X). + Y).

The average crack gap value is calculated by Equation 2 below.

Where b is the average crack crack value, ω _i is the weight, δ _l is the normalized distance, X is the horizontal length of the region of interest, Y is the vertical length of the region of interest, d _i is the distance between the two mechanics, and im is i The number of nested values in.

Next, in a block without a crack gap value, the crack gap value is estimated using a geographical statistical correlation based on the crack gap value of the neighboring blocks. That is, a block to which no crack gap value is assigned using a variation width (σ ² , variance) of the crack gap value distribution in the entire region, a correlation length (λ), and a crack gap value of the neighboring block (hereinafter, referred to as an unassigned block). The crack crack value in () is obtained (S80).

To explain this process in detail, first, the variation width (σ ² ) of the crack gap distribution in the entire region of interest and the correlation distance (λ), which is a value representing the crack gap measurement density in the entire region of interest, are expressed as normal distances.

The change width σ ² and the correlation distance λ of the crack gap distribution in the entire region of interest may be obtained through Equation 3 below.

Where b _i is the crack crack value of block i, b _m is the total mean crack crack value, p _i is the ratio of b _i to the total, δ _m is the average distance between hydraulic test tanks, and Δx and Δy are the The horizontal and vertical dimensions, K is the number of repairers, X and Y are the horizontal and vertical dimensions of the entire region of interest, mn is the total number of blocks (m × n), and λ is the correlation distance.

4 is a diagram illustrating a block to which a crack gap value is not assigned and peripheral blocks distributed around the same. FIG. 4 is not a view of a portion of FIG. 3, but an example in which all neighboring blocks exist.

In FIG. 4, the central block A (x, y) is an unassigned block, and the surrounding blocks surrounding the block are eight except for the center block in the portion indicated by 100.

The next process is to find the crack gap value of the neighboring blocks using the variation width (σ ² ) and the correlation distance (λ) of the crack gap distribution in the entire region of interest.

This process is calculated by Equation 4 below.

Where b _i is the crack gap value calculated from the neighboring block i, σ ² is the change width, λ is the correlation distance, and r _i is the distance from the unassigned block to the neighboring block. This calculation process is performed for eight peripheral blocks of FIG.

When the crack gap value of the neighboring block surrounding the unallocated block is obtained as described above, the crack gap value of the neighboring block calculated in the previous process is determined by using a predetermined weight to determine the crack gap value of the unassigned block.

This process is calculated by Equation 5 below.

Where b _j is the average crack gap value of the unallocated block, im is the number of neighboring blocks, b _i is the crack gap value calculated from the neighboring block i, ωf _i is the weight and is connected to the distance r from the unallocated block to the periphery This is inversely proportional to the mean distance d _mi between hydraulic gauges.

That is, the crack gap value of the unassigned block is obtained by substituting the crack gap values of the eight neighboring blocks obtained in the above process into the above [Equation 5].

In this process, if an unallocated block exists in the neighboring block, the above process may be performed except for the unallocated block. If there are a large number of unallocated blocks, that is, for example, there is no crack gap value among the neighboring blocks. If the number of unallocated blocks is more than half or more than one third of all neighboring blocks, the calculation process may be performed on the outer neighboring block 200 of the neighboring block.

In other words, the crack gap value of the unassigned block is obtained for the neighboring block outside the outer one step. For example, in FIG. 4, blocks between 100 and 200, which are outside of 100, are regarded as neighboring blocks, and [Equation 4] and [Equation 5] are applied to the 16 neighboring blocks, respectively.

As described above, the method for calculating the rock crack gap size distribution geographic statistics using the borehole repair experiment according to the present invention has been described with reference to the illustrated drawings, but the present invention is not limited by the embodiments and drawings disclosed herein. It can be applied within this protected range.

1 is a flow chart illustrating a method for calculating geographic statistics of rock crack gap size distribution using borehole repair experiments according to the present invention;

2 is a view showing the installation of the borehole and the hydraulic conduction test apparatus in the region of interest and the region of the cracked rock;

3 is a diagram illustrating an example in which a region of interest is divided into a plurality of blocks;

4 is a diagram illustrating a block to which a crack gap value is not assigned and peripheral blocks distributed around the same.

<Explanation of symbols for the main parts of the drawings>

1: bedrock

2: crack crack

3: Borehole (repair)

4: measuring equipment

X: the width of the region of interest

Y: height of the region of interest

Claims (12)

Intended for use as an area of interest in the cracked rock region where groundwater flows A first step of determining the size and shape of the area; A second step of installing a measurement device by drilling a plurality of boreholes in consideration of the size and calculation precision of the flow field in the region of interest; Dividing the region of interest into a plurality of blocks; A fourth step of performing hydraulic conduction experiments by setting the two boreholes as one pair and obtaining a crack gap value of a rock bottom existing between the two boreholes; A fifth step of allocating the crack gap value to all blocks existing on a straight line connecting the two boreholes; A sixth step of repeating steps 4 to 5 for all repair experiment sets; A seventh step of obtaining an average crack gap value using a weight that is inversely proportional to the distance between two boreholes in a block in which at least two crack gap values are overlapped; And Rock cracks using borehole repair experiments comprising an eighth step of calculating crack gap values in unassigned blocks that are not assigned crack gap values by using the variation widths and correlation distances of crack gap value distributions in the entire area and the crack gap values of neighboring blocks. Gap size distribution Geographic statistics. The method according to claim 1, The first step is a geographic statistical calculation method for rock crack gap size distribution using a borehole repair experiment, characterized in that the interest is set in the rectangular shape by setting the horizontal and vertical size of the region of interest. The method according to claim 1, In the fourth step, the crack crack size distribution geographic statistical calculation method using a borehole repair experiment, characterized in that calculated by the following equation.

(Wherein, b _i is the i crude given period crack teumgap, Q _i is the flow rate, Δh _i is the pressure applied between the two boreholes, d _i is two drilling clearances, r _w is the radius of the borehole, ρ is ground water weight, g Is the acceleration of gravity) The method according to claim 1, In the seventh step, the weight is a geographic statistical calculation method for rock crack gap size distribution using a borehole repair experiment, characterized in that the distance between the two repairman divided by the length of the entire region of interest. The method according to claim 4, The length of the entire region of interest is a geographic statistical calculation method of rock crack gap size distribution using a borehole repair experiment, characterized in that the sum of the horizontal and vertical length of the region of interest. The method according to claim 1, In the seventh step, the average crack gap value is calculated by the following equation, rock crack crack size distribution geographic statistical estimation method using a borehole repair experiment.

(Where b is the mean crack gap value, ω _i is the weight, δ _l is the normalized distance, X is the horizontal length of the region of interest, Y is the vertical length of the region of interest, d _i is the distance between the two mechanics, and im is the number of assigned values at i) The method of claim 1, wherein the eighth step A first step of obtaining a correlation distance (λ) representing a change width (σ ² ) of the crack gap distribution in the entire region of interest and a normal distance of the crack gap measurement density in the entire region of interest; A second step of obtaining a crack gap value of a neighboring block by using the change width and the correlation distance; Rock crack gap size distribution geography using a borehole repair experiment, comprising a third step of determining an average of crack gap values calculated in the second process using predetermined weights to determine crack gap values of unassigned blocks. Statistical calculation method. The method according to claim 7, The first process is calculated by the following equation, the rock crack crack size distribution geographic statistical estimation method using a borehole repair experiment.

Where b _i is the crack crack value of block i, b _m is the total mean crack crack value, p _i is the proportion of b _i in the total, δ _m is the average distance between hydraulic test tanks, and Δx and Δy are The horizontal and vertical size of the block, K is the number of repairers, X and Y are the horizontal and vertical size of the entire area of interest, mn is the total number of blocks (m × n), and λ is the correlation distance.) The method according to claim 7, The second process is calculated by the following equation, the rock crack crack size distribution geographic statistical estimation method using a borehole repair experiment.

Where b _i is the crack gap calculated from the neighboring block i, σ ² is the change width, λ is the correlation distance, and r _i is the distance from the unassigned block to the neighboring block) The method according to claim 7, The third process is a geographic statistical calculation method of the rock crack crack size distribution using a borehole repair experiment, characterized in that calculated by the following equation.

Where b _j is the average crack gap value of the unallocated block, im is the number of neighboring blocks, b _i is the crack gap value calculated from the neighboring block i, and ωf _i is the weight as the distance r from the unallocated block to the periphery and _Inversely proportional to the average distance d _mi between connected hydraulic instruments) The method according to claim 7, The second to third processes are geographic statistical calculation method for rock crack gap size distribution using a borehole repair experiment, characterized in that if there is an unassigned block in the neighboring block, only the block to which the crack gap value is assigned. The method according to claim 7, In the second to third processes, rock cracks using the borehole repair experiments are calculated for the next neighboring block surrounding the neighboring block when an unassigned block exists in the neighboring block. Method of estimating size distribution geographic statistics.

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