CN116359093A - Quantification method for thermodynamic fracture and anti-reflection effect of coal rock - Google Patents
Quantification method for thermodynamic fracture and anti-reflection effect of coal rock Download PDFInfo
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Abstract
The invention discloses a method for quantifying thermal cracking and anti-reflection effects of coal and rock, which is characterized by comprising the following steps: the method comprises the following steps: A. detecting and obtaining the number N of cracks in the coal rock sample and the length l of all cracks, and calculating and obtaining the fractal dimension D of the length fractal dimension of the cracks in the coal rock f The method comprises the steps of carrying out a first treatment on the surface of the B. Calculation of total volume V by internal crack length of coal rock sample p The method comprises the steps of carrying out a first treatment on the surface of the Total volume of re-passing through crack pores V p Calculating to obtain crack porosity phi p The method comprises the steps of carrying out a first treatment on the surface of the C. Detecting and obtaining the thermal expansion coefficient alpha of the coal rock sample at the temperature T T (T) and mechanical parameters; D. calculating critical crack length L of crack development in the coal rock, and obtaining the relation between the critical crack length L and temperature; E. calculating the thermal permeability coefficient K of the coal rock T And obtain the coal rock thermal permeability coefficient K T And temperature. According to the invention, the thermal permeability coefficient is determined by calculating the porosity of the coal rock after thermal damage cracking and permeability increase, so that the relationship between the thermal damage and the temperature on the permeability increase coefficient is determined, and the aim of more conveniently determining the influence of the thermal damage on the coal rock is fulfilled.
Description
Technical Field
The invention relates to the field of deep gas extraction and coalbed methane development, in particular to a method for quantifying thermal cracking and permeability improvement effects of coal and rock.
Background
The engineering field parts of deep gas thermal recovery, coal bed supercritical carbon dioxide fracturing, liquid nitrogen fracturing, geothermal exploitation and the like relate to the thermal coupling effect of coal and rock, and particularly the crack structure and the permeability of the coal and rock are obviously changed under the action of high temperature or low temperature. When the temperature changes, the internal mismatched thermal expansion stress of the coal rock causes the primary fracture to develop, so that the permeability of the coal rock is increased, but the quantitative characterization method for the internal crack development and permeability evolution of the coal rock caused by the temperature changes still lacks at present. At present, no quantitative calculation method for the thermal effect, crack development and permeability of the coal and rock exists at home and abroad, so that a method for quantifying the relation between the temperature change of the coal and rock, the crack development and the permeability change is needed.
Therefore, the method for quantifying the thermal cracking and permeability increasing effects of the coal and rock is provided, and the method introduces a microscopic fracture theory and a thermal damage coefficient, so that the relation between the temperature change of the coal and rock and the crack development and permeability change can be minimized, and the method has practical significance and good prospect.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method for quantifying the thermal fracture and anti-reflection effect of coal and rock, which is used for determining the thermal anti-reflection coefficient by calculating the porosity after fracture and anti-reflection of the thermal damage of the coal and rock, so as to determine the relationship between the thermal damage and the temperature on the anti-reflection coefficient, thereby achieving the purpose of more conveniently determining the influence of the thermal damage on the coal and rock.
The aim of the invention is achieved by the following technical scheme:
a method for quantifying thermal cracking and anti-reflection effects of coal and rock comprises the following steps:
A. detecting to obtain the number N of cracks in the coal rock sample, measuring the lengths l of all cracks, and calculating to obtain the fractal dimension D of the lengths of the cracks in the coal rock f ；
B. Calculating the volume of crack pores according to the length of the cracks in the coal rock sample, and calculating the total volume V of the crack pores in the coal rock sample p The method comprises the steps of carrying out a first treatment on the surface of the Total volume of re-passing through crack pores V p Calculating to obtain crack porosity phi p ；
C. Heating the coal rock sample, and detecting to obtain the thermal expansion coefficient alpha of the coal rock sample at the temperature T T (T) and mechanical parameters;
D. calculating critical crack length L of crack development in the coal rock, and obtaining the relation between the critical crack length L and temperature;
E. calculating the thermal permeability coefficient K of the coal rock T And obtain the coal rock thermal permeability coefficient K T And temperature.
Preferably, in step A, the internal cracks of the coal rock sample are divided into a plurality of sections according to the range of the crack length l, and the number N of the cracks of the corresponding sections is obtained l The fracture length fractal dimension-D of each fracture length interval is calculated according to the following formula fj ：
Wherein N is j The number of cracks, l, for the jth crack length range interval j A crack length intermediate value, l, of the jth crack length range max For maximum crack length, N m Is the maximum crack lengthNumber of cracks in the span of the degree range;
the calculated fracture length fractal dimension-D of all the crack length range intervals fj Taking an average value to obtain the fractal dimension D of the fracture length inside the coal rock f 。
Preferably, the fracture cell volume in step B is calculated using a sphere calculation formula:
wherein V is pi Volume, l, of the ith crack aperture in the coal rock sample i Crack length for the ith crack aperture;
the total crack pore volume is the sum of the single crack volumes or the integral of the single crack volumes, and is calculated by adopting the following formula:
wherein V is p Is the total volume of crack pores in a coal rock sample, l is the crack length and N i For the number of cracks, l max Is the maximum crack length.
Preferably, the cleavage cell porosity φ in step B p The calculation formula of (2) is as follows:
wherein, kappa is a calibration coefficient, V m Is the original volume of the coal rock sample;
the calculation formula of the calibration coefficient kappa is as follows:
wherein phi is P-test To obtain crack porosity phi in coal rock sample by CT scanning Calculation of p Then go through the formula->
And (5) calculating to obtain the product.
Preferably, the mechanical parameters in step C include the modulus of elasticity E (T), the compressive strength sigma (T) and the Poisson's ratio v (T), the temperature T being a plurality of temperature values between 50℃and 600℃as measured by the plurality of temperatures TCorresponding plurality of thermal expansion coefficients alpha T (T) value and mechanical parameter value, and obtaining thermal expansion coefficient alpha by function fitting respectively T A quantitative relationship between (T) and temperature T, a quantitative relationship between elastic modulus E (T) and temperature T, a quantitative relationship between compressive strength σ (T) and temperature T, and a quantitative relationship between poisson's ratio v (T) and temperature T.
Preferably, in step D by a coefficient of thermal expansion alpha T (T) calculating mismatched thermal stress sigma with mechanical parameters RT When the stress intensity factor of the crack tip is
And material fracture toughness S 0 Crack development at equal time, the calculation formula is expressed as:
the critical crack length L can be calculated.
Preferably, the thermal stress σ is mismatched in step D RT The calculation formula of (2) is as follows:
wherein, deltaT is the temperature increment, namely the difference between the temperature T and the room temperature of 25 ℃; Δα T (T) is the volumetric coefficient of thermal expansion discrete difference;
then
Namely, the relation between the critical crack length L and the temperature is: when the local temperature difference delta T of the coal rock is increased, the length of the critical development cracks in the coal rock is reduced, and the small cracks are developed in turn.
Preferably, the thermodynamic permeability coefficient K of the coal rock in the step E T The calculation formula of (2) is as follows:
wherein phi is pT The calculation formula is as follows:
wherein D is fT The calculation formula is as follows for the fractal dimension of the fracture length in the coal rock under the action of heat:
D fT ＝D f +λ(ΔT/T a )；
wherein, deltaT is the temperature increment, namely the difference between the temperature T and the room temperature of 25 ℃; t (T) a Absolute temperature, i.e., temperature T; lambda is the crack network development coefficient under the action of heat;
then
I.e. coal rock thermodynamic permeability coefficient K T Relationship with temperature: the larger the local temperature difference delta T is, the larger the thermal anti-reflection coefficient value of the coal rock is, and the more obvious the thermal anti-reflection effect is.
Compared with the prior art, the invention has the following advantages:
(1) According to the invention, the thermal permeability coefficient is determined by calculating the porosity of the coal rock after thermal damage cracking and permeability increase, so that the relationship between the thermal damage and the temperature on the permeability increase coefficient is determined, and the aim of more conveniently determining the influence of the thermal damage on the coal rock is fulfilled.
(2) The invention provides a mathematical calculation method for the development of coal rock cracks under the action of heat, which can effectively calculate the development size of the primary coal rock crack size under the temperature change.
(3) The invention provides a method for evaluating the coal rock permeability-increasing effect under the action of heat, which can be used for effectively evaluating the coal rock permeability-increasing effect by defining the coal rock thermal permeability-increasing coefficient and quantifying the relation between the temperature change and the permeability of the coal rock.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The invention is further illustrated by the following examples:
examples
As shown in fig. 1, the method for quantifying the thermal cracking and anti-reflection effects of coal rock comprises the following steps:
A. detecting to obtain the N-most number of internal cracks of the coal rock sample, measuring the lengths l of all cracks, and calculating to obtain the fractal dimension D of the lengths of the internal cracks of the coal rock f The coal rock sample is a standard cylindrical coal rock sample with the diameter of 50mm and the height of 100 mm. The invention adopts an X-ray industrial CT detection system and a dynamic real-time SEM observation system to detect the coal rock sample and obtain the form, the size and the distribution condition of cracks in the coal rock sample, and the invention divides the cracks in the coal rock sample into a plurality of sections according to the crack length range, such as l, because the crack lengths l in the coal rock sample are different<0.001、0.001≤l<0.01、0.01≤l<0.1、0.1≤l<1、1≤l<5、5≤l<10 and 10 is less than or equal to l, and the number of cracks in each crack length interval in the coal rock is obtained by statistics according to a statistical principle, wherein a statistical table is shown in a table I.
List one
In the step A, the internal cracks of the coal rock sample are divided into a plurality of sections according to the range of the crack length l, and the number N of the cracks in the corresponding sections is obtained l Then the fracture length fractal dimension-D of each crack length range interval is calculated according to the following formula fj ：
Wherein j is the number of the partition, N j The number of cracks, l, for the jth crack length range interval j Is the firstCrack length intermediate value, l, of j crack length range intervals max For maximum crack length, N m The number of cracks in the range of maximum crack length.
The invention calculates the fracture length fractal dimension-D of each interval divided according to the range of the crack length l by the formula fj Then the fracture length fractal dimension-D of all the crack length range intervals fj Taking an average value to obtain the fractal dimension D of the fracture length inside the coal rock f I.e. fracture length fractal dimension-D for all crack length range intervals fj The number of the intervals which are added and divided by the intervals of all crack length ranges is the fractal dimension D of the crack length in the coal rock f The number of intervals in table one is 7. The invention divides the internal crack of the coal rock sample into a plurality of sections according to the crack length range, and calculates the crack length fractal dimension-D of each section fj And average value is taken to obtain fractal dimension D of fracture length inside coal rock f The method can ensure the fractal dimension D of the fracture length inside the obtained coal rock f Accuracy of (3).
B. Calculating the volume of crack pores according to the length of the cracks in the coal rock sample, and calculating the total volume V of the crack pores in the coal rock sample p The method comprises the steps of carrying out a first treatment on the surface of the Total volume of re-passing through crack pores V p Calculating to obtain crack porosity phi p . Specifically, the crack pore volume in the invention is calculated by adopting a sphere calculation formula:
wherein i is the number of crack pores, V pi Volume, l, of the ith crack aperture in the coal rock sample i The crack length of the ith crack aperture. The total volume of the crack pores is the sum of the single crack volumes or the integral of the single crack volumes, and is calculated by adopting the following formula: />
Wherein V is p Is the total volume of crack pores in a coal rock sample, l is the crack length and N i For the number of cracks, l max Is the maximum crack length.
Crack porosity phi p The calculation formula of (2) is as follows:
wherein, kappa is a calibration coefficient, V m Is the original volume of the coal rock sample; the calculation formula of the calibration coefficient kappa is as follows: />
Wherein phi is P-test To obtain crack porosity phi in coal rock sample by CT scanning Calculation of p Then go through the formula->
And (5) calculating to obtain the product. The crack porosity phi is calculated by introducing a calculation mode of a calibration coefficient kappa p Can ensure the obtained crack porosity phi p Accuracy of (3).
C. Heating the coal rock sample, and detecting to obtain the thermal expansion coefficient alpha of the coal rock sample at the temperature T T (T) and mechanical parameters. The invention heats the coal rock sample from room temperature to a plurality of temperature values between 50 ℃ and 600 ℃ and keeps the temperature value constant, and the thermal expansion coefficient alpha of the temperature value is measured T (T) and mechanical parameters, the corresponding thermal expansion coefficient alpha can be obtained when a series of temperature values are obtained T (T) and mechanical parameters. In practice, the coal and rock sample can be heated to 50 ℃, 100 ℃, 200 ℃, 300 ℃, 400 ℃, 500 ℃, 600 ℃ or other temperature values and kept at constant temperature, and then the real-time thermal expansion coefficient alpha of the coal and rock sample in the constant temperature state at the corresponding temperature value is measured by a laser heat conduction analyzer T And (T) carrying out a uniaxial compression mechanical test of the coal rock in a constant temperature state when the corresponding temperature value is carried out by sleeving a muffle furnace heating system on the outer side of a high-temperature pressure rod of the MTS810 rock mechanical multi-field coupling test system, so as to obtain the mechanical parameter value in the corresponding temperature state. The mechanical parameters in the invention comprise elastic modulus E (T), compressive strength sigma (T) and Poisson ratio v (T), and the corresponding values at a plurality of temperatures T are measured by the methodMultiple coefficients of thermal expansion alpha T (T), elastic modulus E (T), compressive strength sigma (T) and Poisson's ratio v (T), the thermal expansion coefficient alpha can be obtained by function fitting T A quantitative relationship between (T) and temperature T, a quantitative relationship between elastic modulus E (T) and temperature T, a quantitative relationship between compressive strength σ (T) and temperature T, and a quantitative relationship between poisson's ratio v (T) and temperature T.
D. And calculating the critical crack length L of the crack development in the coal rock, and obtaining the relation between the critical crack length L and the temperature. The invention uses the thermal expansion coefficient alpha T (T) calculating mismatched thermal stress sigma with mechanical parameters RT Mismatch thermal stress sigma RT The calculation formula of (2) is as follows:
wherein, deltaT is the temperature increment, namely the difference between the temperature T and the room temperature of 25 ℃; Δα T And (T) is the difference of the discrete coefficients of thermal expansion of the volumes, and represents the difference of the thermal expansion capacity of the coal matrix in different directions, and the parameter value can be obtained through measurement, and can also be a parameter value which is known and commonly used in the industry.
Stress intensity factor at crack tip
And material fracture toughness S 0 Crack development at equal time, the calculation formula is expressed as: />
Then
Namely, the relation between the critical crack length L and the temperature is: when the local temperature difference delta T of the coal rock is increased, the length of the critical development cracks in the coal rock is reduced, and the small cracks are developed in turn.
E. Calculating the thermal permeability coefficient K of the coal rock T And obtain the heat of coal and rockForce anti-reflection coefficient K T And temperature. Coal rock thermodynamic permeability coefficient K T The calculation formula of (2) is as follows:
wherein phi is pf The calculation formula is as follows:
wherein D is fT The calculation formula is as follows for the fractal dimension of the fracture length in the coal rock under the action of heat:
D fT ＝D f +λ(ΔT/T a )；
wherein, deltaT is the temperature increment, namely the difference between the temperature T and the room temperature of 25 ℃; t (T) a Obtaining the thermal expansion coefficient alpha for absolute temperature, i.e. maintaining a constant temperature state when heating the coal rock sample T (T) and a temperature T at the mechanical parameter; lambda is the crack network development coefficient under the action of heat and can be obtained through repeated CT test.
Then
I.e. coal rock thermodynamic permeability coefficient K T Relationship with temperature: the larger the local temperature difference delta T is, the larger the thermal anti-reflection coefficient value of the coal rock is, and the more obvious the thermal anti-reflection effect is.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (8)
1. A method for quantifying thermal cracking and anti-reflection effects of coal and rock is characterized by comprising the following steps: the method comprises the following steps:
A. detecting and obtaining the inside of the coal rock sampleThe number N of cracks is measured, the length l of all cracks is measured, and the fractal dimension D of the length of the cracks in the coal rock is calculated f ；
B. Calculating the volume of crack pores according to the length of the cracks in the coal rock sample, and calculating the total volume V of the crack pores in the coal rock sample p The method comprises the steps of carrying out a first treatment on the surface of the Total volume of re-passing through crack pores V p Calculating to obtain crack porosity phi p ；
C. Heating the coal rock sample, and detecting to obtain the thermal expansion coefficient alpha of the coal rock sample at the temperature T T (T) and mechanical parameters;
D. calculating critical crack length L of crack development in the coal rock, and obtaining the relation between the critical crack length L and temperature;
E. calculating the thermal permeability coefficient K of the coal rock T And obtain the coal rock thermal permeability coefficient K T And temperature.
2. The method for quantifying the thermal cracking and anti-reflection effects of coal and rock according to claim 1, which is characterized by comprising the following steps: in the step A, the internal cracks of the coal rock sample are divided into a plurality of sections according to the range of the crack length l, and the number N of the cracks in the corresponding sections is obtained l The fracture length fractal dimension-D of each fracture length interval is calculated according to the following formula fj ：
Wherein N is j The number of cracks, l, for the jth crack length range interval j A crack length intermediate value, l, of the jth crack length range max For maximum crack length, N m The number of cracks being the range of maximum crack length;
the calculated fracture length fractal dimension-D of all the crack length range intervals fj Taking an average value to obtain the fractal dimension D of the fracture length inside the coal rock f。
3. A method according to claim 1 or 2The method for quantifying the thermodynamic rupture and permeability-increasing effects of the coal rock is characterized by comprising the following steps of: in the step B, the crack pore volume is calculated by adopting a sphere calculation formula:
wherein V is pi Volume, l, of the ith crack aperture in the coal rock sample i Crack length for the ith crack aperture;
the total crack pore volume is the sum of the single crack volumes or the integral of the single crack volumes, and is calculated by adopting the following formula:
wherein V is p Is the total volume of crack pores in a coal rock sample, l is the crack length and N i For the number of cracks, l max Is the maximum crack length.
4. A method for minimizing thermal cracking and anti-reflection effects of coal rock according to claim 3, wherein: step B, the crack porosity phi p The calculation formula of (2) is as follows:
wherein, kappa is a calibration coefficient, V m Is the original volume of the coal rock sample;
the calculation formula of the calibration coefficient kappa is as follows:
wherein phi is P-test To obtain crack porosity phi in coal rock sample by CT scanning p The algorithm is +.>
And (5) calculating to obtain the product.
5. The method for quantifying the thermal cracking and anti-reflection effects of coal and rock according to claim 2, which is characterized in that: the mechanical parameters in the step C comprise elastic modulus E (T), compressive strength sigma (T) and Poisson ratio v (T), and the temperature T is 50 ℃ to the rangeA plurality of temperature values between 600 ℃ and a plurality of corresponding thermal expansion coefficients alpha are measured through a plurality of temperatures T T (T) value and mechanical parameter value, and obtaining thermal expansion coefficient alpha by function fitting respectively T A quantitative relationship between (T) and temperature T, a quantitative relationship between elastic modulus E (T) and temperature T, a quantitative relationship between compressive strength σ (T) and temperature T, and a quantitative relationship between poisson's ratio v (T) and temperature T.
6. A method for minimizing thermal cracking and anti-reflection effects of coal rock according to claim 5, wherein: by the coefficient of thermal expansion alpha in step D T (T) calculating mismatched thermal stress sigma with mechanical parameters RT When the stress intensity factor of the crack tip is
And material fracture toughness S 0 Crack development at equal time, the calculation formula is expressed as:
the critical crack length L can be calculated.
7. The method for quantifying the thermal cracking and anti-reflection effects of coal and rock according to claim 6, wherein the method comprises the following steps: mismatch thermal stress sigma in step D RT The calculation formula of (2) is as follows:
wherein, deltaT is the temperature increment, namely the difference between the temperature T and the room temperature of 25 ℃; Δα T (T) is the volumetric coefficient of thermal expansion discrete difference;
then
Namely, the relation between the critical crack length L and the temperature is: when the local temperature difference delta T of the coal rock is increased, the length of the critical development cracks in the coal rock is reduced, and the small cracks are developed in turn.
8. The method for quantifying the thermal cracking and anti-reflection effects of coal and rock according to claim 2, which is characterized in that: coal rock thermodynamic permeability coefficient K in step E T The calculation formula of (2) is as follows:
wherein phi is pT The calculation formula is as follows:
wherein D is fT The calculation formula is as follows for the fractal dimension of the fracture length in the coal rock under the action of heat:
D fT ＝D f +λ(ΔT/T a )；
wherein, deltaT is the temperature increment, namely the difference between the temperature T and the room temperature of 25 ℃; t (T) a Absolute temperature, i.e., temperature T; lambda is the crack network development coefficient under the action of heat;
then
I.e. coal rock thermodynamic permeability coefficient K T Relationship with temperature: the larger the local temperature difference delta T is, the larger the thermal anti-reflection coefficient value of the coal rock is, and the more obvious the thermal anti-reflection effect is.
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| CN105136837A (en) * | 2015-07-24 | 2015-12-09 | 中国矿业大学 | Test system and test method of liquid nitrogen circulation freeze-thawing permeability-increasing simulation of coal rock sample |
| CN112102487A (en) * | 2020-09-17 | 2020-12-18 | 西南石油大学 | Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal |
| CN113390906A (en) * | 2021-06-11 | 2021-09-14 | 内蒙古科技大学 | Evaluation method for crack permeability increasing effect of low-permeability coal rock mass under microscopic scale |
| CN113504125A (en) * | 2021-07-27 | 2021-10-15 | 辽宁工程技术大学 | True triaxial physical and chemical combination coal rock permeability increasing test device and method |
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| CN105136837A (en) * | 2015-07-24 | 2015-12-09 | 中国矿业大学 | Test system and test method of liquid nitrogen circulation freeze-thawing permeability-increasing simulation of coal rock sample |
| CN112102487A (en) * | 2020-09-17 | 2020-12-18 | 西南石油大学 | Unconventional reservoir three-dimensional permeability determination method based on multiple mixed fractal |
| CN113390906A (en) * | 2021-06-11 | 2021-09-14 | 内蒙古科技大学 | Evaluation method for crack permeability increasing effect of low-permeability coal rock mass under microscopic scale |
| CN113504125A (en) * | 2021-07-27 | 2021-10-15 | 辽宁工程技术大学 | True triaxial physical and chemical combination coal rock permeability increasing test device and method |
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