CN113204928A - Method for calculating heat-induced flow conductivity of micro-cracks of hot dry rock mass - Google Patents
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Abstract
The invention discloses a method for calculating the heat-induced flow conductivity of a hot dry rock microfracture, which comprises the following steps: s1, collecting a dry-hot rock reservoir core containing the microcracks, obtaining two-dimensional morphology data of the microcracks through laser scanning, and S2, calculating the roughness coefficient of the microcracks according to the two-dimensional morphology data; s3, calculating the initial mechanical opening of the microfractures of the hot dry rock according to the in-situ stress state and the mechanical strength of the hot dry rock; s4, calculating a temperature field of the microcrack wall surface in the long-term injection process of hydraulic fracturing by combining the thermal physical parameters of the hot dry rock and the hot dry rock; s5, calculating the thermal induction opening of the microcrack wall surface in the long-term injection process of hydraulic fracturing according to the temperature drop and the mechanical parameters of the microcrack wall surface of the dry-hot rock mass; and S6, calculating the flow guide opening, the heat-induced flow guide capacity and the comprehensive flow guide capacity of the microcracks of the hot and dry rock according to the initial mechanical opening and the heat-induced opening. The method can accurately calculate the comprehensive flow conductivity of the microcracks after the hot dry rock transformation.
Description
Technical Field
The invention relates to the technical field of yield increase transformation of fractured dry-hot rock masses, in particular to a method for calculating the flow conductivity of micro-fracture heat induction of the dry-hot rock masses.
Background
The hydraulic fracturing technology is one of the most effective reconstruction means for economic and efficient development of deep dry and hot rock geothermal resources, and aims to activate micro cracks in the dry and hot rock by utilizing a thermal induction stress-strain mechanism of the rock to form a water flow channel with high thermal induction flow conductivity and realize the purposes of efficient injection and extraction and heat exchange.
The thermal induction flow conductivity consists of an original mechanical opening and a thermal induction opening, wherein the original mechanical opening is an opening of the hot dry rock micro-cracks determined by self roughness in an in-situ state, and the thermal induction opening is a strain opening generated by rapid temperature drop of the high-temperature hot dry rock micro-cracks in the process of continuously injecting hydraulic fracturing cold fluid. Therefore, accurately calculating the roughness and the heat-induced opening degree of the microfractures of the hot dry rock is the key of the hydraulic fracturing optimization design of the hot dry rock.
At present, the roughness of the hot and dry rock body microcracks is often calibrated for a plurality of times by using an outcrop core, and artificial calibration for a plurality of times can not cover the whole two-dimensional plane and can not accurately measure the height of the microscopic microcracks, so that the deviation of the roughness calibration result and real data is overlarge; the hot and dry rock body microcracks are usually assumed to be plane cracks and are in a closed compression state under the action of in-situ stress, an invalid flow guide channel is defaulted in flow guide calculation, and the original mechanical opening formed by self-supporting of the surface of the rough microcrack is ignored; the temperature drop of the microcrack wall surface of the high-temperature rock mass is often directly expressed by the difference between the temperature of the high-temperature rock mass and the temperature of injected cold fluid, the effect of a stable heat source of the high-temperature dry-hot rock mass is neglected, the temperature drop change cannot be accurately calculated in the length direction of the microcrack, and the calculated temperature drop and the heat induction opening degree are both larger than actual values.
Disclosure of Invention
The invention aims to provide a novel method for calculating the microcrack heat-induced flow conductivity of a hot dry rock body aiming at the defects of the conventional method for measuring the microcrack heat-induced flow conductivity of the hot dry rock body.
The invention provides a method for calculating the heat-induced flow conductivity of a microfracture of a hot and dry rock mass, which comprises the following steps:
s1, collecting the dry-hot rock reservoir core containing the microcracks, and obtaining the two-dimensional plane topography data of the microcracks by laser scanning.
The specific method comprises the following steps: collecting a dry hot rock reservoir rock core containing microcracks, splitting along the direction of the microcracks, cutting and preparing a sample into a rectangular rock plate, and acquiring the appearance data of a two-dimensional plane of the microcracks by laser scanning.
Taking the length direction of the microcracks as the x direction, and measuring the length of the microcracks as L in units of m; taking the width direction of the microcracks as the y direction, measuring the width of the microcracks as W and measuring the width in m; and scanning the microcracks at equal intervals by using a laser scanner, wherein the scanning interval in the x direction is delta x, the scanning interval in the y direction is delta y, and the height of any scanning point on the microcrack two-dimensional plane is Z.
And S2, calculating the roughness coefficient of the microcracks according to the topography data of the two-dimensional plane. The specific method comprises the following steps:
(1) according to the shape data of the two-dimensional plane of the microcrack, the position y with a certain width is obtainediWhere the number of scanning points in the longitudinal direction is N ═ L/Δx, in the length direction, the height of any scanning point is ZijWherein i · · ·, M, W/Δ y, j ·1,2,3 · · · · · · ·, N, calculating an average height difference D of the microcrack two-dimensional plane according to formula (1):
in the formula, Di is an intermediate parameter and has no specific meaning.
(2) Calculating the roughness coefficient JRC of the microcracks according to the average height difference of the two-dimensional planes of the microcracks and a formula (2):
JRC＝32.3+0.25D2+31.53log(D) (2)。
and S3, calculating the initial mechanical opening of the micro-cracks of the hot dry rock according to the in-situ stress state and the mechanical strength of the hot dry rock. The method specifically comprises the following two substeps:
s31, calculating the normal stress sigma applied to the micro-cracks of the hot and dry rock mass according to the formula (3) according to the in-situ stress state of the micro-cracks of the hot and dry rock massn：
In the formula: sigma1、σ3Respectively the maximum and minimum principal stress of the hot and dry rock mass in situ, MPa; beta is the inclination angle of the microcrack, °;
s32, calculating the initial mechanical opening b of the micro-cracks of the hot dry rock mass in the in-situ state according to the formula (4) by combining the mechanical strength of the hot dry rock mass and the normal stress applied to the micro-cracks according to the normal stress applied to the micro-cracks:
in the formula, JCS is the compressive strength of the hot dry rock mass, MPa.
And S4, calculating the temperature field of the microcrack wall surface in the long-term injection process of hydraulic fracturing by combining the thermal physical parameters of the hot dry rock and the hot dry rock. The method comprises the following specific steps:
in the long-term injection process of the dry-hot rock micro-fracture hydraulic fracturing, fluid in the fracture and the dry-hot rock both satisfy an energy balance equation, the fluid property is supposed not to change along with the temperature and the wall surface of the micro-fracture has no filtration loss, only the heat exchange in the direction vertical to the wall surface of the micro-fracture is considered, and the heat transfer equation in the dry-hot rock and the micro-fracture is expressed as follows:
in the formula, TfThe temperature of the fluid in the microcracks is measured at DEG C; k is a radical off,effThe heat conduction coefficient of the fluid in the microcrack is J/(m.s.K); c. CfThe specific heat of the fluid in the microcrack is J/(kg. K); rhofIs the density of the fluid in the microcrack, kg/m3；TmThe temperature of the dry-hot rock mass is DEG C; k is a radical ofm,effThe heat conductivity coefficient of the dry-heat rock mass is J/(m.s.K); c. CmThe specific heat of the hot and dry rock mass is J/(kg.K); rhomIs the density of the dry-hot rock mass in kg/m3；hmfThe heat transfer coefficient from the rock on the wall surface of the crack to the fluid in the micro-crack is J/(m.s.DEG C); μ is the fluid injection linear velocity, m/min; b is the initial mechanical opening.
Meanwhile, x and y are defined as two-dimensional positions of the hot dry rock mass underground, and the length of a micro-crack in a hot dry rock mass reservoir is assumed to be LfAnd m. The direction of the microcracks in the reservoir is x, and the direction perpendicular to the x is the dry-hot rock mass matrix, namely y.
The heat transfer of the dry-hot rock mass matrix is heat conduction, and the heat transfer equation is expressed as follows:
heat transfer within the microcracks includes: the heat storage, the heat convection in the crack direction, the longitudinal dispersion and the heat conduction between the fluid and the crack wall surface, and the heat transfer equation is expressed as follows:
in the formula, DfLongitudinal diffusion coefficient.
Obtaining a two-dimensional temperature distribution equation of the hot and dry rock by utilizing Laplace transform, and calculating a two-dimensional temperature field T of the hot and dry rock according to a formula (8):
in the formula, x and y are two-dimensional positions of the dry-hot rock mass underground, and the length of the microcrack in the dry-hot rock mass reservoir is LfM; the direction of the microcracks in the reservoir is x, and the direction vertical to the x is the dry-hot rock mass matrix, namely y; t isfThe temperature of the fluid in the microcracks is measured at DEG C; t ismThe temperature of the dry-hot rock mass is DEG C; k is a radical ofm,effThe heat conductivity coefficient of the dry-heat rock mass is J/(m.s.K); c. CmThe specific heat of the hot and dry rock mass is J/(kg.K); rhomIs the density of the dry-hot rock mass in kg/m3；ρwIs the water density in kg/m3，cwIs the specific heat of water, J/(kg. K); mu is the linear velocity of water injection, m/min; b is the initial mechanical opening; when y is 0, the temperature field distribution of the microcrack wall surface is obtained; t is a certain moment of the long-term pumping process of hydraulic fracturing, day and H are the height of the microcracks in the dry-hot rock reservoir and m; q is the long-term injection displacement m of the hydraulic fracturing of the hot dry rock mass3/min。
S5, calculating the thermal induction opening of the microcrack wall surface in the long-term injection process of hydraulic fracturing according to the temperature drop and the mechanical parameters of the microcrack wall surface of the dry-hot rock mass. The method comprises the following specific steps:
s51, calculating the temperature drop Delta T of the microcrack wall surface at a certain moment according to the formula (9) according to the temperature field of the microcrack wall surface:
ΔT＝Tm-T(x,0,t) (9)
s52, inducing the hot and dry rock to generate stress and strain under the condition of temperature change, combining a heat induced stress model under the condition of a green function continuous heat source, and expressing the strain equation of the hot and dry rock as follows according to a hole elasticity mechanism:
in the formula, v is the Poisson's ratio of the dry-hot rock mass and has no dimension; alpha is alphaTIs the linear thermal expansion coefficient of the hot and dry rock, G is the volume modulus, MPa, muy(x, y, t) is the injection linear velocity in the y direction, m/min;
and (3) obtaining a thermal induction opening model of the long-term injection process of the hydraulic fracturing at different positions of the microcrack wall surface under the condition of heat exchange by derivation in the y direction, and calculating the thermal induction opening w (x, t) at the different positions of the microcrack wall surface according to a formula (11):
in the formula, v is the Poisson's ratio of the dry-hot rock mass and has no dimension; alpha is alphaTThe coefficient of linear thermal expansion of the dry-hot rock mass is 1/K; q is the displacement of the long-term injection process of hydraulic fracturing, m3/day；cfThe specific heat of the fluid in the microcrack is J/(kg. K); rhofIs the density of the fluid in the microcrack, kg/m3。
And S6, calculating the flow guide opening, the heat-induced flow guide capacity and the comprehensive flow guide capacity of the microcracks of the hot and dry rock according to the initial mechanical opening and the heat-induced opening. The method specifically comprises the following steps:
s61, calculating the total opening W of the hot dry rock body at any position of the microcracks according to the formula (12) according to the initial mechanical opening and the thermal induction openingTAnd diversion opening degree UT：
S62, according to the microcrack diversion opening U of the dry and hot rock massTCalculating the heat-induced flow conductivity K at any position of the microcracks of the hot dry rock according to the formula (13)dAnd micro-crack comprehensive conductivity K:
in the formula, NfIs the micro-crack of the hot and dry rock mass in the length LfA discrete number of directions; and K is the comprehensive flow conductivity (mD) after the hot dry rock micro-fracture hydraulic fracturing is completed for long-term injection.
Compared with the prior art, the invention has the advantages that:
firstly, introducing calculation of a flow guide opening degree, and introducing roughness and an original mechanical opening degree; and secondly, the temperature drop is calculated by utilizing the temperature field of the wall surface of the microcrack, the method is more accurate than directly calculating the temperature difference between the fluid and the rock mass, and the comprehensive flow conductivity of the microcrack after the hot dry rock transformation can be accurately calculated by the method.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
Drawings
FIG. 1 is a two-dimensional plane of a hot dry rock microcracked rectangular rock slab after laser scanning.
FIG. 2 shows the distribution of the microcrack wall temperature along the longitudinal direction.
Fig. 3 distribution of microcrack thermally induced opening along the length direction.
Fig. 4 distribution of microcrack thermally-induced conductivity openings along the length direction.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
And step S1, collecting the dry hot rock reservoir rock core containing the microcracks, splitting along the direction of the microcracks, and cutting and preparing a sample into a rectangular rock plate with the length of 150cm and the width of 35 cm. The scanning precision of the rectangular rock plate in the length direction and the width direction is set to be 0.1mm, and the shape data of the microcracks on a two-dimensional plane is obtained through laser scanning, as shown in figure 1.
And step S2, calculating according to the formula (1) and the formula (2) to obtain the roughness coefficient of the microcracks to be 21.3.
Step S3, setting the maximum principal stress sigma of the hot dry rock in the in-situ state of the microcracks1100MPa, minimum principal stress sigma380MPa and the compressive strength JCS of the dry-hot rock mass is 80 MPa. And (4) calculating according to the formula (3) and the formula (4) to obtain the initial mechanical opening of the microcrack in the in-situ state to be 0.58 mm.
Step S4, obtaining the density of the fluid in the micro-cracks in the hydraulic fracturing process as 1000kg/m3The specific heat of the fluid is 3900J/(kg.K), the heat conduction coefficient of the dry-hot rock mass is 2.6J/(m.s.K), and the density of the dry-hot rock mass is 2650kg/m3The specific heat of the dry and hot rock mass is 1100J/(kg.K), the temperature of the dry and hot rock mass is 180 ℃, the temperature of the fluid injected into the micro-cracks is 20 ℃, the height of the micro-cracks in the reservoir of the dry and hot rock mass is 300m, and the long-term injection displacement of the dry and hot rock mass in hydraulic fracturing is 3.0m3And/min, and the total time of hydraulic fracturing long-term pumping is 5 day.
Assuming that the length of the microcracks of the hot dry rock is 300m, calculating according to the formulas (5) to (8), after the long-term pumping injection of the hydraulic fracturing for 5 days, the temperature at the injection port of the microcrack is reduced from 180 ℃ to 21.2 ℃, and the temperature distribution of the wall surface of the microcrack along the length direction of the microcrack is shown in figure 2.
And step S5, firstly, calculating the temperature reduction value of each position of the wall surface of the microcrack according to the formula (9) according to the temperature distribution of the wall surface of the microcrack after the long-term pumping injection of the hydraulic fracturing for 5 days. Meanwhile, the Poisson ratio of the dry-hot rock mass is 0.28, and the linear thermal expansion coefficient of the dry-hot rock mass is 4.61 multiplied by 10-6K-1And calculating the thermally induced opening degrees of the different positions of the microcrack wall surface according to the formulas (10) to (11).
The thermally induced opening of the microcrack injection port was calculated to be 0.9118mm, and the thermally induced opening of the microcrack wall surface along the microcrack longitudinal direction is shown in fig. 3.
And step S6, respectively calculating the total opening, the diversion opening, the heat-induced diversion capacity and the comprehensive diversion capacity of the microcracks along the length direction of the microcracks according to the formulas (12) to (13). The calculation shows that the heat-induced conductivity of the microcrack injection port is 42.6mD, the comprehensive conductivity of the hot dry rock microcracks is 15.16mD, and the heat-induced conductivity along the length direction of the microcracks is shown in FIG. 4.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (8)
1. A method for calculating the heat-induced flow conductivity of the microcracks of the hot and dry rock mass is characterized by comprising the following steps:
s1, collecting a dry-hot rock reservoir core containing the microcracks, and obtaining the two-dimensional plane topography data of the microcracks by laser scanning;
s2, calculating the roughness coefficient of the microcracks according to the topography data of the two-dimensional plane;
s3, calculating the initial mechanical opening of the microfractures of the hot dry rock according to the in-situ stress state and the mechanical strength of the hot dry rock;
s4, calculating a temperature field of the microcrack wall surface in the long-term injection process of hydraulic fracturing by combining the thermal physical parameters of the hot dry rock and the hot dry rock;
s5, calculating the thermal induction opening of the microcrack wall surface in the long-term injection process of hydraulic fracturing according to the temperature drop and the mechanical parameters of the microcrack wall surface of the dry-hot rock mass;
and S6, calculating the flow guide opening, the heat-induced flow guide capacity and the comprehensive flow guide capacity of the microcracks of the hot and dry rock according to the initial mechanical opening and the heat-induced opening.
2. The method for calculating the heat-induced conductivity of the microfractures of the hot and dry rock mass according to claim 1, wherein the step S1 is specifically as follows: collecting a dry hot rock reservoir rock core containing microcracks, splitting along the direction of the microcracks, cutting and preparing a sample into a rectangular rock plate, and acquiring the appearance data of a two-dimensional plane of the microcracks by laser scanning.
3. The method for calculating the heat-induced conductivity of the microfractures of the hot and dry rock body according to claim 2, wherein in the step S1, the specific method of laser scanning is as follows: taking the length direction of the microcracks as the x direction, and measuring the length of the microcracks as L in units of m; taking the width direction of the microcracks as the y direction, measuring the width of the microcracks as W and measuring the width in m; and scanning the microcracks at equal intervals by using a laser scanner, wherein the scanning interval in the x direction is delta x, the scanning interval in the y direction is delta y, and the height of any scanning point on the microcrack two-dimensional plane is Z.
4. The method for calculating the heat-induced conductivity of the hot and dry rock micro-cracks according to claim 2, wherein the method for calculating the roughness coefficient in the step S2 is as follows:
(1) according to the shape data of the two-dimensional plane of the microcrack, the position y with a certain width is obtainediThe number of scanning points in the longitudinal direction is N ═ L/Δ x, and the height of any scanning point in the longitudinal direction is ZijWherein i · · ·, M, W/Δ y, j ·1,2,3 · · · · · · ·, N, calculating an average height difference D of the microcrack two-dimensional plane according to formula (1):
(2) calculating the roughness coefficient JRC of the microcracks according to the average height difference of the two-dimensional planes of the microcracks and a formula (2):
JRC＝32.3+0.25D2+31.53log(D) (2)。
5. the method for calculating the heat-induced conductivity of the microfractures of the hot and dry rock mass according to claim 1, wherein the step S3 comprises the following two substeps:
s31, calculating the positive stress sigma applied to the micro-cracks of the hot dry rock according to the formula (3)n：
In the formula: sigma1、σ3Respectively the maximum and minimum principal stress of the hot and dry rock mass in situ, MPa; beta is the inclination angle of the microcrack, °;
s32, calculating the initial mechanical opening b of the hot dry rock micro-cracks in the in-situ state according to the formula (4):
in the formula, JCS is the compressive strength of the hot dry rock mass, MPa.
6. The method for calculating the microcrack heat-induced conductivity of the hot and dry rock according to claim 1, wherein in step S4, the two-dimensional temperature field T of the hot and dry rock is calculated according to the formula (8):
in the formula, x and y are two-dimensional positions of the dry-hot rock mass underground, and the length of the microcrack in the dry-hot rock mass reservoir is LfM; the direction of the microcracks in the reservoir is x, and the direction vertical to the x is the dry-hot rock mass matrix, namely y; t isfThe temperature of the fluid in the microcracks is measured at DEG C; t ismThe temperature of the dry-hot rock mass is DEG C; k is a radical ofm,effThe heat conductivity coefficient of the dry-heat rock mass is J/(m.s.K); c. CmThe specific heat of the hot and dry rock mass is J/(kg.K); rhomIs the density of the dry-hot rock mass in kg/m3；ρwIs the water density in kg/m3，cwIs the specific heat of water, J/(kg. K); mu is the linear velocity of water injection, m/min; b is the initial mechanical opening; when y is 0, isTemperature field distribution of the microcrack wall surface; t is a certain moment of the long-term pumping process of hydraulic fracturing, day and H are the height of the microcracks in the dry-hot rock reservoir and m; q is the long-term injection displacement m of the hydraulic fracturing of the hot dry rock mass3/min。
7. The method for calculating the heat-induced conductivity of the microfractures of the hot and dry rock mass according to claim 6, wherein the step S5 specifically comprises the following steps:
s51, calculating the temperature drop Delta T of the microcrack wall surface at a certain moment according to the formula (9) according to the temperature field of the microcrack wall surface:
ΔT＝Tm-T(x,0,t) (9)
s52, inducing the dry-hot rock to generate stress and strain under the condition of temperature change, and expressing the strain equation of the dry-hot rock as follows:
in the formula, v is the Poisson's ratio of the dry-hot rock mass and has no dimension; alpha is alphaTThe linear thermal expansion coefficient of the dry-hot rock mass, G is the volume modulus, MPa; mu.sy(x, y, t) is the injection linear velocity in the y direction; m/min;
and (3) obtaining a thermal induction opening model of the long-term injection process of the hydraulic fracturing at different positions of the microcrack wall surface under the condition of heat exchange by derivation in the y direction, and calculating the thermal induction opening w (x, t) at the different positions of the microcrack wall surface according to a formula (11):
in the formula, v is the Poisson's ratio of the dry-hot rock mass and has no dimension; alpha is alphaTThe coefficient of linear thermal expansion of the dry-hot rock mass is 1/K; q is the displacement of the long-term injection process of hydraulic fracturing, m3/day；cfThe specific heat of the fluid in the microcrack is J/(kg. K); rhofIs the density of the fluid in the microcrack, kg/m3。
8. The method for calculating the heat-induced conductivity of the microfractures of the hot and dry rock mass according to claim 6, wherein the step S6 specifically comprises the following steps:
s61, calculating the total opening W of the hot dry rock body at any position of the microcracks according to the formula (12) according to the initial mechanical opening and the thermal induction openingTAnd diversion opening degree UT：
S62, according to the microcrack diversion opening U of the dry and hot rock massTCalculating the heat-induced flow conductivity K at any position of the microcracks of the hot dry rock according to the formula (13)dAnd micro-crack comprehensive conductivity K:
in the formula, NfIs the micro-crack of the hot and dry rock mass in the length LfA discrete number of directions; and K is the comprehensive flow conductivity (mD) after the hot dry rock micro-fracture hydraulic fracturing is completed for long-term injection.
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| CN112033812A (en) * | 2020-08-12 | 2020-12-04 | 成都北方石油勘探开发技术有限公司 | Method and system for testing shear-swelling flow conductivity of hydraulic shear fracturing |
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| CN112033812A (en) * | 2020-08-12 | 2020-12-04 | 成都北方石油勘探开发技术有限公司 | Method and system for testing shear-swelling flow conductivity of hydraulic shear fracturing |
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