CN109283118B - Characterization method of crack surface roughness, seepage test system and test method - Google Patents
Characterization method of crack surface roughness, seepage test system and test method Download PDFInfo
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Abstract
The invention discloses a characterization method of crack surface roughness, a seepage test system and a test method, wherein the characterization method takes the height difference and the slope of a rough contour line micro-segment as a judgment standard, ignores a line segment with little influence on pressure drop in the seepage process, and combines various parameters such as contour peak density, fractal box counting dimension and the like to the roughness phi 1 、φ 2 Description will be made on itWhen the method is used in a non-Darcy flow region formula, the method can be consistent in both mathematical form and physical sense; the relation between the non-Darcy coefficient beta and the crack roughness characteristic is established through the establishment of a new characterization method and a new formula, and the method highlights the influence of the roughness characteristic along the water flow direction on the pressure drop in the fluid flow process; through the special design of the seepage test system, the change of the gap width can be accurately measured, and the dimensionless quantity A can be researched by combining different prefabricated fracture surfaces D 、B D And roughness parameter phi 1 、φ 2 Specific functional forms and change laws of the system.
Description
Technical Field
The invention relates to a characterization method of crack surface roughness, a seepage test system and a seepage test method, and belongs to the field of seepage research.
Background
Fluid momentum transfer in fractured rock mass is commonly applied to a large number of engineering sites, including mine geothermal work, underground tunnels, geothermal energy extraction, oil and gas exploitation, pollutant sequestration and the like, and discrete fracture network models (DFN models) extracted for engineering problems are commonly applied to seepage research, wherein single fracture seepage is the research foundation. The flowing process of the water in the single fracture meets the N-S equation, and the condition is simplified to obtain the Darcy flow areaThe relationship, i.e., the flow Q through a flat plate slot is proportional to the cube of the slot width b, as shown by the following equation:
in the above formula, Q is seepage flow, m 3 S; w is the width of the overflow surface and m; b is the mechanical gap width of the crack, m; mu is the dynamic viscosity of the fluid and Pa.s;is the pressure gradient across the fracture, pa/m. Wherein A is D Has a value of f (12 phi) 1 )，φ 1 To represent a dimensionless number of roughness, phi when the fracture surface is completely smooth 1 =1, when the fracture surface is rough, Φ 1 ＞1。
In seepage characteristic analysis of a series of actual engineering construction such as hydraulic power, tunnel, petroleum exploitation and the like, more and more test data and monitoring data prove that a plurality of phenomena deviating from Darcy seepage rules exist, namely seepage speed and hydraulic power gradient are not in linear relation, and the main reasons for the nonlinear occurrence are as follows at present: (1) due to the rough flow line tortuosity of the cracks, when the flow rate of water is increased, the inertia force is not negligible due to the change of the flow speed and the direction. (2) The turbulence created during turbulence causes energy dissipation and the pressure drop caused by this condition is greater. (3) The roughened surface causes an increase in the resistance of the flowing water. It can be seen that the rough characteristic of the fracture surface has an important influence on the single fracture seepage process, and the domestic and external Forchheimer formula is used for describing the flow Q and the pressure drop of the non-Darcy flow areaThe relationship between these is dimensionless, and the following formula is shown:
wherein B is D/b Beta, beta is the fidaxy coefficient, m -1 ，B D Is a dimensionless number representing fracture roughness and is more biased to reflect pressure nonlinear losses during fluid seepage.
From the above formulas, it can be seen that the rough characteristic of the fracture surface has an important influence on the description of the fluid state no matter the fluid is in the darcy flow stage or the non-darcy flow stage, and the fracture rough surface is described by most of statistical methods or fractal geometric methods at home and abroad due to the complex shape of the fracture rough surface, but the research results have larger deviation.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide a characterization method for the crack surface roughness, which can characterize the influence condition of the surface crack roughness on the fidaxy seepage, and also provides a seepage test system and a test method for researching the crack surface roughness.
In order to achieve the above purpose, the invention adopts the following technical scheme: a method for characterizing the roughness of the surface of crack includes such steps as providing a segment of randomly generated rough curve with straight reference line, which is composed of N equally-spaced points whose abscissa is x i The ordinate is z i (i is more than or equal to 1 and less than or equal to N), and establishing a dimensionless number A D 、B D Relationship with roughness:
A D ＝f(12φ 1 )
B D ＝f(φ 2 )，
in phi 1 、φ 2 Is roughness, phi 1 Reflects the rough characteristic of the whole curve, represents the influence of the rough characteristic on the linear part of the Forchheimer formula, phi 2 Reflecting the influence of the roughness of the curve along the water flow direction on the water flow pressure drop, representing the influence of the roughness characteristic on the nonlinear part of the Forchheimer formula, phi 1 、φ 2 The expression is as follows:
φ 1 ＝D B
wherein D is B The fractal box counting dimension of the rough curve is l is the length of a datum line of the rough curve, S m For the average pitch of the contour micro-irregularities, the contour micro-irregularities pitch is a length of a reference line containing one contour peak and an adjacent contour valley, then l/S m Is the density of contour peaks on the roughness curve; m refers to all line segments included in the rough curve; m is the number of line segments that simultaneously satisfy the following conditions:
(1) the slope of each segment is determined and,
wherein Z is 2 The root mean square of the first derivative of the surface contour is obtained by the following formula:
wherein N is the number of points contained in the rough curve;
(2) the height difference of each section is judged,
z i distance to midline +z i+1 Distance to midline < 2R a
Wherein R is a The arithmetic mean deviation of the profile, i.e. the arithmetic mean of the distances of each point from the reference line,
the number of line segments satisfying the conditions (1) and (2) is m;
in summary, the forshheimer formula for the fidaxl stage in the single fracture water seepage process can be expressed as formula (1):
namely:
the invention also discloses a seepage test system for the crack surface roughness characterization, which comprises a clamp holder, wherein the clamp holder comprises a sleeve, a rubber sleeve is coaxially arranged in the sleeve, a confining pressure cavity is arranged between the inner wall of the sleeve and the outer wall of the rubber sleeve, and a confining pressure loading device is arranged outside the sleeve; an inlet false rock core and an inlet plug are sequentially plugged into the rubber sleeve from the inlet side of the clamp holder, an inlet end cover is arranged on the inlet side of the clamp holder, an outlet false rock core and an outlet plug are sequentially plugged into the rubber sleeve from the outlet side of the clamp holder, water flow channels are respectively arranged on the inlet false rock core and the outlet false rock core along respective central axes, and a plurality of seepage grooves are respectively arranged on the opposite side surfaces of the inlet false rock core and the outlet false rock core along the radial direction from the centers;
the inlet plug is internally provided with a water flow hole along the central axis, the water flow hole is communicated to an external constant-current constant-pressure pump through an inlet pipeline, the inlet pipeline is provided with a three-way valve I, and a branch port of the three-way valve I is provided with an inlet pressure gauge;
a single-crack sample is arranged in a cavity surrounded by the inlet false core, the outlet false core and the rubber sleeve, a water flow leading-out hole is arranged in the outlet plug along the central axis of the outlet plug, one end of the water flow leading-out hole, which is exposed out of the outlet plug, is connected to a water outlet flowmeter through an outlet pipeline, and a three-way valve II and a back pressure valve are arranged on the outlet pipeline; an outlet pressure gauge is arranged on a branch port of the three-way valve II, a gap width measuring device is arranged outside the sleeve, and a probe of the gap width measuring device penetrates through the sleeve and the rubber sleeve perpendicular to the fracture surface and props against the outer wall of the single fracture sample.
The confining pressure loading device comprises a ring pressure pump, wherein the sleeve is provided with an oil inlet hole, and the oil inlet hole is communicated to the outside of the sleeve from the confining pressure cavity; the outlet of the annular pressure pump is connected to the oil inlet through a pressurizing pipeline. The annular pressure pump can pump out pressure oil, and the pressure oil is injected into the oil inlet hole through the pressurizing pipeline and then enters the confining pressure cavity to pressurize the rubber sleeve.
Preferably, the gap width measuring device comprises an LVDT displacement sensor, a probe of the gap width measuring device is connected with the LVDT displacement sensor, the measuring range can be selected according to the gap width, the vertical deformation quantity delta b of the sample gap can be measured, and the LVDT displacement sensor is connected to the data collector. The measured fracture deformation can be directly displayed on a data acquisition device. The data collector can be PCI720 type collector of Minghua technology.
Preferably, the outer wall of the rubber sleeve is provided with a positioning column, the positioning column can be embedded into a hole in the inner wall of the sleeve in a matching way, and when the positioning column is embedded into the hole in the inner wall of the sleeve, the crack surface of the single crack sample is just vertical to the probe of the crack width measuring device. When the single-slit sample is loaded, the single-slit sample is pushed into the rubber sleeve, and then the rubber sleeve is positioned in the sleeve through the positioning column, so that the positioning of the slit surface is facilitated by the positioning column, and the slit surface of the single-slit sample after loading can be ensured to be always perpendicular to the probe of the slit width measuring device.
The fracture surface of the single fracture sample is designed in advance and is cut by a sand wire cutting machine.
Preferably, in order to ensure a stable connection, the inlet end cap is fixed to the inlet side of the sleeve through the inlet protecting cap, and the outlet plug is fixed to the outlet side of the sleeve through the outlet protecting cap.
Further, the inlet pressure gauge, the outlet pressure gauge, the gap width measuring device and the water outlet flowmeter are commonly connected to a data acquisition device. The data collector can receive the detection data of each detection component in real time and display the detection data in real time.
The seepage test method for the crack surface roughness characterization comprises the following steps:
1) Finding the least square center line of N points forming the rough curve, and taking the least square center line as a datum line of the rough curve, wherein a datum line equation is z=ax+b;
2) Calculating roughness-related parameters of the curve according to matlab program, including fractal box-counting dimension D B Root mean square Z of first derivative of surface contour line 2 Arithmetic mean deviation R of contours a Density of contour peaks l/S m According to Z 2 、R a The (M-M)/M of the curve is found, and the roughness of the curve can be expressed as:
φ 1 ＝D B
3) Cutting the cracks of the single-crack sample into a rough curve by using a diamond wire with the wire diameter of 0.33mm on a sand wire cutting machine, wherein the curve has rough characteristics only in the water flow direction, and the roughness is obtained in the step 2);
4) Sealing two sides of a single-fracture sample fracture with AB glue in a copper sheet with the thickness of 300um in the fracture, pushing the single-fracture sample fracture into a clamp holder, positioning the single-fracture sample fracture with a positioning column, ensuring that a fracture width measuring device is vertical to a fracture surface, screwing an inlet end cover and an outlet plug of the clamp holder after the sample is placed, and enabling the initial fracture width of the fracture to be b0;
5) Applying confining pressure sigma 3 At this time, the crack deformation Δb was measured, and it was found that the confining pressure σ was obtained 3 The crack gap width under the condition is b 0-delta b;
6) After the confining pressure is stable, the pressure of a back pressure valve is set, and the constant-flow constant-pressure pump is used for injecting the pressure P 1 The outlet pressure value P measured by the outlet pressure meter after the flow is stable 2 Is equal to the pressure of the back pressure valve, and the pressure gradient (P is measured by an outlet flow meter 1 -P 2 ) Flow rate Q of/l 1 Then pressurizing step by step, respectively measuring different pressure gradientsLower flow rate Q i Can obtain a stripIs a relationship of (2);
7) Changing the confining pressure condition, applying different confining pressures to the single-fracture sample to obtain different fracture gap widths b, and then performing the tests of the steps 5) to 6), so that the fracture gap width condition of the formula (1) can be changed to obtain the corresponding working conditionA curve;
8) Regenerating a different roughness curve, so that 12 phi in equation (1) can be changed 1 And phi 2 And (3) repeating the steps 1) to 7) to obtain the corresponding working conditionA curve;
9) As can be seen, in the following equation,q, b, w, mu and rho are all available quantities, and test data under each working condition are respectively processed in origin softwareFitting the sub-polynomial, fitting the following formula form, and obtaining A under corresponding working conditions D And B D Value:
10 Through A under different working conditions obtained above D And B D The value can be researched and obtained to obtain dimensionless quantity A in Darcy and non-Darcy areas under the conditions of the same surface roughness, different gap widths and different surface roughness D 、B D And the roughness characterization quantity phi 1 And phi 2 Specific forms and change laws of the functions.
Compared with the prior art, the invention has the following advantages:
(1) The characterization method of the crack surface roughness can be consistent in both mathematical form and physical sense when applied to the Forchheimer formula of the non-Darcy flow region; the relation between the non-Darcy coefficient beta and the crack roughness characteristics is established through the establishment of a new characterization method and a new formula, wherein the relation comprises the crack width, the height difference, the slope and the contour peak density;
(2) The invention takes the slope and the height difference of the micro-segment of the rough contour line as the judgment standard, ignores the line segment with little influence on the pressure drop in the seepage process (such as the line segment with small height difference and small gradient), and combines various parameters such as the contour peak density, the fractal box counting dimension and the like to the roughness phi 1 、φ 2 The method is described, so that the research amount is greatly reduced and the research emphasis is highlighted;
(3) The invention designs a corresponding seepage test system, and obtains corresponding seepage tests on single-fracture rock samples with different rough characteristicsCurve, A under different working conditions can be obtained through quadratic term fitting D 、B D Is used as a reference to the value of (a),final establishment A D 、B D Relationship to roughness parameters.
(4) In the seepage test system, in the process of carrying out crack seepage, the designed gap width measuring device can accurately measure the variation of the gap width b (the precision reaches 1 um), and the probe vertical to the gap surface is closely attached to the outer surface of the sample, so that the measuring influence caused by deformation of the rubber sleeve is fully considered, the measuring error is greatly eliminated, and the accuracy and the reliability of a research result are ensured. Because the clamp can accurately measure the deformation of the crack gap width, A can be studied by prefabricating different crack surfaces D ＝f(12φ 1 )、B D ＝f(φ 2 ) Specific functional forms and change laws of the system.
Drawings
FIG. 1 is a schematic diagram of a rough curve generated by a random midpoint method;
FIG. 2 is a schematic view of a rough surface formed by a rough curve with a straight line as a reference line;
FIG. 3 is a rough plot of FIG. 2;
FIG. 4 is a seepage test system used in the present invention;
FIG. 5 is a schematic side view of an inlet pseudo core and an outlet pseudo core of the present invention opposite each other;
in the figure, 1. Inlet piping; 2. an inlet end cap; 2-1, an inlet protecting cover; 3. an inlet plug; 3-1, a water flow hole; 4. an inlet pseudo-core; 5. a single fracture sample; 5-1, a fracture surface; 10-1, positioning columns; 6. a gap width measuring device; 7. a confining pressure cavity; 8. an oil inlet hole; 9. a sleeve; 10. a rubber sleeve; 11. outlet pipeline, 12. Three-way valve II, 13. Outlet plug; 13-1, a water flow leading-out hole; 13-2, an outlet protective cover; 14. a three-way valve I; 15. constant-flow constant-pressure pump; 16. a back pressure valve; 17. a water outlet flowmeter; 18. an outlet pressure gauge; 19. an inlet pressure gauge; 20. a water flow channel; 21. and a seepage groove.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
In the single-crack seepage process, the influence of the roughness features along the water flow direction on the loss of inlet and outlet pressure drop is the greatest, and only the roughness along the flow direction is considered for highlighting the study object.
Characterization method of roughness:
FIG. 1 is a two-dimensional rough curve generated according to the random midpoint method, which can reflect the contour of the rough plane, and from which it can be seen that the reference line (a straight line reflecting the direction of a crack, typically the least squares centerline) is undulating; for convenience of study, a piece of randomly generated roughness curve with straight datum line was taken for study, as shown in fig. 2. FIG. 3 is a section of the roughness curve of FIG. 2, which curve is composed of 200 points with a spacing of 0.5mm, the abscissa x of 200 points being from 0 to 100mm, and the ordinate z floating (statistically) above and below the reference line, to study the effect of the roughness curve on non-Darcy flow, it is necessary to establish a dimensionless number A D 、B D And the relation between the roughness, and for this purpose, a roughness characterization method is provided:
A D ＝f(12φ 1 )
B D ＝f(φ 2 )
in phi 1 、φ 2 Roughness, but with emphasis on each, phi 1 Mainly reflects the rough characteristic of the whole curve, represents the influence of the rough characteristic on the linear part of the Forchheimer formula, phi 2 Mainly reflects the influence of the roughness of a curve along the water flow direction on the water flow pressure drop, represents the influence of the roughness characteristic on the nonlinear part of the Forchheimer formula, phi 1 、φ 2 The expression is as follows:
φ 1 ＝D B
wherein D is B For the fractal box counting dimension of the rough curve, the value of the two-dimensional curve is 1-2, D is the same as D when the curve is flat B =1, l is the length of the datum line of the roughness curve, S m For the average pitch of the microscopic irregularities of the profile, the microscopic irregularities of the profile refer to the length of a datum line containing one profile peak and adjacent profile valleys, then l/S m Is actually coarseThe density of contour peaks on the curve.
In the above formula, M refers to all the line segments included in the rough curve, which is 199 in this example; m is the number of line segments that simultaneously satisfy the following conditions:
(1) the slope of each segment is determined and,
wherein Z is 2 The root mean square of the first derivative of the surface contour is obtained by the following formula:
wherein N is the number of points contained in the rough curve, in this example 200;
(2) the height difference of each section is judged,
Z(x i ) Distance to midline +Z (x) i+1 ) Distance to midline < 2R a
Wherein R is a Is the arithmetic mean deviation of the profile, i.e. the arithmetic mean of the distances of each point from the reference line.
The number of segments satisfying the conditions (1) and (2) is m.
In summary, the forshheimer formula for the fidaxl stage in the single fracture water seepage process can be expressed as formula (1):
namely:
the formula has definite physical meaning, and when the fluid flow in the single fracture is smaller, the fluid meets Darcy's law, namelySatisfy the linear relation, under the same flow rate Q condition, the pressure drop +.>And roughness phi 1 In relation, this roughness reflects the roughness of the entire fracture surface. When the fluid flow rate in the single fracture is greater than the critical value, the fluid meets the non-Darcy rule, namelyDeviating from the linear relationship, non-linear part +.>Representing the pressure drop caused by crack roughness after the flow is increased, the roughness characterization is more biased to the roughness characteristic along the water flow direction, wherein the height difference and the slope are taken as the judgment standards, the line segment with little influence on the pressure drop of the fluid is ignored (such as the line segment with small height difference and small slope), thus the research amount is greatly reduced, the emphasis is highlighted, and>the non-Darcy coefficient beta is consistent with the non-Darcy coefficient beta in a mathematical form or a physical sense, and the non-Darcy coefficient beta and crack roughness characteristics are related through the establishment of the formula, wherein the relation comprises the gap width, the height difference, the slope and the profile peak density.
To study A when non-Darcy flow of single fracture seepage was performed D ＝f(12φ 1 )、B D ＝f(φ 2 ) The specific function form and expression relation are designed, and the seepage test system has the following structure:
the seepage test system comprises a clamp holder as shown in fig. 4 and 5, wherein the clamp holder comprises a sleeve 9, a rubber sleeve 10 is coaxially arranged in the sleeve 9, a confining pressure cavity 7 is arranged between the inner wall of the sleeve 9 and the outer wall of the rubber sleeve 10, and a confining pressure loading device is arranged outside the sleeve 9; an inlet false core 41 and an inlet plug 3 are sequentially plugged into the rubber sleeve 10 from the inlet side of the holder, an inlet end cover 2 is arranged on the inlet side of the holder, an outlet false core 42 and an outlet plug 13 are sequentially plugged into the rubber sleeve 10 from the outlet side of the holder, the inlet false core 41 and the outlet false core 42 are respectively provided with a water flow channel 20 along respective central axes, and a plurality of seepage grooves 21 are respectively arranged on opposite sides of the inlet false core 41 and the outlet false core 42 along the radial direction from the center;
the inlet plug 3 is internally provided with a water flow hole 3-1 along the central axis thereof, the water flow hole 3-1 is communicated to an external constant-flow constant-pressure pump 15 through an inlet pipeline 1, the inlet pipeline 1 is provided with a three-way valve I14, and a branch port of the three-way valve I14 is provided with an inlet pressure gauge 19;
a single-crack sample 5 is arranged in a cavity surrounded by the inlet false rock core 41, the outlet false rock core 42 and the rubber sleeve 10, a water flow leading-out hole 13-1 is arranged in the outlet plug 13 along the central axis of the outlet plug, one end of the water flow leading-out hole 13-1, which is exposed out of the outlet plug 13, is connected to a water outlet flowmeter 17 through an outlet pipeline 11, and a three-way valve II 12 and a back pressure valve 16 are arranged on the outlet pipeline 11; an outlet pressure gauge 18 is arranged on a branch port of the three-way valve II 12, a gap width measuring device 6 is arranged outside the sleeve 9, and a probe of the gap width measuring device 6 penetrates through the sleeve 9 and the rubber sleeve 10 and props against the outer wall of the single-gap sample 5 perpendicular to the gap surface 5-1.
The confining pressure loading device comprises a ring pressure pump, wherein an oil inlet hole 8 is formed in the sleeve 9, and the oil inlet hole 8 is communicated to the outside of the sleeve 9 from the confining pressure cavity 7; the outlet of the annular pressure pump is connected to the oil inlet hole 8 through a pressurizing pipeline. The annular pressure pump can pump out pressure oil, and the pressure oil is injected into the oil inlet hole 8 through the pressurizing pipeline and then enters the confining pressure cavity 7 to pressurize the rubber sleeve 10.
Preferably, the gap width measuring device 6 comprises an LVDT displacement sensor, the probe of the gap width measuring device 6 is connected with the LVDT displacement sensor, the measuring range can be selected according to the gap width, the vertical deformation quantity delta b of the sample gap can be measured, and the LVDT displacement sensor is connected with the data acquisition device. The measured fracture deformation can be directly displayed on a data acquisition device. The data collector can be PCI720 type collector of Minghua technology.
In order to reduce the heat loss of water flowing into the cracks from the inlet of the clamp, the inlet end cover 2 is designed to be of a hollow structure, the inlet plug 3 is made of nonmetal polyimide material, the inlet pseudo-core 41 is made of polytetrafluoroethylene material, the heat conduction efficiency is low by adopting the material, the water temperature of the inlet of the clamp is ensured to be basically consistent with the water temperature of the inlet of the cracks in the clamp, and the stability of external factors of a test is ensured.
Preferably, the outer wall of the rubber sleeve 10 is provided with a positioning column 10-1, the positioning column 10-1 can be embedded into a hole in the inner wall of the sleeve 9 in a matching way, and when the positioning column 10-1 is embedded into the hole in the inner wall of the sleeve 9, the crack surface 5-1 of the single crack sample 5 is just vertical to the probe of the crack width measuring device 6. When the single-slit sample 5 is put into the rubber sleeve 10, the rubber sleeve 10 is positioned in the sleeve 9 through the positioning column 10-1, the positioning column 10-1 facilitates the positioning of the slit surface 5-1, and the slit surface 5-1 of the single-slit sample 5 after the sample is put into the rubber sleeve can be ensured to be always vertical to the probe of the slit width measuring device 6.
The fracture surface 5-1 of the single fracture sample 5 is designed in advance and is cut by a sand wire cutting machine.
Preferably, to ensure a stable connection, the inlet end cap 2 is fixed to the inlet side of the sleeve 9 by the inlet protecting cap 2-1, and the outlet plug 13 is fixed to the outlet side of the sleeve 9 by the outlet protecting cap 13-2.
Further, the inlet pressure gauge 19, the outlet pressure gauge 18, the gap width measuring device 6 and the outlet flow meter 17 are commonly connected to a data collector. The data collector can receive the detection data of each detection component in real time and display the detection data in real time.
The pressure gradients at two ends in the seepage process can be measured through the inlet pressure gauge 19 and the outlet pressure gauge 18 at two ends of the clamp; the water outlet flowmeter 17 is an electronic balance, the electronic balance measures the weight of water flow injected into the beaker at intervals to obtain the flow, the flow value is equal to the flow Q input into the inlet of the clamp, the water flow coming out of the clamp is more stable, and the measured flow is more accurate and reliable.
The method for carrying out the seepage test by using the system comprises the following steps:
1) Finding a least square center line of 200 points to serve as a reference line of the curve, wherein a reference line equation is z=ax+b;
2) Calculating roughness-related parameters of the curve according to matlab program, including fractal box-counting dimension D B Root mean square Z of first derivative of surface contour line 2 Arithmetic mean deviation R of contours a Density of contour peaks l/S m According to Z 2 、R a The (M-M)/M of the curve is found, and the roughness of the curve can be expressed as:
φ 1 ＝D B
3) Cutting the cracks of the single-crack sample 5 into a curve shown in fig. 3 by using a silicon carbide wire with the wire diameter of 0.33mm on a sand wire cutting machine, wherein the curve has the rough characteristic only in the water flow direction, and the roughness is obtained in the step 2); in order to ensure that the test is more accurate, calibration work can be carried out before the equipment is operated, and the resistance between the probe for measuring fracture deformation and the sleeve is calibrated (the resistance is P);
4) Sealing two sides of a single-slit sample 5 with AB glue in a copper sheet with the thickness of 300um in a slit, pushing the single-slit sample into a clamp holder, positioning the single-slit sample by using a positioning column 10-1, ensuring that a slit width measuring device 6 is vertical to a slit surface 5-1, screwing an inlet end cover 2 and an outlet end cover of the clamp holder after the sample is placed, and at the moment, the initial slit width b0=300 um of the slit;
5) Applying confining pressure sigma 3 At this time, the crack deformation Δb was measured, and it was found that the confining pressure σ was obtained 3 The crack gap width under the condition is b 0-delta b;
6) After the confining pressure was stabilized, the back pressure valve 16 was set to a pressure of 0.1MPa, and the constant-flow constant-pressure pump 15 was used to inject a pressure of P 1 The outlet pressure value measured by the outlet pressure gauge 18 after the flow is stable is equal to the pressure of the back pressure valve 16 of 0.1MPa, and the pressure gradient is thatThe outlet flow meter 17 measures the pressure gradient (P 1 Flow Q of 0.1)/l 1 Then pressurizing step by step at 0.1MPa, and measuring the gradient of the differential pressure>Lower flow rate Q i Can obtain a +.>Is a relationship of (2);
7) Changing the confining pressure condition, applying different confining pressures to the single-fracture sample 5 to obtain different fracture widths b, and then performing the tests of the steps 5) to 6), so that the fracture width condition of the formula (1) can be changed to obtain the corresponding working conditionA curve;
8) Regenerating a different roughness curve, so that 12 phi in equation (1) can be changed 1 And phi 2 And (3) repeating the steps 1) to 7) to obtain the corresponding working conditionA curve;
9) As can be seen, in the following equation,q, b, w, mu and rho are all available quantities, test data under each working condition are respectively subjected to quadratic polynomial fitting in origin software, and A under the corresponding working condition can be obtained by fitting the following formula form D And B D The values and statistical tables of the test data are shown in Table 1.
TABLE 1 statistical tables of test data
10 Obtained by the aboveA D And B D The value can be used for researching dimensionless quantity A in Darcy and non-Darcy areas under the conditions of the same surface roughness and different gap widths D 、B D And the roughness characterization quantity phi presented herein 1 And phi 2 The specific form and change rule of the function between the two are as follows:
A D ＝f(12φ 1 )
B D ＝f(φ 2 )。
Claims (9)
1. a method for characterizing the roughness of the surface of a crack includes such steps as providing a segment of randomly generated rough curve with straight reference line, which is composed of N equally-spaced points whose abscissa is x i The ordinate is z i (i is more than or equal to 1 and less than or equal to N), and establishing a dimensionless number A D 、B D Relationship with roughness:
A D ＝f(12φ 1 )
B D ＝f(φ 2 )，
in phi 1 、φ 2 Is roughness, phi 1 Reflects the rough characteristic of the whole curve, represents the influence of the rough characteristic on the linear part of the Forchheimer formula, phi 2 Reflecting the influence of the roughness of the curve along the water flow direction on the water flow pressure drop, representing the influence of the roughness characteristic on the nonlinear part of the Forchheimer formula, phi 1 、φ 2 The expression is as follows:
φ 1 ＝D B
wherein D is B The fractal box counting dimension of the rough curve is l is the length of a datum line of the rough curve, S m For the average pitch of the contour micro-irregularities, the contour micro-irregularities pitch is a length of a reference line containing one contour peak and an adjacent contour valley, then l/S m Is the density of contour peaks on a rough curveA degree; m refers to all line segments included in the rough curve; m is the number of line segments that simultaneously satisfy the following conditions:
(1) the slope of each segment is determined and,
wherein Z is 2 The root mean square of the first derivative of the surface contour is obtained by the following formula:
wherein N is the number of points contained in the rough curve;
(2) the height difference of each section is judged,
z i distance to midline +z i+1 Distance to midline < 2R a
Wherein R is a The arithmetic mean deviation of the profile, i.e. the arithmetic mean of the distances of each point from the reference line,
the number of line segments satisfying the conditions (1) and (2) is m;
in summary, the forshheimer formula for the fidaxl stage in the single fracture water seepage process can be expressed as formula (1):
namely:
2. the seepage test method for the surface roughness characterization of the crack is characterized by comprising the following steps of:
1) Finding the least square center line of N points forming the rough curve, and taking the least square center line as a datum line of the rough curve, wherein a datum line equation is z=ax+b;
2) Calculating roughness-related parameters of the curve according to matlab program, including fractal box-counting dimension D B Root mean square Z of first derivative of surface contour line 2 Arithmetic mean deviation R of contours a Density of contour peaks l/S m According to Z 2 、R a The (M-M)/M of the curve is found, and the roughness of the curve can be expressed as:
φ 1 ＝D B
wherein m is the number of line segments satisfying the following conditions simultaneously:
(1) the slope of each segment is determined and,
wherein Z is 2 The root mean square of the first derivative of the surface contour is obtained by the following formula:
wherein N is the number of points contained in the rough curve;
(2) the height difference of each section is judged,
z i distance to midline +z i+1 Distance to midline < 2R a
Wherein R is a The arithmetic mean deviation of the profile, i.e. the arithmetic mean of the distances of each point from the reference line,
the number of line segments satisfying the conditions (1) and (2) is m;
3) Cutting the crack of the single-crack sample (5) into a rough curve by using a diamond wire with the wire diameter of 0.33mm on a sand wire cutting machine, wherein the curve has rough characteristics only in the water flow direction, and the roughness is obtained in the step 2);
4) The copper sheet with the thickness of 300um is filled in the gap, the two sides of the gap of a single-gap sample (5) are sealed by AB glue and pushed into a clamp holder, a positioning column (10-1) is used for positioning, the gap width measuring device (6) is ensured to be vertical to the gap surface (5-1), an inlet end cover (2) and an outlet plug (13) of the clamp holder are screwed after the sample is placed, and the initial gap width of the gap is b0;
5) Applying confining pressure sigma 3 At this time, the crack deformation Δb was measured, and it was found that the confining pressure σ was obtained 3 The crack gap width under the condition is b 0-delta b;
6) After the confining pressure is stable, the pressure of a back pressure valve (16) is set, and the constant-flow constant-pressure pump (15) is used for injecting the pressure P 1 The outlet pressure value P measured by an outlet pressure gauge (18) after the flow is stabilized 2 Is equal to the pressure of the back pressure valve (16), and the pressure gradient (P) is measured by the outlet flow meter (17) 1 -P 2 ) Flow rate Q of/l 1 Then pressurizing step by step, respectively measuring different pressure gradientsLower flow rate Q i Can obtain a +.>Is a relationship of (2);
7) Changing the confining pressure condition, applying different confining pressures to the single-slit test specimen (5) to obtain different slit widths b, and then performing the tests of the steps 5) to 6), so that the slit width condition of the formula (1) can be changed to obtain the corresponding working conditionA curve;
8) Regenerating a different roughness curve, so that 12 phi in equation (1) can be changed 1 And phi 2 And (3) repeating the steps 1) to 7) to obtain the corresponding working conditionA curve;
9) As can be seen, in the following equation,q, b, w, mu and rho are all available quantities, test data under each working condition are respectively subjected to quadratic polynomial fitting in origin software, and A under the corresponding working condition can be obtained by fitting the following formula form D And B D Value:
10 Through A under different working conditions obtained above D And B D The value can be researched and obtained to obtain dimensionless quantity A in Darcy and non-Darcy areas under the conditions of the same surface roughness, different gap widths and different surface roughness D 、B D And the roughness characterization quantity phi 1 And phi 2 Specific forms and change laws of the functions.
3. A seepage test system for fracture surface roughness characterization, characterized by implementing the seepage test method for fracture surface roughness characterization of claim 2;
the device comprises a clamp holder, wherein the clamp holder comprises a sleeve (9), a rubber sleeve (10) is coaxially arranged in the sleeve (9), a confining pressure cavity (7) is arranged between the inner wall of the sleeve (9) and the outer wall of the rubber sleeve (10), and a confining pressure loading device is arranged outside the sleeve (9); an inlet false core (41) and an inlet plug (3) are sequentially plugged into the rubber sleeve (10) from the inlet side of the clamp holder, an inlet end cover (2) is arranged on the inlet side of the clamp holder, an outlet false core (42) and an outlet plug (13) are sequentially plugged into the rubber sleeve (10) from the outlet side of the clamp holder, the inlet false core (41) and the outlet false core (42) are respectively provided with a water flow channel (20) along respective central axes, and a plurality of seepage grooves (21) are respectively arranged on opposite side surfaces of the inlet false core (41) and the outlet false core (42) along the radial direction from the centers;
the inlet plug (3) is internally provided with a water flow hole (3-1) along the central axis thereof, the water flow hole (3-1) is communicated to an external constant-flow constant-pressure pump (15) through an inlet pipeline (1), the inlet pipeline (1) is provided with a three-way valve I (14), and a branch port of the three-way valve I (14) is provided with an inlet pressure gauge (19);
a single-crack sample (5) is arranged in a cavity surrounded by the inlet false rock core (41), the outlet false rock core (42) and the rubber sleeve (10), a water flow leading-out hole (13-1) is arranged in the outlet plug (13) along the central axis of the outlet plug, one end of the water flow leading-out hole (13-1) exposed out of the outlet plug (13) is connected to a water outlet flowmeter (17) through an outlet pipeline (11), and a three-way valve II (12) and a back pressure valve (16) are arranged on the outlet pipeline (11); an outlet pressure gauge (18) is arranged on a branch port of the three-way valve II (12), a gap width measuring device (6) is arranged outside the sleeve (9), and a probe of the gap width measuring device (6) penetrates through the sleeve (9) and the rubber sleeve (10) and props against the outer wall of the single-gap sample (5) perpendicular to the gap surface (5-1).
4. A seepage test system for fracture surface roughness characterization according to claim 3, wherein the confining pressure loading device comprises a circular pressure pump, an oil inlet hole (8) is arranged on the sleeve (9), and the oil inlet hole (8) is communicated from the confining pressure cavity (7) to the outside of the sleeve (9); the outlet of the annular pressure pump is connected to the oil inlet hole (8) through a pressurizing pipeline.
5. A seepage test system for the characterization of the surface roughness of a crack as claimed in claim 3, characterized in that the crack width measuring device (6) comprises an LVDT displacement sensor, and the probe of the crack width measuring device (6) is connected with the LVDT displacement sensor.
6. A seepage test system for crack surface roughness characterization according to claim 3, characterized in that the outer wall of the rubber sleeve (10) is provided with a positioning column (10-1), the positioning column (10-1) can be embedded into a hole of the inner wall of the sleeve (9) in a matching way, and when the positioning column (10-1) is embedded into the hole of the inner wall of the sleeve (9), the crack surface (5-1) of the single crack sample (5) is just perpendicular to the probe of the crack width measuring device (6).
7. A seepage test system for fracture surface roughness characterization according to claim 3, wherein the fracture surface (5-1) of the single fracture specimen (5) is cut by a sand wire cutter.
8. A seepage test system for fracture surface roughness characterization according to claim 3, wherein the inlet end cap (2) is fixed to the inlet side of the sleeve (9) by an inlet protecting cap (2-1), and the outlet plug (13) is fixed to the outlet side of the sleeve (9) by an outlet protecting cap (13-2).
9. A seepage test system for fracture surface roughness characterization according to claim 3, wherein the inlet pressure gauge (19), the outlet pressure gauge (18), the gap width measuring device (6), the outlet flow meter (17) are commonly connected to a data collector.
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| CN109946212B (en) * | 2019-04-01 | 2021-08-31 | 东北大学 | Testing device and method for testing seepage characteristics of rough fracture |
| CN110207640B (en) * | 2019-05-31 | 2024-04-05 | 中国矿业大学 | Single-crack micron-sized gap width measuring structure, and mounting method and measuring method thereof |
| CN112630121B (en) * | 2020-11-30 | 2021-10-12 | 中国矿业大学 | Device and method for testing permeability of fractured surrounding rock of deep chamber under stress action |
| CN112903565B (en) * | 2021-02-01 | 2022-10-18 | 核工业北京地质研究院 | Permeability determination method considering internal geometric characteristics of rock fracture |
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