A method of simulating crack width of a test sample

Abstract

The application discloses a method for simulating crack width of a test sample, and belongs to the technical field of oil and gas reservoir development, and is characterized by comprising the following steps: a, calculating the permeability value k' of the sample according to Darcy's law; b, determining the position of the crack and establishing a finite element model; c, setting the input end pressure to 1 MPa, the output end pressure to 0 MPa, and the permeability of the matrix part according to the formula of p m ; d, obtaining different seepage fields under different crack widths through finite element numerical simulation; e, calculating the permeability simulation value k through the seepage field distribution data; f, comparing the permeability simulation value with the actual permeability value measured in the experiment, and if the permeability simulation value is smaller than a preset error value e, then the value of e m is the crack width. The application can effectively determine the crack width by combining the seepage capacity variation law, and provides effective guidance for material development.

Description

Technical Field

[0001] This invention relates to the field of oil and gas reservoir development technology, and in particular to a method for simulating and testing the fracture width of a sample. Background Technology

[0002] For traditional oil and gas reservoirs, carbonate gas reservoirs and shale gas reservoirs often have fractures. The presence of fractures is not only important for gas field development, but also for fracturing operations.

[0003] Current technologies for determining the presence and extent of fractures in porous media, besides visual inspection, generally employ non-destructive testing (NDT) using CT scans. However, the main drawbacks of this method are the long scan time and demanding requirements for the experimental site. Furthermore, determining fracture width is also crucial for the inspection of building materials. Calculating fracture width has always been a challenging task for researchers in oil and gas reservoir development, as fracture parameters are particularly important for oil and gas reservoir development.

[0004] Existing technologies are mostly designed for macroscopic oil and gas reservoirs, but there are no corresponding methods for determining the fracture opening degree of core samples by utilizing changes in seepage capacity. Furthermore, determining the fracture opening degree is also of great significance for materials development.

[0005] Chinese patent document CN 105606775A, published on May 25, 2016, discloses a novel experimental method for simulating and evaluating cracks, characterized by the following specific steps:

[0006] Step 1: Collect the required full-diameter core, grind it, and split it evenly from the middle; the core length should be 5-18cm and the radius 5cm, and this should not be changed.

[0007] Step 2: Place pressure-resistant gaskets of different sizes into the horizontal section end of any half of the split core. By changing the thickness and width of the gaskets, different parameters of cracks can be simulated. Cover with the other half of the core and place it into the core clamping tube.

[0008] Step 3: Tighten the inlet and outlet ends of the fracture simulation evaluation experimental device, adjust the position of the three outlet pipelines at the outlet end, and keep the fracture outlet end aligned with the profile of the core sample that was just placed in.

[0009] Step 4: Open the confining pressure inlet on one side of the core clamping tube, close the confining pressure outlet, inject an appropriate amount of clean water to make the confining pressure reach the required value, and then close the confining pressure inlet; at this time, the crack simulation evaluation device is assembled.

[0010] Step 5: Under the required simulated formation temperature, prepare a weak gel system and inject it into the fracture simulation evaluation device; let it stand for 12-24 hours.

[0011] Step Six: Perform subsequent water flooding and measure the sealing pressure of the weak gel under different fracture sizes; the sealing fracture width is less than 0.69 mm, and the core matrix permeability is 1×10⁻⁶. -3 μm 2 -10×10 -3 μm 2 Within the specified range, if the sealing pressure of the weak gel is greater than 0.5 MPa, then the weak gel has good sealing performance; the core matrix permeability is 0.1 × 10⁻⁶. -3 μm 2 -1×10 -3 μm 2 If the blocking pressure of the weak gel is greater than 2.4 MPa, then the weak gel has good blocking performance.

[0012] Step 7: Measure the liquid volume at the fracture outlet and the matrix outlet respectively to calculate the flow rate of the fracture and the matrix; if the fracture flow rate is less than 25%, that is, the matrix flow rate is greater than 75%, then the weak gel sealing performance is good.

[0013] The novel fracture simulation and evaluation experimental method disclosed in this patent document calculates the flow rates of fractures and the matrix by separately measuring the liquid volume at the fracture outlet and the matrix outlet. This method can quantify fractures of different sizes, study the sealing effect of weak gels on fractures of different sizes, and simulate the flow rates of fractures and the matrix in real oil reservoirs. However, it is designed for macroscopic oil and gas reservoirs and cannot accurately determine the fracture opening of core samples. Summary of the Invention

[0014] In order to overcome the shortcomings of the prior art, this invention provides a method for simulating and testing the crack width of a sample. This invention combines the law of seepage capacity change, which can effectively determine the crack width and provide effective guidance for material development.

[0015] This invention is achieved through the following technical solution:

[0016] A method for simulating the width of a crack in a test sample, characterized by comprising the following steps:

[0017] a. Select two surfaces through which the crack penetrates the sample for testing, applying a constant pressure P to one end of the sample and atmospheric pressure P to the other end. a Other surfaces are reinforced with rubber sleeves and pressure plates. W The permeability value k′ of the sample was calculated using Darcy's law.

[0018]

[0019] Where k′ is the permeability value of the sample, P a At atmospheric pressure, Q a For flow rate, μ gWhere is the gas viscosity, L is the length of the core, L represents the length of the core, A is the cross-sectional area of ​​the sample, and P is the constant pressure.

[0020] b. Determine the location of the crack and establish a finite element model;

[0021] c. Using Darcy's law as the basic equation, assign values, setting the input pressure to 1 MPa and the output pressure to 0 MPa. The permeability of the matrix is ​​calculated according to ρ... m set up;

[0022] d. Different seepage fields under different crack widths were obtained through finite element numerical simulation;

[0023] e. Calculate the simulated permeability value k using seepage field distribution data;

[0024]

[0025] Where k is the simulated permeability value, L is the length of the core, and ∫ B qdh is the line integral of q on the right boundary of the cross section, through The calculations show that H is the height of the cross-section, b is the thickness of the cross-section, and P is the constant pressure. a Atmospheric pressure;

[0026] f. Compare the simulated permeability value with the actual measured permeability value. If the simulated permeability value is less than the preset error value e, then ε m The crack width is set. If the simulated permeability value is greater than the preset error value e, return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e.

[0027] In step a, calculating the permeability value k of the sample using Darcy's law specifically involves finding two opposing surfaces on the sample where a crack is connected, connecting the two opposing surfaces to a constant pressure P and atmospheric pressure Pa respectively, applying a confining pressure Pw to the other surfaces of the sample using a rubber sleeve, calculating and measuring the flow rate Qa using a soap film flow meter, and then calculating it using Darcy's law.

[0028] The gas viscosity μ g This is obtained by looking up a table using pressure.

[0029] The sample is cylindrical.

[0030] The sample is a cuboid.

[0031] In step b, determining the location of the crack specifically means, when the sample is cylindrical, selecting the midpoint of the chord of the circle at the cut end of the crack as the cutting surface.

[0032] In step b, determining the location of the crack specifically means, when the sample is a cuboid, selecting the vertical plane of the end face that runs through the crack and is parallel to the side length as the cutting plane.

[0033] In step c, the permeability value of the matrix is ​​obtained from experimental tests on similar rock samples without cracks.

[0034] Step c also includes the permeability k of the intermediate crack strip, which is set according to k = f(ε).

[0035] In step f, the preset error value e is 1%.

[0036] The formula k = f(ε) in this invention is based on the formula mentioned in Lu Zhanguo's paper "Correction of Cubic Law and Calculation of Critical Velocity in Parallel Cracks" published in Laboratory Research and Exploration, Vol. 29, No. 4, p. 15, 2010. It is derived that, where A is the cross-sectional area of ​​the crack in the flat plate, n is the number of cracks, and ι is the crack length.

[0037] The beneficial effects of this invention are mainly reflected in the following aspects:

[0038] I. This invention, "a) selects two surfaces through which the crack penetrates the sample for testing, and applies a constant pressure P to one end of the sample and an atmospheric pressure P to the other end." a Other surfaces are reinforced with rubber sleeves and pressure plates. W a) Calculate the permeability value k′ of the sample using Darcy's law; b) Determine the location of the crack and establish a finite element model; c) Assign values ​​using Darcy's law as the basic equation, setting the input pressure to 1 MPa and the output pressure to 0 MPa, with the permeability of the matrix portion calculated according to ρ... m d. Obtain different seepage fields under different crack widths through finite element numerical simulation; e. Calculate the simulated permeability value k using the seepage field distribution data; f. Compare the simulated permeability value with the actual experimentally measured permeability value. If the simulated permeability value is less than the preset error value e, then ε m The crack width is set. If the simulated permeability value is greater than the preset error value e, then return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e. Compared with the existing technology, this method can effectively determine the crack width by combining the seepage capacity variation law, and provides effective guidance for material development.

[0039] II. This invention utilizes seepage test data to accurately simulate the crack width of test samples.

[0040] Third, compared with the prior art which describes cracks in samples by CT scanning, the present invention is more cost-effective and convenient in determining the width of the main crack.

[0041] IV. This invention utilizes the variation law of seepage capacity to simulate and test the width of the main crack in porous media. Detailed Implementation

[0042] Example 1

[0043] A method for simulating the crack width of a test sample includes the following steps:

[0044] a. Select two surfaces through which the crack penetrates the sample for testing, applying a constant pressure P to one end of the sample and atmospheric pressure P to the other end. a Other surfaces are reinforced with rubber sleeves and pressure plates. W The permeability value k′ of the sample was calculated using Darcy's law.

[0045]

[0046] Where k′ is the permeability value of the sample, P a At atmospheric pressure, Q a For flow rate, μ g Where is the gas viscosity, L is the length of the core, L represents the length of the core, A is the cross-sectional area of ​​the sample, and P is the constant pressure.

[0047] b. Determine the location of the crack and establish a finite element model;

[0048] c. Using Darcy's law as the basic equation, assign values, setting the input pressure to 1 MPa and the output pressure to 0 MPa. The permeability of the matrix is ​​calculated according to ρ... m set up;

[0049] d. Different seepage fields under different crack widths were obtained through finite element numerical simulation;

[0050] e. Calculate the simulated permeability value k using seepage field distribution data;

[0051]

[0052] Where k is the simulated permeability value, L is the length of the core, and ∫ B qdh is the line integral of q on the right boundary of the cross section, through The calculations show that H is the height of the cross-section, b is the thickness of the cross-section, and P is the constant pressure. a Atmospheric pressure;

[0053] f. Compare the simulated permeability value with the actual measured permeability value. If the simulated permeability value is less than the preset error value e, then ε mThe crack width is set. If the simulated permeability value is greater than the preset error value e, return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e.

[0054] This embodiment is the most basic implementation method. Compared with the prior art, it can effectively determine the crack width by combining the seepage capacity variation law, and provide effective guidance for material development.

[0055] Example 2

[0056] A method for simulating the crack width of a test sample includes the following steps:

[0057] a. Select two surfaces through which the crack penetrates the sample for testing, applying a constant pressure P to one end of the sample and atmospheric pressure P to the other end. a Other surfaces are reinforced with rubber sleeves and pressure plates. W The permeability value k′ of the sample was calculated using Darcy's law.

[0058]

[0059] Where k′ is the permeability value of the sample, P a At atmospheric pressure, Q a For flow rate, μ g Where is the gas viscosity, L is the length of the core, L represents the length of the core, A is the cross-sectional area of ​​the sample, and P is the constant pressure.

[0060] b. Determine the location of the crack and establish a finite element model;

[0061] c. Using Darcy's law as the basic equation, assign values, setting the input pressure to 1 MPa and the output pressure to 0 MPa. The permeability of the matrix is ​​calculated according to ρ... m set up;

[0062] d. Different seepage fields under different crack widths were obtained through finite element numerical simulation;

[0063] e. Calculate the simulated permeability value k using seepage field distribution data;

[0064]

[0065] Where k is the simulated permeability value, L is the length of the core, and ∫ B qdh is the line integral of q on the right boundary of the cross section, through The calculations show that H is the height of the cross-section, b is the thickness of the cross-section, and P is the constant pressure. a Atmospheric pressure;

[0066] f. Compare the simulated permeability value with the actual measured permeability value. If the simulated permeability value is less than the preset error value e, then ε m The crack width is set. If the simulated permeability value is greater than the preset error value e, return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e.

[0067] In step a, calculating the permeability value k of the sample using Darcy's law specifically involves finding two opposing surfaces on the sample where a crack is connected, connecting the two opposing surfaces to a constant pressure P and atmospheric pressure Pa respectively, applying a confining pressure Pw to the other surfaces of the sample using a rubber sleeve, calculating and measuring the flow rate Qa using a soap film flow meter, and then calculating it using Darcy's law.

[0068] This embodiment is a preferred implementation method, which can accurately simulate the crack width of the test sample by using seepage test data.

[0069] Example 3

[0070] A method for simulating the crack width of a test sample includes the following steps:

[0071] a. Select two surfaces through which the crack penetrates the sample for testing, applying a constant pressure P to one end of the sample and atmospheric pressure P to the other end. a Other surfaces are reinforced with rubber sleeves and pressure plates. W The permeability value k′ of the sample was calculated using Darcy's law.

[0072]

[0073] Where k′ is the permeability value of the sample, P a At atmospheric pressure, Q a For flow rate, μ g Where is the gas viscosity, L is the length of the core, L represents the length of the core, A is the cross-sectional area of ​​the sample, and P is the constant pressure.

[0074] b. Determine the location of the crack and establish a finite element model;

[0075] c. Using Darcy's law as the basic equation, assign values, setting the input pressure to 1 MPa and the output pressure to 0 MPa. The permeability of the matrix is ​​calculated according to ρ... m set up;

[0076] d. Different seepage fields under different crack widths were obtained through finite element numerical simulation;

[0077] e. Calculate the simulated permeability value k using seepage field distribution data;

[0078]

[0079] Where k is the simulated permeability value, L is the length of the core, and ∫ B qdh is the line integral of q on the right boundary of the cross section, through The calculations show that H is the height of the cross-section, b is the thickness of the cross-section, and P is the constant pressure. a Atmospheric pressure;

[0080] f. Compare the simulated permeability value with the actual measured permeability value. If the simulated permeability value is less than the preset error value e, then ε m The crack width is set. If the simulated permeability value is greater than the preset error value e, return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e.

[0081] In step a, calculating the permeability value k of the sample using Darcy's law specifically involves finding two opposing surfaces on the sample where a crack is connected, connecting the two opposing surfaces to a constant pressure P and atmospheric pressure Pa respectively, applying a confining pressure Pw to the other surfaces of the sample using a rubber sleeve, calculating and measuring the flow rate Qa using a soap film flow meter, and then calculating it using Darcy's law.

[0082] The gas viscosity μ g This is obtained by looking up a table using pressure.

[0083] The sample is cylindrical.

[0084] In step b, determining the location of the crack specifically means, when the sample is cylindrical, selecting the midpoint of the chord of the circle at the cut end of the crack as the cutting surface.

[0085] This embodiment is another preferred implementation method. Compared with the prior art, which describes the cracks in the sample by CT scanning, it is more cost-effective and convenient to determine the width of the main crack.

[0086] Example 4

[0087] A method for simulating the crack width of a test sample includes the following steps:

[0088] a. Select two surfaces through which the crack penetrates the sample for testing, applying a constant pressure P to one end of the sample and atmospheric pressure P to the other end. a Other surfaces are reinforced with rubber sleeves and pressure plates. W The permeability value k′ of the sample was calculated using Darcy's law.

[0089]

[0090] Where k′ is the permeability value of the sample, P a At atmospheric pressure, Qa For flow rate, μ g Where is the gas viscosity, L is the length of the core, L represents the length of the core, A is the cross-sectional area of ​​the sample, and P is the constant pressure.

[0091] b. Determine the location of the crack and establish a finite element model;

[0092] c. Using Darcy's law as the basic equation, assign values, setting the input pressure to 1 MPa and the output pressure to 0 MPa. The permeability of the matrix is ​​calculated according to ρ... m set up;

[0093] d. Different seepage fields under different crack widths were obtained through finite element numerical simulation;

[0094] e. Calculate the simulated permeability value k using seepage field distribution data;

[0095]

[0096] Where k is the simulated permeability value, L is the length of the core, and ∫ B qdh is the line integral of q on the right boundary of the cross section, through The calculations show that H is the height of the cross-section, b is the thickness of the cross-section, and P is the constant pressure. a Atmospheric pressure;

[0097] f. Compare the simulated permeability value with the actual measured permeability value. If the simulated permeability value is less than the preset error value e, then ε m The crack width is set. If the simulated permeability value is greater than the preset error value e, return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e.

[0098] In step a, calculating the permeability value k of the sample using Darcy's law specifically involves finding two opposing surfaces on the sample where a crack is connected, connecting the two opposing surfaces to a constant pressure P and atmospheric pressure Pa respectively, applying a confining pressure Pw to the other surfaces of the sample using a rubber sleeve, calculating and measuring the flow rate Qa using a soap film flow meter, and then calculating it using Darcy's law.

[0099] The gas viscosity μ g This is obtained by looking up a table using pressure.

[0100] The sample is a cuboid.

[0101] In step b, determining the location of the crack specifically means, when the sample is a cuboid, selecting the vertical plane of the end face that runs through the crack and is parallel to the side length as the cutting plane.

[0102] In step c, the permeability value of the matrix is ​​obtained from experimental tests on similar rock samples without cracks.

[0103] Step c also includes the permeability k of the intermediate crack strip, which is set according to k = f(ε).

[0104] In step f, the preset error value e is 1%.

[0105] This embodiment is the best implementation method, which utilizes the law of seepage capacity variation to simulate and test the width of the main crack in porous media.

[0106] The invention will be further illustrated below with specific examples:

[0107] A rock sample with a crack running through both ends is given. The rock sample is 1.5m long, 1m wide, and 1m thick. The crack runs parallel to the side length of the sample. A confining pressure of 1MPa is applied to the left end of the sample, atmospheric pressure to the right end, and 2.5MPa is applied around the sample. The flow rate of the gas discharged from the right end is 79.12mL / s, as measured by a flow meter. The permeability of the sample at this time is calculated to be 0.01545mD.

[0108] The experimentally measured permeability of the rock matrix is ​​0.15 mD (n = 1, l = 1.72 m, A = 1 * 1 = 1 m). 2 The estimated crack width is ε = 0.025m, based on... The crack permeability is 2.08 mD. A numerical model is established based on the above conditions, with the upper temperature set to 1 MPa and the lower temperature set to atmospheric pressure. The corresponding finite element model is then established.

[0109] The permeability of the sample was then calculated to be 0.01548 mD, which is greater than the measured permeability. Therefore, the previously assumed crack width was too large. The crack width should be appropriately reduced, and the estimated crack width is ε = 0.0125 m. The crack permeability is 1.04 mD; substituting this into the finite element model and performing numerical simulation, the seepage field is obtained.

[0110] Finally, the permeability of the sample was calculated to be 0.01409 mD, which is less than the measured permeability of the sample. This indicates that the estimated crack width is too small, so the crack width should be appropriately increased. Therefore, the crack width is determined to be between 0.0125 and 0.025 m.

[0111] After several assumptions, it was found that when the crack width is 0.024m, the crack permeability is 1.997mD. Substituting this into step e, the sample permeability was calculated to be 0.01545mD through numerical simulation, which is equal to the experimentally measured permeability value. Therefore, the crack width of the sample should be 0.024m.

Claims

1. A method for simulating the width of a crack in a test sample, characterized in that, Includes the following steps: a. Select two surfaces through which the crack penetrates the sample for testing, applying a constant pressure P to one end of the sample and atmospheric pressure P to the other end. a Other surfaces are reinforced with rubber sleeves and pressure plates. W The permeability value of the sample was calculated using Darcy's law. ; Formula 1 in, P represents the permeability value of the sample. a Atmospheric pressure For traffic, Let L be the gas viscosity, L be the length of the core, A be the cross-sectional area of ​​the sample, and P be the constant pressure. b. Determine the location of the crack and establish a finite element model; c. Using Darcy's law as the basic equation, assign values, setting the input pressure to 1 MPa and the output pressure to 0 MPa. The permeability of the matrix is ​​calculated according to ρ... m The permeability values ​​of the matrix are set based on experimental tests of similar rock samples without cracks, and the permeability k of the middle fracture strip is set according to k=f(ε). d. Different seepage fields under different crack widths were obtained through finite element numerical simulation; e. Calculate the simulated permeability value k using seepage field distribution data; Where k is the simulated permeability value, and L is the length of the core sample. For the line integral of q on the right boundary of the section, through The calculations show that H is the height of the cross-section, b is the thickness of the cross-section, and P is the constant pressure. a Atmospheric pressure; f. Compare the simulated permeability value with the actual measured permeability value. If the simulated permeability value is less than the preset error value e, then ε is the crack width. If the simulated permeability value is greater than the preset error value e, then return to step c, reset the crack width, recalculate the crack permeability and substitute it into the finite element model for calculation until it is less than the preset error value e.

2. The method for simulating the width of a crack in a sample according to claim 1, characterized in that: In step a, calculating the permeability value k of the sample using Darcy's law specifically involves finding two opposing surfaces on the sample where a crack is connected, connecting the two opposing surfaces to a constant pressure P and atmospheric pressure Pa respectively, applying a confining pressure Pw to the other surfaces of the sample using a rubber sleeve, calculating and measuring the flow rate Qa using a soap film flow meter, and then calculating it using Darcy's law.

3. The method for simulating the width of a crack in a sample according to claim 1, characterized in that: The gas viscosity This is obtained by looking up a table using pressure.

4. The method for simulating the width of a crack in a sample according to claim 1, characterized in that: The sample is cylindrical.

5. The method for simulating the width of a crack in a sample according to claim 1, characterized in that: The sample is a cuboid.

6. The method for simulating the width of a crack in a sample according to claim 1, characterized in that: In step b, determining the location of the crack specifically means, when the sample is cylindrical, selecting the midpoint of the chord of the circle at the cut end of the crack as the cutting surface.

7. The method for simulating the width of a crack in a sample according to claim 5, characterized in that: In step b, determining the location of the crack specifically means, when the sample is a cuboid, selecting the vertical plane of the end face that runs through the crack and is parallel to the side length as the cutting plane.

8. The method for simulating the width of a crack in a sample according to claim 1, characterized in that: In step f, the preset error value e is 1%.

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