A rapid calculation method for shale hydration expansion stress-strain and hydration expansion amount

Abstract

The present invention provides a rapid calculation method for shale hydration expansion stress-strain and hydration expansion amount, comprising the following steps: obtaining the petrophysical and mechanical parameters of the shale layer, calculating the in-situ stress of the shale layer, calculating the hydration degree of the shale layer, calculating the hydration expansion amount of the shale layer, and then obtaining the hydration expansion stress-strain of the shale layer; wherein key parameters A, B, and C are introduced in the calculation of the hydration expansion amount, and the optimal calculation parameters A, B, and C under two working conditions are determined by separately changing the hydration degree and simultaneously changing the hydration degree and in-situ stress in the field test. The present invention controls the water injection volume through the "standard injection process" to achieve different hydration degrees of the shale layer and simulate the hydration expansion phenomenon. The rapid calculation method for shale hydration expansion stress-strain proposed by the present invention has a calculation accuracy that can reach 90%, and compared with the existing calculation method, the calculation accuracy of the hydration expansion stress-strain is improved by more than 15%.

Description

Technical Field

[0001] The invention belongs to the field of oil and gas drilling engineering and relates to a method for quickly calculating shale hydration expansion stress strain and hydration expansion amount. Background Art

[0002] The hydration effect in the shale gas drilling process cannot be ignored. The expansion stress and strain caused by shale hydration will aggravate the expansion of formation cracks and cause drilling problems such as drilling fluid leakage. In this context, accurate prediction of hydration expansion stress and strain has always been a key issue to be solved in drilling engineering. At present, the prediction of shale hydration expansion stress and strain is mainly based on empirical formulas, and the empirical parameters in the formula are relatively arbitrary and have a large range of values, which makes the prediction accuracy of hydration expansion stress and strain difficult to meet the requirements of field engineering. In view of this, it is urgent to propose a fast calculation method for shale hydration expansion stress and strain, and optimize the key parameters in the calculation method through field tests to obtain the hydration expansion amount, so as to improve the prediction accuracy of hydration expansion stress and strain in the shale formation drilling process.

[0003] Through patent research, it was found that there are a few hydration expansion test simulation devices at this stage, such as a shale hydration expansion stress test device and method (CN202011227743.4), an expansive rock hydration expansion force test device (CN202121920077.2), an expansive rock hydration expansion force test device and test method (CN201910386441.2), etc. However, the above devices are only used for indoor testing of hydration expansion stress and strain, and do not involve the calculation of hydration expansion stress and strain. In addition, the above test device is an indoor test, and it is impossible to carry out field tests to optimize the key parameters in the calculation method to obtain the hydration expansion amount. In response to the above problems, a rapid calculation method for shale hydration expansion stress and strain and hydration expansion amount is proposed. Summary of the invention

[0004] The present invention provides a method for quickly calculating shale hydration expansion stress-strain and hydration expansion amount, optimizes key parameters A, B and C in the calculation method through field tests, and considers the influence of hydration degree on hydration expansion stress-strain, so as to improve the calculation accuracy of shale hydration expansion stress-strain.

[0005] To achieve the above object, the first aspect of the present invention provides a method for quickly calculating shale hydration expansion stress and strain, the calculation steps of which are:

[0006] (1) Calculation of hydration expansion of shale layer L i , obtain the hydration expansion L of the shale layer in the x, y, and z directions x , L y , L z ;

[0007] (2) Calculate the hydration swelling strain ε of the shale i

[0008] Substitute the hydration swelling amounts L x 、L y 、L z of the shale layer in the x, y, and z directions into the true strain calculation formula to calculate the hydration swelling strain ε x 、ε y 、ε z :

[0009]

[0010] In the formula, L i is the hydration swelling amount; ε i is the hydration swelling strain; l i is the length, width, and height of the shale layer; i takes x, y, z;

[0011] (3) Calculate the hydration swelling stress of the shale

[0012] Substitute the hydration swelling strain ε i into Hooke's law under the triaxial stress state to calculate the hydration swelling stresses

[0013]

[0014]

[0015]

[0016] In the formula, E is the elastic modulus of the shale layer, obtained from the uniaxial compression experiment; μ is the Poisson's ratio of the shale layer, obtained from the uniaxial compression experiment.

[0017] Furthermore, the second aspect of the present invention provides a rapid calculation method for the hydration swelling amount of shale, and its calculation steps are:

[0018] S1 Obtain the petrophysical and mechanical parameters of the shale layer

[0019] Use the sidewall coring technology to sample the shale layer to obtain rock samples, record the depth of sampling of the shale layer, denoted as H, and then conduct tests on the porosity φ, pore fluid density ρ l 、skeleton density ρ m of the rock samples, and record the corresponding test data;

[0020] S2 Calculate the in-situ stress σ of the shale layer i

[0021] Substitute the parameters obtained in S1 into the Huang's model of in-situ stress to calculate the in-situ stresses σ x 、σ y 、σ z ;

[0022]

[0023]

[0024] σ z = gH[(1 - φ)ρ m + φρ l

[0025] In the formula: σ x 、σ y 、σ z are the in-situ stresses of the shale layer in the x, y, and z directions; μ is the Poisson's ratio; α is the Biot coefficient, generally 0.85; P P is the formation pore pressure; β1 and β2 are the tectonic in-situ stress coefficients, obtained by fitting the measured in-situ stress data of the shale layer through the Huang's model; g is the acceleration due to gravity; H is the depth of the shale layer; φ is the porosity; ρ l is the pore fluid density; ρ m is the skeleton density;

[0026] S3 Calculate the hydration degree w0 of the shale layer

[0027] The hydration degree is defined as the ratio of the water content L c at any time during the hydration process to the water content R m after complete hydration, that is, the water content after complete hydration of the same volume of rock and the same volume of water; the water content at any time during the hydration process is determined by measuring the mass of the basic chemically bound water inside the sample, and the water content after complete hydration is determined by measuring the mass of the chemically bound water after the sample is completely hydrated; obtain two rock samples from the shale layer, measure L c of the first rock sample and R m of the second rock sample, and then obtain the hydration degree of the shale layer by calculating the ratio of L c and R m , as shown in the following formula:

[0028] L c = m0 - m 100 R m = R1 - R0

[0029]

[0030] In the formula: m0 is the mass of the first rock sample at room temperature; m 100 is the mass of the first rock sample after drying at 100°C; L​c is the water content at any moment during the hydration process of the first rock sample; R0 is the mass of the second rock sample at normal temperature; R1 is the mass of the second rock sample after complete hydration; R m is the water content of the second rock sample after complete hydration; w0 is the degree of hydration of the shale layer, %;

[0031] S4 calculates the hydration swelling amount L of the shale layer i

[0032] Based on the coupled action model of the degree of hydration and in-situ stress load, the hydration swelling amounts of the shale layer in the x, y, and z directions are derived as follows:

[0033]

[0034]

[0035]

[0036] In the formula: L x 、L y 、L z are the hydration swelling amounts of the shale layer in the x, y, and z directions; A, B, and C are all calculation parameters optimized by in-situ tests; w0 is the degree of hydration of the shale layer; σ x 、σ y 、σ z are the in-situ stresses of the shale layer in the x, y, and z directions; S x 、S y 、S z are the cross-sectional area sizes of the shale layer along the x, y, and z directions; P0 is the atmospheric pressure.

[0037] In the above rapid calculation method of the hydration swelling amount of the shale layer, the calculation parameters A, B, and C are optimized and determined according to the following in-situ test method, and the specific steps are:

[0038] S41: Build the basic formation in the in-situ test;

[0039] S42: Fill the shale layer in the in-situ test to obtain the initial degree of hydration of the shale layer;

[0040] Determine the position, shape, size, and material consumption of the shale layer; according to the position, shape, and size of the shale layer, fill the organosilicon-modified cement mortar (mass ratio of hydrated neat paste to quartz sand 1:2) layer by layer every 50 cm to form the shale layer; during the filling process of the shale layer, lay a set of capillary tubes (diameter 1 mm, strength 30 MPa) made of rigid plastic every 50 cm of the filled shale layer; calculate the initial degree of hydration w0 of the shale layer according to S3;

[0041] S43: Start the field test to obtain the experimental data of the hydration expansion stress and strain of the shale layer;

[0042] (1) Apply confining pressure and axial pressure;

[0043] (2) Hydrate the shale layer through the "standard injection process" and calculate the degree of hydration;

[0044] The "standard injection process" includes the following steps: ① Set the water injection pressure of the water pump to be lower than 0.3 kPa to ensure that the shale layer will not be damaged due to too high injection pressure; ② Control the flow rate of each set of capillaries through a mass flow meter to ensure that the flow rate at the injection end of each layer of capillaries is less than 10 L / h, so as to realize the slow outflow of the fluid from the outlet end of the capillary; ③ Turn on the water pump and synchronously inject the water in the water tank into each set of capillaries through the pipeline to ensure synchronous hydration of each position of the shale layer; ④ During the water injection process, monitor the injection volume of each set of capillaries through a mass flow meter to ensure that the injection volume of each set of capillaries is the same; ⑤ When the sum of the injection volumes of all mass flow meters reaches the total injection volume, turn off the water pump and wait quietly for 3 h - 5 h to complete a complete hydration of the shale layer;

[0045] (3) Monitor and record the hydration expansion stress and strain of the shale layer during the field test;

[0046] S44: Conduct optimization tests of calculation parameters under two different working conditions to determine the optimal values of calculation parameters A, B, and C

[0047] (1) Keep the in-situ stress unchanged, change the degree of hydration by the water injection volume, repeat the field test according to S43, record the hydration expansion stress and strain, and use the Matlab function to fit the test data to optimize the calculation parameters A, B, and C in the hydration expansion stress and strain formula; the optimal values of the calculation parameters obtained under this condition are applicable to the working condition where the drilling fluid continuously leaks into the shale layer;

[0048] (2) Change the in-situ stress and at the same time change the degree of hydration by the water injection volume, repeat the field test according to S43, record the hydration expansion stress and strain, and use the Matlab function to fit the test data to optimize the calculation parameters A, B, and C in the hydration expansion stress and strain formula; the optimal values of the calculation parameters obtained under this condition are applicable to the working condition where the drilling fluid continuously leaks into the shale layer and the crack propagation causes the change of the in-situ stress of the shale layer.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] 1. The present invention proposes a rapid calculation method for the hydration expansion stress and strain of shale, and the calculation accuracy can reach 90%. Compared with the existing calculation methods, the calculation accuracy of the hydration expansion stress and strain is increased by more than 15%;

[0051] 2. The present invention designs a rapid calculation method for the shale hydration expansion amount, customizes calculation parameters A, B, and C, optimizes and determines the optimal values of A, B, and C through field tests, and determines the optimal calculation parameters under two working conditions by separately changing the degree of hydration and simultaneously changing the degree of hydration and in-situ stress;

[0052] 3. The present invention proposes a method for realizing controllable hydration degree of shale layers. By controlling the water injection volume through the "standard injection process", different hydration degrees of shale layers are achieved, and the hydration expansion phenomenon is simulated. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a step diagram of the rapid calculation method for the shale hydration expansion stress and strain according to the present invention;

[0054] Figure 2 is a schematic diagram of the field test;

[0055] Figure 3 is Figure 2 the top view of

[0056] Figure 4 is a step diagram of the field test optimization of the calculation parameters A, B, and C;

[0057] Figure 5 is a comparison diagram of the calculation results after optimizing the calculation parameters A, B, and C;

[0058] In the figure: 1. Power supply; 2. Circuit; 3. "◎"-shaped foundation pit; 4. "⌒"-shaped thin steel plate; 5. Type I hydraulic device; 51. Hydraulic outer wall; 52. Hydraulic cavity; 53. Hydraulic column; 6. Stress sensor; 7. Strain sensor; 8. Pipeline; 9. Water tank; 10. Water pump; 11. Mass flowmeter; 12. Data processor; 13. Capillary; 14. Counterweight; 15. Foundation stratum; 16. Shale layer; 17. Bearing plate; 18. Pressure sensor. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] Combined with the description of the specific embodiments of the present invention and the drawings, the details of the present invention can be more clearly understood. However, the specific embodiments of the present invention described herein are only for the purpose of explaining the present invention and cannot be understood in any way as a limitation of the present invention. Under the teaching of the present invention, those skilled in the art can conceive any possible deformation based on the present invention, and all of these should be regarded as belonging to the scope of the present invention.

[0060] The first embodiment provides a rapid calculation method for the shale hydration expansion amount, and its calculation steps are as follows:

[0061] (1) Obtain the rock physical and mechanical parameters of the shale layer

[0062] Two rock samples of the shale layer are obtained using the borehole wall coring technique, and the depth of sampling of the shale layer is recorded, denoted as H. Then, porosity, pore fluid density, and matrix density tests of the rock samples are carried out, and the corresponding test data are recorded;

[0063] (2) Calculate the in-situ stresses σ x 、σ y 、σ z

[0064] Substitute the parameters obtained in step (1) above into the Huang's in-situ stress model to calculate the in-situ stresses σ x 、σ y 、σ z ;

[0065]

[0066]

[0067] σ z =gH[(1 - φ)ρ m + φρ l

[0068] In the formula: σ x 、σ y 、σ z are the in-situ stresses of the shale layer in the x, y, and z directions; μ is the Poisson's ratio; α is the Biot coefficient, generally 0.85; P P is the formation pore pressure; β1 and β2 are tectonic in-situ stress coefficients, obtained by fitting the measured in-situ stress data of the shale layer through the Huang's model; g is the acceleration due to gravity; H is the depth of the shale layer; φ is the porosity; ρ l is the pore fluid density; ρ m is the matrix density;

[0069] (3) Calculate the degree of hydration w0 of the shale layer

[0070] Carry out comparative tests on the two rock samples taken in (1); for one rock sample, first measure its mass, denoted as m0, then place the rock sample in a vacuum drying oven at 100 °C for 24 h, and measure the mass of the dried rock sample, denoted as m 100 ; for the other rock sample, directly measure its mass, denoted as R0, then completely hydrate the rock sample, and weigh the mass of the completely hydrated rock sample, denoted as R1; calculate the degree of hydration of the shale layer according to the definition of the degree of hydration, as shown in formula (2):

[0071] L c =m0 - m 100 R m =R1 - R0

[0072] ​

[0073] Where: m0 is the mass of the first rock sample at room temperature; m 100 is the mass of the first rock sample after drying at 100 °C; L c is the water content of the first rock sample at any time during the hydration process; R0 is the mass of the second rock sample at room temperature; R1 is the mass of the second rock sample after complete hydration; R m is the water content of the second rock sample after complete hydration; w0 is the hydration degree of the shale layer, %;

[0074] (4) Calculate the hydration swelling amount L of the shale layer i

[0075] Based on the coupling action model of hydration degree and in-situ stress load, the hydration swelling amounts of the shale layer in the x, y, and z directions are deduced, as shown in Equation (3):

[0076]

[0077]

[0078]

[0079] Where: L x 、L y 、L z are the hydration swelling amounts of the shale layer in the x, y, and z directions; A, B, and C are all calculation parameters optimized by in-situ tests; w0 is the hydration degree of the shale layer; σ x 、σ y 、σ z are the in-situ stresses of the shale layer in the x, y, and z directions; S x 、S y 、S z are the cross-sectional areas of the shale layer along the x, y, and z directions; P0 is the atmospheric pressure.

[0080] The calculation parameters A, B, and C in the above calculation method of shale hydration swelling amount are all obtained according to the following in-situ test method, and the specific steps are as follows:

[0081] Step 1: Build the basic formation for in-situ tests

[0082] Such as Figures 1-4As shown in the figure, a field test for optimizing the calculation parameters of the hydration swelling amount mainly includes a power supply 1, a circuit 2, an "◎"-shaped foundation pit 3, a "⌒"-shaped thin steel plate 4, a type-I hydraulic device 5, a hydraulic outer wall 51, a hydraulic cavity 52, a hydraulic column 53, a stress sensor 6, a strain sensor 7, a pipeline 8, a water tank 9, a water pump 10, a mass flowmeter 11, a data processor 12, a capillary 13, a counterweight 14, a foundation stratum 15, a shale layer 16, a bearing plate 17, and a pressure sensor 18;

[0083] Excavate an "◎"-shaped foundation pit with an outer diameter of 30 m, an inner diameter of 20 m, and a depth of 30 m; inside the "◎"-shaped foundation pit, use four "⌒"-shaped thin steel plates 4 to form a cylinder with a diameter of 20 m and a height of 30 m; inside the cylinder surrounded by the "⌒"-shaped thin steel plates 4, use sandstone slurry to fill in layers at a thickness of 50 cm each to form the foundation stratum 15. When filling to the preset position of the shale layer, fill the shale layer according to the following step 2, and finally complete the filling of the entire field test stratum;

[0084] A bearing plate 17 is set on the outer circle of the "◎"-shaped foundation pit 3, and a type-I hydraulic device 5 is set between the bearing plate 17 and the "⌒"-shaped thin steel plate 4. One type-I hydraulic device 5 is set every 18° in the circumferential direction and one circle is set every 3 m in the height direction, with a total of 200; by injecting liquid into the hydraulic cavity 52 of the type-I hydraulic device 5, the hydraulic column 53 is pushed to squeeze the "⌒"-shaped thin steel plate 4 to apply the confining pressure; a bearing plate 17 is set on the top of the foundation stratum 15, and a counterweight 14 is set on the bearing plate 17 to apply the axial pressure;

[0085] Inside the "⌒"-shaped thin steel plate 4, one 2 pressure sensor 18 is set every 1 m to monitor the confining pressure; one pressure sensor 18 is set every 1 m on the bottom surface of the bearing plate 17 to monitor the axial pressure; the stress sensor 6 and the strain sensor 7 are evenly distributed at the contact position between the shale layer and the foundation stratum 15, and one stress sensor 6 and one strain sensor 7 are set every 0.5 m 2 to be responsible for monitoring the hydration swelling stress and strain of the shale layer; 2

[0086] Step 2: Fill the shale layer in the field test to obtain the initial hydration degree w0 of the shale layer

[0087] Determine the position, shape, size, and material consumption of the shale layer 16; according to the position, shape, and size of the shale layer 16, fill the organic silicone-modified cement mortar (mass ratio of hydrated pure paste to quartz sand is 1:2) layer by layer at a thickness of 50 cm each to form the shale layer 16, and record the filling amount m of the organic silicone-modified cement mortar s ​; During the process of filling the shale layer 16, a set of capillary tubes 13 (with a diameter of 1 mm and a strength of 30 MPa) made of rigid plastic are laid every 50 cm of the filled shale layer 16; the water tank 9, the water pump 10, the mass flowmeter 11 and the capillary tubes 13 are connected in series through the pipeline 8, and a mass flowmeter 11 is set at the connection of each set of capillary tubes 13 and the pipeline 8 to control the amount of water injected into the shale layer 16 through the capillary tubes 13; the water outlet ends of the capillary tubes 13 are distributed in a dot matrix within the shale layer 16 to ensure that the shale layer 16 can be evenly hydrated; stress sensors 6 and strain sensors 7 are evenly laid on the six surfaces of the shale layer 16; calculate the initial hydration degree w0 of the shale layer 16 according to formula (2);

[0088] Step 3: Start the in-situ test to obtain the hydration expansion stress-strain test data of the shale layer

[0089] (1) Apply confining pressure and axial pressure;

[0090] (2) Hydrate the shale layer through the "standard injection process" and calculate the hydration degree w1;

[0091] The "standard injection process" includes the following steps: ① Set the water injection pressure of the water pump 10 to be lower than 0.3 kPa to ensure that the shale layer 16 will not be damaged due to excessive injection pressure; ② Control the flow rate of each set of capillary tubes 13 through the mass flowmeter 11 to ensure that the flow rate at the injection end of each layer of capillary tubes 13 is less than 10 L / h, so that the fluid slowly flows out from the outlet end of the capillary tubes 13; ③ Turn on the water pump 10 and synchronously inject the water in the water tank 9 into each set of capillary tubes 13 through the pipeline 8 to ensure that all positions of the shale layer 16 are hydrated synchronously; ④ During the water injection process, monitor the injection volume of each set of capillary tubes 13 through the mass flowmeter 11 to ensure that the injection volume of each set of capillary tubes 13 is the same; ⑤ When the sum of the injection volumes of all mass flowmeters 11 reaches the total water injection volume, turn off the water pump 10 and wait for 3 h - 5 h to complete a complete hydration of the shale layer 16;

[0092] Calculate the hydration degree after water injection: Determine the total mass of water injection as m through the mass flowmeter 11, and calculate the hydration degree after injecting water m using the definition of hydration degree, as shown in formula (4):

[0093]

[0094] In the formula, w1 is the hydration degree after injecting water m; m s is the filling mass of the silicone-modified cement mortar;

[0095] (3) Monitor the hydration expansion stress-strain of the shale layer during the in-situ test;

[0096] Record the strain data of the shale layer 16 monitored by all strain sensors 7, and then classify the strain data of the monitoring points on each surface into a group. Take the average value of all strain data within this group as the actual expansion strain at the position of this surface; there are 6 surfaces in the shale layer 16, and 6 actual expansion strains (along 3 directions) are obtained; superpose 2 actual expansion strains in the same direction to obtain the actual expansion strains ε′ x , ε′ y , ε′ z in the x, y, and z directions of the shale layer 16; use the same method to obtain the actual expansion stresses σ′ xx , σ′ yy , σ′ zz in the x, y, and z directions of the shale layer 16; record ε′ x , ε′ y , ε′ z , σ′ xx , σ′ yy , σ′ zz , and complete one field test;

[0097] Step 4: Conduct calculation parameter optimization tests under two different working conditions to determine the optimal values of the calculation parameters

[0098] (1) Keep the in-situ stress unchanged, change the degree of hydration by the water injection volume, repeat the field test according to Step 3 to record the hydration expansion stress and strain, and use the Matlab function to fit the test data to optimize the calculation parameters A, B, and C in the hydration expansion stress and strain formula; the optimal values of the calculation parameters obtained under this condition are applicable to the working condition where the drilling fluid continuously leaks into the shale layer 16;

[0099] Set the degree of hydration w1 as the independent variable x, the hydration expansion strain ε′ i as the dependent variable y, and the in-situ stress as a constant. Use the polyfit function p = polyfit(x,1) provided by Matlab to fit the field test data of this working condition to determine the optimal values of the three parameters A, B, and C. The type of the fitting formula is shown in Formula (5):

[0100]

[0101] In the formula: x is the independent variable, representing the degree of hydration of the shale layer after water injection in the field test, that is, substituting w1 during the fitting process; y is the dependent variable, representing the expansion strain of the shale layer after water injection in the field test, that is, substituting ε′ i ; l i is the length, width, and height of the shale layer in the field test; σ i is the in-situ stress of the shale layer in different directions in the field test, obtained from the axial pressure and confining pressure monitoring data in the field test; S iis the cross-sectional area of the shale layer in different directions during the in-situ test; i takes values of x, y, and z; P0 is the atmospheric pressure;

[0102] (2) While changing the in-situ stress, change the degree of hydration by adjusting the water injection volume. According to Step 3, repeat the in-situ test to record the hydration expansion stress and strain. Use Matlab functions to fit the test data and optimize the calculation parameters A, B, and C in the hydration expansion stress and strain formula; the optimal values of the calculation parameters obtained under this condition are applicable to the working condition where the drilling fluid continuously leaks into the shale layer and the crack propagation causes changes in the in-situ stress of the shale layer 16;

[0103] Set the degree of hydration w1 as the independent variable x, and the in-situ stress σ i as the independent variable z, and the hydration expansion strain ε i ′ as the dependent variable y′. Use the polyfit function p = polyfit(x, y, 2) provided by Matlab to fit the in-situ test data of this working condition and determine the optimal values of the three parameters A, B, and C. The type of the fitting formula is shown in Formula (6):

[0104]

[0105] In the formula: x is the independent variable, representing the degree of hydration of the shale layer after water injection in the in-situ test, that is, substitute w1 during the fitting process; z is the independent variable, representing the in-situ stress of the shale layer in different directions during the in-situ test, that is, substitute σ i , which is obtained from the axial pressure and confining pressure monitoring data in the in-situ test; y′ is the dependent variable, representing the expansion strain of the shale layer after water injection in the in-situ test, that is, substitute ε i ′ during the fitting process, which is obtained from the monitoring data in the in-situ test; l i is the length, width, and height of the shale layer in the in-situ test; S i is the cross-sectional area of the shale layer in different directions during the in-situ test, i takes values of x, y, and z; P0 is the atmospheric pressure.

[0106] Based on the rapid calculation method of shale hydration expansion amount, Embodiment 2 provides a rapid calculation method for shale hydration expansion stress and strain. Its calculation steps are as follows:

[0107] (1) Calculate the hydration expansion amount L of the shale layer i , and obtain the hydration expansion amounts L x 、L y 、L z of the shale layer in the x, y, and z directions;

[0108] (2) Calculate the hydration expansion strain ε of the shale layer i

[0109] Take the hydration expansion amounts L of the shale layer in the x, y, and z directionsx and L y and L z Substitute into the true strain calculation formula to calculate the hydration expansion strain ε of the shale layer x and ε y and ε z , see formula (7):

[0110]

[0111] In the formula, L i is the hydration expansion amount; ε i is the hydration expansion strain; l i is the length, width, and height of the shale layer; i takes x, y, z;

[0112] (3) Calculate the hydration expansion stress of the shale layer

[0113] Substitute the hydration expansion strain ε i into Hooke's law under the triaxial stress state to calculate the hydration expansion stress of the shale layer in the x, y, and z directions see formula (8):

[0114]

[0115]

[0116]

[0117] In the formula, E is the elastic modulus of the shale layer, obtained from the uniaxial compression experiment; μ is the Poisson's ratio of the shale layer, obtained from the uniaxial compression experiment.

[0118] Example 1:

[0119] Example 1 is a field test used to obtain the test data of the hydration expansion strain caused by the continuous loss of drilling fluid into the shale layer.

[0120] When Well W5 in the JZ block was drilled to the well section with a vertical depth of 2412m - 2420m, a problem of wellbore shrinkage occurred. After on-site investigation and analysis, it was found that: the loss of drilling fluid in the well section with a vertical depth of 2415m - 2417m caused the hydration expansion of the shale layer, inducing the problem of wellbore shrinkage; immediately after the problem was discovered, drilling was stopped on-site, and strain sensors were promptly set at the wellbore shrinkage position to monitor the deformation of the wellbore shrinkage; through on-site monitoring, the hydration expansion strain data of the shale layer in the two horizontal directions were: ε x = 0.35%, ε y= 0.35%; In addition, the in-situ stress of the shale layer at the time of drill stoppage and the degree of hydration of the shale layer at the time of drill stoppage are also required for Example 2 and Example 3; the in-situ stresses of the shale layer in the x, y, and z directions are obtained as 34 MPa, 34 MPa, and 40 MPa using the logging-while-drilling data before drill stoppage; the degree of hydration of the shale layer is obtained as 30.48% using data such as the mud loss volume, the range of the mud loss area (a circle centered on the wellbore), and the thickness of the mud loss area.

[0121] Example 2:

[0122] Example 2 uses the field test method described in the present invention to calculate the hydration expansion strain in Example 1 by optimizing the calculation parameters A, B, and C in the calculation method of the hydration expansion amount of the mud lost to the shale layer.

[0123] Build the site basic formation 15 according to test step 1, and obtain the porosity φ, density ρ, pore fluid density ρ l of the basic formation 15, and the skeleton density ρ m . The specific values are 3.35%, 2.42 g / cm 3 , 1.05 g / cm 3 , and 2.17 g / cm 3 respectively; fill the shale layer in layers according to step 2. The shale layer is a cuboid with a length of 10 m, a width of 5 m, and a height of 1 m, and is located 5 m above the center of the site; obtain the initial degree of hydration w0 of the shale layer as 3.2%; start the field test according to step 3, set the confining pressure and axial pressure as the on-site data 34 MPa and 40 MPa in Example 1, control the water injection volume m through the mass flowmeter 24 and calculate the degree of hydration w1, monitor and record the hydration expansion stress and strain, and complete one field test; according to (1) in step 4, keep the in-situ stress unchanged and change the degree of hydration to repeat the field test, and use the Matlab function to fit the field test data to obtain the optimized calculation parameters A = 14.66, B = 49.16, C = -14.75; substitute A, B, C, the degree of hydration 30.48% in Example 1, and the in-situ stresses 34 MPa, 34 MPa, and 40 MPa in Example 1 into formula (7) to calculate the hydration expansion strains ε x = 0.317%, ε y = 0.317%. The results are shown in Figure 5 .

[0124] Example 3:

[0125] Example 3 is a conventional calculation method (source: Xue Yanjin, et al. Swelling calculation model of expansive soil foundation of ballastless track for high-speed railway [J]. Journal of Railway Science and Engineering, 2017, 14(07): 1347-1353.), which can calculate the hydration swelling strain in Example 1. Substitute the hydration degree of 30.48% in Example 1, the in-situ stresses of 34 MPa, 34 MPa, and 40 MPa in Example 1 into the above conventional calculation method to calculate the hydration swelling strains ε x = 0.268%, ε y = 0.268%. The results are shown in Figure 5 .

[0126] Comparing the hydration swelling strain results of Examples 1 and 2, see Figure 5 . It can be known that the accuracy of the calculation method described in the present invention is 90.6%; comparing the hydration swelling strain results of Examples 1 and 3, see Figure 5 . It can be known that the accuracy of the conventional calculation method is 76.8%; comparing the above calculation accuracies, it can be known that the calculation accuracy of the method described in the present invention is 17.8% higher than that of the conventional method.

Claims

1. A rapid calculation method for the hydration swelling amount of shale, characterized in that, The specific calculation steps include: S1 Obtain the petrophysical and mechanical parameters of the shale formation Samples are taken from the shale layer using the borehole wall coring technique, and the sampling depth of the shale layer is recorded as H. Then, physical and mechanical parameter tests of the rock samples are carried out, including porosity φ, pore fluid density ρ l , skeleton density ρ m , and the corresponding test data are recorded; S2 Calculate the in-situ stress σ of the shale formation i Substitute the parameters obtained in S1 into the Huang's model of in-situ stress to calculate the in-situ stresses σ x 、σ y 、σ z in the x, y, and z directions of the shale formation; S3 Calculate the degree of hydration w0 of the shale formation The degree of hydration is defined as the water content L at any time during the hydration process c and the water content R after complete hydration m The ratio is the water content after complete hydration of an equal volume of rock and an equal volume of water; the water content at any time during the hydration process is determined by measuring the mass of the basic chemically bound water inside the sample, and the water content after complete hydration is determined by measuring the mass of the chemically bound water after the sample is completely hydrated; two rock samples are obtained from the shale layer, and the L of the first rock sample is tested c and the R of the second rock sample m , and then by calculating the ratio of L c and R m the degree of hydration of the shale layer is obtained, as shown in the following formula: L c = m0 - m 100 R m = R1 - R0 Where: m0 is the mass of the first rock sample at room temperature; m 100 is the mass of the first rock sample after drying at 100 °C; L c is the water content of the first rock sample at any time during the hydration process; R0 is the mass of the second rock sample at room temperature; R1 is the mass of the second rock sample after complete hydration; R m is the water content of the second rock sample after complete hydration; w0 is the hydration degree of the shale layer, %; S4 Calculate the hydration swelling amount L of the shale layer i Based on the coupling action model of the degree of hydration and in-situ stress load, deduce the hydration swelling amounts of the shale formation in the x, y, and z directions, as shown in the following formula: Where: L x 、L y 、L z are the hydration swelling amounts of the shale layer in the x, y, and z directions; A, B, and C are all calculation parameters optimized by in-situ tests; w0 is the degree of hydration of the shale layer; σ x 、σ y 、σ z are the in-situ stresses of the shale layer in the x, y, and z directions; S x 、S y 、S z are the cross-sectional area sizes of the shale layer along the x, y, and z directions; P0 is the atmospheric pressure.

2. The rapid calculation method for the hydration swelling amount of shale according to claim 1, characterized in that, In the Huang's in-situ stress model, Where: σ x , σ y , σ z are the in-situ stresses of the shale formation in the x, y, and z directions; μ is the Poisson's ratio; α is the Biot coefficient, generally 0.85; P P is the formation pore pressure; β1 and β2 are the tectonic in-situ stress coefficients, obtained by fitting the measured in-situ stress data of the shale formation through the Huang's model; g is the acceleration due to gravity; H is the depth of the shale formation; φ is the porosity; ρ l is the pore fluid density; ρ m is the skeleton density.

3. The rapid calculation method for the shale hydration swelling amount according to claim 1, characterized in that The calculation parameters A, B, and C are optimized and determined according to the following site test method. The specific steps include: S41: Build the basic formation in the site test; S42: Fill the shale formation in the site test to obtain the initial degree of hydration of the shale formation; Determine the position, shape, size, and material consumption of the shale formation; according to the position, shape, and size of the shale formation, fill the organosilicon-modified cement mortar layer by layer every 50 cm to form the shale formation; during the filling process of the shale formation, lay a set of capillary tubes made of rigid plastic every 50 cm of the filled shale formation; calculate the initial degree of hydration w0 of the shale formation according to S3; S43: Start the site test to obtain the hydration swelling stress-strain test data of the shale formation (1) Apply confining pressure and axial pressure; (2) Hydrate the shale formation through the "standard injection process" and calculate the degree of hydration w1; The "standard injection process" includes the following steps: ① Set the water injection pressure of the water pump to be lower than 0.3 kPa to ensure that the shale formation will not be damaged due to excessive injection pressure; ② Control the flow rate of each set of capillary tubes through a mass flowmeter to ensure that the flow rate at the injection end of each layer of capillary tubes is less than 10 L / h, so that the fluid slowly flows out from the outlet end of the capillary tubes; ③ Turn on the water pump and synchronously inject the water in the water tank into each set of capillary tubes through the pipeline to ensure that all positions of the shale formation are hydrated synchronously; ④ During the water injection process, monitor the injection volume of each set of capillary tubes through a mass flowmeter to ensure that the injection volume of each set of capillary tubes is the same; ⑤ When the sum of the injection volumes of all mass flowmeters reaches the total injection volume, turn off the water pump and wait for 3 h - 5 h to complete a complete hydration of the shale formation; (3) Monitor and record the hydration swelling stress-strain of the shale formation in the site test S44: Conduct calculation parameter optimization tests under two different working conditions to determine the optimal values of the calculation parameters A, B, and C (1) Keep the in-situ stress unchanged, change the degree of hydration by the water injection volume, repeat the site test according to S43, record the hydration swelling stress-strain, and use the Matlab function to fit the test data to optimize the calculation parameters A, B, and C in the hydration swelling amount formula; the optimal values of the calculation parameters obtained under this condition are applicable to the working condition where the drilling fluid continuously leaks into the shale formation; (2) Change the in-situ stress and at the same time change the degree of hydration by the water injection volume, repeat the site test according to S43, record the hydration swelling stress-strain, and use the Matlab function to fit the test data to optimize the calculation parameters A, B, and C in the hydration swelling amount formula; the optimal values of the calculation parameters obtained under this condition are applicable to the working condition where the drilling fluid continuously leaks into the shale formation and the in-situ stress of the shale formation changes due to crack propagation.

4. A rapid calculation method for the shale hydration expansion amount according to claim 3, characterized in that In step (1) of S44, the degree of hydration w1 is set as the independent variable x, the hydration expansion strain ε i ′ as the dependent variable y, and the in-situ stress σ i as a constant. The in-situ test data of this working condition is fitted by the polyfit function p = polyfit(x, 1) provided by Matlab to determine the optimal values of the three parameters A, B, and C. The fitting formula type is shown in the following formula: Where: x is the independent variable, representing the degree of hydration after water injection in the shale layer during the in-situ test, i.e., substituting w1 during the fitting process; y is the dependent variable, representing the swelling strain after water injection in the shale layer during the in-situ test, i.e., substituting ε′ during the fitting process i ; l i is the length, width, and height of the shale layer in the in-situ test; σ i is the in-situ stress of the shale layer in different directions during the in-situ test, obtained from the axial pressure and confining pressure monitoring data in the in-situ test; S i is the cross-sectional area size of the shale layer in different directions during the in-situ test; i takes values of x, y, z; P0 is the atmospheric pressure; In step (2) of S44, the degree of hydration w1 is set as the independent variable x, and the in-situ stress σ i is set as the independent variable z, and the hydration expansion strain ε′ i is set as the dependent variable y′. The in-situ test data of this working condition are fitted by the polyfit function p = polyfit(x, y, 2) provided by Matlab to determine the optimal values of the three parameters A, B, and C. The fitting formula type is shown in the following formula: In the formula: x is the independent variable, representing the degree of hydration after water injection in the shale layer during the in-situ test, that is, substituting w1 during the fitting process; z is the independent variable, representing the in-situ stress in different directions of the shale layer during the in-situ test, that is, substituting σ i , which is obtained from the axial pressure and confining pressure monitoring data during the in-situ test; y′ is the dependent variable, representing the swelling strain after water injection in the shale layer during the in-situ test, that is, substituting ε′ i , which is obtained from the monitoring data during the in-situ test; l i is the length, width, and height of the shale layer during the in-situ test; S i is the cross-sectional area size of the shale layer in different directions during the in-situ test; i takes values of x, y, z; P0 is the atmospheric pressure.

5. A rapid calculation method for the shale hydration expansion amount according to claim 3, characterized in that The site test device mainly includes a power supply, a circuit, an "◎"-shaped foundation pit, a "⌒"-shaped thin steel plate, a type-I hydraulic device, a hydraulic outer wall, a hydraulic cavity, a hydraulic column, a stress sensor, a strain sensor, a pipeline, a water tank, a water pump, a mass flowmeter, a data processor, a capillary tube, a counterweight, a foundation stratum, a shale stratum, a bearing plate, and a pressure sensor; In the inner circle of the "◎"-shaped foundation pit, four "⌒"-shaped thin steel plates are used to enclose a cylinder; a bearing plate is arranged on the outer circle of the "◎"-shaped foundation pit, and a type-I hydraulic device is arranged between the bearing plate and the "⌒"-shaped thin steel plate. The type-I hydraulic devices are arranged at intervals of 18° in the circumferential direction and at intervals of 3 m in the height direction, with a total of 200; by injecting liquid into the hydraulic cavity of the type-I hydraulic device, the hydraulic column is pushed to extrude the "⌒"-shaped thin steel plate to apply confining pressure; a bearing plate is arranged on the top of the foundation stratum, and a counterweight is arranged on the bearing plate to apply axial pressure; One pressure sensor is set every 1 m on the inner side of the "⌒"-shaped thin steel plate to monitor the confining pressure; one pressure sensor is set every 1 m on the bottom surface of the bearing plate to monitor the axial pressure; stress sensors and strain sensors are evenly distributed at the contact position between the shale layer and the foundation stratum, and one stress sensor and one strain sensor are set every 0.5 m to be responsible for monitoring the hydration expansion stress and strain of the shale layer. 2 One pressure sensor is set every 1 m on the inner side of the "⌒"-shaped thin steel plate to monitor the confining pressure; one pressure sensor is set every 1 m on the bottom surface of the bearing plate to monitor the axial pressure; stress sensors and strain sensors are evenly distributed at the contact position between the shale layer and the foundation stratum, and one stress sensor and one strain sensor are set every 0.5 m to be responsible for monitoring the hydration expansion stress and strain of the shale layer. 2 One pressure sensor is set every 1 m on the inner side of the "⌒"-shaped thin steel plate to monitor the confining pressure; one pressure sensor is set every 1 m on the bottom surface of the bearing plate to monitor the axial pressure; stress sensors and strain sensors are evenly distributed at the contact position between the shale layer and the foundation stratum, and one stress sensor and one strain sensor are set every 0.5 m to be responsible for monitoring the hydration expansion stress and strain of the shale layer. 2 One pressure sensor is set every 1 m on the inner side of the "⌒"-shaped thin steel plate to monitor the confining pressure; one pressure sensor is set every 1 m on the bottom surface of the bearing plate to monitor the axial pressure; stress sensors and strain sensors are evenly distributed at the contact position between the shale layer and the foundation stratum, and one stress sensor and one strain sensor are set every 0.5 m to be responsible for monitoring the hydration expansion stress and strain of the shale layer. A water tank, a water pump, a mass flowmeter, and a capillary tube are connected in series through a pipeline. A mass flowmeter is arranged at the connection of each set of capillary tubes and pipelines to control the water volume injected into the shale stratum through the capillary tubes.

6. The rapid calculation method of the shale hydration expansion amount according to claim 5, characterized in that, In S41, the "◎"-shaped foundation pit is excavated; in the cylinder enclosed by the "⌒"-shaped thin steel plate, sandstone slurry is filled in a layered filling method with a layer thickness of 50 cm to form a foundation stratum. When filling to the preset position of the shale stratum, the shale stratum is filled, and finally the filling of the entire site test stratum is completed; after the filling is completed, rock samples are obtained from the foundation stratum to test the physical and mechanical parameters of the rock samples of the foundation stratum.

7. A rapid calculation method for the shale hydration swelling amount according to claim 3, characterized in that In the silicone-modified cement mortar, the mass ratio of hydrated pure paste to quartz sand is 1:

2. The diameter of the capillary tube is 1 mm and the strength is 30 MPa; the water outlet ends of the capillary tubes are distributed in a lattice pattern in the shale stratum to ensure uniform hydration of the shale stratum.

8. A rapid calculation method for the shale hydration swelling amount according to claim 3, characterized in that In step (3) of S43, record the strain data of the shale layer monitored by all strain sensors, then classify the strain data of the monitoring points on each surface into a group, and take the average value of all strain data within this group as the actual expansion strain at the surface position; there are 6 surfaces in the shale layer, and obtain the actual expansion strains in 6 directions along 3 directions; superimpose 2 actual expansion strains in the same direction to obtain the actual expansion strains ε′ x 、ε′ y 、ε′ z ; of the shale layer in the x, y, and z directions; use the same method to obtain the actual expansion stresses σ′ xx 、σ′ yy 、σ′ zz ; of the shale layer in the x, y, and z directions; record ε′ x 、ε′ y 、ε′ z 、σ′ xx 、σ′ yy 、σ′ zz , and complete a site test.

9. A rapid calculation method for the stress and strain of shale hydration swelling, characterized in that, Specifically, it includes the following calculation steps: (1) Calculate the hydration swelling amount L of shale by using the method described in any one of claims 1-7 i , and obtain the hydration swelling amounts L in the x, y, and z directions of the shale layer x , L y , L z ; (2) Calculate the hydration swelling strain ε of the shale i Substitute the hydration swelling amounts L x 、L y 、L z in the x, y, and z directions of the shale layer into the true strain calculation formula to calculate the hydration swelling strain ε x 、ε y 、ε z : Where L i is the hydration swelling amount; ε i is the hydration swelling strain; l i is the length, width and height of the shale layer; i takes x, y, z; (3) Calculate the hydration swelling stress of the shale formation Substitute the hydration expansion strain ε i into Hooke's law under the triaxial stress state to calculate the hydration expansion stresses of the shale layer in the x, y, and z directions In the formula, E is the elastic modulus of the shale stratum, which is obtained from a uniaxial compression experiment; μ is the Poisson's ratio of the shale stratum, which is obtained from a uniaxial compression experiment.

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