# US 11,028,689 B2 · Method for experimentally determining the conductivity of unpropped fracture in hydraulic fracturing of shale reservoir > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,028,689 B2 - Document ID: US11028689B2 - Status: Granted - Kind: B2 - Application number: 17/005,382 - Filed: 2020-08-28 - Published: 2020-12-17 - Granted: 2021-06-08 - Earliest claimed: 2020-08-28 - Assignees: Southwest Petroleum University - Applicants: Southwest Petroleum University - Inventors: Zhihong Zhao; Chi Chen; Shouxin Wang; Kun Wang; Cong Lu; Jie Lai; Yuxuan Liu; Ye Zhong; Yuhang Zhao - Web page: https://patentgrep.com/patent/US11028689B2 ## CPC - E21B 49/00: Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells - G01N 1/286: {involving mechanical work, e.g. chopping, disintegrating, compacting, homogenising (microtomes G01N1/06; pulverising in general B02C; mixing in general B01F)} - G01N 3/24: by applying steady shearing forces (G01N3/26, G01N3/28 take precedence) - G01N 15/0826: {and measuring fluid flow rate, i.e. permeation rate or pressure change} - G01N 15/088: {Investigating volume, surface area, size or distribution of pores; Porosimetry} - G01N 33/24: Earth materials (G01N33/42 takes precedence) - G06T 5/70: Denoising; Smoothing - G06T 7/62: of area, perimeter, diameter or volume - G06T 17/30: Polynomial surface description - E21B 43/26: by forming crevices or fractures - G01N 2001/2866: {Grinding or homogeneising} - G01N 2001/2873: {Cutting or cleaving} - G01N 2001/2893: {Preparing calibration standards} - G01N 2015/0846: {by use of radiation, e.g. transmitted or reflected light} - G06T 2207/10028: Range image; Depth image; 3D point clouds - G06T 2207/30181: Earth observation - E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS - G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q) - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract The invention discloses a method for experimentally determining the conductivity of an unpropped fracture in hydraulic fracturing of a shale reservoir, comprising: select an outcrop sample with a natural fracture in the shale reservoir, and cut the outcrop sample with along the extension direction of the natural fracture into no less than eight square rock slabs; use a laser scanner to obtain the rough topography data of the fracture surface of each square rock slab and calculate the area tortuosity; pick out the rock samples; model the rough surface of the selected rock samples; import the treated surface model into the engraving machine, and select the downhole core or outcrop rocks in the same horizon for repeated production; calculate the shear slippage at different positions of unpropped fracture according to the data of the shale reservoir; finally test the conductivity of the shale rock samples after shear slip. ## Claims ### Claim 1 A method for experimentally determining a conductivity of an unpropped fracture in hydraulic fracturing of a shale reservoir, comprising the following steps: Step 1: Collect an outcrop sample with a natural fracture in the shale reservoir, and cut the sample into no less than eight square rock slabs with the natural fracture along an extension direction of the natural fracture; the extension direction of the natural fracture is considered as the length of the slab, which ensures that a height difference between any two points on the natural fracture and a fracture surface of each square rock slab is less than 10 mm; Step 2: Use a laser scanner to obtain a rough topography data of the fracture surface of each square rock slab, and calculate an area tortuosity; Step 3: Select one square rock slab that represents a surface topography of the natural fracture in the shale reservoir according to the area tortuosity obtained in Step 2; Step 4: Denoise a point cloud data of each square rock slab selected in Step 3 by standard deviation filtering method, interpolate and normalize the point cloud data by a Kriging interpolation method after noise reduction, then import the point cloud data into Geomagic software to convert the point cloud data into a Non-uniform rational basis spline (NURBS) surface model, and finally, import the surface model into an engraving machine and use a computer-aided manufacturing (CAM) software that comes with the engraving machine to establish an engraving machine toolpath; Step 5: Use a downhole core of the shale reservoir or an outcrop rock in a formation on an identical horizontal plane to make smooth square slabs with smooth and straight surfaces; Step 6: Engrave the smooth square rock slabs in Step 5 with the engraving machine to produce artificial rock samples with uniform surface topography; Step 7: Calculate a shear slippage of the unpropped fracture by the following formula, and then divide the fracture into sections by every 0.5 mm of change in slippage from the center of the fracture, and calculate an average shear slippage of each section; u s = ( k + 1 4 ⁢ ⁢ G ) ⁢  - δ 3 - δ 1 2 ⁢ sin ⁢ ⁢ 2 ⁢ ⁢ θ  ⁢ l ⁢ 1 - ( x ⁢ / ⁢ l ) 2 Where, us is the shear slippage of the unpropped fracture surface, in mm; k is Kolosov constant, k=3-4v; v is Poisson's ratio, dimensionless; G is a shear modulus, in MPa; δ3 is a maximum horizontal principal stress, in MPa; δ1 is a minimum horizontal principal stress, in MPa; θ is the angle between the natural fracture and the maximum horizontal principal stress, in °; l is a half-length of the unpropped fracture, in m; and x is a coordinate of any point along the length of the fracture, in m; Step 8: Shear and stagger the artificial rock samples described in Step 6 in the length direction respectively according to the average shear slippage of each section of the unpropped fracture calculated in Step 7, then use a grinding miller to grind the artificial rock samples at both ends of the length direction to be flush, and bond semi-circular arc-shaped polymethyl methacrylate pads at both ends of the artificial rock sample to obtain shear-slip shale slabs at different positions on the unpropped fracture surface; Step 9: Determine a closing pressure in an unpropped fracture conductivity test according to the maximum horizontal principal stress, minimum horizontal principal stress, formation pressure, and effective stress coefficient of the shale reservoir, and determine an experimental temperature of the fracture conductivity test based on a formation temperature; and Step 10: Put the shear-slip shale slabs at different positions on the unpropped fracture surface obtained in Step 8 into a diversion chamber, put the diversion chamber into a conductivity test device, heat the diversion chamber and load the closing pressure according to the closing pressure and experimental temperature determined in Step 9, and test the conductivity of the unpropped fracture at different positions to obtain the conductivity and a distribution of unpropped fractures in hydraulic fracturing of the shale reservoir. ### Claim 2 (depends on 1) The method for experimentally determining the conductivity of an unpropped fracture in hydraulic fracturing of a shale reservoir according to claim 1, wherein a specific calculation process of the area tortuosity in Step 2 is described as follows: R s = A s A n Where, Rs is the area tortuosity; As is an actual area of the rough fracture surface; and An is a projected area of the rough fracture surface; According to the point cloud data of the surface topography obtained by the laser scanner, the actual area of the rough fracture surface can be calculated in the following way: A s = ∫ [ 1 + ( ∂ z ⁡ ( x , y ) ∂ x ) 2 + ( ∂ z ⁡ ( x , y ) ∂ y ) 2 ] 1 ⁢ / ⁢ 2 ⁢ dxdy Where, As is the actual area of the rough fracture surface; x is the x-coordinate of the point cloud data; y is the y-coordinate of the point cloud data; and z is the z-coordinate of the point cloud data; The projected area of the fracture surface is calculated by the following formula: An=l×w Where, An is the projected area of the rough fracture surface; l is the length of the rock slab; and w is the width of the rock slab. ### Claim 3 (depends on 1) The method for experimentally determining the conductivity of an unpropped fracture in hydraulic fracturing of a shale reservoir according to claim 1, wherein the square rock slab in Step 3 is selected by the following steps: calculate an average area tortuosity of the square rock slabs, and then select the square rock slab with the area tortuosity closest to the average area tortuosity. ### Claim 4 (depends on 1) The method for experimentally determining the conductivity of an unpropped fracture in hydraulic fracturing of a shale reservoir according to claim 1, wherein the specific calculation process of standard deviation filtering method in Step 4 is described as follows: (1) Calculate the distance between each point {Xn, Yn, Zn} and its adjacent eight neighborhood points in the point cloud data {Xi, Yi, Zi} of the fracture surface obtained by scanning, and the X and Y coordinates of the neighborhood points are {Xn−1, Yn−1}, {Xn−1, Yn}, {Xn−1, Yn+1}, {Xn, Yn−1}, {Xn, Yn+1}, {Xn+1, Yn−1}, {Xn+1, Yn} and {Xn+1, Yn+1} respectively; (2) Make statistics of the distance calculated in Step (1), and calculate the average u and standard deviation r of an average distance; and (3) Determine a relationship between the average distance u from the point {Xn, Yn, Zn} to eight neighborhood points and a distance threshold d=u±5r; if the average distance u is greater than the distance threshold d, a noise will be eliminated. ### Claim 5 (depends on 4) The method for experimentally determining the conductivity of an unpropped fracture in hydraulic fracturing of a shale reservoir according to claim 4, wherein a step size is set as 0.1 mm×0.1 mm when the point cloud data is interpolated by the Kriging interpolation method in Step 4.