Method for experimentally determining the conductivity of unpropped fracture in hydraulic fracturing of shale reservoir

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;
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• 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.