| CPC G01N 23/046 (2013.01) [G01N 15/0806 (2013.01); G01N 15/082 (2013.01); G01N 23/083 (2013.01); G01N 33/24 (2013.01); G01N 2223/04 (2013.01); G01N 2223/419 (2013.01); G01N 2223/616 (2013.01)] | 7 Claims |
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1. A method for measuring the relative permeability of propped fractures in shale considering probability distribution, comprising using a device for measuring the relative permeability of propped fractures in shale considering probability distribution, comprising a displacement system, a CT scanning imaging system and a metering system; wherein
the displacement system comprises a gas cylinder (1), a water pump (5), a booster pump (14), a rock slab holder (8), and a differential pressure sensor (9); the CT scanning imaging system comprises a directional X-ray source (7), an X-ray detector (10), and an X-ray shielding box (16); the metering system comprises a tee, a liquid meter (17), a gas meter (18), an electronic balance (11), and a vacuum pump (23);
an inlet of the rock slab holder (8) is respectively connected with the gas cylinder (1) and the water pump (5) by a pipe, an outlet of the rock slab holder is connected with the liquid meter (17) and the vacuum pump (23) by the tee, and the differential pressure sensor (9) is connected with both ends of the rock slab holder (8); the booster pump (14) is connected with the rock slab holder (8) by the pipe;
the directional X-ray source (7), the X-ray detector (10), the rock slab holder (8), and the electronic balance (11) are all placed in the X-ray shielding box (16), the rock slab holder (8) is placed on the electronic balance (11) and located between the directional X-ray source (7) and the X-ray detector (10);
an inlet of the gas meter (18) is connected with the liquid meter (17), and an outlet of the gas meter is connected to the external atmosphere;
a gas source control valve (2), a gas flow meter (3) and a gas pressure sensor (4) are installed between the gas cylinder (1) and the rock slab holder (8);
the method specifically comprising the following steps:
Step 1: preparing two cuboid shale slabs of the same size, stacking them together, and laying proppants on the contact surface of the stacked slabs to form a whole shale slab;
Step 2: putting the whole shale slab into the rock slab holder (8), applying confining pressure on the upper, lower, left and right sides of the whole shale slab with the booster pump (14), and measuring the mass (denoted as m1) of the whole shale slab with proppant by the electronic balance (11);
Step 3: turning on the directional X-ray source (7), adjusting CT scanning parameters according to a shale rock slab size and a fracture size and determining a set of appropriate scanning parameters;
Step 4: determining the attenuation coefficient of pure substance with the scanning parameters set in Step 3;
filling the rock slab holder (8) with air and pressurizing to a specified fluid pressure acquiring CT projection images of pure air continuously after the pressure is stabilized; averaging multiple projection images to obtain the X-ray projection result of pure air, which is denoted as projection image A; then, conducting the same measurement for the gas and liquid used in relative permeability test and a standard block made of the same material as the proppant respectively to obtain the corresponding X-ray projection results, denoted as projection image B, projection image C and projection image D respectively; then, calculating the difference of attenuation coefficients of pure substances by the following equation;
 where IA, IB, IC and ID are the intensity of each pixel point in the projection images A, B, C and D, respectively; L is the inner length of the holder cavity of the rock slab holder; μair, μgas, μliquid and μproppant stand for the attenuation coefficients of X-ray passing through air, experimental gas, experimental liquid and proppant successively;
Step 5: putting the whole shale slab into the rock slab holder (8), and applying confining pressure on the upper, lower, left and right sides of the slab with the booster pump (14); injecting air and pressurizing to the fluid pressure p required for the relative permeability experiment;
acquiring the CT projection images continuously after the pressure is stabilized, averaging multiple projection images to obtain the X-ray projection result of the rock slab, denoted as projection image E;
Step 6: calculating the porosity and pore volume in the propped fractures of the shale rock slab;
 where L is the inner length of the holder cavity of the rock slab holder; ϕ is the porosity; IE is the intensity of each pixel point in the projected image E;
 where A is the area of a single pixel in the projection image; ϕj is the calculated porosity at each pixel point; Vp is the pore volume in the propped fracture;
Step 7: turning on the directional X-ray source (7) and recording projected images per second; adjusting the flow rates of the flow meter (3) and the water pump (5), injecting gas and water into the whole shale slab in a certain proportion, and recording the following data per second for a period of time: projection image of the whole shale slab, the gas rate qs at the holder outlet, the water rate qw, pressure p1 at the holder inlet, the pressure difference Δp between the two ends of the whole shale slab, and the value m of the electronic balance; maintaining the injection process of each ratio for the same time and changing another ratio until the gas volume ratio drops to 0;
Step 8: calculating the saturation and permeability at each moment under various gas-water injection ratio; wherein
the water saturation at each pixel point in the projection image at each moment is calculated by the following equation:
 the overall average water saturation in the fracture is calculated by the following equation:
 the mass of water imbibed into matrix is calculated by the following equation:
 effective permeabilities of gas and water at corresponding time are calculated by the following equation:
 where, Kge is the effective permeability of gas; Kwe is the effective permeability of liquid; pa is atmospheric pressure; p1 is the pressure at the inlet; qg is gas flow rate; qw is liquid flow rate; l is the length of propped fracture; A is the sectional area of the fracture; μg and μw are gas and liquid viscosity at the test temperature and pressure, respectively;
the relative permeabilities of gas and water are calculated by the following equation:
 where, Kg is the effective permeability of pure gas; krg and krw are the relative permeability of gas and water respectively; and
Step 9: calculating a fracture relative permeability curve considering the probability distribution according to the saturation and permeability at each time;
wherein Step 9 specifically comprises:
Step 91: counting the gas phase relative permeability value Krg under the same water saturation sw at all times, and working out a frequency distribution histogram of Krg; calculating the gas relative permeability values corresponding to a Rth percentile; similarly, working out the water relative permeability values corresponding to the Rth percentile;
Step 92: repeating Step 91 with different water saturation sw and counting the relative permeability values of gas and water phases corresponding to each Rth percentile at different water saturations; and
Step 93: based on the relative permeability values of gas and water phases corresponding to different water saturations under the same Rth percentile, obtaining the fracture relative permeability curve considering probability distribution.
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