CN114622905B - System and method for testing conductivity of low concentration proppants - Google Patents
System and method for testing conductivity of low concentration proppants Download PDFInfo
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- 238000012360 testing method Methods 0.000 title claims abstract description 95
- 238000000034 method Methods 0.000 title claims abstract description 48
- 239000012530 fluid Substances 0.000 claims abstract description 58
- 239000003795 chemical substances by application Substances 0.000 claims description 125
- 239000011435 rock Substances 0.000 claims description 23
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- 208000010392 Bone Fractures Diseases 0.000 description 69
- 206010017076 Fracture Diseases 0.000 description 69
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 27
- 239000006004 Quartz sand Substances 0.000 description 26
- 229910001220 stainless steel Inorganic materials 0.000 description 11
- 239000010935 stainless steel Substances 0.000 description 11
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- 230000008569 process Effects 0.000 description 9
- 229910000619 316 stainless steel Inorganic materials 0.000 description 8
- 229910052782 aluminium Inorganic materials 0.000 description 8
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 8
- 239000011888 foil Substances 0.000 description 8
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 8
- 239000012153 distilled water Substances 0.000 description 7
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- 239000004215 Carbon black (E152) Substances 0.000 description 2
- 208000013201 Stress fracture Diseases 0.000 description 2
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—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
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- E—FIXED CONSTRUCTIONS
- E21—EARTH OR ROCK DRILLING; MINING
- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/25—Methods for stimulating production
- E21B43/26—Methods for stimulating production by forming crevices or fractures
- E21B43/267—Methods for stimulating production by forming crevices or fractures reinforcing fractures by propping
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Abstract
The invention discloses a system and a method for testing the flow conductivity of a low-concentration propping agent, and belongs to the technical field of propping agent flow conductivity testing. The technical proposal is as follows: the method comprises the steps of putting propping agents into an upper core and a lower core with arched end faces, and then packaging a simulated propping crack by using a cushion block with a filter screen on one side and a thermal shrinkage sleeve; the method comprises the steps of optimizing a high-pressure core holder, a high-pressure confining pressure pump with a worm and gear labor-saving transmission system and a differential pressure sensor with a proper range, and assembling a test flow; injecting test fluid into the support fracture model, obtaining fluid flow pressure difference and flow parameters under set closing pressure, and calculating the flow conductivity of the support fracture; the propping fracture opening is calculated based on the equivalent volume. The invention not only makes up the testing limitation of the existing proppant diversion capability testing system and method, but also widens the testing limit, reduces the configuration difficulty of the testing device, and more importantly greatly reduces the testing cost.
Description
1.1 Technical field
The invention relates to the technical field of proppant diversion capability test, in particular to a system and a method for testing diversion capability of a low-concentration proppant.
1.2 Background art
Propping agent is a key material for fracturing construction, and is used for supporting cracks, preventing the cracks from closing and keeping the high flow conductivity of the cracks. Proppant conductivity testing is a main way to evaluate proppant performance, optimize proppant application schemes, and recognize and understand proppant conductivity change rules under reservoir conditions. With the continuous development of the propping agent technology, the propping agent not only can effectively prop the main fracture of the artificial fracturing, but also can enter the secondary fracture and the natural micro fracture to generate propping. The main fracture and other fracture proppant placement conditions differ by: the propping agent in the main fracture has large particle size and high laying concentration; the propping agent in the secondary cracks and the microcracks has small particle size and low laying concentration. In order to better understand and understand the proppant conductivity in the secondary cracks and the microcracks, the research of the low-concentration proppant conductivity test method is significant, wherein the concentration range of the low-concentration proppant is the sand paving concentration corresponding to the filling thickness of less than or equal to 2mm, namely <0.2ρ vg/cm2,ρv is the volume density, and g/cm 3.
Under the current situation, there are 2 main methods for testing the flow conductivity, namely, the test method using the recommended standard flow guiding chamber as the main body for simulating the supporting crack: the standard diversion chamber is an experimental device for simulating a supporting crack recommended by SY/T6302-2019 industry standard, and consists of an upper piston, a lower piston, an experimental table, a metal filter screen and the like, wherein the laying area of a diversion cavity propping agent formed by the upper piston, the lower piston and the experimental table is 64.5cm 2; secondly, the test method of using the artificial fracture core as a supporting fracture simulation main body comprises the following steps: selecting a reservoir rock sample or an outcrop rock sample, preparing the rock sample with a rough fracture surface by using a manual fracturing and joint making method, simulating a subsurface propping fracture by filling a propping agent or sliding combination, and obtaining the diversion capacity of the propping fracture by using a propping fracture model fluid flow experiment. Although the methods are feasible, the application limit and the application limit exist, and the test method established based on the standard diversion chamber is easy to cause the problems of blockage of the pressure measuring end, the inlet end and the outlet end or fluid bypass in the experimental process of the standard diversion chamber under the condition of low concentration of propping agent, so that the diversion capability of the propping agent cannot be obtained effectively; the test method established based on the artificial fracture core method has the following problems: firstly, the roughness of the crack wall surface is uncontrollable, so that the test result is large in difference and unstable; secondly, the low pressure bearing capacity of the conventional core holder and the confining pressure pump leads to a narrow closing pressure test range, and the problem of low closing pressure can be solved by introducing a large loading system, but the experimental device is difficult to assemble and inconvenient; thirdly, the application limitation that the opening degree of the supporting crack cannot be represented exists.
At present, the method for testing the flow conductivity of the proppants has more researches: the invention patent with application publication number of CN 110608037A and patent number of CN 107806339B establishes a proppant diversion capacity evaluation method considering the influence of crack wall morphology and proppant distribution conditions on the diversion capacity of the proppant based on a standard diversion chamber; the invention patent with application publication numbers of CN 104295281A and CN 104295281 sets a fracture network model formed by combining a metal plate, a metal patch or a rock plate and a propping agent into a standard diversion chamber, and establishes a fracture diversion capability test method under the condition of complex fracture network; the invention patent number CN 110593842B sets up a self-supporting crack flow conductivity test method by placing an artificial rock plate into a standard flow guide chamber through a self-supporting crack model formed by shearing and sliding, but in the test process, particularly when the opening of a supporting crack is narrower, the problems that the standard flow guide chamber is easy to generate an inlet and outlet end, a pressure measuring port is blocked, fluid flows around the gap between the rock plate and the inner wall of the flow guide chamber and the like cannot be effectively conducted. The invention with the application publication number of CN 113029898A establishes a self-supporting fracture conductivity test method based on a designed square core holder, and has the problems that the closing pressure test range is narrow, and the fracture opening cannot be characterized; the invention patent with the application publication number of CN 111103222A establishes a self-supporting fracture conductivity test based on a cylindrical core sample by using a triaxial tester, the invention patent with the application publication number of CN 113295537A establishes an unconventional reservoir fracturing fracture permeability evaluation method considering the water rock effect based on a cylindrical core sample by using an MTS rock mechanical test system, and the problem of narrow closing pressure test range is solved due to the introduction of a large loading system, but the problem that the opening of a supporting fracture cannot be characterized still exists, and the large loading system limits the application popularity of the device.
In summary, the proppant conductivity testing method based on the standard diversion chamber or the artificial core sample at present has some defects in the low-concentration proppant conductivity test, and is difficult to develop the proppant application scheme optimization in the secondary fracture and the microcrack conveniently, stably and effectively.
1.3 Summary of the invention
The invention aims to solve the technical problems that: the system and the method for testing the flow conductivity of the low-concentration propping agent can effectively solve the problems that the pressure measuring end and the inlet and outlet ends of a standard flow guide chamber are blocked or fluid flows around, and simultaneously can effectively solve the problems that the flow conductivity difference of the propping agent is large and the flow conductivity of the propping agent in the deep part of the fracture, the secondary fracture and the micro fracture cannot be represented due to uncontrollable roughness of the core wall surface of the artificial fracture, and effectively improve the understanding and understanding of the flow conductivity of the propping agent in the fracture.
In one aspect, the invention provides a system for testing the conductivity of a low-concentration propping agent, which comprises a core holder, wherein the core holder is internally provided with a core; the inlet of the core holder is connected with a constant flow pump through a pipeline, the outlet of the core holder is communicated with a fluid container through a pipeline, and the fluid container is arranged on a precision balance; the side wall of the core holder is connected with a confining pressure pump through a pipeline; a differential pressure sensor is also connected between the inlet and the outlet of the core holder; the rock core comprises an upper rock core and a lower rock core which are symmetrically arranged, and propping agents are paved between the upper rock core and the lower rock core; the contact surfaces of the upper core and the lower core with the propping agent are rectangular, and two end surfaces of the upper core and the lower core, which are perpendicular to the contact surfaces, are arched; the two ends of the core are respectively provided with a cushion block, the center of each cushion block is provided with a through hole, and a filter screen is arranged at the position, close to the through hole, of one side surface of the core, of each cushion block. The filter screen is used for blocking propping agent between the upper core and the lower core when fluid can enter, so that the propping agent cannot flow into the fluid channel along the flowing direction of the fluid.
Preferably, the core holder further comprises an intermediate container, wherein the inlet of the intermediate container is connected with the outlet of the constant flow pump through a pipeline, and the outlet of the intermediate container is connected with the inlet of the core holder through a pipeline; valves are respectively arranged on the pipeline between the constant flow pump and the core holder, the pipeline between the constant flow pump and the intermediate container, the pipeline between the intermediate container and the core holder and the pipeline between the outlet of the core holder and the fluid container.
Preferably, a screw rod in the working cylinder of the confining pressure pump is connected with the handle through a worm wheel and a worm.
Preferably, the range of the differential pressure sensor is selected by a differential pressure estimation formula, wherein the differential pressure estimation formula is:
Wherein Δp is the estimated differential pressure, pa; mu is the viscosity of the fluid, pa.s; q is fluid flow, m 3/s; τ is the tortuosity of the seepage channel of the propping agent layer, the value is taken according to the particle size of propping agent, the larger value of the particle size is lower, otherwise, the value is higher, and the value range is 1.5-5.5; M is the length of the support fracture model; w f is the width of the propping fracture model, m; h f Estimation of is the estimated crack opening, m;
Wherein, h f Estimation of can be calculated according to the porosity change, and the calculation formula is:
，；
Wherein phi is the porosity of the propping agent at different closing pressures, and the fraction; p is closing pressure, MPa; alpha is a constant, the compressive strength of the propping agent is high, the compressive strength is low, and conversely, the compressive strength is high, and the value range is 0.010-0.027; c s is proppant placement concentration, g/cm 2;ρs is proppant apparent density, g/cm 3;ρv is proppant bulk density, g/cm 3.
In another aspect, the present invention provides a method for testing the conductivity of a low concentration proppant using the above system, comprising the steps of:
S1: paving propping agent between an upper core and a lower core, assembling upper cushion blocks at two ends of the core to form a supporting crack model, and putting the supporting crack model into a core holder; loading the confining pressure to a closing pressure value, and obtaining fluid flow pressure difference and fluid flow parameters under the closing pressure value;
S2: and calculating the conductivity of the low-concentration propping agent by using a Darcy formula in combination with the geometric dimension of the propping fracture model, wherein the Darcy formula is as follows:
wherein kh f is the flow conductivity of the propping agent, um 2 cm; q is the fluid flow, cm 3/min;wf is the width of the propped fracture model, cm; h f is the opening degree of the support crack model, cm; Δp is the flow differential, kpa; mu is the viscosity of the fluid, mpa.s; To support the length of the fracture model, cm.
Preferably, the method further comprises a characterization step S31 of the opening degree of the propping fracture: based on capillary seepage model, calculating equivalent capillary radius and corresponding pore volume of the proppant layer by using poise She Gongshi:
Wherein r p is equivalent capillary radius, cm; mu is viscosity, pa.s; The length of the crack model is supported by cm; q is the fluid flow, cm 3/s; Δp is the test differential pressure, pa; v p is the pore volume of the proppant layer, mL;
s32: the volume density and apparent density of the propping agent are obtained by using the precise zenith and the fluid container, and then the volume of the propping fracture skeleton is calculated:
Wherein, C s is the proppant placement concentration, g/cm 2;ρv is the proppant bulk density, g/cm 3;Vs is the proppant skeleton volume in the proppant layer, and mL; w f is the width of the support fracture model, cm; The length of the crack model is supported by cm; ρ s is proppant apparent density, g/cm 3;
S33: calculating the opening degree of the propping fracture of the propping agent under different closing pressures:
Wherein h f is the opening degree of the supporting crack, cm; v p is the pore volume of the proppant layer, mL; v s is proppant skeleton volume in the proppant layer, mL; w f is the width of the support fracture model, cm; To support the length of the fracture model, cm.
Compared with the prior art, the invention has the following beneficial effects:
The test system for simulating the supporting crack by the circular arc column core and the cushion block can effectively solve the problem that the pressure measuring end and the inlet and outlet end of a standard diversion chamber are blocked or fluid flows around, and meanwhile, can effectively solve the problem that the diversion capacity difference of propping agents is large due to uncontrollable roughness of the core wall surface of the manual splitting crack, and effectively improves the understanding and understanding of the diversion capacity of propping agents in deep parts of the crack, secondary cracks and micro cracks. The core holder and the high-pressure confining pressure pump with the worm and gear labor-saving transmission system solve the problems of narrow testing range, complicated loading system and inconvenience caused by low pressure range of the conventional core holder and loading system. By adopting the method, the dependence degree of large-scale loading systems such as a pressure testing machine or a triaxial testing machine can be effectively reduced, the convenience of the testing process of the flow conductivity of the propping agent is improved, and the testing cost of the flow conductivity of the propping agent is reduced. The propping crack opening characterization method can effectively obtain propping crack opening in the test process, effectively describe the change rule of propping cracks of propping agents, and solve the problem that propping crack opening can not be monitored in the test process of fully sealing the sample. 1.4 description of the drawings
Fig. 1 is a schematic diagram of the system of the present invention.
Fig. 2 is a schematic structural view of a core according to the present invention.
Fig. 3 is a front view of the spacer of the present invention.
In the figure, a 1-core holder, a 2-constant flow pump, a 3-fluid container, a 4-precision balance, a 5-confining pressure pump, a 6-differential pressure sensor, a 7-upper core, an 8-lower core, a 9-propping agent, a 10-cushion block, 11-through holes, a 12-intermediate container, 13-valves and 14-grooves are arranged.
1.5 Detailed description of the invention
The proppant conductivity is the product of the permeability of the proppant pack and the opening of the propping fracture and is used to describe the flow capacity of the hydrocarbon-bearing percolation path in the hydrocarbon reservoir. The proppant conductivity under different conditions obtained through experimental tests has the following significance: firstly, the method is used for optimizing the proppant application scheme in the fracturing construction design; secondly, the method is used for optimizing the production system of the reservoir after hydraulic fracturing of the reservoir; third, the proppant performance was evaluated.
The propping crack opening degree refers to the relative distance between two crack walls in the direction perpendicular to the crack walls, and is an important parameter for quantitatively describing the fracturing crack. The propping crack opening obtained through experimental tests has the following significance: firstly, on the basis of the flow conductivity of the propping agent, the permeability of the propping agent filling layer is obtained; and secondly, the method is used for quantitatively describing the change process and the rule of the fracturing fracture under the oil reservoir condition.
The invention discloses a system for testing the flow conductivity of a low-concentration propping agent, wherein the low-concentration propping agent is the sand-spreading concentration which is lower than the proppant filling thickness by less than or equal to 2mm, namely <0.2ρ vg/cm2,ρv is the volume density, g/cm 3. Referring to fig. 1, the system comprises a core holder 1, wherein the core holder 1 contains a core; the inlet of the core holder 1 is connected with a constant flow pump 2 through a pipeline, the outlet is communicated with a fluid container 3 (such as a measuring cylinder) through a pipeline, and the fluid container 3 is arranged on a precision balance 4; the side wall of the core holder 1 is connected with a confining pressure pump 5 through a pipeline; a differential pressure sensor 6 is also connected between the inlet and the outlet of the core holder 1; the rock core comprises an upper rock core 7 and a lower rock core 8 which are symmetrically arranged, and a propping agent 9 is paved between the upper rock core 7 and the lower rock core 8; the contact surfaces of the upper core 7 and the lower core 8 and the propping agent 9 are rectangular, and two end surfaces of the upper core 7 and the lower core 8, which are perpendicular to the contact surfaces, are arched; two ends of the core are respectively provided with a cushion block 10, a through hole 11 is formed in the center of each cushion block 10, and a filter screen is arranged on one side surface, close to the core, of each cushion block 10.
According to the size of the test closing pressure, a proper core holder 1 and a high-range confining pressure pump 5 with a worm and gear labor-saving transmission system can be selected, and a screw rod in a working cylinder of the confining pressure pump 5 is connected with a handle through a worm gear and a worm. When the electric hydraulic pump is used for driving the surrounding pump, the electric hydraulic pump system is too large, the occupied area is large and the cost is high; when the manual confining pressure pump is used, the manual pressure can not reach 69MPa, so that the confining pressure pump overcomes the defects of the two modes, the electric hydraulic pump system is abandoned, and the manual closing pressure can reach 69MPa on the premise of saving labor.
Wherein, utilize the speed reduction ratio formula to calculate worm gear transmission system's speed reduction ratio i:
Wherein i is a reduction ratio, and is dimensionless; p p is confining pressure, pa; d p is the diameter of the plunger of the confining pressure pump, m; The lead of the lead screw is mm; f is the applied force, N; r is the radius of the hand wheel, mm; η is the transmission efficiency, decimal.
And selecting a constant flow pump with the flow range of 1-10mL/min, estimating the pressure difference according to parameters such as the volume density of the propping agent, the apparent density, the laying concentration of the propping agent, the test closing pressure and the like, and optimizing the measuring range of the sensor. The differential pressure sensor selected empirically can cause flow differential pressure to exceed a measuring range during experiments, or the flow differential pressure can not be accurately obtained due to overlarge measuring range. Therefore, the differential pressure estimation method overcomes the defect of selection mode based on experience, provides the selection basis of the measuring range of the differential pressure sensor, and can ensure the accuracy of flow differential pressure test within the accuracy range of the differential pressure sensor.
Wherein the differential pressure Δp is estimated using a differential pressure estimation formula:
Wherein Δp is the estimated differential pressure, pa; mu is viscosity, pa.s; q is fluid flow, m 3/s; τ is the tortuosity of the seepage channel of the propping agent layer, the value is taken according to the particle size of propping agent, the larger value of the particle size is lower, otherwise, the value is higher, and the value range is 1.5-5.5; M is the length of the support fracture model; w f is the width of the propping fracture model, m; h f Estimation of is the estimated crack opening, m.
Wherein, h f Estimation of can be calculated according to the porosity change, and the calculation formula is:
，
Wherein phi is the porosity of the propping agent at different closing pressures, and the fraction; p is closing pressure, MPa; alpha is a constant, the compressive strength of the propping agent is high, the compressive strength is low, and conversely, the compressive strength is high, and the value range is 0.010-0.027; c s is proppant placement concentration, g/cm 2;ρs is proppant apparent density, g/cm 3;ρv is proppant bulk density, g/cm 3.
Referring to fig. 2, a standard cylindrical core sample of Φ25x50-80 mm is prepared from 316 stainless steel or natural outcrop core, cut along the axial section, and cut into circular-arc column cores with complete symmetry up and down, the chord length L of the end face bow is 23.9-24.8mm, and the height H of the bow arc is 8.9-11.0mm.
Referring to fig. 3, two Φ25x10-20 mm packing pads 10, in which stainless steel screens can be placed, were prepared using 316 stainless steel for supporting the packing of the end faces of the crack mold. A groove 14 is formed in the surface, close to the core, of the cushion block 10, and a filter screen is placed in the groove 14.
Preparing a low-concentration propping agent propping crack model by using an aluminum foil tape and a heat shrinkage film:
(1) Aligning the lower core 7 with two cushion blocks 10 provided with stainless steel filter screens by using an aluminum foil tape to form a propping agent cavity;
(2) And adding a propping agent 9 into the propping agent cavity, covering the core 7, and then sleeving a heat shrinkage film for packaging, so that the propping crack model with the low-concentration propping agent is prepared.
Finally, referring to fig. 1, the test system of the present invention is assembled to construct a flow of low concentration proppant conductivity test.
The system of the invention further comprises an intermediate container 12, wherein the inlet of the intermediate container 12 is connected with the outlet of the constant flow pump 2 through a pipeline, and the outlet of the intermediate container 12 is connected with the inlet of the core holder 1 through a pipeline; valves 13 are respectively arranged on the pipelines between the constant flow pump 2 and the core holder 1, between the constant flow pump 2 and the intermediate container 12, between the intermediate container 12 and the core holder 1 and between the outlet of the core holder 1 and the fluid container 3.
The intermediate container 12 is used for pumping special liquid (such as fracturing fluid gel breaking liquid, etc.) which cannot be directly pumped by the constant flow pump 2 into the core holder 1. If the fluid is distilled water, the fluid can be directly pumped into the core holder 1 along a pipeline by the constant flow pump 2 without passing through the intermediate container 12; when the fluid is special liquid, valves at two ends of the intermediate container 12 are required to be opened, valves on the distilled water pipeline are required to be closed, distilled water is pumped into the lower end space of the intermediate container 12 through the constant flow pump 2, and therefore the special liquid at the upper end is pushed into the core holder 1.
Based on the above work, the fluid flow experiment of the low-concentration propping agent propping fracture model is used for obtaining the flow parameters of the test liquid layer under the flowing seepage, and the current conductivity of the low-concentration propping agent is calculated by using the Darcy formula, and the specific operation is as follows:
s1: placing the low-concentration propping agent propping fracture model into a core holder shown in fig. 1, and loading a confining pressure 1MPa fixed sample; starting a constant flow pump to inject test liquid, and discharging air of the differential pressure sensor and the test system; loading confining pressure to a closed pressure value, and obtaining parameters such as fluid flow pressure difference, flow and the like of a support fracture model under the closed pressure;
S2: and calculating the diversion capacity of the low-concentration propping agent by using a Darcy formula in combination with the geometric dimension of the low-concentration propping agent propping fracture model, wherein the Darcy formula is as follows:
wherein kh f is the flow conductivity of the propping agent, um 2 cm; q is the fluid flow, cm 3/min;wf is the width of the propped fracture model, cm; h f is the opening degree of the support crack model, cm; Δp is the flow differential, kpa; mu is the viscosity of the fluid, mpa.s; To support the length of the fracture model, cm.
The method further comprises a characterization step S31 of the opening degree of the supporting crack: based on capillary seepage model, calculating equivalent capillary radius and corresponding pore volume of the proppant layer by using poise She Gongshi:
Wherein r p is equivalent capillary radius, cm; mu is viscosity, pa.s; The length of the crack model is supported by cm; q is the fluid flow, cm 3/s; Δp is the test differential pressure, pa; v p is the pore volume of the proppant layer, mL;
s32: the volume density and apparent density of the propping agent are obtained by using the precise zenith and the fluid container, and then the volume of the propping fracture skeleton is calculated:
Wherein, C s is the proppant placement concentration, g/cm 2;ρv is the proppant bulk density, g/cm 3;Vs is the proppant skeleton volume in the proppant layer, and mL; w f is the width of the support fracture model, cm; The length of the crack model is supported by cm; ρ s is proppant apparent density, g/cm 3;
S33: calculating the opening degree of the propping fracture of the propping agent under different closing pressures:
Wherein h f is the opening degree of the supporting crack, cm; v p is the pore volume of the proppant layer, mL; v s is proppant skeleton volume in the proppant layer, mL; w f is the width of the support fracture model, cm; To support the length of the fracture model, cm.
Example 1
Taking a proppant flow conductivity test of 40/70 mesh quartz sand with a laying concentration as low as 0.16g/cm 2 as an example, the low-concentration proppant flow conductivity test method of the invention is further described, and specifically comprises the following steps:
1. preferred equipment and method for constructing flow conductivity test flow of low-concentration propping agent
(1) When the maximum value of the closing pressure is 69 MPa, a core holder with pressure resistance of 80 MPa and a high-range confining pressure pump with a worm and gear labor-saving transmission system are selected, and parameters such as the diameter of a plunger (25 mm), the lead (10 mm), the radius of a hand wheel (10 cm), the transmission efficiency of the worm and gear (0.6), the applied force (100-200N) and the like of the known confining pressure pump are known according to the formulaThe reduction ratio i=5-10 of the worm and gear transmission system can be calculated;
(2) A constant flow pump with the flow rate range of 1-10 mL/min is selected, the known propping agent has the volume density of 1.632 g/cm 3, the apparent density of 2.646 g/cm 3, the laying concentration of 0.16g/cm 2 and the maximum closing pressure of 69. 69 MPa, the differential pressure under the maximum flow rate is estimated by utilizing a differential pressure estimation formula, and a differential pressure sensor with the measuring range of 200 kPa (mu=1 mpa.s) is preferably selected. The evaluation results are shown in the following table:
(3) The optimized equipment is assembled according to the flow shown in the figure 1, and a flow conductivity testing flow of the low-concentration propping agent is constructed.
2. Preparation of circular-arc column core and cushion block
(1) Preparing a standard cylinder sample with phi 25 multiplied by 50mm by using 316 stainless steel, cutting the standard cylinder sample into an upper core and a lower core which are completely symmetrical in the upper and lower arc columns along the axial section, wherein the chord length L=24.5 mm of the arc shape of the end face, and the height H=10.0 mm of the arc shape;
(2) Two phi 25 multiplied by 20 mm cushion blocks capable of placing a stainless steel filter screen are prepared by using 316 stainless steel, and are placed into a 200-mesh stainless steel filter screen for supporting end face encapsulation of a crack model.
3. Preparation of low-concentration propping agent propping crack model by using aluminum foil adhesive tape and heat shrinkage film
(1) Aligning the lower core with two cushion blocks filled with a stainless steel filter screen by using an aluminum foil tape to form a propping agent cavity;
(2) And uniformly adding 1.96 g and 40/70 meshes of quartz sand propping agent into the propping agent cavity, covering a core, and then covering a heat shrinkage film for packaging to prepare the low-concentration quartz sand propping crack model.
4. Fluid flow experiment of low-concentration quartz sand supporting crack model is utilized to obtain flow parameters of distilled water layer under flowing and seepage conditions, and Darcy formula is utilized to calculate flow conductivity of low-concentration propping agent
(1) Placing the low-concentration quartz sand supporting crack model into a core holder in a test flow, loading a confining pressure 1MPa fixed sample, starting a constant flow pump to inject distilled water, and discharging air of a differential pressure sensor and a test system; loading confining pressure to different preset closing pressure values, bearing pressure for a certain time, and obtaining parameters such as fluid flow pressure difference and flow under the closing pressure;
(2) And calculating the flow conductivity of the propping agent by using a Darcy formula in combination with the geometric dimension of the low-concentration quartz sand propping crack model, wherein the calculation result is shown in the following table:
5. Calculating equivalent capillary radius, pore volume and proppant skeleton volume of the quartz sand proppant layer, and further calculating the opening of the propping crack
(1) Based on capillary seepage model, using poise She Gongshi to calculate equivalent capillary radius and corresponding pore volume of quartz sand propping agent layer, the calculation result is shown in the following table:
(2) The volume density of the quartz sand with 40/70 meshes is 1.632 g/cm 3 and the apparent density is 2.646 g/cm 3, the mass of the quartz sand is 1.96 g, the initial opening degree of the supporting crack is calculated to be 0.098 cm, and the skeleton volume of the quartz sand is 0.741 mL by using a precision balance (precision 0.001 g) and a 100 mL density bottle;
(3) The opening degree of the 40/70 mesh quartz sand supporting crack under different closing pressures is calculated, and the calculation results are shown in the following table:
6. stability analysis of low concentration proppant conductivity test method
For three experimental data of 1.96 g and 40/70 meshes of quartz sand propping agent, the fluctuation of the test is analyzed by using standard deviation, the standard deviation of the three diversion capacity is 0.01-1.03, and the standard deviation of the opening of the three propping cracks is 0.0001-0.0003, which are all relatively stable. The following table shows the standard deviation of the flow conductivity and the opening of the supporting crack obtained by the three tests:
Example 2
Taking a proppant flow conductivity test of 70/140 mesh quartz sand with a laying concentration as low as 0.2g/cm 2 as an example, the low-concentration proppant flow conductivity test method of the invention is further described, and specifically comprises the following steps:
1. preferred equipment and method for constructing flow conductivity test flow of low-concentration propping agent
(1) The method for calculating the worm gear ratio is the same as that of the embodiment 1;
(2) A constant flow pump with the flow rate range of 1-10 mL/min is selected, the volume density of the propping agent is 1.550 g/cm 3, the apparent density is 2.639 g/cm 3, the laying concentration is 0.2g/cm 2, the maximum closing pressure is tested for 69: 69 MPa, the differential pressure under the maximum flow rate is estimated by utilizing a differential pressure estimation formula, and a differential pressure sensor with the measuring range of 300 kPa (mu=1 mpa.s) is preferably selected, wherein the estimation result is shown in the following table:
(3) The optimized equipment is assembled according to the flow shown in the figure 1, and a flow conductivity testing flow of the low-concentration propping agent is constructed.
2. Preparation of circular-arc column core and cushion block
(1) Preparing a standard cylinder sample with phi 25 multiplied by 80 mm by using 316 stainless steel, cutting the standard cylinder sample into an upper core and a lower core which are completely symmetrical in the upper and lower arc columns along the axial section, wherein the chord length L=24.8 mm of the arc shape of the end face, and the height H=11.0 mm of the arc shape;
(2) Two cushion blocks of phi 25 multiplied by 10 mm capable of placing a stainless steel filter screen are prepared by using 316 stainless steel, and are placed into a 200-mesh stainless steel filter screen for supporting end face encapsulation of a crack model.
3. Preparation of low-concentration propping agent propping crack model by using aluminum foil adhesive tape and heat shrinkage film
(1) Aligning the lower core with two cushion blocks filled with a stainless steel filter screen by using an aluminum foil tape to form a propping agent cavity;
(2) And uniformly adding 3.968 g, 70/140 meshes of quartz sand propping agent into the propping agent cavity, covering a core, and then sleeving a heat shrinkage film for packaging to prepare the low-concentration quartz sand propping crack model.
4. Fluid flow experiments of a low-concentration quartz sand supporting crack model are utilized to obtain flow parameters of a distilled water layer under the flowing and seepage condition, and then a Darcy formula is utilized to calculate the flow conductivity of the low-concentration propping agent
(1) Placing the low-concentration quartz sand supporting crack model into a core holder in a test flow, loading a confining pressure 1MPa fixed sample, starting a constant flow pump to inject distilled water, and discharging air of a differential pressure sensor and a test system; loading confining pressure to different preset closing pressure values, bearing pressure for a certain time, and obtaining parameters such as fluid flow pressure difference and flow under the closing pressure;
(2) And calculating the flow conductivity of the propping agent by using a Darcy formula in combination with the geometric dimension of the low-concentration quartz sand propping fracture model, wherein the calculation result is shown in the following table:
5. Calculating equivalent capillary radius, pore volume and proppant skeleton volume of the quartz sand proppant layer, and further calculating the opening of the propping crack
(1) Based on capillary seepage model, using poise She Gongshi to calculate equivalent capillary radius and corresponding pore volume of quartz sand propping agent layer, the calculation result is shown in the following table:
(2) The volume density of the quartz sand with 70/140 meshes is 1.550 g/cm 3 and the apparent density is 2.639 g/cm 3 by using a precision balance (precision is 0.001 g) and a 100 mL density bottle, the mass of the quartz sand is 3.968 g, the initial opening of the supporting crack is calculated to be 0.129 cm, and the skeleton volume of the quartz sand is 1.504 mL;
(3) The opening degree of the quartz sand supporting crack of 70/140 meshes under different closing pressures is calculated, and the calculation results are shown in the following table:
6. stability analysis of low concentration proppant conductivity test method
(1) For three experimental data of 3.968 g and 70/140 meshes of quartz sand propping agents, the standard deviation is utilized to analyze the fluctuation of the test, the standard deviation of the three diversion capacity is 0.02-0.13, the standard deviation of the opening degree of the three propping cracks is 0.0002-0.0007, and the three experimental data are all relatively stable. The following table shows the standard deviation of the flow conductivity and the opening of the supporting crack obtained by the three tests:
Example 3:
Taking a proppant conductivity test with 30/50 mesh ceramsite fluid with a laying concentration as low as 0.1g/cm 2 as a supernatant fluid of a fracturing fluid gel breaking liquid (viscosity mu= mpa.s) as an example, the method for testing the conductivity of the low-concentration proppant of the invention is further described, and specifically comprises the following steps of:
1. The method comprises the following steps of (1) optimizing equipment, and constructing a low-concentration propping agent flow conductivity testing flow:
(1) The method for calculating the worm gear ratio is the same as that of the embodiment 1;
(2) A constant flow pump with the flow rate range of 1-10 mL/min is selected, the volume density of the propping agent is 1.660 g/cm 3, the apparent density is 3.059 g/cm 3, the laying concentration is 0.1 g/cm 2, the maximum closing pressure is tested to be 69 MPa, the differential pressure under the maximum flow rate is estimated by utilizing a differential pressure estimation formula, and a differential pressure sensor with the measuring range of 50 kPa (mu=3 mpa.s) is preferably selected. The evaluation results are shown in the following table:
(3) The optimized equipment is assembled according to the flow shown in the figure 1, and a flow conductivity testing flow of the low-concentration propping agent is constructed.
2. Preparation of circular-arc column core and cushion block
(1) Preparing a standard cylinder sample with phi 25 multiplied by 80 mm by using 316 stainless steel, cutting the standard cylinder sample into an upper core and a lower core which are completely symmetrical in the upper and lower arc columns along the axial section, wherein the chord length L=24.8 mm of the arc shape of the end face, and the height H=11.0 mm of the arc shape;
(2) Two cushion blocks of phi 25 multiplied by 10 mm capable of placing a stainless steel filter screen are prepared by using 316 stainless steel, and are placed into a 200-mesh stainless steel filter screen for supporting end face encapsulation of a crack model.
3. Preparation of low-concentration propping agent propping crack model by using aluminum foil adhesive tape and heat shrinkage film
(1) Aligning the lower core with two cushion blocks filled with a stainless steel filter screen by using an aluminum foil tape to form a propping agent cavity;
(2) Uniformly adding 1.984 g and 30/50 meshes of ceramsite propping agent into the propping agent cavity, covering a core, and then covering a heat shrinkage film for packaging to prepare the low-concentration ceramsite propping crack model.
4. Fluid flow experiments of a low-concentration ceramsite supporting crack model are utilized to obtain flow parameters of a fracturing fluid gel breaking liquid supernatant (viscosity mu=3 mpa & s) under laminar flow seepage, and then a Darcy formula is utilized to calculate the diversion capacity of a low-concentration propping agent
(1) Placing the low-concentration ceramsite supporting crack model into a core holder in a test flow, adding a fracturing fluid gel breaking liquid supernatant into an intermediate container, opening a channel valve of the intermediate container, closing a bypass valve of the intermediate container, loading a confining pressure 1MPa fixed sample, starting a constant flow pump, injecting liquid, and discharging air of a differential pressure sensor and a test system; loading confining pressure to different preset closing pressure values, bearing pressure for a certain time, and obtaining parameters such as fluid flow pressure difference and flow under the closing pressure;
(2) And calculating the flow conductivity of the low-concentration ceramsite by using a Darcy formula in combination with the geometric dimension of the support crack model, wherein the calculation result is shown in the following table:
5. calculating equivalent capillary radius, pore volume and proppant skeleton volume of the ceramic proppant layer, and further calculating the opening of the propping crack
(1) Based on a capillary seepage model, calculating equivalent capillary radius and corresponding pore volume of the ceramic proppant layer by using a poise She Gong formula, wherein the calculation results are shown in the following table:
(2) The 30/50 mesh ceramsite is obtained by a precision balance (precision 0.001 g) and a 100 mL density bottle, the volume density is 1.660 g/cm 3 and the apparent density is 3.059 g/cm 3, the mass of the ceramsite is known to be 1.984/g, the initial opening of a supporting crack is calculated to be 0.060 cm, and the framework volume of the ceramsite is 0.649 mL;
(3) The opening degree of 30/50 mesh ceramsite supporting cracks under different closing pressures is calculated, and the calculation results are shown in the following table:
comparative example 1
For 20/40 mesh haydite, comparing the artificial crack core method with the proppant conductivity testing method under the condition that the paving concentration is as low as 0.1g/cm 2, the low-concentration proppant conductivity testing method is further described, and specifically comprises the following steps:
1. preferred equipment and method for constructing flow conductivity test flow of low-concentration propping agent
According to the method, according to parameters such as the volume density of the 20/40 mesh ceramsite (1.54 g/cm 3), the apparent density (2.68 g/cm 3), the laying concentration of the propping agent (0.1 g/cm 2), the test closing pressure (69 MPa), the plunger diameter (25 mm), the lead (10 mm), the efficiency of a transmission system (0.6), the radius of a hand wheel (10 cm), the applied force (100-200N) and the like, the labor-saving high-range confining pressure pump (80 MPa, the reduction ratio of 5-10) and the pressure difference sensor with the range of 10 KPa can be optimized, so that the flow conductivity of the propping agent in the high closing pressure range can be accurately measured.
In the manual fracture core method, due to the lack of a speed reducing system, the confining pressure pump for simulating the closing pressure can only be loaded to 40MPa, and the diversion capability test under the condition of high closing pressure (> 40 MPa) can not be tested; and because of lacking corresponding differential pressure estimation, a differential pressure sensor with a proper measuring range cannot be effectively selected, and the problem of inaccurate differential pressure test caused by exceeding the testing measuring range or overlarge measuring range in the testing process possibly exists, so that the accuracy of test data of the differential pressure sensor is limited.
2. Preparation of low concentration proppant propping fracture model
In the method, the propping agent crack model has a simulated crack wall surface and an end surface cushion block with fixed and uniform roughness, can be repeatedly and uniformly paved with propping agent, can prevent the propping agent from moving towards the end surface under high closing pressure, and ensures the stability and the repeatability of the propping agent crack model.
In the artificial fracture core method, the roughness of the fracture wall surface is uncontrollable, no packaging cushion block is arranged, the laying state of the propping agent is uncontrollable and unrepeatable, the propping agent cannot be prevented from moving to the end surface under high closing pressure, and the limitations of instability and unrepeatable propping agent fracture model exist.
3. Calculation of low concentration proppant conductivity
In the method, under the condition that the closing pressure is 69MPa, the standard deviation of the three test results of the flow conductivity of the low-concentration propping agent is 0.03, the stability is good, the more accurate flow conductivity of propping agent cracks can be obtained, and the change rule analysis of the flow conductivity of the propping agent can be well developed.
In the manual fracture core method, the closing pressure can only be loaded to 40MPa difficultly and cannot be higher any more, and the standard deviation of the three-time test result of the flow conductivity of the low-concentration propping agent is larger and is 5.67, so that the stability is poor. The method can not obtain the flow conductivity of the propping agent under the condition of high closing pressure, and can not effectively conduct regular analysis of the flow conductivity of the propping agent.
4. Low concentration propping agent propping fracture opening
In the method, a calculation method of the opening degree of the propping crack is provided, the opening degree of the propping crack under different closing pressure conditions can be obtained, the stability is good, the change rule of the fracturing crack can be quantitatively described, and the permeability of the propping crack can also be obtained.
In the artificial fracture core method, no corresponding characterization method exists, the opening parameters of the propping fracture cannot be obtained, the change rule of the fracturing fracture cannot be quantitatively described, and the permeability of the propping fracture cannot be obtained.
Comparative example 2
For 40/70 mesh ceramsite, the flow conductivity test method of the low-concentration propping agent is further described by comparing the flow conductivity tests of different circular arc column core propping agents under the condition that the paving concentration is as low as 0.1g/cm 2, and specifically comprises the following steps:
1. Core sizes of different circular arc columns
According to parameters such as 40/70 mesh ceramsite volume density (1.60 g/cm 3), apparent density (3.18 g/cm 3), proppant laying concentration (0.1 g/cm 2), test closing pressure (69 MPa), plunger diameter (25 mm), lead (10 mm), transmission system efficiency (0.6), hand wheel radius (10 cm), applied force (100-200N) and the like, a labor-saving high-range confining pressure pump and a pressure difference sensor are preferably selected, and a low-concentration proppant diversion capability test flow is constructed:
2. Preparation of low concentration proppant propping fracture model
Weighing 1.195 g of 40/70 mesh ceramsite and preparing a low-concentration propping agent supporting crack model by the model; weighing 1.165 g of 40/70 mesh ceramsite and other models to prepare the low-concentration propping agent propping crack model.
3. Proppant conductivity calculation of support fracture model prepared by different circular-arc column cores
As can be seen from the comparison of the data, the circular arc column core model and the low-concentration propping agent supporting crack model prepared from 1.195 g of 40/70 mesh ceramsite: under the same closing pressure and flow, the three-time test flow pressure difference is relatively stable, the pressure difference change trend in each test process is relatively stable, and the pressure difference is increased along with the increase of the closing pressure and accords with a theoretical rule, so that the circular arc column core model can obtain relatively stable proppant diversion capability.
Other circular arc column core models and a low-concentration propping agent supporting crack model prepared from 1.165 g of 40/70 mesh ceramsite: under the same closing pressure and flow rate, the fluctuation of the differential pressure of the three-time test flow is larger (except 6.9 MPa), the fluctuation of the differential pressure variation trend in each test process is larger, the differential pressure is sometimes increased and sometimes decreased along with the increase of the closing pressure, and the differential pressure does not accord with the theoretical rule, so that the circular arc column core model cannot obtain the relatively accurate proppant diversion capability.
4. Calculation of opening degree of propping cracks of propping agents of different core models
The equivalent capillary radius, the pore volume and the propping crack opening degree of the arc column core model and the low-concentration propping crack model prepared from the 1.195 g 40/70 mesh ceramsite show a decreasing trend along with the increase of the closing pressure, and are consistent with a theoretical rule, so that the arc column core model can obtain the accurate propping crack opening degree.
The overall trend of the equivalent capillary radius, the pore volume, the propping fracture opening and other parameter values of other circular arc column core models and a low-concentration propping fracture model prepared from the 40/70 mesh ceramsite is that the equivalent capillary radius, the pore volume, the propping fracture opening and other parameter values are reduced along with the increase of the closing pressure, but the phenomenon of increasing occurs at certain closing pressure points, such as the first 6.9MPa to 13.8MPa, the equivalent capillary radius is increased from 0.025cm to 0.026cm, the pore volume is increased from 0.01cm 3 to 0.011cm 3, and the propping fracture opening is increased from 0.323mm to 0.324mm; there are also 13.8MPa to 27.6MPa for the second time and 6.9MPa to 13.8MPa for the third time. The results of the test points are contrary to the theoretical rules, which indicates that the circular arc column core model cannot obtain the opening degree of the supporting crack accurately.
5. Stability analysis of low concentration proppant conductivity test method
As can be seen from the comparison of the data, the standard deviation of the flow conductivity test of the circular arc column core model propping agent is 0.04-0.07, the standard deviation of the propping agent propping crack opening degree test is 0.0002-0.0004, and the stability is good and reliable. The standard deviation of the proppant flow conductivity test of other circular arc column core models is 0.26-2.21, the standard deviation of the proppant support crack opening degree test is 0.0002-0.0019, the stability is relatively poor, and the proppant support crack opening degree test is unreliable.
Although the present invention has been described in detail by way of preferred embodiments with reference to the accompanying drawings, the present invention is not limited thereto. Various equivalent modifications and substitutions may be made in the embodiments of the present invention by those skilled in the art without departing from the spirit and scope of the present invention, and it is intended that all such modifications and substitutions be within the scope of the present invention/be within the scope of the present invention as defined by the appended claims. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (5)
1. The system for testing the flow conductivity of the low-concentration propping agent comprises a core holder (1), wherein the core holder (1) is internally provided with a core; the inlet of the core holder (1) is connected with a constant flow pump (2) through a pipeline, the outlet is communicated with a fluid container (3) through a pipeline, and the fluid container (3) is arranged on a precision balance (4); the side wall of the core holder (1) is connected with a confining pressure pump (5) through a pipeline; a differential pressure sensor (6) is also connected between the inlet and the outlet of the core holder (1); the rock core is characterized by comprising an upper rock core (7) and a lower rock core (8) which are symmetrically arranged, wherein a propping agent (9) is paved between the upper rock core (7) and the lower rock core (8); the contact surfaces of the upper core (7) and the lower core (8) and the propping agent (9) are rectangular, and two end surfaces of the upper core (7) and the lower core (8) which are perpendicular to the contact surfaces are arched; two ends of the core are respectively provided with a cushion block (10), a through hole (11) is formed in the center of each cushion block (10), and a filter screen is arranged on one side surface, close to the core, of each cushion block (10);
The measuring range of the differential pressure sensor is selected by a differential pressure estimation formula, wherein the differential pressure estimation formula is as follows:
Wherein Δp is the estimated differential pressure, pa; mu is the viscosity of the fluid, pa.s; q is fluid flow, m 3/s; tau is the tortuosity of the seepage channel of the propping agent layer, and the value is 1.5-5.5; M is the length of the support fracture model; w f is the width of the propping fracture model, m; h f Estimation of is the estimated crack opening, m;
Wherein, h f Estimation of can be calculated according to the porosity change, and the calculation formula is:
，；
Wherein phi is the porosity of the propping agent at different closing pressures, and the fraction; p is closing pressure, MPa; alpha is a constant, and the value is 0.010-0.027; c s is proppant placement concentration, g/cm 2;ρs is proppant apparent density, g/cm 3;ρv is proppant bulk density, g/cm 3.
2. The system of claim 1, further comprising an intermediate vessel (12), wherein an inlet of the intermediate vessel (12) is connected to an outlet of the constant flow pump (2) via a pipeline, and an outlet of the intermediate vessel (12) is connected to an inlet of the core holder (1) via a pipeline; valves (13) are respectively arranged on a pipeline between the constant flow pump (2) and the core holder (1), a pipeline between the constant flow pump (2) and the intermediate container (12), a pipeline between the intermediate container (12) and the core holder (1) and a pipeline between an outlet of the core holder (1) and the fluid container (3).
3. The system according to claim 1, characterized in that the screw in the working cylinder of the confining pressure pump (5) is connected with the handle by means of a worm wheel and a worm.
4. A method of testing the conductivity of a low concentration proppant using the system of any one of claims 1-3, comprising the steps of:
S1: a propping agent (9) is paved between an upper core (7) and a lower core (8), upper cushion blocks (10) are assembled at two ends of the core to form a supporting crack model, and the supporting crack model is placed into a core holder (1); loading the confining pressure to a closing pressure value, and obtaining fluid flow pressure difference and fluid flow parameters under the closing pressure value;
S2: and calculating the conductivity of the low-concentration propping agent by using a Darcy formula in combination with the geometric dimension of the propping fracture model, wherein the Darcy formula is as follows:
wherein kh f is the flow conductivity of the propping agent, um 2 cm; q is the fluid flow, cm 3/min;wf is the width of the propped fracture model, cm; h f is the opening degree of the support crack model, cm; Δp is the flow differential, kpa; mu is the viscosity of the fluid, mpa.s; To support the length of the fracture model, cm.
5. The method of claim 4, further comprising a characterization step S31 of propping fracture opening: based on capillary seepage model, calculating equivalent capillary radius and corresponding pore volume of the proppant layer by using poise She Gongshi:
Wherein r p is equivalent capillary radius, cm; mu is viscosity, pa.s; The length of the crack model is supported by cm; q is the fluid flow, cm 3/s; Δp is the test differential pressure, pa; v p is the pore volume of the proppant layer, mL;
S32: the volume density and apparent density of the propping agent are obtained by using a precision balance (4) and a fluid container (3), and then the volume of the propping fracture skeleton is calculated:
Wherein, C s is the proppant placement concentration, g/cm 2;ρv is the proppant bulk density, g/cm 3;Vs is the proppant skeleton volume in the proppant layer, and mL; w f is the width of the support fracture model, cm; The length of the crack model is supported by cm; ρ s is proppant apparent density, g/cm 3;
S33: calculating the opening degree of the propping fracture of the propping agent under different closing pressures:
Wherein h f is the opening degree of the supporting crack, cm; v p is the pore volume of the proppant layer, mL; v s is proppant skeleton volume in the proppant layer, mL; w f is the width of the support fracture model, cm; To support the length of the fracture model, cm.
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