CN110006788B - Device and method for measuring spreadability of water shutoff agent at porous medium air-water interface - Google Patents
Device and method for measuring spreadability of water shutoff agent at porous medium air-water interface Download PDFInfo
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 97
- 239000003795 chemical substances by application Substances 0.000 title claims abstract description 48
- 238000000034 method Methods 0.000 title claims abstract description 16
- 239000004576 sand Substances 0.000 claims abstract description 88
- 230000007480 spreading Effects 0.000 claims abstract description 62
- 238000007789 sealing Methods 0.000 claims abstract description 8
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- 238000009530 blood pressure measurement Methods 0.000 claims description 12
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
- G01N2013/003—Diffusion; diffusivity between liquids
Abstract
The invention discloses a device and a method for measuring the spreadability of a water shutoff agent at a porous medium air-water interface, wherein the device comprises a piston cylinder 1, an outlet pump 2, a sand filling pipe 3, a sensor group 4, a computer data acquisition system 5, a constant temperature box 6, an intermediate container 7 and an inlet pump 8, the center of a sealing cover of the sand filling pipe 3 is provided with a through hole a, a conduit is screwed into the middle part A of the sand filling pipe through the through hole a, a high-position pressure measuring pipe 3-3 and a low-position pressure measuring pipe 3-4 are arranged in the cylinder, and the part of the high-position pressure measuring pipe above the low-position pressure measuring pipe is a conductor and is alternately connected with a positive electrode and a negative electrode. The method comprises the following steps: (1) Filling sand samples with different granularities and an adhesive into a sand filling pipe; (2) measuring the initial differential pressure and pressure gradient prior to occlusion: (3) establishing a gas-water interface; (4) determining the spreading speed; (5) determining the spreading area; (6) determining the spreading thickness. The invention can simulate the spreading process of the water shutoff agent on the air-water interface of the porous medium, and provides a basis for evaluating the spreading performance of the water shutoff agent.
Description
Technical Field
The invention relates to a device and a method for measuring the spreadability of a water shutoff agent at a sand filling pipe gas-water interface in the field of oilfield chemical profile control and water shutoff in the petroleum industry.
Background
Gas-liquid two-phase seepage caused by gas reservoir water invasion can increase seepage resistance, reduce gas well productivity and finally reduce gas reservoir recovery ratio. If the side bottom water can be prevented from invading the gas reservoir by a reasonable means, the development benefit of the gas reservoir can be greatly improved, wherein the water shutoff by the water shutoff agent is an effective means for controlling the water invasion of the gas reservoir.
Different water shutoff agents are widely explored abroad as early as the 30 th century, and the domestic water shutoff technology is started from the 50 th century. Through long-term research and development, a series of testing methods for the performance (such as rheological property, plugging strength, thickening property, temperature resistance, salt resistance, long-term stability and the like) of the water shutoff agent are formed initially. According to the visual testing device and method for the spreading performance of the water shutoff agent (CN 2018103276401), the spreading performance of the water shutoff agent at the air-water interface is evaluated, so that the water shutoff agent with excellent spreading performance at the air-water interface is preferably obtained, but the device can only test the spreading performance parameters of the water shutoff agent at the air-water interface of a container and cannot simulate the spreading performance of the water shutoff agent at the air-water interface of a porous medium. Xue Chen et al (Xue Chen, wei Yufeng, fu Wenxi, et al) analysis of a composite porous media seepage field embedded with watertight spheres [ J ]. Engineering science and technology, 2017 (S2): 36-42) found that embedding spheres of different diameters in a sand filling pipe changed the pressure distribution in the sand filling pipe, and similarly, when the size of the plugging area formed by the plugging agent at the gas-water interface of the sand filling pipe changed the pressure distribution in the sand filling pipe, conversely, if the pressure distribution in the sand filling pipe could be measured by a pressure measuring pipe, the spreading thickness and area of the plugging agent at the gas-water interface of the porous media could be determined. Meanwhile, the insulating plugging area formed by spreading the water shutoff agent on the air-water interface can enable the resistance value between adjacent high-level piezometric tubes to change, and the spreading speed of the water shutoff agent is measured and calculated through the position of the adjacent high-level piezometric tubes with the changed resistance value and the moment of the change of the resistance value. The determination of the spreading thickness, spreading area and spreading speed of the water shutoff agent at the porous medium air-water interface provides reasonable basic parameters for quantitatively evaluating the spreading performance of the water shutoff agent.
Disclosure of Invention
The invention aims to provide a device for measuring the spreading performance of a water shutoff agent at a porous medium air-water interface, which has reliable principle, ingenious structure and convenient operation, and the spreading thickness, spreading area and spreading speed of the water shutoff agent are tested at the air-water interface of a sand filling pipe, so that the measured spreading performance parameter of the water shutoff agent is closer to the spreading condition in a real stratum.
The invention further aims to provide a method for measuring the spreading performance of the water shutoff agent on the air-water interface of the porous medium by using the device, by the method, the spreading thickness, the spreading area and the spreading speed of the water shutoff agent on the air-water interface of the porous medium can be measured under the conditions of high temperature and high pressure, and reasonable basic data are provided for quantitatively evaluating the spreading performance of the water shutoff agent on the air-water interface of a stratum.
In order to achieve the technical purpose, the invention provides the following technical scheme.
The technical principle of the invention is as follows: the insulating plugging area formed by spreading the water shutoff agent on the air-water interface can change the resistance value between the adjacent high-level piezometric tubes, and the spreading speed of the water shutoff agent can be determined by the positions of the two adjacent high-level piezometric tubes with the changed resistance values and the moment of the change of the resistance values; after spreading, under constant-speed displacement, the size of a plugging area formed by the water shutoff agent on the air-water interface of the sand filling pipe can change the pressure distribution in the sand filling pipe, a plurality of high-low pressure measuring pipe groups are used for determining the pressure difference distribution in the sand filling pipe, the area controlled by the pressure measuring pipe with large pressure difference is the plugging area, and the corresponding cross-sectional area is the spreading area of the water shutoff agent; after the spreading area is determined, the Darcy law is respectively used for the two states before and after the blocking, the flow before and after the blocking is the same as the bridge, and the blocking thickness can be immediately obtained by the joint.
The device for measuring the spreadability of the water shutoff agent at the porous medium air-water interface comprises a piston cylinder, an outlet pump, a sand filling pipe, a sensor group, a computer data acquisition system, an incubator, an intermediate container, an inlet pump, an inlet flowmeter, an inlet pressure gauge, an outlet pressure gauge and an outlet flowmeter, wherein the bottom of the sand filling pipe is connected with the intermediate container filled with stratum water and the inlet pump through the inlet pressure gauge and the inlet flowmeter, the top of the sand filling pipe is connected with the piston cylinder and the outlet pump through the outlet pressure gauge and the outlet flowmeter, the sand filling pipe is connected with the sensor group and the computer data acquisition system, and the sand filling pipe is positioned in the incubator.
The sand filling pipe consists of a sealing cover, a guide pipe, a high-position pressure measuring pipe, a low-position pressure measuring pipe and a cylinder body, wherein the center of the sealing cover is provided with a through hole a, the through hole a is provided with internal threads, the guide pipe is provided with external threads, the guide pipe can be screwed into the middle part A of the sand filling pipe through the through hole a, the guide pipe and the cylinder body are insulators, and the tail end of the guide pipe is connected with a hollow conductor and is connected with an electrode. The sand filling pipe is characterized in that a through hole b is formed in the center of the bottom end of the sand filling pipe body, a high-position pressure measuring pipe and a low-position pressure measuring pipe are arranged in the body, and the high-position pressure measuring pipe and the low-position pressure measuring pipe are placed in pairs to form a high-position pressure measuring pipe group and a low-position pressure measuring pipe group. A rectangular coordinate system is made on a horizontal section cut at a certain position of the lower part of the sand filling pipe, the horizontal direction is taken as an x axis, the vertical direction is taken as a y axis, pressure measuring points are equidistantly distributed on the x axis and the y axis, and each pressure measuring point is x i Or y i Corresponds to a high-low pressure measuring tube group.
The high-level piezometer tube is connected with the positive and negative electrodes alternately by taking the part above the low-level piezometer tube as a conductor, namely the polarities of the electrodes connected with the adjacent high-level piezometer tubes are different, and the part below the low-level piezometer tube and the low-level piezometer tube are insulators, and each group of high-level piezometer tubes and each group of low-level piezometer tubes have the same property.
The method for measuring the spreadability of the water shutoff agent on the air-water interface of the porous medium by using the device sequentially comprises the following steps:
(1) Sand filling pipe sand filling: filling sand samples with different granularities and adhesives into a sand filling pipe, so that the sand filling pipe has the same porosity and permeability as those of the original stratum;
(2) Initial differential pressure and pressure gradient were measured prior to occlusion: firstly, cleaning a sand filling pipe by petroleum ether, then drying by nitrogen, vacuumizing the sand filling pipe, further saturating stratum water of a rock core, and simultaneously measuring and calculating the pore volume V of the sand filling pipe P Finally, an inlet pump is used for driving the sand filling pipe through the intermediate container at a constant speed, and the inlet pressure P is measured by an inlet pressure gauge 10 and an outlet pressure gauge 11 6 Outlet pressure P 1 By DeltaP 1 =P 6 -P 1 Calculating an initial differential pressure ΔP 1 And the pressure gradient ΔP is obtained by the following formula ot :
L is the length of the sand filling pipe;
(3) Establishing a gas-water interface: after the sand filling pipe is dried, the sand filling pipe is injected from the bottom of the sand filling pipe through an intermediate container by an inlet pumpInjecting natural gas from the top of the sand filling pipe by using an outlet pump to reach the pressure required by the test, namely establishing a gas-water interface on the plane of the point A in the middle of the sand filling pipe;
(4) Determining the spreading speed: setting the temperature and pressure of a sand filling pipe, injecting a water shutoff agent into a gas-water interface of the sand filling pipe through a guide pipe, blocking the guide pipe, starting timing at the same time, when an electrode connected with a high-level pressure measuring pipe detects that a resistance value changes, indicating that the water shutoff agent spreads to the position of the high-level pressure measuring pipe, setting the distance from the intersection point of the high-level pressure measuring pipe and the gas-water interface to be S, and determining the spreading speed v of the water shutoff agent from the timing to the time when the electrode connected with the high-level pressure measuring pipe detects that the resistance value changes to be t according to the following formula:
(5) Determining the spreading area: when the resistance value monitored by the electrodes connected with all the high-level piezometric tubes is not changed any more, namely, the spreading of the water shutoff agent is completed, the sand filling tube is driven by the inlet pump through the intermediate container at the same displacement speed and constant speed as in the step (2), and the pressure difference between the upper end and the lower end of the spreading area measured by the high-level piezometric tubes and the low-level piezometric tubes is larger than that of the non-spreading area due to the separation of the water shutoff agent, so that the spreading area can be determined by the relative size of the pressure difference, namely, the pressure difference is relatively smaller and is a seepage area, and the corresponding cross section area is a seepage area 2 The spreading area with relatively large pressure difference corresponds to the spreading area A 1 -A 2 ,A 1 Is the cross section area of the sand filling pipe;
(6) Determining the spreading thickness: the spreading thickness H corresponding to different pressure measuring points on the x axis and the y axis is determined by xi 、H yi :
P in the formula 5xi Pressure measurement point x i The pressure measured by the low-level piezometer tube;
P 2xi pressure measurement point x i The pressure measured by the high-level piezometer tube;
P 5yi pressure measurement point y i The pressure measured by the low-level piezometer tube;
P 2yi pressure measurement point y i The pressure measured by the high-level piezometer tube;
ΔP ot -a pressure gradient;
x-vertical distance between high-position piezometer tube and low-position piezometer tube.
Compared with the prior art, the invention has the following beneficial effects:
the device for testing the spreading thickness and the spreading area of the water shutoff agent has ingenious structure, reasonable design and strong operability, and the device can simulate the spreading process of the water shutoff agent at the air-water interface of the porous medium; the method is novel, can rapidly and accurately obtain the spreading thickness, spreading area and spreading speed of the water shutoff agent, provides a basis for evaluating the spreading performance of the water shutoff agent, and has wide market application prospect.
Drawings
FIG. 1 is a schematic diagram of a device for measuring the spreadability of a water shutoff agent at a porous medium air-water interface.
In the figure:
1-a piston cylinder; 2-outlet pump; 3-sand filling pipe; a 4-sensor group; 5-a computer data acquisition system; 6-a constant temperature box; 7-an intermediate container; 8-an inlet pump; 9-inlet flow meter; 10-an inlet pressure gauge; 11-outlet pressure gauge; 12-outlet flow meter.
Fig. 2 is a schematic structural view of the sand filling pipe.
In the figure:
3-1: sealing cover; 3-2: a conduit; 3-3: a high-level piezometer tube; 3-4: a low-level piezometer tube; 3-5: a cylinder body.
Fig. 3 is a horizontal sectional view of the sand filling pipe B of fig. 2.
Fig. 4 (a) and fig. 4 (b) are schematic diagrams of water flooding flow before and after plugging, respectively.
Detailed Description
The present invention is further described below with reference to the accompanying drawings to facilitate understanding of the present invention by those skilled in the art. It should be understood that the invention is not limited to the precise embodiments, and that various changes may be effected therein by one of ordinary skill in the art without departing from the spirit or scope of the invention as defined and determined by the appended claims.
See fig. 1.
The device for measuring the spreadability of the water shutoff agent at the porous medium air-water interface comprises a piston cylinder 1, an outlet pump 2, a sand filling pipe 3, a sensor group 4, a computer data acquisition system 5, an incubator 6, an intermediate container 7, an inlet pump 8, an inlet flowmeter 9, an inlet pressure gauge 10, an outlet pressure gauge 11 and an outlet flowmeter 12, wherein the bottom of the sand filling pipe 3 is connected with the intermediate container 7 filled with stratum water through the inlet pressure gauge 10 and the inlet flowmeter 9, the intermediate container is connected with the inlet pump 8, the top of the sand filling pipe 3 is connected with the piston cylinder 1 through the outlet pressure gauge 11 and the outlet flowmeter 12, the piston cylinder is connected with the outlet pump 2, the sand filling pipe is connected with the sensor group 4, the sensor group is connected with the computer data acquisition system 5, and the sand filling pipe is placed in the incubator 6.
See fig. 2.
The sand filling pipe 3 consists of a sealing cover 3-1, a guide pipe 3-2, a high-position pressure measuring pipe 3-3, a low-position pressure measuring pipe 3-4 and a cylinder body 3-5, wherein a through hole a is formed in the center of the sealing cover 3-1, internal threads are formed in the through hole a, external threads are formed in the guide pipe 3-2, the guide pipe can be screwed into the middle part A of the sand filling pipe through the through hole a, and the guide pipe 3-2 and the cylinder body are arranged in the middle of the sand filling pipeThe body 3-5 is an insulator, and the end of the catheter is connected with a hollow conductor and connected with an electrode. The center of the bottom end of the cylinder body 3-5 is provided with a through hole B, a high-position pressure measuring pipe 3-3 and a low-position pressure measuring pipe 3-4 are arranged in the cylinder body, the high-position pressure measuring pipe and the low-position pressure measuring pipe are arranged in pairs to form a high-position pressure measuring pipe group, a rectangular coordinate system is adopted as a cross section of the lower part B of the sand filling pipe, the horizontal direction is taken as an x axis, the vertical direction is taken as a y axis, pressure measuring points are equidistantly distributed on the x axis and the y axis, and each pressure measuring point is x i Or y i Corresponds to a high-low pressure measuring tube group. The high-level piezometer tube 3-3 is connected with positive and negative electrodes alternately by taking the part above the low-level piezometer tube 3-4 as a conductor.
See fig. 3.
FIG. 3 is a cross-sectional view of the sand pack taken from the horizontal plane at B in FIG. 2, and the stack number is given in rectangular coordinates on the horizontal plane: the horizontal direction is taken as the x axis, the vertical direction is taken as the y axis, and the numbering principle is as follows: starting from the origin of coordinates, the positive directions are numbered 1, 2, 3 and … … in sequence, and the negative directions are numbered-1, -2, -3 and … … in sequence, namely a pressure measuring point x i Or y i Corresponds to a high-low pressure measuring tube group, and each pressure measuring point on the x and y axes is distributed equidistantly.
See fig. 4 (a), fig. 4 (b).
In the figure: p (P) 1 、P 6 Outlet pressure and inlet pressure respectively; p (P) 2 、P 5 The pressure measured by the high-position piezometer tube and the low-position piezometer tube respectively; p (P) 3 、P 4 The pressure of the upper end face and the pressure of the lower end face of the plugging area are respectively; x is x 1 、x 2 The distance from the high-position piezometer tube to the upper end face of the plugging area and the distance from the low-position piezometer tube to the lower end face of the plugging area are respectively; x is the distance between the high-order piezometer tube and the low-order piezometer tube; l is the length of the piezometer tube; h is the plugging thickness; q (Q) 1 、Q 2 The displacement flow before and after the plugging is respectively; μ is the viscosity of the formation water.
Taking two states before and after the sand filling pipe is plugged for research, and spreading thicknesses H corresponding to different pressure measuring points on an x axis and a y axis in the sand filling pipe xi 、H yi The calculation formula of (2) is derived as follows:
as shown in fig. 4 (a), darcy's law is applied to the water flooding process before sand filling pipe plugging:
ΔP 1 =P 6 -P 1 (2)
as shown in fig. 4 (b), darcy's law is applied to the water flooding process after the sand filling pipe is plugged:
ΔP 2 =P 4 -P 3 (4)
assuming that the water flow is steady and symmetrical flowing around the plugging area, the pressure gradient of the upper and lower seepage areas of the plugging section is the same, and the flow before and after plugging is the same, namely Q 1 =Q 2 The pressure gradient of the upper and lower seepage areas of the plugging section is the same as the pressure gradient before plugging, and is delta P ot 。
The directions of the seepage of the broken lines in fig. 4 (b) are selected as follows:
i.e.
P 4 =P 5 -x 2 ·ΔP ot (6)
P 3 =P 2 +x 1 ·ΔP ot (7)
Carrying out the following formulas (6) and (7) into formula (4) to obtain the following formula:
ΔP 2 =P 4 -P 3 =P 5 -P 2 -ΔP ot (x 1 +x 2 ) (8)
x 1 +x 2 =x-H (9)
ΔP 2 =P 5 -P 2 -ΔP ot (x-H) (10)
carrying out the following formula (10) to the formula (3) to obtain:
due to Q 1 =Q 2 The simultaneous formulas (1) and (11) are obtained:
bringing (13) into (12) for simplification to obtain:
then:
pressure P brought to different pressure taps 5xi 、P 2xi And P 5yi 、P 2yi The spreading thickness H corresponding to different pressure measuring points on the x axis and the y axis in the sand filling pipe is obtained by the following two formulas xi 、H yi :
P in the formula 5xi Pressure measurement point x i The pressure measured by the low-level piezometer tube;
P 2xi pressure measurement point x i Pressure measured by high-level pressure measuring tube;
P 5yi Pressure measurement point y i The pressure measured by the low-level piezometer tube;
P 2yi pressure measurement point y i The pressure measured by the high-level piezometer tube;
ΔP ot -a pressure gradient;
x-vertical distance between high and low pressure measuring tubes.
Claims (1)
1. The method for measuring the spreadability of the water shutoff agent on the porous medium air-water interface by using the device comprises a piston cylinder (1), an outlet pump (2), a sand filling pipe (3), a sensor group (4), a computer data acquisition system (5), a constant temperature box (6), an intermediate container (7), an inlet pump (8), an inlet flowmeter (9), an inlet pressure gauge (10), an outlet pressure gauge (11) and an outlet flowmeter (12), wherein the bottom of the sand filling pipe (3) is connected with the intermediate container (7) filled with stratum water through the inlet pressure gauge (10) and the inlet flowmeter (9), the intermediate container is connected with the inlet pump (8), the top of the sand filling pipe (3) is connected with the piston cylinder (1) through the outlet pressure gauge (11) and the outlet flowmeter (12), the piston cylinder is connected with the outlet pump (2), the sand filling pipe is connected with the sensor group (7), the sensor group is connected with the computer data acquisition system (5), and the sand filling pipe is placed in the constant temperature box (6). The sand filling pipe (3) consists of a sealing cover (3-1), a guide pipe (3-2), a high-position pressure measuring pipe (3-3), a low-position pressure measuring pipe (3-4) and a cylinder (3-5), a through hole a is formed in the center of the sealing cover (3-1), the guide pipe (3-2) is screwed into the middle part A of the sand filling pipe through the through hole a, and the tail end of the guide pipe is connected with a hollow conductor and is connected with an electrode; the center of the bottom end of the cylinder body (3-5) is provided with a through hole b, a high-position pressure measuring pipe (3-3) and a low-position pressure measuring pipe (3-4) are arranged in the cylinder body, the high-position pressure measuring pipe and the low-position pressure measuring pipe are arranged in pairs to form a high-position pressure measuring pipe group, and the part of the high-position pressure measuring pipe above the low-position pressure measuring pipe is a conductor and is alternately connected with positive and negative electrodes; taking a transverse section at the lower part B of the sand filling pipe as a rectangular coordinate system, taking the horizontal direction as an x axis and the vertical direction as a y axis, and equally distributing pressure measuring points on the x axis and the y axis, wherein each pressure measuring point is x i Or y i Corresponding to a high-low pressure measuring tube group, the method sequentially comprises the following steps of:
(1) Sand filling pipe sand filling: filling sand samples with different granularities and adhesives into a sand filling pipe, so that the sand filling pipe has the same porosity and permeability as those of the original stratum;
(2) Initial differential pressure and pressure gradient were measured prior to occlusion: vacuumizing the sand filling pipe to saturate stratum water, and measuring and calculating the pore volume V of the sand filling pipe P Finally, the inlet pump is used for measuring the inlet pressure P through the constant-speed water-driven sand filling pipe of the intermediate container 6 Outlet pressure P 1 By DeltaP 1 =P 6 -P 1 Calculating an initial differential pressure ΔP 1 And the pressure gradient ΔP is obtained by the following formula ot :
L is the length of the sand filling pipe;
(3) Establishing a gas-water interface: after the sand filling pipe is dried, the sand filling pipe is injected from the bottom of the sand filling pipe through an intermediate container by an inlet pumpInjecting natural gas from the top of the sand filling pipe by using an outlet pump to reach the pressure required by the test, namely establishing a gas-water interface on the plane of the point A in the middle of the sand filling pipe;
(4) Determining the spreading speed: setting the temperature and pressure of a sand filling pipe, injecting a water shutoff agent into a gas-water interface of the sand filling pipe through a guide pipe, blocking the guide pipe, starting timing at the same time, when an electrode connected with a high-level pressure measuring pipe detects that a resistance value changes, indicating that the water shutoff agent spreads to the position of the high-level pressure measuring pipe, setting the distance from the intersection point of the high-level pressure measuring pipe and the gas-water interface to be S, and determining the spreading speed v of the water shutoff agent from the timing to the time when the electrode connected with the high-level pressure measuring pipe detects that the resistance value changes to be t according to the following formula:
(5) Determining the spreading area: when the resistance value monitored by the electrodes connected with all the high-level piezometric tubes is not changed any more, the sand filling tube is driven by the inlet pump through the intermediate container at the same displacement speed and constant speed as in the step (2), and the pressure difference between the upper end and the lower end of the spreading area measured by the high-level piezometric tubes and the low-level piezometric tubes is larger than that of the non-spreading area due to the separation of the water shutoff agent, so that the seepage area is a seepage area with relatively smaller pressure difference, and the corresponding cross section area is a seepage area A 2 The spreading area with relatively large pressure difference corresponds to the spreading area A 1 -A 2 ,A 1 Is the cross section area of the sand filling pipe;
(6) Determining the spreading thickness: the spreading thickness H corresponding to different pressure measuring points on the x axis and the y axis is determined by xi 、H yi :
P in the formula 5xi Pressure measurement point x i The pressure measured by the low-level piezometer tube;
P 2xi pressure measurement point x i The pressure measured by the high-level piezometer tube;
P 5yi pressure measurement point y i The pressure measured by the low-level piezometer tube;
P 2yi pressure measurement point y i The pressure measured by the high-level piezometer tube;
ΔP ot -a pressure gradient;
x-vertical distance between high-position piezometer tube and low-position piezometer tube.
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