CN112818503B - Method for determining moving speed of temporary plugging ball - Google Patents
Method for determining moving speed of temporary plugging ball Download PDFInfo
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Abstract
The application discloses a method for determining the moving speed of a temporary plugging ball, and belongs to the technical field of fracturing. The method comprises the following steps: establishing a shaft mesh model of a target oil and gas well, wherein the shaft mesh model is a model which divides a shaft of the target oil and gas well into N rectangular meshes with the same height, and N is a preset positive integer; determining a diameter equation of the temporary plugging ball in the current rectangular grid; and determining a motion equation of the temporary plugging ball based on the external force borne by the temporary plugging ball and a diameter equation and a moving time equation of the temporary plugging ball in the current rectangular grid, and determining the moving speed of the temporary plugging ball in the current rectangular grid based on the motion equation of the temporary plugging ball. By the adoption of the method and the device, the cost for detecting the moving speed of the temporary blocking ball can be saved.
Description
Technical Field
The application relates to the technical field of fracturing, in particular to a method for calculating moving speed of a temporary plugging ball based on parabolic trajectory tracking.
Background
In the exploitation of petroleum and natural gas, the fracturing technology is a relatively common means for increasing the yield. When the staged fracturing transformation is carried out on the oil-gas well, the oil-gas well is perforated and injected with liquid fracturing liquid, so that the perforation is enlarged to achieve the fracturing purpose. Because the liquid absorption capacity of the completed perforation is larger, the fracturing liquid can not effectively enter the perforation section which is not fractured. At present, when staged fracturing is carried out, a temporary plugging ball is put into an oil-gas well to plug the perforations which are already fractured so as to force fracturing fluid to enter the perforations which are not fractured so as to carry out fracturing reconstruction on the perforations. Therefore, it is very important to perform effective stress analysis on the temporary plugging ball to know the moving track of the temporary plugging ball in the oil and gas well. Then, the precondition for carrying out effective stress analysis on the temporary plugging ball is to know the moving speed of the temporary plugging ball in the oil and gas well.
At present, a mode of arranging a detector underground is mostly adopted to detect the moving speed of the temporary plugging ball in an oil-gas well.
In the process of implementing the present application, the inventor finds that the prior art has at least the following problems:
the detector is arranged under the oil gas well to detect the moving speed of the temporary plugging ball, and the cost is high.
Disclosure of Invention
The embodiment of the application provides a method and a device for determining the moving speed of a temporary plugging ball, and can solve the problem of high cost caused by the detection of the moving speed of the temporary plugging ball by using detection equipment. The technical scheme is as follows:
in a first aspect, a method for determining a moving speed of a temporary blocking ball is provided, the method comprising:
establishing a shaft mesh model of a target oil and gas well, wherein the shaft mesh model is a model which divides a shaft of the target oil and gas well into N rectangular meshes with the same height, and N is a preset positive integer;
determining a diameter equation of the temporary plugging ball in the current rectangular grid;
and determining a motion equation of the temporary blocking ball based on the external force applied to the temporary blocking ball and a diameter equation and a moving time equation of the temporary blocking ball in the current rectangular grid, and determining the moving speed of the temporary blocking ball in the current rectangular grid based on the motion equation of the temporary blocking ball.
Optionally, the determining a diameter equation of the temporary blocking ball in the current mesh includes:
determining the dissolution speed of the temporary plugging ball, and determining a mass equation of the temporary plugging ball in the current rectangular grid based on the dissolution speed;
and determining a diameter equation of the temporary plugging ball based on the mass equation of the temporary plugging ball.
Optionally, temporarily stifled ball is in the straight well section of target oil gas well removes, the external force that temporarily blocks the ball and receives includes: buoyancy, gravity, drag, mass forces, and bessel base forces.
Optionally, temporarily stifled ball is in the oblique section of making of target oil gas well removes, the external force that temporarily blocks up the ball and receives includes: the temporary plugging ball comprises buoyancy, gravity, resistance and centripetal force, wherein the centripetal force is the centripetal force applied to the temporary plugging ball when the deflecting section moves along the elliptical track, and the direction of the centripetal force points to the focus of the elliptical track.
In a second aspect, there is provided an apparatus for temporarily blocking ball movement speed determination, the apparatus comprising:
the system comprises an establishing module, a calculating module and a judging module, wherein the establishing module is used for establishing a shaft mesh model of a target oil and gas well, the shaft mesh model is a model which divides a shaft of the target oil and gas well into N rectangular meshes with the same height, and N is a preset positive integer;
the determining module is used for determining a diameter equation of the temporary plugging ball in the current rectangular grid; and determining a motion equation of the temporary blocking ball based on the external force applied to the temporary blocking ball and a diameter equation and a moving time equation of the temporary blocking ball in the current rectangular grid, and determining the moving speed of the temporary blocking ball in the current rectangular grid based on the motion equation of the temporary blocking ball.
Optionally, the determining module is configured to:
determining the dissolution speed of the temporary plugging ball, and determining a mass equation of the temporary plugging ball in the current rectangular grid based on the dissolution speed;
and determining a diameter equation of the temporary plugging ball based on the mass equation of the temporary plugging ball.
Optionally, work as the ball of temporarily stifled is in the straight well section of target oil gas well removes, the external force that the ball of temporarily stifled receives includes: buoyancy, gravity, drag, mass, and bessel base force.
Optionally, work as the temporary plugging ball is in the deflecting section of target oil and gas well removes, the external force that temporary plugging ball receives includes: the temporary plugging ball comprises buoyancy, gravity, resistance and centripetal force, wherein the centripetal force is the centripetal force applied to the temporary plugging ball when the deflecting section moves along the elliptical track, and the direction of the centripetal force points to the focus of the elliptical track.
In a third aspect, a computer device is provided, the computer device includes a processor and a memory, the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the method for determining the speed of moving the temporary ball according to the first aspect.
In a fourth aspect, a computer-readable storage medium is provided, in which at least one instruction is stored, and the at least one instruction is loaded and executed by the processor to implement the method for determining the moving speed of the temporary ball according to the first aspect.
The technical scheme provided by the embodiment of the application has the following beneficial effects:
and (3) simulating the target oil-gas well into which the temporary plugging ball needs to be put, and establishing a shaft mesh model. Then, the motion equation of the temporary plugging ball can be determined according to the external force possibly applied to the temporary plugging ball when the temporary plugging ball moves in the shaft and the diameter equation of the temporary plugging ball, and the moving speed of the temporary plugging ball in the rectangular grid can be obtained according to the motion equation. Therefore, by adopting the method, the moving speed of the temporary plugging ball can be obtained through simulation before the temporary plugging ball is put into the well, a detector does not need to be arranged under the oil gas well, and the cost is lower.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a method for determining a moving speed of a temporary blocking ball according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a wellbore mesh model provided by an embodiment of the present application;
FIG. 3 is a schematic view of a force analysis of a temporary plugging ball according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a wellbore mesh model provided by an embodiment of the present application;
FIG. 5 is a schematic view of a force analysis of a temporary plugging ball provided in an embodiment of the present application;
FIG. 6 is a schematic structural diagram of an apparatus for determining a moving speed of a temporary blocking ball according to an embodiment of the present application;
fig. 7 is a schematic structural diagram of a computer device according to an embodiment of the present application.
Detailed Description
To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
The method provided by the embodiment of the application can be adopted to calculate the moving speed of the temporary plugging ball in the oil and gas well according to the simulated shaft mesh model before the temporary plugging ball is thrown into the oil and gas well.
Referring to fig. 1, the process flow of the method for determining the moving speed of the temporary blocking ball may include the following steps:
The target oil-gas well is an oil-gas well to be put into the temporary plugging ball, and the shaft grid model is a model which divides a shaft of the target oil-gas well into N rectangular grids with the same height.
In practice, the technician may record data relating to all existing wells, such as well depth, wellbore diameter, wellbore configuration, and the like. The technician can simulate the target oil-gas well needing to input the temporary plugging ball. And firstly, acquiring relevant data of the target oil and gas well, and modeling the oil and gas well by using modeling software based on the data to obtain a wellbore mesh model corresponding to the oil and gas well. Fig. 2 is a schematic diagram of a wellbore mesh model of a target oil and gas well, in the wellbore mesh model, the height of each mesh corresponds to the actual wellbore length L, it should be noted that fig. 2 only shows a part of rectangular meshes by way of example, in this case, for more accurate calculation, L may be set to be small, for example, several meters, and may be divided into thousands of meshes for a wellbore of several kilometers.
And 102, determining a diameter equation of the temporary blocking ball in the current rectangular grid.
In practice, the mass of the temporary plugging ball in the fracturing fluid will decrease over time, given that the ball will dissolve as it moves in the fracturing fluid. When the temporary plugging ball moves in the fracturing fluid, the mass and the volume of the temporary plugging ball do not change from the top of the ith rectangular grid to the bottom of the ith rectangular grid, and the temporary plugging ball changes stepwise from the bottom of the ith rectangular grid to the top of the (i + 1) th rectangular grid. The mass equation of the temporary plugging ball is as follows: m isi+1＝mi- γ t, wherein γ is the previously measured dissolution speed of the temporary plugging ball in the fracturing fluid, and is expressed in kg/s, miThe mass of the temporary blocking ball in the ith rectangular grid, t is the moving time of the temporary blocking ball in the ith rectangular grid, and mi+1The mass of the temporary blocking ball in the (i + 1) th rectangular grid. The inner diameter of the temporary plugging ball in the ith rectangular grid is
Wherein r isiTo temporarily block the inner diameter of the ball in the ith rectangular grid. When i is 0, ri+1＝r1The initial radius of the temporary blocking ball is indicated.
And 103, determining a motion equation of the temporary blocking ball based on the external force applied to the temporary blocking ball and a diameter equation and a moving time equation of the temporary blocking ball in the current rectangular grid, and determining the moving speed of the temporary blocking ball in the current grid based on the motion equation of the temporary blocking ball.
In the implementation, the moving conditions of the temporary plugging ball in the vertical well section and the deflecting section are respectively explained.
In case one, the temporary plugging ball moves in the vertical well section, as shown in fig. 3, the force analysis of the temporary plugging ball is shown, wherein the force applied to the temporary plugging ball includes buoyancy, mass force, resistance (frictional resistance) of the fracturing fluid to the temporary plugging ball, gravity and bessel base force.
Based on the stress condition of the temporary plugging ball, a motion equation of the temporary plugging ball can be established:
wherein d is the diameter of the temporary plugging ball, ubFor temporarily blocking the ball movement speed, rhobFor temporary blocking of the ball density, ρfAs fracturing fluid density, g is acceleration of gravity, CDIs the drag coefficient, ufFor fluid velocity, tmift time, μ fracturing fluid viscosity, ζ is the profile parameter.
In the above equation of motion, the Basset force is:
integrating the motion equations, and combining the same terms and the like on the motion equations to obtain:
simplifying this equation yields the following equation:
in order to ensure that the water-soluble organic acid,
since the initial moving speed of the temporary plugging ball at the time of just putting into the wellbore is 0, there is the following equation:
make the temporary blocking ball accelerate
Thus, the Basset force expression is transformed into:
based on the viscous fracturing fluid mechanics principle, the bounded regular of the temporary plugging sphere acceleration f (zeta) can be determined, namely, if a positive number M < + ∞exists, then:
|f(ζ)|≤M，
thus, there are:
the equation for the Basset force is divided into integral intervals as follows:
wherein d is the diameter of the temporary plugging ball, and:
as a result of this, it is possible to prevent,
wherein h is the step length. Then for equation:
by adopting a trapezoidal integral calculation formula, the following can be obtained:
working out this equation yields:
wherein, the expression of Basset is as follows:
the moving speed of the temporary blocking ball can be dispersed as:
working up this equation yields:
so that the raw materials are mixed and stirred,
the product is obtained by adopting Runge-Kutta (Longgedata) method:
K1＝gn(ubm-1)
K4＝gn(ubn-1+hK3)
wherein u isbn-1For temporary blockingThe speed of the ball in the (n-1) th rectangular grid is solved by the above formula, and the moving speed u of the temporary ball-blocking speed in the (n) th rectangular grid can be obtainedbn。
In case two, in the wellbore mesh model as shown in fig. 2, after the kick-off point is a kick-off section. As shown in fig. 4, the oil and gas well after the deflecting point may be referred to as a deflecting segment, and in the embodiment of the present application, the temporary plugging ball is considered to be an elliptical track when moving in the deflecting segment, that is, the motion track is approximately the edge of the ellipse, and the solid part on the ellipse in fig. 4 is the motion track of the approximate temporary plugging ball. The elliptical trajectory is obtained according to the actual situation of the deflecting segment after a technician establishes the wellbore mesh model, namely the shape of the elliptical trajectory is determined by the technician. When the temporary plugging ball moves in the deflecting section, the stress analysis of the temporary plugging ball is shown in fig. 5, wherein the temporary plugging ball is subjected to buoyancy, gravity, resistance and centripetal force.
The major axis of the ellipse track is 2a, the minor axis of the ellipse is 2b, the curvature radius is
Based on the stress analysis of the temporary plugging ball, the motion equation of the temporary plugging ball at the deflecting section is as follows:
wherein θ is shown in fig. 5 and is an included angle between the centripetal force of the temporary plugging ball and the axis, and the rest parameters are the same as the motion equation of the straight well section, which is not described herein again.
The motion equation is arranged to obtain:
boundary conditions: when the included angle between the axis of the elliptical track and the horizontal line is 0, ub|θ＝0＝ub1。
Order:
u(θ)＝uf-ub。
the equation can thus be obtained:
by using the Euler method, the program can be obtained by arranging:
solving the equation to obtain the moving speed u (theta) of the temporary plugging ball in the nth rectangular gridn。
According to the embodiment of the application, a shaft mesh model is established by simulating the target oil-gas well into which the temporary plugging ball needs to be put. Then, a motion equation of the temporary plugging ball can be determined according to the external force possibly applied to the temporary plugging ball when the temporary plugging ball moves in the shaft and a diameter equation of the temporary plugging ball, and the moving speed of the temporary plugging ball in the rectangular grid can be obtained according to the motion equation. Therefore, by adopting the method, the moving speed of the temporary plugging ball can be obtained through simulation before the temporary plugging ball is put into the well, a detector does not need to be arranged under the oil gas well, and the cost is lower.
All the above optional technical solutions may be combined arbitrarily to form the optional embodiments of the present disclosure, and are not described herein again.
Based on the same technical concept, an embodiment of the present application further provides an apparatus for tracking a target, where the apparatus may be a server in the foregoing embodiment, as shown in fig. 6, the apparatus includes: a setup module 610 and a determination module 620.
The building module 610 is used for building a shaft mesh model of a target oil and gas well, wherein the shaft mesh model is a model which divides a shaft of the target oil and gas well into N rectangular meshes with the same height;
a determining module 620, configured to determine a diameter equation of the temporary plugging ball in the current rectangular grid; determining a motion equation of the temporary blocking ball based on the external force applied to the temporary blocking ball and a diameter equation and a moving time equation of the temporary blocking ball in the current rectangular grid; and determining the moving speed of the temporary plugging ball in the current rectangular grid based on the motion equation of the temporary plugging ball.
Optionally, the determining module 620 is configured to:
determining the dissolving speed of the temporary plugging balls, and determining a mass equation of the temporary plugging balls in the current rectangular grid based on the dissolving speed;
and determining a diameter equation of the temporary plugging ball based on the mass equation of the temporary plugging ball.
Optionally, when temporarily stifled ball is in the straight section of well of target oil gas well removes, the external force that temporarily blocks up the ball receives includes: buoyancy, gravity, drag, mass forces, and bessel base forces.
Optionally, work as the temporary plugging ball is in the deflecting section of target oil and gas well removes, the external force that temporary plugging ball receives includes: the temporary plugging ball comprises buoyancy, gravity, resistance and centripetal force, wherein the centripetal force is the centripetal force applied to the temporary plugging ball when the deflecting section moves along the elliptical track, and the direction of the centripetal force points to the focus of the elliptical track.
With regard to the apparatus in the above embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment related to the method, and will not be described in detail here.
It should be noted that: in the device for determining the moving speed of the temporary plugging ball provided by the above embodiment, when determining the moving speed of the temporary plugging ball, only the division of the functional modules is taken as an example, and in practical application, the functions may be distributed to different functional modules according to needs, that is, the internal structure of the device may be divided into different functional modules to complete all or part of the functions described above. In addition, the device for determining the moving speed of the temporary plugging ball and the method for determining the moving speed of the temporary plugging ball provided by the embodiments belong to the same concept, and specific implementation processes thereof are detailed in the method embodiments and are not described herein again.
In an exemplary embodiment, a computer-readable storage medium is further provided, in which at least one instruction is stored, and the at least one instruction is loaded and executed by a processor to implement the method for identifying an action category in the foregoing embodiments. For example, the computer readable storage medium may be a ROM, a Random Access Memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like.
Fig. 7 is a schematic structural diagram of a computer device 700 according to an embodiment of the present application, where the computer device 700 may have a relatively large difference due to different configurations or performances, and may include one or more processors (CPUs) 701 and one or more memories 702, where the memory 702 stores at least one instruction, and the at least one instruction is loaded and executed by the processor 701 to implement the above method for determining a speed of moving a temporary ball.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, where the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The above description is only exemplary of the present application and should not be taken as limiting the present application, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (4)
1. A method of determining a velocity of movement of a temporarily blocked ball, the method comprising:
establishing a shaft mesh model of a target oil and gas well, wherein the shaft mesh model is a model which divides a shaft of the target oil and gas well into N rectangular meshes with the same height, and N is a preset positive integer;
determining the dissolution speed of the temporary plugging ball, and determining a mass equation of the temporary plugging ball in the current rectangular grid based on the dissolution speed;
determining a diameter equation of the temporary plugging ball based on the mass equation of the temporary plugging ball;
based on the external force that temporary plugging ball received with the diameter equation of temporary plugging ball in current rectangular grid, confirm the equation of motion of temporary plugging ball, and based on the equation of motion of temporary plugging ball, confirm the moving speed of temporary plugging ball in current rectangular grid, wherein, temporary plugging ball is in the straight section of well of target oil gas well removes, the external force that temporary plugging ball received includes: buoyancy, gravity, resistance, mass force and Bessel Basset force, the temporary plugging ball moves in the deflecting section of the target oil-gas well, and the external force applied to the temporary plugging ball comprises: the temporary plugging ball is characterized by comprising buoyancy, gravity, resistance and centripetal force, wherein the centripetal force is the centripetal force borne by the temporary plugging ball when the deflecting section moves along the elliptical track, and the direction of the centripetal force points to the focus of the elliptical track.
2. An apparatus for determining a moving speed of a temporary blocking ball, the apparatus comprising:
the system comprises an establishing module, a calculating module and a judging module, wherein the establishing module is used for establishing a shaft mesh model of a target oil and gas well, the shaft mesh model is a model which divides a shaft of the target oil and gas well into N rectangular meshes with the same height, and N is a preset positive integer;
the determining module is used for determining the dissolving speed of the temporary plugging ball and determining a mass equation of the temporary plugging ball in the current rectangular grid based on the dissolving speed; determining a diameter equation of the temporary plugging ball based on the mass equation of the temporary plugging ball; determining a motion equation of the temporary plugging ball based on the external force applied to the temporary plugging ball and a diameter equation and a moving time equation of the temporary plugging ball in the current rectangular grid; based on the motion equation of the temporary plugging ball, determining the moving speed of the temporary plugging ball in the current rectangular grid, wherein the temporary plugging ball moves in the vertical well section of the target oil-gas well, and the external force applied to the temporary plugging ball comprises the following steps: buoyancy, gravity, resistance, mass force and Bessel Basset force, wherein the temporary plugging ball moves in the deflecting section of the target oil-gas well, and the external force applied to the temporary plugging ball comprises the following steps: the temporary plugging ball is characterized by comprising buoyancy, gravity, resistance and centripetal force, wherein the centripetal force is borne by the temporary plugging ball when the temporary plugging ball moves along an elliptic track at the deflecting section, and the direction of the centripetal force points to the focus of the elliptic track.
3. A computer device comprising a processor and a memory, the memory having stored therein at least one instruction, the at least one instruction being loaded and executed by the processor to implement the method of determining a velocity of a ball break as claimed in claim 1.
4. A computer-readable storage medium having stored therein at least one instruction, which is loaded and executed by a processor, to implement the method of determining a velocity of movement of a ball of a temporary blockage according to claim 1.
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