CN111624124A - Method and device for determining crushing performance of proppant - Google Patents
Method and device for determining crushing performance of proppant Download PDFInfo
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- CN111624124A CN111624124A CN201910151176.XA CN201910151176A CN111624124A CN 111624124 A CN111624124 A CN 111624124A CN 201910151176 A CN201910151176 A CN 201910151176A CN 111624124 A CN111624124 A CN 111624124A
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Abstract
The invention discloses a method and a device for determining the crushing performance of a proppant, and belongs to the technical field of proppant quality detection. The method is characterized in that a crushing experiment is carried out based on a small amount of proppant, experiment data are obtained, and then a crushing function between the accumulated mass proportion and the particle size and pressure of the proppant before crushing and a replenishing function between the particle size and the pressure of the proppant before crushing and after crushing are obtained; in the mixed proppant consisting of the proppants with different particle sizes, after the crushing experiment, the variation of the mass of the proppant with the first particle size is as follows: the crushing mass of the original first particle size and the mass of the proppant of the first particle size formed by crushing the proppant of the second particle size are added, and based on the crushing function and the replenishment function, a particle number balance equation between the particle sizes of the proppant before and after the crushing experiment is obtained, so that based on the particle number balance equation, the pressure in the production process and the requirements on the crushing performance of the proppant, the matched proppant is selected for the production process.
Description
Technical Field
The invention relates to the technical field of proppant quality detection, in particular to a method and a device for determining the crushing performance of a proppant.
Background
The proppant is natural sand or artificial high-strength ceramic particles with certain granularity and gradation, and is used for entering a stratum along with a high-pressure solution in the fracturing construction of an oil and gas field, and a proppant filling layer formed by the proppant and the high-pressure solution is filled in a fracture of the stratum to play a role in supporting the fracture not to be closed due to stress release, so that the high flow conductivity of the fracture of the stratum is maintained, oil and gas can smoothly pass through, and the yield of the oil and gas is increased.
The determination method of the fracturing performance of the proppant commonly used at present comprises the following steps: based on a crushing experiment, the crushing rates of different proppants are obtained, so that the proppant with lower crushing rate is selected for the production process. The crushing rate obtained by the method can only represent the crushing proportion of the proppant under high pressure, and the evaluation of the crushing performance of the proppant by only depending on the crushing rate is not accurate enough, which is not beneficial to guiding the actual production.
Disclosure of Invention
The embodiment of the invention provides a method and a device for determining the fracturing performance of a proppant, which can solve the problems that the fracturing rate obtained by the conventional method for determining the fracturing performance of the proppant can only represent the fracturing proportion of the proppant under high pressure, and the fracturing performance of the proppant is not accurate enough to be evaluated only by the fracturing rate, so that the actual production is not guided. The technical scheme is as follows:
there is provided a method of determining proppant fracturing performance, the method comprising:
carrying out multiple groups of first crushing experiments by adopting a plurality of proppants with different first particle sizes under a plurality of different pressures respectively to obtain experiment results of the multiple groups of first crushing experiments, wherein the first particle sizes are the initial particle sizes of the proppants in each group of first crushing experiments;
obtaining a first accumulated mass ratio after each group of first crushing experiments based on the experiment results of the plurality of groups of first crushing experiments, wherein the first accumulated mass ratio refers to: in the proppant after each group of the first crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size of the group of the first crushing experiments to the total mass of the proppant in the group of the first crushing experiments;
obtaining a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass proportion after each group of first crushing experiments and a crushing function model, wherein the crushing function represents the relationship between the mass of the proppant in each group of first crushing experiments, which is reduced due to crushing, and the pressure of each group of first crushing experiments and the first particle size;
carrying out a plurality of groups of second crushing experiments by adopting a plurality of proppants with different second particle sizes under a plurality of different pressures respectively to obtain experiment results of the plurality of groups of second crushing experiments, wherein the second particle sizes are the initial particle sizes of the proppants in each group of second crushing experiments, and the first particle sizes are the target particle sizes of each group of second crushing experiments;
based on the experimental results of the multiple groups of second crushing experiments, obtaining a second accumulated mass proportion and a third accumulated mass proportion after each group of second crushing experiments, wherein the second accumulated mass proportion refers to: in each group of the second fracturing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of the second fracturing experiments is as follows: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the second particle size to the total mass of the proppant in the group of second crushing experiments;
obtaining a replenishment function based on the first particle size of each group of second crushing experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second crushing experiments, and a replenishment function model, wherein the replenishment function represents the proportion of the proppant crushed into the first particle size from the second particle size in each group of second crushing experiments;
and obtaining a particle number balance equation based on the crushing function, the replenishment function and the particle number balance model, wherein the particle number balance equation represents the relationship between the particle size of the proppant before and after crushing of the mixed proppant formed by the proppants with different particle sizes under a preset pressure, the preset pressure and the accumulated mass ratio based on the first particle size.
In one possible implementation, the obtaining a particle number balance equation based on the fragmentation function, the replenishment function, and a particle number balance model includes:
carrying out differential discretization on the particle number balance model to obtain a differential model;
and acquiring the particle number balance equation based on the difference model, the crushing function and the replenishment function.
In one possible implementation, the fragmentation function model includes:
wherein x represents a first particle size in μm, σ represents the pressure of the first fracturing experiment in MPa, and S (x, σ) represents the value of the fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ in MPa-1And P (x, σ) represents the first cumulative mass fraction, dimensionless.
In one possible implementation, the replenishment function model includes:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless.
In one possible implementation, the grain number balance model includes:
wherein x represents a first particle size, the unit is μm, y represents a second particle size, the unit is μm, σ represents a pressure of a crushing experiment, the unit is MPa, B (y, x, σ) represents a replenishment function value when the second particle size is y after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the dimensionless degree is not provided, P (x, σ) represents a first accumulated mass proportion and the dimensionless degree is provided, P (y, σ) represents a third accumulated mass proportion and the dimensionless degree is provided, S (x, σ) represents a crushing function value after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the unit is MPa-1。
In one aspect, there is provided an apparatus for determining fracturing performance of a proppant, the apparatus comprising:
the crushing module is used for performing multiple groups of first crushing experiments under multiple different pressures by adopting multiple proppants with different first particle sizes to obtain experiment results of the multiple groups of first crushing experiments, wherein the first particle sizes are initial particle sizes of the proppants in each group of first crushing experiments;
the data acquisition module is configured to acquire a first accumulated mass ratio after each group of first crushing experiments based on experiment results of the plurality of groups of first crushing experiments, where the first accumulated mass ratio is: in the proppant after each group of the first crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size of the group of the first crushing experiments to the total mass of the proppant in the group of the first crushing experiments;
a crushing function obtaining module, configured to obtain a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass ratio after each group of first crushing experiments, and a crushing function model, where the crushing function represents a relationship between a mass of the proppant in each group of first crushing experiments, which is reduced due to crushing, and the pressure of each group of first crushing experiments and the first particle size;
the crushing module is further used for performing a plurality of groups of second crushing experiments under a plurality of different pressures by adopting a plurality of proppants with different second particle sizes to obtain experiment results of the plurality of groups of second crushing experiments, wherein the second particle sizes are the initial particle sizes of the proppants in each group of second crushing experiments, and the first particle sizes are the target particle sizes of the second crushing experiments in each group;
the data acquisition module is further configured to acquire a second accumulated mass proportion and a third accumulated mass proportion after each group of second crushing experiments based on the experiment results of the plurality of groups of second crushing experiments, where the second accumulated mass proportion refers to: in each group of the second fracturing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of the second fracturing experiments is as follows: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the second particle size to the total mass of the proppant in the group of second crushing experiments;
a replenishment function obtaining module, configured to obtain a replenishment function based on the first particle size of each group of second fragmentation experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second fragmentation experiments, and a replenishment function model, where the replenishment function represents a proportion of the proppant crushed into the first particle size from the second particle size in each group of second fragmentation experiments;
and the particle number balance equation obtaining module is used for obtaining a particle number balance equation based on the crushing function, the replenishment function and the particle number balance model, wherein the particle number balance equation represents the relationship among the particle size of the proppant before and after crushing of the mixed proppant formed by multiple different particle sizes under preset pressure, the preset pressure and the accumulated mass ratio based on the first particle size.
In one possible implementation, the grain number balance equation obtaining module is configured to:
carrying out differential discretization on the particle number balance model to obtain a differential model;
and acquiring the particle number balance equation based on the difference model, the crushing function and the replenishment function.
In one possible implementation, the fragmentation function model includes:
wherein x represents a first particle size in μm, σ represents the pressure of the first fracturing experiment in MPa, and S (x, σ) represents the value of the fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ in MPa-1And P (x, σ) represents the first cumulative mass fraction, dimensionless.
In one possible implementation, the replenishment function model includes:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless.
In one possible implementation, the grain number balance model includes:
wherein x represents a first particle size, the unit is μm, y represents a second particle size, the unit is μm, σ represents a pressure of a crushing experiment, the unit is MPa, B (y, x, σ) represents a replenishment function value when the second particle size is y after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the dimensionless degree is not provided, P (x, σ) represents a first accumulated mass proportion and the dimensionless degree is provided, P (y, σ) represents a third accumulated mass proportion and the dimensionless degree is provided, S (x, σ) represents a crushing function value after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the unit is MPa-1。
The technical scheme provided by the embodiment of the invention has the following beneficial effects:
according to the method provided by the embodiment of the invention, a first crushing experiment is carried out based on a small amount of proppant to obtain experiment data, and then a crushing function between the accumulated mass proportion and the particle size and pressure of the proppant before crushing is obtained; further, a second crushing experiment is carried out based on a small amount of groups of proppants, and a replenishment function between the particle size and the pressure before and after crushing of the proppants is obtained; in the mixed proppant consisting of the proppants with different particle sizes, after the crushing experiment, the variation of the mass of the proppant with the first particle size is as follows: the crushing mass of the original first particle size and the mass of the proppant of the first particle size formed by crushing the proppant of the second particle size are added, and based on the crushing function and the replenishment function, a particle number balance equation between the particle sizes of the proppant before and after the crushing experiment is obtained, so that based on the particle number balance equation, the pressure in the production process and the requirements on the crushing performance of the proppant, the matched proppant is selected for the production process.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method for determining proppant fracturing performance provided by an embodiment of the present invention;
FIG. 2 is a flow chart of a method for determining proppant fracturing performance provided by an embodiment of the present invention;
FIG. 3 is a graph of the fracture function of a proppant provided by an embodiment of the present invention;
FIG. 4 is a graph of a proppant make-up function provided by an embodiment of the present invention;
FIG. 5 is a graph of a particle number balance equation for a proppant provided by an embodiment of the present invention;
FIG. 6 is a schematic structural diagram of a proppant fracturing performance determining device provided by an embodiment of the present invention;
fig. 7 is a schematic device structure diagram of a computer apparatus according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Fig. 1 is a flowchart of a method for determining proppant fracturing performance according to an embodiment of the present invention. The method may be applied to a computer device, see fig. 1, the embodiment comprising:
101. and respectively carrying out multiple groups of first crushing experiments under multiple different pressures by adopting a plurality of proppants with different first particle sizes to obtain the experiment results of the multiple groups of first crushing experiments.
Wherein the first particle size is the primary particle size of the proppant in each set of first fracturing experiments.
102. And acquiring a first accumulated mass proportion of each group of the first crushing experiments based on the experiment results of the plurality of groups of the first crushing experiments.
Wherein the first accumulated mass ratio is: in the proppant of each set after the first fracturing experiment, the ratio of the mass of the proppant having a particle size smaller than the first particle size of the set of the first fracturing experiments to the total mass of the proppant of the set of the first fracturing experiments.
103. And acquiring a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass proportion after each group of first crushing experiments and the crushing function model.
Wherein the fragmentation function represents a relationship between the mass of proppant reduced by fragmentation in each set of first fragmentation experiments and the pressure, the first particle size of each set of first fragmentation experiments.
104. And carrying out multiple groups of second crushing experiments by adopting a plurality of proppants with different second particle sizes under a plurality of different pressures respectively to obtain the experiment results of the multiple groups of second crushing experiments.
The second particle size is the initial particle size of the proppant in each group of second crushing experiments, and the first particle size is the target particle size of each group of second crushing experiments.
105. And acquiring a second accumulated mass proportion and a third accumulated mass proportion after each group of second crushing experiments based on the experiment results of the plurality of groups of second crushing experiments.
Wherein the second accumulated mass ratio is: in each group of the second fracturing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of the second fracturing experiments is as follows: in the proppant of each set after the second fracturing experiment, the ratio of the mass of the proppant having a particle size smaller than the second particle size to the total mass of the proppant of the set in the second fracturing experiment.
106. And obtaining a replenishment function based on the first particle size of each group of second crushing experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second crushing experiments and the replenishment function model.
Wherein the replenishment function represents a proportion of the proppant crushed from the second particle size to the first particle size in each set of second crushing experiments.
107. And acquiring a particle number balance equation based on the crushing function, the supply function and the particle number balance model.
Wherein the particle number balance equation represents a relationship between a particle size of a proppant before and after crushing of a mixed proppant formed of a plurality of different particle sizes under a preset pressure, the preset pressure, and a cumulative mass ratio based on the first particle size.
According to the method provided by the embodiment of the invention, a first crushing experiment is carried out based on a small amount of proppant to obtain experiment data, and then a crushing function between the accumulated mass proportion and the particle size and pressure of the proppant before crushing is obtained; further, a second crushing experiment is carried out based on a small amount of groups of proppants, and a replenishment function between the particle size and the pressure before and after crushing of the proppants is obtained; in the mixed proppant consisting of the proppants with different particle sizes, after the crushing experiment, the variation of the mass of the proppant with the first particle size is as follows: the crushing mass of the original first particle size and the mass of the proppant of the first particle size formed by crushing the proppant of the second particle size are added, and based on the crushing function and the replenishment function, a particle number balance equation between the particle sizes of the proppant before and after the crushing experiment is obtained, so that based on the particle number balance equation, the pressure in the production process and the requirements on the crushing performance of the proppant, the matched proppant is selected for the production process.
In one possible implementation, the obtaining a particle number balance equation based on the fragmentation function, the replenishment function, and a particle number balance model includes:
carrying out differential discretization on the particle number balance model to obtain a differential model;
and acquiring the particle number balance equation based on the difference model, the crushing function and the replenishment function.
In one possible implementation, the fragmentation function model includes:
wherein x represents a first particle size in μm, σ represents the pressure of the first fracturing experiment in MPa, and S (x, σ) represents the value of the fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ in MPa-1And P (x, σ) represents the first cumulative mass fraction, dimensionless.
In one possible implementation, the replenishment function model includes:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless.
In one possible implementation, the grain number balance model includes:
wherein x represents a first particle size, the unit is μm, y represents a second particle size, the unit is μm, σ represents a pressure of a crushing experiment, the unit is MPa, B (y, x, σ) represents a replenishment function value when the second particle size is y after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the dimensionless degree is not provided, P (x, σ) represents a first accumulated mass proportion and the dimensionless degree is provided, P (y, σ) represents a third accumulated mass proportion and the dimensionless degree is provided, S (x, σ) represents a crushing function value after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the unit is MPa-1。
Fig. 2 is a flowchart of a method for determining proppant fracturing performance according to an embodiment of the present invention. The method may be applied to a computer device, see fig. 2, the embodiment comprising:
201. and respectively carrying out multiple groups of first crushing experiments under multiple different pressures by adopting a plurality of proppants with different first particle sizes to obtain the experiment results of the multiple groups of first crushing experiments.
Wherein the first particle size is the primary particle size of the proppant in each set of first fracturing experiments. In this step 201, the computer device may obtain experimental results of the plurality of sets of first fragmentation experiments and process them in a subsequent step in order to obtain a first cumulative mass fraction. In particular, the experimental results of the sets of first fragmentation experiments may be directly obtained by the computer device from the experimental device.
For any one kind of proppant with the primary particle size, the multiple groups of first crushing experiments are used for obtaining the mass of any one kind of proppant with the primary particle size, which is reduced due to crushing after the crushing experiments are carried out. In particular, the experiment may be performed with proppants of a plurality of common particle sizes and a plurality of pressures at a gradient, for example, the plurality of different first particle sizes may be: 300 μm, 400 μm, 500 μm and 700 μm, while the plurality of different pressures may be: 30MPa, 40MPa, 50MPa, 60MPa and 70 MPa. Each first particle size and each pressure are combined to perform a first fracturing experiment, each set of first fracturing experiments having the same initial mass of proppant in order to obtain accurate experimental results.
202. And acquiring a first accumulated mass proportion of each group of the first crushing experiments based on the experiment results of the plurality of groups of the first crushing experiments.
Wherein the first accumulated mass ratio is: in the proppant of each set after the first fracturing experiment, the ratio of the mass of the proppant having a particle size smaller than the first particle size of the set of the first fracturing experiments to the total mass of the proppant of the set of the first fracturing experiments.
The first crushing experiment is used for acquiring the crushing characteristics of a small group of proppants under certain pressure, the first accumulated mass proportion is used for reflecting the crushing characteristics, and the accumulated mass proportion is used for acquiring the crushing function in the subsequent step. In the process of obtaining the first accumulated mass proportion, after the pressurized proppant sample is taken out from the experimental equipment, in order to ensure the accuracy of the experimental result, the mass of the proppant is firstly measured, if the mass loss of the proppant exceeds 1%, the set of experiments are considered to be invalid, and the set of experiments need to be carried out again. Further, samples are taken at a plurality of different positions respectively, the first cumulative mass proportions of the samples are measured, and the average of the first cumulative mass proportions of the samples is obtained as the first cumulative mass proportion after the set of first crushing experiments.
203. And acquiring a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass proportion after each group of first crushing experiments and the crushing function model.
Wherein the fragmentation function represents a relationship between the mass of proppant reduced by fragmentation in each set of first fragmentation experiments and the pressure, the first particle size of each set of first fragmentation experiments.
In one possible implementation, the fragmentation function model includes:
wherein x represents a first particle size in μm, σ represents a pressure of the first fracturing experiment in MPa, and S (x, σ) represents a value of a fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ, and MPa-1And P (x, σ) represents the first cumulative mass fraction, dimensionless. For example, according to the items of data obtained in the above steps, the fragmentation function can be obtained as follows:
S(x,σ)＝(-0.0022σ+0.1864)x(0.0031σ-0.4149)
in one possible implementation, the step 203 further includes: the pressure in the crushing function is respectively assigned to make a crushing function graph, and fig. 3 is a crushing function graph of the proppant provided by the embodiment of the invention, wherein the abscissa represents the particle diameter in mum, and the ordinate represents the value of the crushing function in MPa-1. The accuracy between the calculated value and the experimental value of the crushing function can be reflected more intuitively by the crushing function graph.
204. And carrying out multiple groups of second crushing experiments by adopting a plurality of proppants with different second particle sizes under a plurality of different pressures respectively to obtain the experiment results of the multiple groups of second crushing experiments.
The second particle size is the initial particle size of the proppant in each group of second crushing experiments, and the first particle size is the target particle size of each group of second crushing experiments. The second crushing experiment is used for obtaining the mass of the first particle size in the proppant after the crushing experiment.
205. And acquiring a second accumulated mass proportion and a third accumulated mass proportion after each group of second crushing experiments based on the experiment results of the plurality of groups of second crushing experiments.
Wherein the second accumulated mass ratio is: in each group of the second fracturing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of the second fracturing experiments is as follows: in the proppant of each set after the second fracturing experiment, the ratio of the mass of the proppant having a particle size smaller than the second particle size to the total mass of the proppant of the set in the second fracturing experiment.
In this step 205, the computer device may obtain experimental results of the plurality of sets of second fragmentation experiments and process them in a subsequent step in order to obtain the second and third cumulative mass proportions. In particular, the experimental results of the plurality of sets of second fragmentation experiments may be directly obtained from the experimental apparatus by the computer apparatus.
The second crushing experiment is used for obtaining the crushing characteristics of a small group of proppants under a certain pressure, the second accumulated mass proportion is used for reflecting the crushing characteristics, and the second accumulated mass proportion and the third accumulated mass proportion are both used for obtaining a replenishment function in the subsequent process. The process of acquiring the second cumulative mass proportion and the third cumulative mass proportion is similar to the process of acquiring the first cumulative mass proportion, and is not repeated herein.
The first crushing experiment and the second crushing experiment aim at obtaining the proportion of the proppant with one particle size in the obtained proppants under a certain pressure of a plurality of proppants with different particle sizes. Carrying out experiments based on a small amount of groups of proppants, acquiring experimental data, and acquiring the mass of the proppants with the first particle size, which is reduced due to crushing, under a certain pressure based on the first crushing experiment; based on the second crushing experiment, the proportion of the second particle size to the first particle size of the proppant under a certain pressure is obtained. Based on the data, the obtained particle number balance equation can reflect the proportion of the proppant with the first particle size in the proppant with various initial particle sizes, and the proppant with the first particle size is crushed under a certain pressure and is used for comprehensively evaluating the crushing characteristics of the various proppants, so that the matched proppant can be selected for the production process based on the particle number balance equation.
206. And obtaining a replenishment function based on the first particle size of each group of second crushing experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second crushing experiments and the replenishment function model.
Wherein the replenishment function represents a proportion of the proppant crushed from the second particle size to the first particle size in each set of second crushing experiments.
In one possible implementation, the replenishment function model includes:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless. For example, according to the items of data obtained in the above steps, the replenishment function can be obtained as follows:
wherein, B1＝-0.0015σ+1.0961，B2＝0.0111x2+0.7066x+17.316，
B3＝0.0036σ+0.4418
In one possible implementation, the step 206 further includes: assigning the pressure in the replenishment function respectively, and making a replenishment function graph, wherein fig. 4 is the replenishment function graph of the proppant provided by the embodiment of the invention, the abscissa represents the dimensionless particle size, namely the value of x/y, and the ordinate represents the value of the replenishment function, and the unit is MPa-1. The accuracy between the calculated value and the experimental value of the replenishment function can be reflected more intuitively by the replenishment function graph.
207. And acquiring a particle number balance equation based on the crushing function, the supply function and the particle number balance model.
Wherein the particle number balance equation represents a relationship between a particle size of a proppant before and after crushing of a mixed proppant formed of a plurality of different particle sizes under a preset pressure, the preset pressure, and a cumulative mass ratio based on the first particle size.
In the actual production process, a plurality of proppants with different particle sizes are mixed and then enter the stratum along with the high-pressure solution, so that the research on the crushing characteristics of the plurality of proppants with different particle sizes under high pressure has good practical significance, and the guidance on the use process of the proppants on site is facilitated.
In one possible implementation, the grain number balance model includes:
the initial conditions were:
P(x,0)＝f(x)
the boundary conditions are as follows:
wherein f (x) is the initial particle size cumulative distribution of the proppant, dimensionless.
Wherein x represents a first particle size in μm, y represents a second particle size in μm, σ represents a pressure of a crushing experiment, andthe bit is MPa, B (y, x, sigma) represents a supply function value when the second particle size of the proppant with the first particle size of x is y after the crushing experiment is carried out under the condition of pressure of sigma, and has no dimension, P (x, sigma) represents a first accumulated mass proportion and has no dimension, P (y, sigma) represents a third accumulated mass proportion and has no dimension, and S (x, sigma) represents a crushing function value of the proppant with the first particle size of x after the crushing experiment is carried out under the condition of pressure of sigma, and the unit is MPa-1。
In one possible implementation, the obtaining a particle number balance equation based on the fragmentation function, the replenishment function, and a particle number balance model includes: carrying out differential discretization on the particle number balance model to obtain a differential model; and acquiring the particle number balance equation based on the difference model, the crushing function and the replenishment function. The method of difference is adopted to facilitate the solution of the particle number balance equation, and specifically, the step length in the x direction is taken as delta x ═ xmaxN, the node is { x1,x2,…,xNStep size in σ direction is Δ σ ═ σ }minPer M, node is { σ1,σ2,…,σM}. The difference equation is established as follows:
wherein, Pi nRepresents the cumulative mass ratio at which the first particle diameter is x and the pressure is n.
In one possible implementation, step 207 further includes: and (3) respectively assigning the pressure in the particle number balance equation, and making a particle number balance equation graph, wherein the abscissa represents the particle size, the unit is mum, and the ordinate represents the accumulated mass ratio without dimension, and fig. 5 is the particle number balance equation graph of the proppant provided by the embodiment of the invention. The particle number balance equation graph can reflect the accuracy between the calculated value and the experimental value of the particle number balance equation more intuitively.
208. And determining the particle size of the proppant meeting the first preset condition based on the particle number balance equation.
The first preset condition can be set according to the actual pressure of the oil well and the requirement of the accumulated mass proportion of the proppant under the pressure, and is used for selecting the combination of the proppants meeting the use requirement from the aspect of particle size.
209. And obtaining the breakage rate of each group of first breakage experiments and each group of second breakage experiments, and further determining the particle size of the proppant meeting a second preset condition based on the breakage rate of each group of first breakage experiments and each group of second breakage experiments.
The second preset condition can be set according to the actual pressure of the oil well and the requirement of the fracture rate of the proppant under the pressure, and is used for selecting the combination of the proppants meeting the use requirement from the aspect of the fracture rate.
The method is used for detecting the quality of the proppant from two aspects of the breaking rate and the particle number balance equation of the proppant, and the proppant meeting the use requirement is obtained based on the quality, so that the accuracy of the performance detection of the proppant is improved.
All the above-mentioned optional technical solutions can be combined arbitrarily to form the optional embodiments of the present invention, and are not described herein again.
According to the method provided by the embodiment of the invention, a first crushing experiment is carried out based on a small amount of proppant to obtain experiment data, and then a crushing function between the accumulated mass proportion and the particle size and pressure of the proppant before crushing is obtained; further, a second crushing experiment is carried out based on a small amount of groups of proppants, and a replenishment function between the particle size and the pressure before and after crushing of the proppants is obtained; in the mixed proppant consisting of the proppants with different particle sizes, after the crushing experiment, the variation of the mass of the proppant with the first particle size is as follows: the crushing mass of the original first particle size and the mass of the proppant of the first particle size formed by crushing the proppant of the second particle size are added, and based on the crushing function and the replenishment function, a particle number balance equation between the particle sizes of the proppant before and after the crushing experiment is obtained, so that based on the particle number balance equation, the pressure in the production process and the requirements on the crushing performance of the proppant, the matched proppant is selected for the production process.
Furthermore, the breaking rate of each group of first breaking experiments and each group of second breaking experiments can be obtained, the propping agent meeting the use requirement is obtained based on the breaking rate and the particle number balance equation of each group of first breaking experiments and each group of second breaking experiments, and the accuracy of propping agent performance detection is favorably improved.
Fig. 6 is a schematic structural diagram of a proppant crushing performance determining apparatus provided by an embodiment of the present invention, and referring to fig. 6, the apparatus includes:
the crushing module 601 is configured to perform multiple groups of first crushing experiments under multiple different pressures by using multiple proppants with different first particle sizes, so as to obtain experiment results of the multiple groups of first crushing experiments, where the first particle size is an initial particle size of the proppant in each group of first crushing experiments;
a data obtaining module 602, configured to obtain, based on the experiment results of the multiple groups of first crushing experiments, a first accumulated mass ratio after each group of first crushing experiments, where the first accumulated mass ratio is: in the proppant after each group of the first crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size of the group of the first crushing experiments to the total mass of the proppant in the group of the first crushing experiments;
a crushing function obtaining module 603, configured to obtain a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass ratio after each group of first crushing experiments, and a crushing function model, where the crushing function represents a relationship between a mass of the proppant in each group of first crushing experiments, which is reduced due to crushing, and the pressure of each group of first crushing experiments and the first particle size;
the crushing module 601 is further configured to perform multiple groups of second crushing experiments under multiple different pressures by using multiple proppants with different second particle sizes, so as to obtain experiment results of the multiple groups of second crushing experiments, where the second particle size is an initial particle size of the proppant in each group of second crushing experiments, and the first particle size is a target particle size of each group of second crushing experiments;
the data obtaining module 602 is further configured to obtain, based on the experiment results of the multiple groups of second crushing experiments, a second accumulated mass ratio and a third accumulated mass ratio after each group of second crushing experiments, where the second accumulated mass ratio is: in each group of the second fracturing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of the second fracturing experiments is as follows: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the second particle size to the total mass of the proppant in the group of second crushing experiments;
a replenishment function obtaining module 604, configured to obtain a replenishment function based on the first particle size of each group of second fragmentation experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second fragmentation experiments, and a replenishment function model, where the replenishment function represents a proportion of the proppant crushed into the first particle size from the second particle size in each group of second fragmentation experiments;
a particle number balance equation obtaining module 605, configured to obtain a particle number balance equation based on the crushing function, the replenishment function, and the particle number balance model, where the particle number balance equation represents a relationship between a particle size of a proppant before and after crushing of a mixed proppant formed by multiple different particle sizes under a preset pressure, the preset pressure, and an accumulated mass ratio based on the first particle size.
In one possible implementation, the grain number balance equation obtaining module 605 is configured to:
carrying out differential discretization on the particle number balance model to obtain a differential model;
and acquiring the particle number balance equation based on the difference model, the crushing function and the replenishment function.
In one possible implementation, the fragmentation function model includes:
wherein x represents a first particle size in μm, σ represents the pressure of the first fracturing experiment in MPa, and S (x, σ) represents the value of the fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ in MPa-1，P(xσ) represents the first cumulative mass fraction, dimensionless.
In one possible implementation, the replenishment function model includes:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless.
In one possible implementation, the grain number balance model includes:
wherein x represents a first particle size, the unit is μm, y represents a second particle size, the unit is μm, σ represents a pressure of a crushing experiment, the unit is MPa, B (y, x, σ) represents a replenishment function value when the second particle size is y after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the dimensionless degree is not provided, P (x, σ) represents a first accumulated mass proportion and the dimensionless degree is provided, P (y, σ) represents a third accumulated mass proportion and the dimensionless degree is provided, S (x, σ) represents a crushing function value after the crushing experiment is performed on the proppant with the first particle size being x under the condition that the pressure is σ, and the unit is MPa-1。
It should be noted that: the device for determining the fragmentation performance of a proppant provided in the above embodiments is only illustrated by the division of the above functional modules when determining the fragmentation performance of a proppant, and in practical applications, the above function distribution may be performed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to perform all or part of the above described functions. In addition, the device for determining the fragmentation performance of the proppant provided by the above embodiment and the method embodiment for determining the fragmentation performance of the proppant belong to the same concept, and the specific implementation process thereof is described in the method embodiment and is not described again.
According to the device provided by the embodiment of the invention, a first crushing experiment is carried out based on a small amount of proppant to obtain experiment data, and then a crushing function between the accumulated mass proportion and the particle size and pressure of the proppant before crushing is obtained; further, a second crushing experiment is carried out based on a small amount of groups of proppants, and a replenishment function between the particle size and the pressure before and after crushing of the proppants is obtained; in the mixed proppant consisting of the proppants with different particle sizes, after the crushing experiment, the variation of the mass of the proppant with the first particle size is as follows: the crushing mass of the original first particle size and the mass of the proppant of the first particle size formed by crushing the proppant of the second particle size are added, and based on the crushing function and the replenishment function, a particle number balance equation between the particle sizes of the proppant before and after the crushing experiment is obtained, so that based on the particle number balance equation, the pressure in the production process and the requirements on the crushing performance of the proppant, the matched proppant is selected for the production process.
Fig. 7 is a schematic structural diagram of a computer device 700 according to an embodiment of the present invention, where the computer device 700 may generate 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 method for determining the proppant breaking performance provided by the above-mentioned method embodiments. Certainly, the computer device may further have components such as a wired or wireless network interface, a keyboard, and an input/output interface, so as to perform input and output, and the computer device may further include other components for implementing the functions of the device, which is not described herein again.
In an exemplary embodiment, a computer-readable storage medium, such as a memory, is also provided that includes instructions executable by a processor in a computer device to perform the method of proppant fracturing performance determination of the above 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.
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 for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A method of determining proppant fracturing performance, the method comprising:
carrying out multiple groups of first crushing experiments by adopting a plurality of proppants with different first particle sizes under a plurality of different pressures respectively to obtain experiment results of the multiple groups of first crushing experiments, wherein the first particle sizes are the initial particle sizes of the proppants in each group of first crushing experiments;
obtaining a first accumulated mass ratio after each group of first crushing experiments based on the experiment results of the plurality of groups of first crushing experiments, wherein the first accumulated mass ratio refers to: in each group of the proppants after the first crushing experiment, the ratio of the mass of the proppants with the particle size smaller than the first particle size of the group of the first crushing experiment to the total mass of the proppants in the group of the first crushing experiment;
obtaining a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass proportion after each group of first crushing experiments and a crushing function model, wherein the crushing function represents the relation between the mass of the proppant in each group of first crushing experiments, which is reduced due to crushing, and the pressure of each group of first crushing experiments and the first particle size;
carrying out multiple groups of second crushing experiments by adopting a plurality of proppants with different second particle sizes under a plurality of different pressures respectively to obtain experiment results of the multiple groups of second crushing experiments, wherein the second particle sizes are the initial particle sizes of the proppants in each group of second crushing experiments, and the first particle sizes are the target particle sizes of each group of second crushing experiments;
obtaining a second accumulated mass proportion and a third accumulated mass proportion after each group of second crushing experiments based on the experiment results of the plurality of groups of second crushing experiments, wherein the second accumulated mass proportion refers to: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of second crushing experiments is as follows: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the second particle size to the total mass of the proppant in the group of second crushing experiments;
obtaining a replenishment function based on the first particle size of each group of second crushing experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second crushing experiments, and a replenishment function model, wherein the replenishment function represents the proportion of the proppant crushed into the first particle size from the second particle size in each group of second crushing experiments;
and acquiring a particle number balance equation based on the crushing function, the replenishment function and a particle number balance model, wherein the particle number balance equation represents the relationship between the particle size of the proppant before and after crushing of the mixed proppant formed by the proppants with different particle sizes under a preset pressure, the preset pressure and the accumulated mass ratio based on the first particle size.
2. The method of claim 1, wherein obtaining a particle number balance equation based on the fragmentation function, the replenishment function, and a particle number balance model comprises:
carrying out differential discretization on the particle number balance model to obtain a differential model;
and acquiring the particle number balance equation based on the difference model, the crushing function and the supply function.
3. The method of claim 1, wherein the fragmentation function model comprises:
wherein x represents a first particle size in μm, σ represents a pressure of the first fracturing experiment in MPa, and S (x, σ) represents a value of a fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ, and MPa-1And P (x, σ) represents the first cumulative mass fraction, dimensionless.
4. The method of claim 1, wherein the replenishment function model comprises:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless.
5. The method of claim 1, wherein the grain number balance model comprises:
wherein x represents the first particle size in μm, y represents the second particle size in μm, σ represents the pressure in the crushing test in MPa, and B (y, x, σ) is shown in TableShowing a replenishment function value when a second particle size is y after a fracturing experiment is carried out on a proppant with a first particle size of x under the condition of pressure of sigma, without dimension, P (x, sigma) showing a first accumulated mass proportion, without dimension, P (y, sigma) showing a third accumulated mass proportion, without dimension, and S (x, sigma) showing a fracturing function value after the fracturing experiment is carried out on the proppant with the first particle size of x under the condition of pressure of sigma, and the unit is MPa-1。
6. An apparatus for determining proppant fracturing performance, the apparatus comprising:
the crushing module is used for performing multiple groups of first crushing experiments under multiple different pressures by adopting multiple proppants with different first particle sizes respectively to obtain experiment results of the multiple groups of first crushing experiments, wherein the first particle sizes are initial particle sizes of the proppants in each group of first crushing experiments;
a data obtaining module, configured to obtain, based on the experiment results of the multiple groups of first crushing experiments, a first accumulated mass ratio after each group of first crushing experiments, where the first accumulated mass ratio is: in each group of the proppants after the first crushing experiment, the ratio of the mass of the proppants with the particle size smaller than the first particle size of the group of the first crushing experiment to the total mass of the proppants in the group of the first crushing experiment;
a crushing function obtaining module, configured to obtain a crushing function based on the first particle size of each group of first crushing experiments, the pressure of each group of first crushing experiments, the first accumulated mass ratio after each group of first crushing experiments, and a crushing function model, where the crushing function represents a relationship between a mass of the proppant in each group of first crushing experiments, which is reduced due to crushing, and the pressure of each group of first crushing experiments and the first particle size;
the crushing module is further used for performing a plurality of groups of second crushing experiments under a plurality of different pressures by using a plurality of proppants with different second particle sizes respectively to obtain experiment results of the plurality of groups of second crushing experiments, wherein the second particle sizes are initial particle sizes of the proppants in each group of second crushing experiments, and the first particle sizes are target particle sizes of the second crushing experiments;
the data obtaining module is further configured to obtain, based on the experiment results of the plurality of groups of second crushing experiments, a second accumulated mass proportion and a third accumulated mass proportion after each group of second crushing experiments, where the second accumulated mass proportion refers to: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the first particle size to the total mass of the proppant in the group of second crushing experiments is as follows: in the proppant after each group of second crushing experiments, the ratio of the mass of the proppant with the particle size smaller than the second particle size to the total mass of the proppant in the group of second crushing experiments;
a replenishment function obtaining module, configured to obtain a replenishment function based on the first particle size of each group of second fragmentation experiments, the second accumulated mass proportion and the third accumulated mass proportion after each group of second fragmentation experiments, and a replenishment function model, where the replenishment function represents a proportion of the proppant in each group of second fragmentation experiments that is fragmented from the second particle size to the first particle size;
and the particle number balance equation obtaining module is used for obtaining a particle number balance equation based on the crushing function, the replenishment function and the particle number balance model, wherein the particle number balance equation represents the relationship among the particle size of the proppant before and after crushing of the mixed proppant formed by a plurality of proppants with different particle sizes under preset pressure, the preset pressure and the accumulated mass ratio based on the first particle size.
7. The apparatus of claim 6, wherein the grain number balance equation obtaining module is configured to:
carrying out differential discretization on the particle number balance model to obtain a differential model;
and acquiring the particle number balance equation based on the difference model, the crushing function and the supply function.
8. The apparatus of claim 6, wherein the fragmentation function model comprises:
wherein x represents a first particle size in μm, σ represents a pressure of the first fracturing experiment in MPa, and S (x, σ) represents a value of a fracturing function of the proppant having the first particle size x after the first fracturing experiment under the pressure of σ, and MPa-1And P (x, σ) represents the first cumulative mass fraction, dimensionless.
9. The apparatus of claim 6, wherein the replenishment function model comprises:
wherein x represents a first particle size, and is expressed in μm, y represents a second particle size, and is expressed in μm, σ represents pressure of a second crushing experiment, and is expressed in MPa, B (y, x, σ) represents a replenishment function value when the first particle size is x after a proppant having the second particle size of y is subjected to the second crushing experiment under the condition that the pressure is σ, and is dimensionless, P (x, σ) represents a second accumulated mass ratio, and is dimensionless, and P (y, σ) represents a third accumulated mass ratio, and is dimensionless.
10. The apparatus of claim 6, wherein the grain number balance model comprises:
wherein x represents a first particle diameter, in μm, y represents a second particle diameter, in μm, σ represents a pressure of a crushing experiment, in MPa, B (y, x, σ) represents a replenishment function value when the second particle diameter is y after the crushing experiment of the proppant having the first particle diameter of x is performed under the pressure of σ, and is dimensionless, P (x, σ) represents a first cumulative mass ratio, and is dimensionless, and P (y, σ) represents a third cumulative mass ratio,dimensionless, S (x, σ) denotes the value of the fracture function of a proppant having a first particle size x after fracturing experiments under pressure σ, in MPa-1。
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