CN108661623B - Pump diagram calculation method and device based on pumping unit suspension point load fluctuation analysis - Google Patents

Pump diagram calculation method and device based on pumping unit suspension point load fluctuation analysis Download PDF

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CN108661623B
CN108661623B CN201810412474.5A CN201810412474A CN108661623B CN 108661623 B CN108661623 B CN 108661623B CN 201810412474 A CN201810412474 A CN 201810412474A CN 108661623 B CN108661623 B CN 108661623B
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load
pump
suspension point
calculating
displacement
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CN108661623A (en
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尹教建
孙东
马秀波
尹玉芳
杨新建
李静
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China University of Petroleum East China
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China University of Petroleum East China
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells
    • E21B47/008—Monitoring of down-hole pump systems, e.g. for the detection of "pumped-off" conditions
    • E21B47/009—Monitoring of walking-beam pump systems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Abstract

The invention discloses a pump diagram calculation method and a device based on pumping unit suspension point load fluctuation analysis, wherein the method comprises the following steps: step 1: obtaining a longitudinal wave equation of the sucker rod; step 2: calculating the wave equation and obtaining an analytic solution of the wave equation; and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point; and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump; and 5: calculating a pump diagram according to the suspension point indicator diagram; step 6: analyzing the fluctuation form of the pump valve under the action of pulse load; and 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr. The technical problems that in the prior art, partial parameters of the sucker rod are not suitable to be accurately obtained, and parameters such as the length and the diameter of the sucker rod are not available sometimes, and calculation and application of a pump diagram are influenced are solved, and the technical effects that the pump diagram is convenient to obtain, the length of the sucker rod, the cross-sectional area of the sucker rod and the damping coefficient are convenient to calculate are achieved.

Description

Pump diagram calculation method and device based on pumping unit suspension point load fluctuation analysis
Technical Field
The invention relates to the technical field of oil exploitation, in particular to a pump diagram calculation method and device based on analysis of pumping unit suspension point load fluctuation.
Background
The pumping unit pump diagram is a direct reflection of the operation condition of an oil well pump in a rod pump pumping system, and the obtained pumping unit pump diagram has important significance for the production and management of an oil field. The oil well pump is generally located at a depth of thousands of meters underground and cannot be directly measured. The method is to measure the indicator diagram of the suspension point by a dynamic instrument, solve the wave equation of the sucker rod by a complex separation variable method, and calculate the indicator diagram according to the parameters of the sucker rod such as material, length, diameter, viscous damping coefficient and the like. In practical application, some parameters are not suitable for being accurately obtained, such as a viscous damping system, and even parameters such as the length and the diameter of the pumping rod are not available under some conditions, so that the calculation and the application of a pump diagram are influenced.
Disclosure of Invention
The invention provides a pump work diagram calculation method and device based on analysis of pumping unit suspension point load fluctuation, which are used for solving the technical problems that in the prior art, partial parameters of a pumping rod are not suitable for being accurately obtained, such as a viscous damping system, and parameters such as the length and the diameter of the pumping rod are not available sometimes, so that calculation and application of the pump work diagram are influenced, and the technical effects of conveniently obtaining the pump work diagram, and conveniently calculating the length of the pumping rod, the cross-sectional area of the pumping rod and the damping coefficient are achieved.
In one aspect, the invention provides a pump diagram calculation method based on analysis of pumping unit suspension point load fluctuation, which comprises the following steps: step 1: obtaining a longitudinal wave equation of the sucker rod; step 2: calculating the wave equation and obtaining an analytic solution of the wave equation; and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point; and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump; and 5: calculating a pump diagram according to the suspension point indicator diagram; step 6: analyzing the fluctuation form of the pump valve under the action of pulse load; and 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr。
Preferably, in step 1, according to that the propagation speed of sound in the sucker rod is c, the damping coefficient of the oil well fluid to the sucker rod is ν, and the sucker rod is in an underdamped state, the upper boundary condition displacement time function is p (t), the lower boundary condition load time function is q (t), the initial moment displacement and speed are zero, the length of the sucker rod is l, and the longitudinal wave equation of the sucker rod is obtained as follows:
Figure GDA0003475966670000021
preferably, the calculating the wave equation and obtaining an analytic solution of the wave equation further includes: obtaining a preset solution of the wave equation as: obtaining a solution problem of the homogeneous boundary condition according to the preset solution and the wave equation, wherein u (x, t) ═ w (x, t) + q (t) x + p (t) (2), and the solution problem is as follows:
Figure GDA0003475966670000022
wherein f (x, t) — v (q 'x + p') - (q "x + p") (4); according to the boundary condition w (0, t) ═ wx(l, t) ═ 0, the eigenfunctions for obtaining the solution problem are: sin omeganx，
Figure GDA0003475966670000023
Figure GDA0003475966670000024
According to the eigenfunction sin omeganx expands W (x, t) and f (x, t) respectively, and the expansion result is as follows:
Figure GDA0003475966670000025
and
Figure GDA0003475966670000026
Figure GDA0003475966670000027
bringing equations (5), (6), (7) into equation (3) results in: wn"+vWn'+(ωnc)2Wn＝fn(t) (8); according to the preset values w (x,0) ═ 0, wt (x,0) ═ 0, the following results are obtained: wn(0)＝Wn' (0) ═ 0 (9); substituting equation (4) into
Figure GDA0003475966670000028
Obtaining: f. ofn(t)＝fpn(t)+fqn(t) (10); wherein the content of the first and second substances,
Figure GDA0003475966670000029
shifting the upper bound condition by timeThe function p (T) and the lower boundary condition load time function q (T) are obtained by expansion according to a periodic T Fourier series:
Figure GDA00034759666700000210
and
Figure GDA00034759666700000211
wherein the content of the first and second substances,
Figure GDA00034759666700000212
to obtain
Figure GDA00034759666700000213
Figure GDA0003475966670000031
Wherein the content of the first and second substances,
Figure GDA0003475966670000032
Figure GDA0003475966670000033
is calculated to obtain
Figure GDA0003475966670000034
Obtained according to equation (8):
Figure GDA0003475966670000035
the solution of the equation (21) is:
Figure GDA0003475966670000036
according to the under-damping characteristic when
Figure GDA0003475966670000037
When the temperature of the water is higher than the set temperature,
Figure GDA0003475966670000038
from equation (9) we can obtain: cn＝D n0; according to Cn＝DnSubstituting equation (22) into equation (21) yields 0:
Figure GDA0003475966670000039
and calculating to obtain:
Figure GDA00034759666700000310
Figure GDA00034759666700000311
calculated according to equation (5):
Figure GDA00034759666700000312
substituting equation (25) into equation (2) yields an analytical solution for the wave equation as:
Figure GDA00034759666700000313
preferably, the calculating the pump load according to the fourier coefficient of the suspension point load further includes: according to
Figure GDA00034759666700000314
Performing Fourier series expansion on the first suspension point load: calculating the suspension point load according to said formula (26) as:
Figure GDA0003475966670000041
wherein E isrYoung's modulus of sucker rod, ArThe sectional area of the sucker rod; substituting the equation (14) into the equation (28) yields:
Figure GDA0003475966670000042
comparing said formula (27) with said formula (29) to obtain:
Figure GDA0003475966670000043
will QnmAnd PnmThe calculation formulas are respectively substituted into the calculation to obtain: erAra0＝ace0(30)，
Figure GDA0003475966670000044
Figure GDA0003475966670000045
Said formulas (31) and (32) are developed
Figure GDA0003475966670000046
Figure GDA0003475966670000047
Wherein the content of the first and second substances,
Figure GDA0003475966670000048
and
Figure GDA0003475966670000049
respectively forming suspension point load parameters for suspension point displacement; will be a formula
Figure GDA00034759666700000410
And formula
Figure GDA00034759666700000411
Both substituting said formula (33) and said (34) into being available:
Figure GDA00034759666700000412
Figure GDA00034759666700000413
from said formula (39) and said formula (40) it follows:
Figure GDA0003475966670000051
wherein the content of the first and second substances,
Figure GDA0003475966670000052
Figure GDA0003475966670000053
a is obtained by calculation according to the formulas (17), (18), (19), (20), (23) and (24)qmAnd bqmBringing the lower boundary conditions to obtain a pump load of:
Figure GDA0003475966670000054
preferably, the calculating of the pump displacement according to the suspension point displacement and the fourier coefficient of the pump load further comprises the fourier coefficient a of the suspension point displacementpm、bpmAnd pump load Fourier coefficient aqm、bqmSubstituting the equations (17), (18), (19), (20), (23) and (24) to respectively obtain parameters A of the wave equation analytic solutionpnm、Aqnm、Bpnm、Bqnm、Qnm、PnmSubstituting the equation (2) can result in a pump displacement of:
Figure GDA0003475966670000055
preferably, the calculating a pump diagram according to the suspension point indicator diagram further includes: and obtaining a pump work diagram according to the fact that the pump displacement is an abscissa and the pump load is an ordinate.
Preferably, the calculating a pump diagram according to the suspension point indicator diagram further includes: obtaining a second differential equation of the pump load and using the second differential equation as a pulse function q' (t) ═ q0δ (t- τ) (45), where δ (t- τ) is a unit pulse function indicating that a pulse acts at time t ═ τ; when the influence caused by the displacement of the suspension point and the characteristic of the small damping coefficient are not considered, the calculation result is obtained
Figure GDA0003475966670000056
According to the fact that the instant time of pulse action is short, displacement can not be changed in time, and the speed can be changed suddenly to obtain
Figure GDA0003475966670000057
Then
Figure GDA0003475966670000058
The fluctuation part on the suspension point load is obtained as follows:
Figure GDA0003475966670000061
when consideringWhen the fundamental frequency of the sucker rod vibrates,
Figure GDA0003475966670000062
wherein E isrArq0Is the maximum of the second derivative of the pump load function, and ErArq0The pulse value is the pulse value when the fixed valve or the traveling valve is suddenly loaded; obtaining the suspension point load part formed by the suspension point displacement
Figure GDA0003475966670000063
Figure GDA0003475966670000064
According to the pump load being constant F after the standing valve is opened0When the traveling valve is opened, the pump load is 0, and according to the superposition principle, the fluctuation form of the fluctuation stage is obtained as follows: upper stroke part
Figure GDA0003475966670000065
Down stroke part
Figure GDA0003475966670000066
Preferably, the length l of the sucker rod, the damping coefficient v and the cross section area A of the sucker rod are determined according to the fluctuation form of the suspension point loadrThe method also comprises the following steps: step 71: obtaining a suspension point displacement and load time sequence of a period; obtaining a fluctuating load signal, wherein the fluctuating load signal is a point of maximum load PRL (t) during the overshootpm) Or, a point of minimum load during undershoot; determining the time t at which the fluctuating load signal is obtainedSm(ii) a Selecting an original fluctuation signal PRL (t) from a maximum load point to an upper dead pointpm:tSm) Resetting the time with the time point at the maximum load point as the starting 0 point, wherein tc＝(0:tSm-tpm) (ii) a Step 72: for the original wobble signal PRL (t)pm:tSm) Linear trend is removed to obtain a fluctuation signal PRL' (t)c) Performing a spectral analysis, wherein the time t is calculatedcTotal length N oftcFor PRL' (t)c) Performing amplitude spectrum divisionAnalytically calculating a frequency series
Figure GDA0003475966670000067
Taking the first half part of the amplitude spectrum; selecting the frequency with the maximum amplitude as the initial fundamental frequency f0(ii) a Step 73: for the fluctuating signal PRL' (t)c) Normalization was performed to obtain PRL' (t)c)＝PRL'(tc)/PRL'(tpm) (ii) a For vibration frequency f0Optimizing to obtain
Figure GDA0003475966670000068
Obtaining a fundamental frequency f0yCalculating the pole length
Figure GDA0003475966670000069
Step 74: determining the law of the damped fundamental frequency cosine vibration as
Figure GDA00034759666700000610
Extracting a damping coefficient of the fluctuation signal according to the minimum difference value of the attenuated cosine vibration law and the actually measured vibration signal as an optimization target to obtain
Figure GDA0003475966670000071
Obtaining a damping coefficient v after optimizationce(ii) a Step 75: the original fluctuation signal is used for subtracting the attenuated fundamental frequency cosine vibration signal to obtain
Figure GDA0003475966670000072
Wherein, PRLh(tc)＝PRLp(tc)+F0(54) Said equation (54) having a suspension point load formed by a suspension point displacement and a pump load constant; according to PRLh'(tc)＝PRLh(tc)-PRLh(tcend) Eliminating the influence of constants, wherein, PRLh(tcend) Is PRLh(tc) The suspension point load corresponding to the medium final time; (ii) a
Step 76: obtaining the floating weight W of the sucker rod according to the minimum value of the suspension point loadfMin (PRL), calculating the initial value of the cross section of the sucker rod
Figure GDA0003475966670000073
Where ρ isrIs the density of the steel, pwIs the standard density of water; step 77: the displacement time function p (T) of the upper boundary condition is expanded according to the periodic T Fourier series
Figure GDA0003475966670000074
Wherein the content of the first and second substances,
Figure GDA0003475966670000075
m ═ 40; calculating system parameters
Figure GDA0003475966670000076
Calculating a suspension point load parameter formed by the displacement of the suspension point
Figure GDA0003475966670000077
Figure GDA0003475966670000078
Obtaining an expression as a function of the cross-sectional area of the sucker rod:
Figure GDA0003475966670000079
calculating to obtain PRLp'(Ar,tc)＝PRLp(tc)-PRLp(tcend) (ii) a Step 78: obtaining an optimization equation of
Figure GDA00034759666700000710
Obtaining the sectional area A of the sucker rod according to the optimization equationr。
In another aspect, the present invention further provides a pump diagram calculating apparatus based on analysis of pumping unit suspension point load fluctuation, where the apparatus includes: a measurement module for measuring a suspension displacement and a suspension load time series; the acquisition module is used for acquiring a suspension point displacement and a suspension point load time sequence of one period and is connected with the measurement module; the analysis module is used for analyzing the fluctuation characteristics of the suspension point load and is connected with the acquisition module; the calculation module is used for calculating a pump diagram and is connected with the analysis module; and the output module is used for outputting the calculation result and is connected with the calculation module.
One or more technical solutions in the embodiments of the present invention at least have one or more of the following technical effects:
the embodiment of the invention provides a pump diagram calculation method based on analysis of load fluctuation of a suspension point of an oil pumping unit, which comprises the following steps: step 1: obtaining a longitudinal wave equation of the sucker rod; step 2: calculating the wave equation and obtaining an analytic solution of the wave equation; and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point; and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump; and 5: calculating a pump diagram according to the suspension point indicator diagram; step 6: analyzing the fluctuation form of the pump valve under the action of pulse load; and 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr. The technical problems that in the prior art, partial parameters of the sucker rod are not suitable to be accurately obtained, such as a viscous damping system, and parameters such as the length and the diameter of the sucker rod are not available at times, and calculation and application of a pump diagram are influenced are solved, and the technical effects of conveniently obtaining the pump diagram, calculating the length of the sucker rod, the cross-sectional area of the sucker rod and calculating the damping coefficient are achieved.
The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.
Drawings
Fig. 1 is a schematic flow chart of a pump diagram calculation method based on analysis of pumping unit suspension point load fluctuation in an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a pump diagram calculation apparatus based on analysis of pumping unit suspension point load fluctuation in an embodiment of the present invention;
fig. 3 is a flow chart of a suspension point load vibration analysis of a pump diagram calculation method based on a pumping unit suspension point load fluctuation analysis in the embodiment of the present invention;
FIG. 4 is a graph of the displacement of the suspension point in an embodiment of the present invention;
FIG. 5 is a time series of the suspension point loads in an embodiment of the present invention;
FIG. 6 is a fluctuation curve of the suspension point load during the upstroke in the embodiment of the present invention, with the linear trend removed, and the fluctuation signal;
FIG. 7 is a first half amplitude spectrum of a wobble signal according to an embodiment of the present invention;
FIG. 8 is a comparison graph of the calculated fluctuation curve and the original fluctuation curve in the optimization in the embodiment of the present invention;
FIG. 9 is a load curve and optimization curve relating to the displacement of the suspension point in the embodiment of the present invention;
FIG. 10 shows the optimized cross-sectional area of the sucker rod in the embodiment of the present invention;
FIG. 11 is a flow chart of a suspension point indicator diagram for calculating pump power in an embodiment of the present invention;
fig. 12 is a pump diagram calculated from a suspension point indicator diagram in an embodiment of the present invention.
Detailed Description
The embodiment of the invention provides a pump work diagram calculation method and device based on analysis of pumping unit suspension point load fluctuation, which are used for solving the technical problems that in the prior art, partial parameters of a pumping rod are not suitable for being accurately obtained, such as a viscous damping system, and parameters such as the length and the diameter of the pumping rod are not available at times, so that calculation and application of the pump work diagram are influenced, and the technical effects of conveniently obtaining the pump work diagram, and conveniently calculating the length of the pumping rod, the cross-sectional area of the pumping rod and the damping coefficient are achieved.
The technical scheme in the embodiment of the invention has the following general idea:
the embodiment of the invention provides a pump diagram calculation method and device based on analysis of pumping unit suspension point load fluctuation, which comprises the following steps of: obtaining a longitudinal wave equation of the sucker rod; step 2: meterCalculating the wave equation and obtaining an analytic solution of the wave equation; and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point; and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump; and 5: calculating a pump diagram according to the suspension point indicator diagram; step 6: analyzing the fluctuation form of the pump valve under the action of pulse load; and 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr. The technical effects of obtaining the pump diagram conveniently, and calculating the length of the sucker rod, the cross-sectional area of the sucker rod and the damping coefficient conveniently are achieved.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example one
Fig. 1 is a schematic flow chart of a pump diagram calculation method based on analysis of pumping unit suspension point load fluctuation in an embodiment of the present invention, and as shown in fig. 1, the method includes:
step 1: obtaining a longitudinal wave equation of the sucker rod;
furthermore, according to the fact that the propagation speed of sound in the sucker rod is c, the damping coefficient of oil well liquid to the sucker rod is v, the oil well liquid is in an underdamped state, the displacement time function of the upper boundary condition is p (t), the load time function of the lower boundary condition is q (t), the displacement and the speed at the initial moment are zero, the length of the sucker rod is l, and the longitudinal wave equation of the sucker rod is obtained as follows:
Figure GDA0003475966670000101
step 2: calculating the wave equation and obtaining an analytic solution of the wave equation;
further, the calculating the wave equation and obtaining an analytic solution of the wave equation further includes: obtaining a preset solution of the wave equation as: obtaining a solution problem of the homogeneous boundary condition according to the preset solution and the wave equation, wherein u (x, t) ═ w (x, t) + q (t) x + p (t) (2), and the solution problem is as follows:
Figure GDA0003475966670000102
wherein f (x, t) — v (q 'x + p') - (q "x + p") (4);
according to the boundary condition w (0, t) ═ wx(l, t) ═ 0, the eigenfunctions for obtaining the solution problem are: sin omeganx，
Figure GDA0003475966670000103
According to the eigenfunction sin omeganx expands W (x, t) and f (x, t) respectively, and the expansion result is as follows:
Figure GDA0003475966670000111
and
Figure GDA0003475966670000112
Figure GDA0003475966670000113
bringing equations (5), (6), (7) into equation (3) results in: wn"+vWn'+(ωnc)2Wn＝fn(t)(8)；
According to the preset value w (x,0) being 0, wt(x,0) ═ 0 gave: wn(0)＝Wn'(0)＝0(9)；
Substituting equation (4) into
Figure GDA0003475966670000114
Obtaining: f. ofn(t)＝fpn(t)+fqn(t)(10)；
Wherein the content of the first and second substances,
Figure GDA0003475966670000115
expanding an upper boundary condition displacement time function p (T) and a lower boundary condition load time function q (T) according to a periodic T Fourier series to obtain:
Figure GDA0003475966670000116
and
Figure GDA0003475966670000117
wherein the content of the first and second substances,
Figure GDA0003475966670000118
to obtain
Figure GDA0003475966670000119
Wherein the content of the first and second substances,
Figure GDA00034759666700001110
Figure GDA00034759666700001111
is calculated to obtain
Figure GDA00034759666700001112
Obtained according to equation (8):
Figure GDA00034759666700001113
the solution of the equation (21) is:
Figure GDA00034759666700001114
according to the under-damping characteristicWhen is coming into contact with
Figure GDA0003475966670000121
When the temperature of the water is higher than the set temperature,
Figure GDA0003475966670000122
from equation (9) we can obtain: cn＝Dn＝0；
According to Cn＝DnSubstituting equation (22) into equation (21) yields 0:
Figure GDA0003475966670000123
and calculating to obtain:
Figure GDA0003475966670000124
Figure GDA0003475966670000125
calculated according to equation (5):
Figure GDA0003475966670000126
substituting equation (25) into equation (2) yields an analytical solution for the wave equation as:
Figure GDA0003475966670000127
and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point;
further, the calculating the pump load according to the fourier coefficient of the suspension point load further includes: according to
Figure GDA0003475966670000128
Suspending the first suspensionPerforming Fourier series expansion on the point load:
calculating the suspension point load according to said formula (26) as:
Figure GDA0003475966670000129
wherein E isrYoung's modulus of sucker rod, ArThe sectional area of the sucker rod;
substituting the equation (14) into the equation (28) yields:
Figure GDA0003475966670000131
comparing said formula (27) with said formula (29) to obtain:
Figure GDA0003475966670000132
will QnmAnd PnmThe calculation formulas are respectively substituted into the calculation to obtain:
ErAra0＝ace0(30)，
Figure GDA0003475966670000133
Figure GDA0003475966670000134
expanding the equations (31) and (32) yields:
Figure GDA0003475966670000135
Figure GDA0003475966670000136
wherein the content of the first and second substances,
Figure GDA0003475966670000137
and
Figure GDA0003475966670000138
respectively forming suspension point load parameters for suspension point displacement;
will be a formula
Figure GDA0003475966670000139
And formula
Figure GDA00034759666700001310
Both substituting said formula (33) and said (34) into being available:
Figure GDA0003475966670000141
Figure GDA0003475966670000142
from said formula (39) and said formula (40) it follows:
Figure GDA0003475966670000143
wherein the content of the first and second substances,
Figure GDA0003475966670000144
Figure GDA0003475966670000145
a is obtained by calculation according to the formulas (17), (18), (19), (20), (23) and (24)qmAnd bqmBringing the lower boundary conditions to obtain a pump load of:
Figure GDA0003475966670000146
and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump;
further, the calculating the pump displacement according to the suspension point displacement and the fourier coefficient of the pump load further includes: fourier coefficient a of displacement of suspension pointpm、bpmAnd pump load Fourier coefficient aqm、bqmSubstituting the equations (17), (18), (19), (20), (23) and (24) to respectively obtain parameters A of the wave equation analytic solutionpnm、Aqnm、Bpnm、Bqnm、Qnm、PnmSubstituting the equation (2) can result in a pump displacement of:
Figure GDA0003475966670000147
and 5: calculating a pump diagram according to the suspension point indicator diagram;
further, the calculating a pump diagram according to the suspension point indicator diagram further includes: and obtaining a pump work diagram according to the fact that the pump displacement is an abscissa and the pump load is an ordinate.
Specifically, the above scheme illustrates that calculating the pump diagram from the suspension point diagram requires knowledge of three parameters: respectively the length l of the sucker rod, the damping coefficient v and the cross section area A of the sucker rodr. When the parameters are known, the pump load and the pump displacement time series can be calculated according to the suspension point displacement and the suspension point load time series, and therefore a pump work diagram is obtained. The method comprises the following specific steps:
step 51: for suspension point displacement p (t) and suspension point load PRLce(T) is developed according to a periodic T Fourier series to obtain:
Figure GDA0003475966670000151
Figure GDA0003475966670000152
wherein the content of the first and second substances,
Figure GDA0003475966670000153
M＝40。
step 52: calculating system parameters:
Figure GDA0003475966670000154
Figure GDA0003475966670000155
step 53: calculating a suspension point load coefficient formed by suspension point displacement:
Figure GDA0003475966670000156
step 54: calculating pump load matrix parameters
Figure GDA0003475966670000157
Step 55: solving the matrix to obtain the Fourier series a of the pump loadqm、bqmAnd pump load Pp(t) solving the matrix to obtain the pump load Fourier coefficient aqm、bqm
Figure GDA0003475966670000158
Calculating the pump load:
Figure GDA0003475966670000159
step 56: calculating pump displacement parameters to obtain pump displacement, and calculating wave equation analytic solution parameters
Figure GDA0003475966670000161
Figure GDA0003475966670000162
Figure GDA0003475966670000163
The pump displacement can be found as:
Figure GDA0003475966670000164
and 57: and taking the pump displacement as an abscissa and the pump load as an ordinate to obtain a pump diagram.
Step 6: analyzing the fluctuation form of the pump valve under the action of pulse load;
further, a second differential equation of the pump load is obtained and taken as a pulse function q ″ (t) ═ q0δ (t- τ) (45), where δ (t- τ) is a unit pulse function indicating that a pulse acts at time t ═ τ;
when the influence caused by the displacement of the suspension point and the characteristic of the small damping coefficient are not considered, the calculation result is obtained
Figure GDA0003475966670000165
According to the fact that the instant time of pulse action is short, displacement can not be changed in time, and the speed can be changed suddenly to obtain
Figure GDA0003475966670000166
Then
Figure GDA0003475966670000167
The fluctuation part on the suspension point load is obtained as follows:
Figure GDA0003475966670000168
when the fundamental frequency vibration of the sucker rod is considered,
Figure GDA0003475966670000169
wherein E isrArq0Is the maximum of the second derivative of the pump load function, and ErArq0The pulse value is the pulse value when the fixed valve or the traveling valve is suddenly loaded;
obtaining the suspension point load part formed by the suspension point displacement
Figure GDA0003475966670000171
Figure GDA0003475966670000172
According to the pump load being constant F after the standing valve is opened0When the traveling valve is opened, the pump load is 0, and according to the superposition principle, the fluctuation form of the fluctuation stage is obtained as follows:
upper stroke part
Figure GDA0003475966670000173
Down stroke part
Figure GDA0003475966670000174
And 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr。
Further, the length l of the sucker rod, the damping coefficient v and the cross section area A of the sucker rod are determined according to the fluctuation form of the suspension point loadrThe method also comprises the following steps:
step 71: obtaining a suspension point displacement and load time sequence of a period;
obtaining a fluctuating load signal, wherein the fluctuating load signal is the maximum load during the overshootCharge point PRL (t)pm) Or, a point of minimum load during undershoot;
determining the time t at which the fluctuating load signal is obtainedSm；
Selecting an original fluctuation signal PRL (t) from a maximum load point to an upper dead pointpm:tSm) Resetting the time with the time point at the maximum load point as the starting 0 point, wherein tc＝(0:tSm-tpm)；
Step 72: for the original wobble signal PRL (t)pm:tSm) Linear trend is removed to obtain a fluctuation signal PRL' (t)c) Performing a spectral analysis, wherein the time t is calculatedcTotal length N oftcFor PRL' (t)c) Calculating frequency sequence by amplitude spectrum analysis
Figure GDA0003475966670000175
Taking the first half part of the amplitude spectrum; selecting the frequency with the maximum amplitude as the initial fundamental frequency f0；
Step 73: for the fluctuating signal PRL' (t)c) Normalization was performed to obtain PRL' (t)c)＝PRL'(tc)/PRL'(tpm)；
For vibration frequency f0Optimizing to obtain
Figure GDA0003475966670000181
Obtaining a fundamental frequency f0yCalculating the pole length
Figure GDA0003475966670000182
Step 74: determining the law of the damped fundamental frequency cosine vibration as
Figure GDA0003475966670000183
Extracting a damping coefficient of the fluctuation signal according to the minimum difference value of the attenuated cosine vibration law and the actually measured vibration signal as an optimization target to obtain
Figure GDA0003475966670000184
Obtaining a damping coefficient v after optimizationce；
Step 75: the original fluctuation signal is used for subtracting the attenuated fundamental frequency cosine vibration signal to obtain
Figure GDA0003475966670000185
Wherein, PRLh(tc)＝PRLp(tc)+F0(54) Said equation (54) having a suspension point load formed by a suspension point displacement and a pump load constant;
according to PRLh'(tc)＝PRLh(tc)-PRLh(tcend) Eliminating the influence of constants, wherein, PRLh(tcend) Is PRLh(tc) The suspension point load corresponding to the medium final time;
step 76: obtaining the floating weight W of the sucker rod according to the minimum value of the suspension point loadfMin (PRL), calculating the initial value of the cross section of the sucker rod
Figure GDA0003475966670000186
Where ρ isrIs the density of the steel, pwIs the standard density of water;
step 77: the displacement time function p (T) of the upper boundary condition is expanded according to the periodic T Fourier series
Figure GDA0003475966670000187
Wherein the content of the first and second substances,
Figure GDA0003475966670000188
M＝40；
calculating system parameters
Figure GDA0003475966670000189
Calculating a suspension point load parameter formed by suspension point displacement:
Figure GDA00034759666700001810
obtaining an expression as a function of the cross-sectional area of the sucker rod:
Figure GDA00034759666700001811
calculating to obtain PRLp'(Ar,tc)＝PRLp(tc)-PRLp(tcend)；
Step 78: obtaining an optimization equation of
Figure GDA0003475966670000191
Obtaining the sectional area A of the sucker rod according to the optimization equationr。
Example two
Fig. 2 is a schematic structural diagram of a pump diagram calculation apparatus based on analysis of pumping unit suspension point load fluctuation in an embodiment of the present invention, as shown in fig. 2, the apparatus includes:
a measuring module 21, the measuring module 21 being configured to measure a suspension displacement and a suspension load time series;
an obtaining module 22, where the obtaining module 22 is configured to obtain a suspension displacement and a suspension load time sequence of one cycle, and the obtaining module 22 is connected to the measuring module 21;
the analysis module 23 is used for analyzing the fluctuation characteristics of the suspension point load, and the analysis module 23 is connected with the acquisition module 22;
a calculating module 24, where the calculating module 24 is configured to calculate a pump diagram, and the calculating module 24 is connected to the analyzing module 23;
an output module 25, where the output module 25 is configured to output a calculation result, and the output module 25 is connected to the calculation module 24.
Specifically, the measurement module 21 is configured to measure a suspension displacement and a suspension load time sequence, the acquisition module 22 acquires a suspension displacement and a suspension load time sequence of one cycle, the analysis module 23 analyzes a suspension load fluctuation characteristic, the calculation module 24 calculates a pump diagram, and the output module 25 outputs a calculation result.
EXAMPLE III
The following describes in detail a pump diagram calculation method based on analysis of pumping unit suspension point load fluctuation, specifically as follows:
when vibration analysis is performed on the suspension point load, as shown in FIG. 3, taking the measured suspension point displacement and load time sequence of a certain well in the victory oil field as an example, the sucker rod material is carbon steel, and the density is 7890kg/m3The Young modulus is 206GPa, and the specific implementation steps are as follows:
step 31: a periodic time series of the displacement of the suspension point and the load is selected, as shown in fig. 4 and 5. Selecting a fluctuating load signal: finding the maximum load point PRL (t) during overshootpm) (or minimum load point during undershoot, taking overshoot as an example), the time t at this time is determinedSmSelecting the original fluctuation signal PRL (t) from the maximum load point to the top dead centerpm:tSm) The time is reset with the time point at the maximum load point as the starting 0 point, which is tc＝(0:tSm-tpm) As shown in FIG. 6, single-1 is the original wobble signal PRL (t)pm:tSm) Single-2 is a fluctuating signal PRL' (t) with linear trend removedc)；
Step 32: carrying out spectrum analysis to obtain a fundamental frequency initial value: for the original wobble signal PRL (t)pm:tSm) Linear trend is removed to obtain a fluctuation signal PRL' (t)c) And performing spectrum analysis. The spectral analysis is as follows: calculating the time tcTotal length N oftcFor PRL' (t)c) Performing amplitude spectrum analysis to calculate a frequency sequence:
Figure GDA0003475966670000201
the first half of the amplitude spectrum is taken as shown in fig. 7. Selecting the frequency with the maximum amplitude as the initial fundamental frequency f0I.e. 0.6250 Hz.
Step 33: obtaining a fundamental frequency through optimization: for the fluctuating signal PRL' (t)c) Normalization is carried out, namely: PRL "(t)c)＝PRL'(tc)/PRL'(tpm) For vibration frequency f0The optimization is carried out, that is,
Figure GDA0003475966670000202
the optimization result is shown in FIG. 8, in which single-1 is the optimized fluctuation signal cos2 π f0ytcCurve, single-2, is the normalized fluctuation signal PRL' (t)c) Further obtain the fundamental frequency f0yThe rod length was calculated to be 0.6517Hz
Figure GDA0003475966670000203
Step 34: obtaining a damping coefficient through optimization: determining an attenuated fundamental frequency cosine vibration law:
Figure GDA0003475966670000204
extracting the damping coefficient of the fluctuation signal according to the minimum difference between the attenuated cosine vibration law and the actually measured vibration signal as an optimization target, namely
Figure GDA0003475966670000205
As shown in FIG. 9, single-1 is the optimized wobble signal
Figure GDA0003475966670000211
Curve, single-2, is the normalized fluctuation signal PRL' (t)c) Obtaining a damping coefficient v after optimizationce＝0.3661。
Step 35: obtaining the suspension point load related to the suspension point displacement: subtracting the attenuated fundamental frequency cosine vibration signal, i.e. PRL, from the original undulation signalh(tc)：
Figure GDA0003475966670000212
Obviously: PRLh(tc)＝PRLp(tc)+F0I.e. the suspension load and pump load constants including the suspension displacement. For signal PRLh(tc) The following processing is carried out to eliminate the influence of constants: PRLh'(tc)＝PRLh(tc)-PRLh(tcend)
Step 36: calculating the initial value A of the cross section according to the floating weight of the sucker rodr0: obtaining the float weight of the sucker rod from the minimum value of the load of the suspension point, i.e. WfMin (prl), calculated to yield:
Figure GDA0003475966670000213
in the formula, ρrIs the density of the steel, pwIs the standard density of water. The initial value of the cross-sectional area was calculated to be 4.6215 × 10-4m2。
Step 37: calculating the suspension point load formed by the suspension point displacement taking the cross section area of the sucker rod as a function, and expanding the suspension point displacement p (T) according to the periodic T Fourier series to obtain:
Figure GDA0003475966670000214
wherein the content of the first and second substances,
Figure GDA0003475966670000215
M＝40。
the following parameters were calculated:
Figure GDA0003475966670000216
calculating the influence of the suspension point displacement on the suspension point load:
Figure GDA0003475966670000217
obtaining an expression as a function of the cross-sectional area of the sucker rod:
Figure GDA0003475966670000218
the treatment can obtain:
PRLp'(Ar,tc)＝PRLp(tc)-PRLp(tcend)；
step 38: the cross section A of the sucker rod is obtained through optimizationr：
The resulting optimization equation is then:
Figure GDA0003475966670000221
thereby obtaining the sectional area A of the sucker rodr. As shown in FIG. 10, single-1 in the figure is a fluctuation signal PRL for the optimization result of the cross section area of the sucker rodh'(tc) Fluctuation signal PRL with single-2 as initial valuep'(Ar0,tc) Single-3 is the optimized fluctuating signal PRLp'(Ar,tc) The calculated value of the cross section area of the sucker rod is 3.5721 multiplied by 10-4m2。
So far, three parameters necessary for calculating the pump diagram from the suspension point indicator diagram are calculated: sucker rod length l, damping coefficient v and sucker rod cross-sectional area Ar。
With reference to the flow chart of the suspension point indicator diagram to calculate the pump diagram, as shown in fig. 11, the specific implementation of calculating the pump diagram from the suspension point load and displacement time sequence diagrams 4 and 5 is as follows:
step 111: for suspension point displacement p (t) and suspension point load PRLce(T) is developed according to a periodic T Fourier series to obtain:
Figure GDA0003475966670000222
wherein the content of the first and second substances,
Figure GDA0003475966670000223
M＝40。
step 112: calculating system parameters:
Figure GDA0003475966670000224
step 113: calculating a suspension point load parameter formed by suspension point displacement:
Figure GDA0003475966670000225
step 114: calculating pump load matrix parameters
Figure GDA0003475966670000226
Step 115: solving the matrix to obtain the Fourier series a of the pump loadqm、bqmAnd pump load Pp(t)
Solving the matrix to obtain the pump load Fourier coefficient aqm、bqm
Figure GDA0003475966670000231
Calculating the pump load:
Figure GDA0003475966670000232
step 116: calculating pump displacement parameters to obtain pump displacement:
calculating wave equation analytic solution parameters:
Figure GDA0003475966670000233
Figure GDA0003475966670000234
Figure GDA0003475966670000235
the pump displacement is obtained as follows:
Figure GDA0003475966670000236
step 117: the pump work diagram is obtained with the pump displacement as the abscissa and the pump load as the ordinate, and the calculation result is shown in fig. 12. In the figure, single-1 is a pump indicator diagram obtained by calculation, and single-2 is a suspension point indicator diagram.
By the method, the analytical solution of the sucker rod wave equation can be obtained when the displacement of the suspension point and the boundary condition of the pump load are known; when the suspension point displacement and the suspension point load time sequence are known, the calculation of the pump load and the pump displacement can be realized, and a pump diagram is obtained; analyzing the fluctuation part of the suspension point load to obtain the length of the sucker rod, the cross section area of the sucker rod and the damping coefficient; when the suspension point displacement and the suspension point load time sequence are known, the technical effect of calculating the pump work diagram can be realized only by knowing the material characteristics of the sucker rod without providing other parameters.
One or more technical solutions in the embodiments of the present invention at least have one or more of the following technical effects:
the embodiment of the invention provides a pump diagram calculation method based on analysis of load fluctuation of a suspension point of an oil pumping unit, which comprises the following steps: step 1: obtaining a longitudinal wave equation of the sucker rod; step 2: calculating the wave equation and obtaining an analytic solution of the wave equation; and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point; and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump; and 5: calculating a pump diagram according to the suspension point indicator diagram; step 6: analyzing the fluctuation form of the pump valve under the action of pulse load; and 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr. The technical problems that in the prior art, partial parameters of the sucker rod are not suitable to be accurately obtained, such as a viscous damping system, and parameters such as the length and the diameter of the sucker rod are not available at times, and calculation and application of a pump diagram are influenced are solved, and the technical effects of conveniently obtaining the pump diagram, calculating the length of the sucker rod, the cross-sectional area of the sucker rod and calculating the damping coefficient are achieved. While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made in the embodiments of the present invention without departing from the spirit or scope of the embodiments of the invention. Thus, if such modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to encompass such modifications and variations.

Claims (9)

1. A pump work diagram calculation method based on pumping unit suspension point load fluctuation analysis is characterized by comprising the following steps:
step 1: obtaining a longitudinal wave equation of the sucker rod;
step 2: calculating the wave equation and obtaining an analytic solution of the wave equation;
and step 3: calculating the load of the pump according to the Fourier coefficient of the load of the suspension point;
and 4, step 4: calculating the displacement of the pump according to the displacement of the suspension point and the Fourier coefficient of the load of the pump;
and 5: calculating a pump diagram according to the suspension point indicator diagram;
step 6: analyzing the fluctuation form of the pump valve under the action of pulse load;
and 7: determining the length l of the sucker rod, the damping coefficient v and the cross-sectional area A of the sucker rod according to the fluctuation form of the suspension point loadr。
2. The method of claim 1, wherein, in step 1,
according to the fact that the propagation speed of sound in the sucker rod is c, the damping coefficient of oil well liquid to the sucker rod is v, the oil well liquid is in an underdamping state, the displacement time function of the upper boundary condition is p (t), the load time function of the lower boundary condition is q (t), the displacement and the speed at the initial moment are zero, the length of the sucker rod is l, and the longitudinal wave equation of the sucker rod is obtained:
Figure FDA0003475966660000011
3. the method of claim 2, wherein the calculating the wave equation and obtaining an analytical solution for the wave equation further comprises:
obtaining a preset solution of the wave equation as: obtaining a solution problem of the homogeneous boundary condition according to the preset solution and the wave equation, wherein u (x, t) ═ w (x, t) + q (t) x + p (t) (2), and the solution problem is as follows:
Figure FDA0003475966660000012
wherein f (x, t) — v (q 'x + p') - (q "x + p") (4);
according to the boundary condition w (0, t) ═ wx(l, t) ═ 0, the eigenfunctions for obtaining the solution problem are: sin omeganx，
Figure FDA0003475966660000021
According to the eigenfunction sin omeganx expands W (x, t) and f (x, t) respectively, and the expansion result is as follows:
Figure FDA0003475966660000022
and
Figure FDA0003475966660000023
Figure FDA0003475966660000024
bringing equations (5), (6), (7) into equation (3) results in: wn+vW′n+(ωnc)2Wn＝fn(t)(8)；
According to the preset value w (x,0) being 0, wt(x,0) ═ 0 gave: wn(0)＝Wn'(0)＝0 (9)；
Substituting equation (4) into
Figure FDA0003475966660000025
To obtain：fn(t)＝fpn(t)+fqn(t) (10)；
Wherein the content of the first and second substances,
Figure FDA0003475966660000026
expanding an upper boundary condition displacement time function p (T) and a lower boundary condition load time function q (T) according to a periodic T Fourier series to obtain:
Figure FDA0003475966660000027
and
Figure FDA0003475966660000028
wherein the content of the first and second substances,
Figure FDA0003475966660000029
to obtain
Figure FDA00034759666600000210
Wherein the content of the first and second substances,
Figure FDA00034759666600000211
Figure FDA00034759666600000212
is calculated to obtain
Figure FDA00034759666600000213
Obtained according to equation (8):
Figure FDA00034759666600000214
the solution of the equation (21) is:
Figure FDA0003475966660000031
according to the under-damping characteristic when
Figure FDA0003475966660000032
When the temperature of the water is higher than the set temperature,
Figure FDA0003475966660000033
from equation (9) we can obtain: cn＝Dn＝0；
According to Cn＝DnSubstituting equation (22) into equation (21) yields 0:
Figure FDA0003475966660000034
and calculating to obtain:
Figure FDA0003475966660000035
Figure FDA0003475966660000036
calculated according to equation (5):
Figure FDA0003475966660000037
substituting equation (25) into equation (2) yields an analytical solution for the wave equation as:
Figure FDA0003475966660000038
4. the method of claim 3, wherein calculating the pump load from the Fourier coefficients of the suspension point loads further comprises:
according to
Figure FDA0003475966660000039
Performing Fourier series expansion on the suspension point load:
and calculating according to the formula (26) to obtain the suspension point load as follows:
Figure FDA00034759666600000310
wherein E isrYoung's modulus of sucker rod, ArThe sectional area of the sucker rod;
substituting the equation (14) into the equation (28) yields:
Figure FDA0003475966660000041
comparing said formula (27) with said formula (29) to obtain:
Figure FDA0003475966660000042
will QnmAnd PnmThe calculation formulas are respectively substituted into the calculation to obtain:
ErAra0＝ace0 (30)，
Figure FDA0003475966660000043
Figure FDA0003475966660000044
expanding the equations (31) and (32) yields:
Figure FDA0003475966660000045
Figure FDA0003475966660000046
wherein the content of the first and second substances,
Figure FDA0003475966660000047
Figure FDA0003475966660000048
respectively forming suspension point load parameters for suspension point displacement;
will be a formula
Figure FDA0003475966660000049
And formula
Figure FDA0003475966660000051
Both substituting said formula (33) and said (34) into being available:
Figure FDA0003475966660000052
Figure FDA0003475966660000053
from said formula (39) and said formula (40) it follows:
Figure FDA0003475966660000054
wherein the content of the first and second substances,
Figure FDA0003475966660000055
Figure FDA0003475966660000056
a is obtained by calculation according to the formulas (17), (18), (19), (20), (23) and (24)qmAnd bqmBringing the lower boundary conditions to obtain a pump load of:
Figure FDA0003475966660000057
5. the method of claim 4, wherein calculating the pump displacement from the suspension point displacement, a Fourier coefficient of the pump load, further comprises:
fourier coefficient a of displacement of suspension pointpm、bpmAnd pump load Fourier coefficient aqm、bqmSubstituting the equations (17), (18), (19), (20), (23) and (24) to respectively obtain parameters A of the wave equation analytic solutionpnm、Aqnm、Bpnm、Bqnm、Qnm、PnmSubstituting the equation (2) can result in a pump displacement of:
Figure FDA0003475966660000058
6. the method of claim 5, wherein calculating the pump diagram from the suspension point indicator diagram further comprises:
and obtaining a pump work diagram according to the fact that the pump displacement is an abscissa and the pump load is an ordinate.
7. The method of claim 6, wherein calculating the pump diagram from the suspension point indicator diagram further comprises:
obtaining a second differential equation of the pump load and using the second differential equation as a pulse function q "(t) q ═ q0δ (t- τ) (45), where δ (t- τ) is a unit pulse function indicating that a pulse acts at time t ═ τ;
when the influence caused by the displacement of the suspension point and the characteristic of the small damping coefficient are not considered, the calculation result is obtained
Figure FDA0003475966660000061
According to the fact that the instant time of pulse action is short, displacement can not be changed in time, and the speed can be changed suddenly to obtain
Figure FDA0003475966660000062
Then
Figure FDA0003475966660000063
The fluctuation part on the suspension point load is obtained as follows:
Figure FDA0003475966660000064
when the fundamental frequency vibration of the sucker rod is considered,
Figure FDA0003475966660000065
wherein E isrArq0Is the maximum of the second derivative of the pump load function, and ErArq0The pulse value is the pulse value when the fixed valve or the traveling valve is suddenly loaded;
obtaining the suspension point load part formed by the suspension point displacement
Figure FDA0003475966660000066
Figure FDA0003475966660000067
According to the pump load being constant F after the standing valve is opened0When the traveling valve is opened, the pump load is 0, and according to the superposition principle, the fluctuation form of the fluctuation stage is obtained as follows:
Figure FDA0003475966660000068
Figure FDA0003475966660000069
8. the method of claim 7 wherein determining the sucker rod length l, the damping coefficient v, and the sucker rod cross-sectional area A from the form of the suspension point load fluctuationrThe method also comprises the following steps:
step 71: obtaining a suspension point displacement and load time sequence of a period;
obtaining a fluctuating load signal, wherein the fluctuating load signal is a point of maximum load PRL (t) during the overshootpm) Or, a point of minimum load during undershoot;
determining the time t at which the fluctuating load signal is obtainedSm；
Selecting an original fluctuation signal PRL (t) from a maximum load point to an upper dead pointpm:tSm) Resetting the time with the time point at the maximum load point as the starting 0 point, wherein tc＝(0:tSm-tpm)；
Step 72: for the original wobble signal PRL (t)pm:tSm) Linear trend is removed to obtain a fluctuation signal PRL' (t)c) Performing a spectral analysis, wherein the time t is calculatedcTotal length N oftcFor PRL' (t)c) Calculating frequency sequence by amplitude spectrum analysis
Figure FDA0003475966660000071
Taking the first half part of the amplitude spectrum; selecting the frequency with the maximum amplitude as the initial fundamental frequency f0；
Step 73: for the fluctuating signal PRL' (t)c) Normalization was performed to obtain PRL ″ (t)c)＝PRL'(tc)/PRL'(tpm)；
For vibration frequency f0Optimizing to obtain
Figure FDA0003475966660000072
Obtaining a fundamental frequency f0yCalculating the pole length
Figure FDA0003475966660000075
Step 74: determining the law of the damped fundamental frequency cosine vibration as
Figure FDA0003475966660000076
Extracting a damping coefficient of the fluctuation signal according to the minimum difference value of the attenuated cosine vibration law and the actually measured vibration signal as an optimization target to obtain
Figure FDA0003475966660000073
Obtaining a damping coefficient v after optimizationce；
Step 75: the original fluctuation signal is used for subtracting the attenuated fundamental frequency cosine vibration signal to obtain
Figure FDA0003475966660000074
Wherein, PRLh(tc)＝PRLp(tc)+F0(54) Said equation (54) having a suspension point load formed by a suspension point displacement and a pump load constant;
according to PRLh'(tc)＝PRLh(tc)-PRLh(tcend) Eliminating the influence of constants, wherein, PRLh(tcend) Is PRLh(tc) The suspension point load corresponding to the medium final time;
step 76: obtaining the floating weight W of the sucker rod according to the minimum value of the suspension point loadfMin (PRL), calculating the initial value of the cross section of the sucker rod
Figure FDA0003475966660000081
Where ρ isrIs the density of the steel, pwIs the standard density of water;
step 77: the displacement time function p (T) of the upper boundary condition is expanded according to the periodic T Fourier series
Figure FDA0003475966660000082
Wherein the content of the first and second substances,
Figure FDA0003475966660000083
M＝40；
calculating system parameters
Figure FDA0003475966660000084
Calculating a suspension point load parameter formed by suspension point displacement:
Figure FDA0003475966660000085
obtaining an expression as a function of the cross-sectional area of the sucker rod:
Figure FDA0003475966660000086
calculating to obtain PRLp'(Ar,tc)＝PRLp(tc)-PRLp(tcend)；
Step 78: obtaining an optimization equation of
Figure FDA0003475966660000087
Obtaining the sectional area A of the sucker rod according to the optimization equationr。
9. A pump work diagram calculation device based on analysis of pumping unit suspension point load fluctuation is characterized by comprising the following components:
a measurement module for measuring a suspension displacement and a suspension load time series;
the acquisition module is used for acquiring a suspension point displacement and a suspension point load time sequence of one period and is connected with the measurement module;
the analysis module is used for analyzing the fluctuation characteristics of the suspension point load and is connected with the acquisition module;
the calculation module is used for calculating a pump diagram and is connected with the analysis module;
and the output module is used for outputting the calculation result and is connected with the calculation module.
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