Wherein m is system mass, c is system damping, k is the rigidity of the sucker rod, the simple harmonic vibration formula is substituted into the formula to obtain the absolute motion differential equation of forced vibration of the sucker rod under simple harmonic excitation

The equation is a second-order constant coefficient heterogeneous differential equation, and the solution form of the equation is obtained by superposing a general solution of the homogeneous equation and a special solution of the heterogeneous equation. Homogeneous equationThe general solution of (A) is as follows:

can be written as:

which is that the temperature of the molten steel is controlled,

v₀the speed of movement of the pump is caused to the column of oil applied to the pump.

The special solution of the non-homogeneous equation is:

x^*＝a₁cos(ωt)+b₁sin(ωt)+s/2

wherein,

the general solution of the equation is:

the above equation shows that the vibration of the sucker rod is composed of two parts, the first term represents free vibration, the system free vibration can be attenuated due to the existence of damping, and the second term is forced vibration, the forced vibration is caused by the displacement of a suspension point, and the frequency of the forced vibration is the same as that of the oil pumping unit.

According to the function, a vibration curve of the oil well pump can be drawn, as shown in fig. 8. It can be known from the curve that when the wave crest of free vibration of the sucker rod is identical to the wave crest of forced vibration, the stroke of the oil pump can be maximized under a certain pumping condition. The time for the free vibration to reach the maximum displacement satisfies the following conditions:

the time for the forced vibration to reach the maximum displacement satisfies:

ωt＝π

can obtain the product

\frac{3}{4} t_{n} = \frac{1}{2} T

Considering that the length of the sucker rod is generally more than 1000m, the time is required for the disturbance of the wellhead to be transmitted to the underground, therefore, considering the influence formula can be written as

Wherein, t_nFor the period of vibration of the sucker rod, Δ T is the lag time after the sucker rod is loaded until vibration occurs, T_cyjThe vibration period of the rod-pumped well.

Therefore, the formula is proved to be satisfied, the over-stroke generated by the oil well pump is the largest, and the pump efficiency is the highest.

The concrete realization of the invention is that a plurality of buffers 4 are considered to be arranged on thesucker rod 3, so that the whole sucker rod string satisfies the following formula (1),

wherein t is_nThe vibration period of the sucker rod string, delta T is the lag time after the sucker rod is loaded and before vibration occurs, T_cyjThe working period of the pumping unit. When the formula (1) is met, the over-stroke generated by the oil well pump is maximum, and the pump efficiency is highest.

Wherein:

E_rod-modulus of elasticity of sucker rod string, MPa;

E_slow-individual bumper modulus of elasticity, MPa;

l-total sucker rod string length, m;

l-length of single buffer, m;

x-the number of installed buffers;

Wherein: f-natural frequency of sucker rod string, Hz;

e-the modulus of elasticity of the sucker rod string;

a-cross-sectional area of sucker rod, m²；

qr-kg mass per meter of sucker rod;

l-oil pump depth, m;

k-correction factor;

wherein K is determined according to the following rule:

phi 25 rod phi 83 pump, k equals 271;

phi 25rod phi 70 pump, k 400;

phi 22rod phi 70 pump, k is 291.3;

phi 22 rod phi 57 pump, k 341.3;

phi 22rod phi 44 pump, k 391.3.

The reason why the correction of the sucker rod string natural frequency calculation formula is required is that the value calculated by the conventional formula has a larger error than the actually measured value, and therefore, it is considered necessary to correct the error. The K value was obtained by summarizing a large amount of experimental data.

The following is an example of a specific implementation:

taking north 1-72-555 as an example, the well pump has the depth of 944m, the diameter of the sucker rod is phi 25mm, the diameter of the oil pipe is phi 76mm, the diameter of the oil pump is phi 70mm, the working fluid level depth is 587m, the stroke is 2.93m, and the stroke time is 9.2min^-1And yield 62t, water content 95%.

Therod string 3 of the rod pumped well 1 comprises:sucker rod 3,oil pipe 5, oil-well pump 7 and liquid column quality. Thesucker rod 3 in the pumping well is an elastic body, the lower end of the sucker rod is connected with anoil well pump 7, and thesucker rod 3 and a plunger of theoil well pump 7 reciprocate up and down to pump liquid in the well under the drive of thepumping unit 1 and lift the liquid to the ground. During the up stroke, the weight of the liquid column acts on theoil well pump 7, the 3 columns of the sucker rod generate tensile deformation, the deformation length is lambda, and the deformation time is delta t. On the down stroke, therod string 3 is unloaded, the weight of the fluid column acts on thetubing 5, and therod string 3 undergoes compression deformation. Thesucker rod 3 is continuously stretched and compressed under the action of alternating load of the liquid column, generates longitudinal vibration while reciprocating up and down, and simultaneously stores and releases elastic energy generated by deformation and vibration.

In order to make the whole sucker rod string satisfy the formula (1), the vibration period t of the sucker rod string is first specified according to the formula (3)_nThe calculation of (1):

period t of vibration of sucker rod string_nComprises the following steps:

wherein: f-natural frequency of sucker rod, Hz;

e-the modulus of elasticity of the sucker rod string;

a-cross sectional area ofsucker rod 3, m²；

q_r-mass per meter, kg, of thesucker rod 3;

l-depth ofoil well pump 7, m;

k-correction factor (phi 25rod phi 70 pump, K400).

Secondly, the calculation of the lag time delta t from the loading of the sucker rod to the vibration generation is shown as follows:

the displacement length of the suspension point of the oil pumping unit at any moment is as follows:

the up-stroke liquid column acts on the plunger of the oil well pump, and the deformation of the sucker rod column and the oil pipe is lambda:

when the displacement of the suspension point of the oil pumping unit is equal to the deformation of the oil pumping unit: i.e., λ ═ S, the pumping unit has operated at time Δ t.

This yields:

<math> <mrow> <mi>Δt</mi> <mo>=</mo> <mfrac> <mrow> <mi>arccos</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mfrac> <mrow> <mn>2</mn> <mi>λ</mi> </mrow> <msub> <mi>S</mi> <mi>max</mi> </msub> </mfrac> <mo>)</mo> </mrow> </mrow> <mi>ω</mi> </mfrac> </mrow> </math>

in the formula: s_max-beam-pumping unit suspension point maximum stroke length, m;

s-stroke length m of suspension point of pumping unit at any time;

omega-the angular velocity of rotation of the crank of the pumping unit, rad/s,

P_r-the weight of the liquid column of the working fluid level of the well, N;

f_poil pipe cross-sectional area, m²。

T_CYJ-the time of one stroke of the pumping unit, s;

T_{CYJ} = \frac{60}{n},

n is the stroke frequency of thepumping unit 1, min^-1；

By substituting the above equations into equation (1), since only one E is unknown and other quantities are known or can be measured, the value of E can be determined, i.e., the overall modulus of elasticity of the sucker rod string can be determined when equation (1) is satisfied.

The number of sucker rod buffers 4 that need to be specifically added to achieve the overall modulus of elasticity of the sucker rod string determined in the previous step is determined below.

First, as shown in fig. 6, the concrete structure of the sucker rod buffer 4 used in this example is that the sucker rod buffer 4 is mainly composed of a sucker rod joint 14, atie rod joint 8, an upper nut joint 12, a plurality of annular rubberelastic members 10, anut baffle ring 11, a lower nut joint 13 and asleeve 9, wherein the plurality of rubberelastic members 10 are sequentially connected in thesleeve 9, when the buffer 4 is in operation, a part of well fluid enters from the gap in thesleeve 9, and the sucker rod joint 14 is connected with thesucker rod 3.

When thepumping unit 1 works, the load born by the pumpingrod 3 is alternating load, and the buffer stretches under the action of the alternating load, so that the buffer effect of reducing vibration load and inertia load is achieved. Thesleeve 9 of the downhole buffer 4 is provided with drainage holes to allow drainage of well fluid entering the downhole buffer 4 when it is pressurized.

The calculation formula of the elastic modulus of the sucker rod after the buffer is added is changed as follows:

wherein:

E_{general assembly}-the overall modulus of elasticity, MPa, of the sucker rod string after the bumper has been applied;

E_rod-modulus of elasticity of sucker rod string, MPa;

E_slow-individual bumper modulus of elasticity, MPa;

l-total sucker rod string length, m;

l-length of single buffer, m;

x-the number of the installation buffers;

the above formula for calculating the change of the elastic modulus of the sucker rod after the buffer is added is derived by the following formula:

rigidity of the sucker rod:

total rigidity of the sucker rod after the buffer is added:

the damper stiffness kurtosis can be measured by testing, then:

then

When the cross-sectional area of the sucker rod column is the same as that of the buffer, the cross-sectional area of the sucker rod column is equal to that of the buffer

To this end, since the length of the sucker rod string, the length of the individual buffer, the elastic modulus of the individual buffer, and the original elastic modulus of the sucker rod string are all known or measurable, then the E can be given_{General assembly}The number of buffers to be added is obtained.

And (4) performing simulation calculation on the energy-saving effect of the pumping well after the buffer is installed by adopting a finite element method. The method comprises the steps of establishing a mechanical model according to actual parameters of an oil well, as shown in figure 9, and then dividing units to generate a finite element model, as shown in figure 10; and applying boundary conditions on the well and the well to the finite element model, fixing the displacement of the oil well pump in UX and UZ directions (note: UY direction is the axial direction of the sucker rod) under the well, establishing a mass unit at the upper end of the oil well pump, simulating an oil column, and simulating the change of the mass of the oil column by changing the real constant change of the mass unit. And (3) fixing displacement in the UX and UZ directions at the wellhead, and applying displacement loading, namely applying sinusoidal motion to the suspension point. Then, a transient analysis method is adopted for solving, and loads, axial displacements and the like of all nodes can be obtained.

In this example, it was calculated that 49 sucker rod buffers would need to be installed on the downhole pump to achieve the desired over-stroke condition. After finite element simulation, the diagram of the suspension point is shown in FIG. 11. At this time, compared with the normal state, the stroke of the underground pump is increased by 0.441m, 19 percent and the daily oil increment is 0.589 t.

Claims

1. A method for reducing energy and increasing production by changing the elastic modulus of a sucker rod string is characterized in that: a plurality of buffers (4) are arranged on the sucker rod (3) to ensure that the whole sucker rod string satisfies the following formula (1),

wherein t is_nThe vibration period of the sucker rod string, delta T is the lag time after the sucker rod is loaded and before vibration occurs, T_cyiIs the working period of the oil pumping unit,

2. The method of claim 1 wherein the pumping rod string is modified to reduce the elastic modulus and increase the production yield by: the cross-sectional area of the selected buffer is the same as that of the sucker rod, and the elastic modulus of the sucker rod string is obtained according to the formula (2):

wherein:

E_rod-modulus of elasticity of sucker rod string, MPa;

E_slow-individual bumper modulus of elasticity, MPa;

l-total sucker rod string length, m;

l-length of single buffer, m;

x-the number of installed buffers;

3. a method of stimulation by modifying the rod string elastic modulus lowering according to claim 1 or 2, characterized in that: the natural frequency f of the sucker rod string is obtained according to the following formula (3):

wherein: f-natural frequency of sucker rod string, Hz;

e-the modulus of elasticity of the sucker rod string;

a-cross-sectional area of sucker rod, m²；

q_r-mass per meter of sucker rod, kg;

l-oil pump depth, m;

k-correction factor;

wherein K is determined according to the following rule:

phi 25 rod phi 83 pump, k equals 271;

phi 25 rod phi 70 pump, k 400;

phi 22 rod phi 70 pump, k is 291.3;

phi 22 rod phi 57 pump, k 341.3;

phi 22 rod phi 44 pump, k 391.3.

4. A buffer (4) for use in a method according to claim 1, 2 or 3, characterized in that: the buffer (4) mainly comprises a sucker rod joint (14), a pull rod joint (8), an upper nut joint (12), a plurality of annular rubber elastic pieces (10), a nut retaining ring (11), a lower nut joint (13) and a sleeve (9), wherein the plurality of rubber elastic pieces (10) are sequentially connected into the sleeve (9), and when the buffer (4) works, a gap in the sleeve (9) enters partial well fluid.