Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 4, No. 3, 2022 

 

1 

Analysis	of	Pump	Efficiency	and	Feed	Flow	Under	the	
Condition	of	Flexible	Rate	
Hongbin Liu*, Wei Luo, Haobin Sun 

School of Mechanical Engineering, Southwest Petroleum University, Chengdu, Sichuan 610500, China 

 

Abstract: In this paper, a flexible method of optimizing the velocity of plunger is presented by selecting important oil well 
production parameters through orthogonal test and combining the oil well parameters and the structural parameters of the pump 
barrel. In order to explore the influence of the motion rate of the optimized flexible plunger on the pump efficiency, the motion 
law curves of the plunger before and after the optimization were compared, and the pump efficiency before and after the 
optimization was theoretically analyzed. The flow rate and pump efficiency of the pump before and after optimization were 
simulated by the model. Finally, the pumping unit experimental system is used to test the pumping pump fluid production before 
and after optimization. The results show that the pump efficiency under the optimized flexible rate is 3.7% higher than that before 
the optimization without considering other factors. The model simulation analysis shows that the mass flow rate of the pump in 
a single swabbing period under the condition of optimized flexible rate is increased, and the pump efficiency is increased by 4.9% 
compared with that before optimization. The experimental results of the pumping unit experimental system show that the fluid 
yield under the optimized flexible rate is higher than that before the optimization, and the maximum increase is 4.1%. The 
experimental results are consistent with the theoretical analysis results. 

Keywords: Flexible control, Orthogonal test, Optimize, Velocity of plunger motion, Pump efficiency, Model simulation. 
 

1. Introduction 
Beam pumping unit has many advantages, such as simple 

structure, strong adaptability, economic durability and so on. 
It plays a pivotal role in the field of mechanical oil recovery. 
So far, it is still the main tool of mechanical oil recovery in 
many oil fields around the world. However, due to the 
inherent geometric characteristics of the beam pumping unit 
and the circular rate driving mode (i.e., the crank does 
uniform circular rotation), the pumping system has many 
problems such as large energy consumption and low 
efficiency in the working process. Engineering analysis 
shows that the oil recovery efficiency can be improved by 
using flexible rate drive. Therefore, many oil fields begin to 
study, use and popularize the flexible control pumping 
technology of pumping unit gradually. 

The flexible control pumping technology of pumping unit 
is an optimized variable speed drive technology [1-2]. Its 
main objective is to improve the motion process of the entire 
pumping system, make the oil recovery rate match the current 
pumping system and reservoir characteristics, so as to reduce 
the energy consumption of the pumping well and improve the 
pumping efficiency. 

Most of the existing flexible pumping control technologies 
only focus on the optimization of the pumping speed of 
Pumping unit and motor frequency [3-4], instead of 
corresponding optimization based on downhole physical 
parameter conditions and pump structural parameters, and the 
adjustment ability and control range are limited to a certain 
extent. For the sake of effectively improve pump efficiency 
and optimize oil recovery rate of pumping unit, this paper 
selects key production parameters such as stroke, pumping 
speed and sinking degree through orthogonal test. Based on 
the selected production parameters, combined with the 
physical parameters of the well and the structural parameters 
of the pump barrel, the plunger speed is optimized, and the 
optimized flexible plunger speed curve based on specific well 

conditions is obtained. In order to explore the influence of the 
optimized flexible piston movement rate on the pump, the 
plunger movement laws before and after the optimization 
were compared under the same conditions, and the pump 
efficiency and flow rate of the pump were calculated and 
evaluated. The results can provide some guidance for the 
flexible control strategy of the oil pumping system. 

2. Orthogonal Experimental Design 

2.1. Pump efficiency and liquid production 
The pumping efficiency of the pumping pump is an 

important parameter to reflect the pumping efficiency of the 
pumping well. If the pumping efficiency is high, the pumping 
efficiency of the pumping well is high, and the current suction 
parameters are reasonable. If the pump efficiency is low, the 
relevant parameters should be adjusted or optimized. 
Therefore, the pump efficiency can provide some reference 
for the adjustment of swabbing parameters. The main 
influencing factors of pump efficiency can be summarized 
into the following four aspects: ηS——the effective stroke 
coefficient of the plunger, ηF——the coefficient of the 
fullness degree of pump; ηL——leakage coefficient of the 
pump; ηV——volume coefficient of crude oil under 
submerged pressure. Pumping efficiency η is expressed as 
formula (1) : 

 
 

S F L V      (1) 
 
The calculation method of pump leakage coefficient ηL is 

shown in Equation (2), and the other influencing factors can 
be calculated in reference [5]. 

 
 

P S F V
L

P S F V

A S Q

A S

  


  



 

(2) 

 



 

2 

In the equation: Ap is the cross-sectional area of the plunger 
of the pump, m2;S is the stroke, m; ΔQ is the amount of fluid 
loss during a stroke of the plunger through the gap between 
the plunger and the pump barrel, m3, its calculation formula 
is: 

 3
23

1
12 2 u

c

D p
Q T

L

  

     

   
(3) 

 
In the equation: Δp is the pressure difference between the 

upper and lower plunger, Pa; δ is the mean radius clearance 
between the plunger and the pump barrel, m; Lc is the plunger 
length, m; ε is the relative eccentricity, ε=e/δ; e is the 
eccentricity of the center line of the plunger relative to the 
center line of the pump barrel, m; Tu is the time corresponding 
to the upper stroke of the plunger, s; μ is the dynamic viscosity 
of oil well fluid, Pa·s. 

The formula for calculating liquid production Q is as 
follows: 

  21440
4

Q D
  

 
(4) 

 
In the equation: D is the diameter of the pump, m; η is the 

pump effect, decimal. 

2.2. Introduction to orthogonal test 
Orthogonal experimental method is an efficient research 

design method, which is often used in multi-factor 
optimization. It makes use of mathematical statistics and the 
principle of orthogonality [6], and selects some representative 
points from all the tests according to the orthogonality. These 
representative points also have the characteristics of "evenly 
dispersed, neat and comparable", which can greatly reduce 
the number of tests and workload while ensuring the accuracy 
of results. In the orthogonal test, since the number of different 
factors of each factor is the same, and the probability of each 
factor combination with other different factors is equal. 

Therefore, by analyzing part of the test results, the situation 
of all the tests can be comprehensively and systematically 
known, and the influence degree of each factor on the target 
can be obtained. Finally, the optimal or better test scheme can 
be obtained, so as to achieve the purpose of parameter 
optimization. 

2.3. Orthogonal test scheme and calculation 
According to the measured data of Jiangsu oilfield, the 

main parameters of a pumping well are as follows: The 
pumping unit model is CYJY10-3-53HB, casing pressure is 
0.4MPa, wellhead back pressure is 0.8MPa, crude oil density 
is 870 kg/m3, water cut is 0.68, surface gas/oil ratio of crude 
oil is 14 m3/ m3, formation temperature is 60℃, the oil well 
adopts three stage sucker rod. The diameter of the primary 
sucker rod is 25 mm. The secondary sucker rod is 22 mm. The 
tertiary sucker rod is 19 mm. 

According to the research on the physical parameters of the 
well and the research and analysis of the comprehensive data 
of the oilfield block, the influence factors of orthogonal test 
are determined from four aspects: pumping stroke, stroke 
times, pump diameter and sinking degree. and the pump 
efficiency and liquid production were taken as the objective 
functions to carry out the orthogonal test. In order to reduce 
the influence between the horizontal spans of each impact 
factor, each impact factor was designed by means of 
arithmetic difference, and the orthogonal test scheme was 
developed, as shown in Table 1. 

According to Table 1, the pump efficiency and liquid 
production under the corresponding parameter conditions 
were calculated. According to the common orthogonal test 
table [5]L16(44), an orthogonal test scheme with 4 factors and 
4 factors was designed. A total of 16 tests were conducted, 
and the test results were listed in Table 2, which significantly 
reduced the number of comprehensive tests (44= 256). 
Improve the efficiency of calculation. 

 
Table 2. Scheme of orthogonal test and results of numerical calculation 

Test number 
Each factor Index of test 

submergence depth stroke stroke times Pump diameter pump efficiency 
liquid production 

(m3/d) 
1 1 1 1 1 0.21 1.73 
2 1 2 2 2 0.30 5.83 
3 1 3 3 3 0.37 14.20 
4 1 4 4 4 0.41 27.59 
5 2 1 2 3 0.32 7.04 
6 2 2 1 4 0.37 6.80 
7 2 3 4 2 0.47 17.26 
8 2 4 3 1 0.42 10.11 
9 3 1 3 4 0.33 12.16 

10 3 2 4 3 0.37 15.66 
11 3 3 1 2 0.35 5.14 
12 3 4 2 1 0.46 8.30 
13 4 1 4 2 0.34 9.55 
14 4 2 3 1 0.41 7.80 
15 4 3 2 4 0.38 13.73 
16 4 4 1 3 0.44 9.44 

 
The orthogonal influence test results of each influence 

factor are shown in Table 2. As can be seen from Table 2, with 
the increase of stroke, stroke times and pump diameter, pump 
efficiency and liquid production will be greatly improved. 

With the increase of sinking degree, pump efficiency will 
increase to a certain extent. 

In order to maximize the expected pump efficiency and 
effectively improve the oil production efficiency of the well, 
parameters of the group with the highest pump efficiency 



 

3 

(group 7) in the orthogonal experiment were selected for 
subsequent flexible optimization. 

3. Search for Velocity Curve of 
Flexible Plunger 

The optimization idea of this paper is to first assume the 
plunger movement curve, then construct the optimization 
objective function according to the parameters selected by 
orthogonal experiment, the basic parameters of the well 
condition and the structure of the pump, and carry out the 
corresponding solution calculation combined with the 
constraint conditions. Finally, the optimal plunger movement 
rate curve satisfying the conditions is obtained, which can be 
used for the flexible driving of the pumping unit. 

3.1. Construction of flexible rate curve 
In order to ensure that the expression of the optimized 

curve is characterized by easy solution, strong adaptability, 
and multiple combined solution sets, as well as a certain 
periodicity, the displacement equation of the pump plunger 
movement is assumed to be a function variable expressed by 
Fourier series expansion [7], as shown in Formula (5) : 

 

0
1

2 2
( ) sin( ) cos( ) ( 2)

j

i i
i

t t
x t a a i b i j

T T

 


      


 
(5) 

 
In the formula: ɑ0, ɑ1, b1, …, ɑN and bN are Fourier 

expansion coefficients. 
Because the form of Fourier series is used to represent the 

equation of plunger motion, when we select appropriate 
optimization objectives and constraints to solve x(t) that 
meets the conditions, we can get the coefficients of the 
optimized Fourier series, namely:   

 
  0 1 1 2 2, , , , ,... , ( 2)j jX a a b a b a b j 

 
(6) 

 
According to the solved coefficients, the optimized plunger 

motion equation can be formed, that is, the optimized flexible 
plunger motion rate curve can be obtained. 

3.2. Optimization Objectives 
Since the fullness degree of pump occupies a large part of 

the factors affecting the pump efficiency, and the fullness 
degree of pump is most affected by the plunger movement and 
the structural parameters of the pump, the coefficient of 
pump filling degree is selected as the optimization objective 
in order to facilitate the establishment of an appropriate 
formula. The coefficient of pump filling degree is expressed 
by β(the ratio of the volume of fluid in the suction pump, VL(t), 
to the volume of the up-stroke plunger, VS(t)). 

 

 
Figure 1. Schematic diagram of pump structure 

(1) According to the conservation of mass and energy, 
Bernoulli's equation at the fluid flow section of the pump can 
be written: 

 

 
2 2

1 1 2 2
2 1 2

1 22 2s w i

p v p v
L L L h h

g g g g         
 

(7)

 

 
In the formula: v1 is the flow velocity at section 1-1, m/s; 

v2 is the flow velocity at section 2-2, m/s; p1 is the pump inlet 
pressure, MPa; p2 is the pressure in the pump, MPa; g is the 
acceleration of gravity, g= 9.8m /s2; L2 is the height of liquid 
in the pump, m; LS is the clearance length of the oil pump, m; 
Lw is the length of oil pump liner, m; ρ1 is the fluid density at 
section 1-1, kg/m3; ρ2 is the fluid density at section 2-2, kg/m3; 
h1-2 is fluid drag and head loss, m; hi is inertance drag and 
head loss, m. 

(2) The liquid level height L2 in the pump at time t can be 
calculated as: 

  2
2 0 2

30

( ) ( )

pS

p

v t
L = dx

n x t S x t 


 
(8)

 

 
Then, the liquid volume VL(t) in the pump at time t is: 
 

 
2( )L pV t L A (9)

 

 
In the formula: x(t) is the displacement of the plunger, m; n 

is pumping speed, min-1; Sp is the effective stroke of the 
plunger, m; Ap is the cross-sectional area of the plunger, m2; 
Sp is the effective stroke, m. 

(3) Pump chamber volume VS(t) is: 
 

 ( ) ( )S p sV t A x t V  (10)

 

 
In the formula: Vs is the clearance volume of the pump, m3. 
(4) Finally get the fullness degree of pump expression as 

shown below: 
 ( )

( )
L

S

V t

V t
 

 
(11)

 

 
Then the main optimization objective function can be 

expressed as: 
 

s 0 0 1 1( ) max ( , , , , , , , , , , , , , , , )w l s d N NF x S n D l L L h H a b a b a b     (12) 
 
In the formula: S is stroke, m; n is pumping speed, min-1; D 

is pump diameter, m2; l is length of sucker rod, m; ρ1 is the 
well fluid density, kg/m3; hs is submergence depth, m; Hd is 
the depth of producing fluid level, m. 

3.3. Find the solution 
In order to delimit the solution range, make the 

optimization calculation of the curve have a more appropriate 
and reasonable solution domain, and achieve the purpose of 
improving the pump efficiency and productivity, the 
boundary constraint conditions are set as follows: 

 



 

4 

  
 
   
 

0

0

max max

1 = 0

2 = 0

3 = 0

4 = 0

y

y

f fv

G

G

G

G N N

 

 

 

 


 


 
  

 
(13)

 

 
In the formula: β0 and βv are the fullness degree of pump 

before and after optimization; η0, ηv are the pump efficiency 
before and after optimization; σmax is the maximum working 
stress of the sucker rod, MPa; [σmax] is the maximum 
allowable stress of the sucker rod, MPa; Nf and Nfv are the 
number of stress cycles before rod failure before and after 
optimization. 

Based on the objective function and constraint conditions 
established above, the mathematical model of optimization 
design of the plunger motion curve can be established as 
follows: 

 

s 0 0 1 1( ) max ( , , , , , , , , , , , , , , , )

( ) 0 1, 2, 3, 4
w l s d N NF x S n D l L L h H a b a b a b

G i i

    
     (14)

 

The variable value of optimization solution is: 
 

 0 1 1 2 2, , , , ,... , ( 2)j jX a a b a b a b j  (15)

 

 

In summary, the optimization process is as follows: 
according to the main optimization objective function and 
constraint conditions (14), the solution algorithm is used to 
obtain the optimal variable value in (15) under the condition 
of specific well condition parameters, so as to obtain the 
optimal flexible plunger motion curve equation expressed by 
Fourier series under the condition of the specific well 
condition parameters. 

The above optimization problem is actually a nonlinear 
optimization problem of discrete variables, and the actual 
solving process is relatively complex, considering the 
efficiency and global nature of genetic algorithm, genetic 
algorithm is adopted here to solve the optimization model. 

4. Plunger Movement Law Analysis 
Based on the measured well condition data parameters of 

Jiangsu oilfield, parameters such as stroke and submergence 
depth obtained by orthogonal experiment and corresponding 
constraint conditions, the optimal Fourier series coefficients 
are obtained as follows: 

ɑ0 = 1.3572, ɑ1 = -0.1728, b1 = -1.3482, ɑ2 = 0, b2 = -0.0072 

Therefore, the optimal flexible plunger motion rate curve 
is finally obtained as follows: 

2 2 2
( ) 1.3572 0.1728 sin 1.3482 cos 0.0072 cos 2

20 20 20

t t t
x t

                
     

 

Compare the speed and acceleration characteristics of the 
plunger before and after optimization, as shown in Figure 2: 

 

 
a. Comparison of velocity curves before and after optimization 

 
b. Comparison of acceleration curves before and after optimization 

Figure 2. Comparison of plunger velocity and acceleration before and after optimization 
 



 

5 

 
As can be seen from the figure, compared with the plunger 

motion curve before optimization, the optimized plunger 
motion curve has a higher speed at the initial up stroke, which 
is conducive to the rapid change of pressure in the pump and 
the rapid inflow of liquid into the pump. However, the speed 
change at the maximum speed is more stable. At the same 
time, the speed at the maximum speed of down stroke is larger 
and more stable, which ensures the smooth and rapid 
discharge of liquid.  

According to the well parameters, formula (1) calculated 
that the pump efficiency before optimization was 47% and the 
pump efficiency after optimization was 50.7%. Therefore, the 
optimized flexible rate can improve pump efficiency by 3.7% 
at this well parameter. 

5. Simulation Analysis of Pump Based 
on Finite Element Software 

Compared with the plunger velocity before optimization, 
the plunger movement law of the pump has changed to some 
extent. Different plunger velocities in a pumping cycle will 
lead to different fluid velocity variation laws in the pump, 
which will have a certain degree of influence on the fluid 
production. The internal flow field of the pump and the flow 
rate of the pump were studied by using the finite element 
software. Due to the complex structure of the pump, it is 
difficult to realize the modeling calculation completely 
according to the actual model. Therefore, the following basic 
assumptions are made: (1) The bottom pump valve orifice is 
simplified as the speed inlet, without considering the valve 
housing; (2) The upper end is the exit boundary. (3) There is 
no gap between the plunger and the pump chamber, and the 
leakage between the plunger and the pump chamber is not 
considered [8]; The model is shown in Figure 3: 

 

 

Figure 3. Simplified model of pump 

According to the flow state of bottomhole fluid entering the 
pump barrel of the pump, the simulation model is set as 
follows: the round ball in Figure 3 represents the valve ball, 
and the rest are the wall of the pump; The flow model of the 
fluid in the pump is set as turbulence model. The bottom end 
is the fluid inlet, which is set as the velocity inlet boundary; 
the top end is the fluid outlet, which is set as the pressure 
outlet boundary; the rest part is set as the wall boundary. The 
temperature field of the whole simulation model is set as 
constant, the simulated fluid is an oil-water mixture with a 
density of 870 kg/m3, the viscosity coefficient is 0.24, the 
pump inlet pressure is 3 MPa, the pump outlet pressure is 12 
MPa. The finite element software was used to analyze the 
flow field of pump and the flow rate of the incoming pump 
before and after the optimization, and the cloud diagram of 
the flow rate change in the pump at some time (as shown in 
Figure 4), the flow of fluid into the pump and the pump 
efficiency (as shown in Table 3) were obtained. 

 

Before 
optimization 

 1s 4s 7s 11s 

After 
optimization 

  

Figure 4. Cloud diagram of velocity variation in plunger at partial time 

 
 
 
 
 
 



 

6 

Table 3. Inlet pump flow and pump efficiency before and after optimization 

 Mass of incoming pump fluid during a swabbing cycle (g) 
pump 

efficiency (%) 
Before optimization 1630 43.6 
After optimization 1782 48.5 

Range of optimization 9.3% 4.9% 
 

It can be seen from the results that under the condition that 
the stroke, stroke times and other parameters are the same and 
only the plunger movement law is changed, after optimization, 
the flow rate of the incoming pump increases in a single 
swabbing cycle, and the pump efficiency increases by 4.9%. 
Therefore, the liquid production is higher under the flexible 
rate condition. 

6. Test and Data Analysis 
According to the basic working parameters, a 1∶4 

pumping unit test system is set up to simulate the working 
process of the whole pumping unit under the condition of two 
kinds of piston speed before and after 
optimization(According to the optimized flexible plunger 
speed curve x(t), the motion rate of the suspension point of 
the pumping unit can be inversely derived, and then the motor 
speed can be inversely derived from the motion rate of the 
suspension point of the pumping unit. By adjusting the 
frequency conversion motor speed to the motor speed 
obtained by the above inverse push, the pumping unit 
experiment system device can simulate the working process 
of the whole pumping system under optimized conditions). 
The device is mainly composed of variable speed drive 
system, Support system and oil pumping system. The 
schematic diagram of the test device is shown in Figure 5: 

 
 

 
1. Variable frequency motor 2. Support mechanism 3. 

Crank 4. Connecting rod 5. Walking beam 6. support 
frame 7. Horsehead 8. Capstan 9. fixed pulley 10. friction 
pulley 11. Vertical moving device 12. Support frame 13. 

Oil pumping pump 14. Horizontal moving device 15. 
Bottom guide rail 

Figure 5. Pumping unit test system structure 
 

The solid diagram of the test device is as follows: 

 
Figure 6. Pumping unit test system device 

 
The test period of the experiment was 1min, and the 

experimental medium was clean water and oil-water mixed 
solution, respectively. The fluid production of the pumping 
system was tested under the conditions of two kinds of 
plunger movement rates before and after optimization when 
the borehole deviation was 15°, 30° and 45°, respectively. The 
experimental results are shown in Figure 7: 

 

 
a. Liquid production when the medium is clean water 

 
b. Liquid production when the medium is oil-water 

mixture 
Figure 7. Comparison of experimental results 

 
As can be seen from Figure 7, when the experimental 

medium is clean water and oil-water mixture, the liquid 



 

7 

production after optimization is increased to a certain extent 
compared with that before optimization, and the maximum 
increase is 4.1%. Therefore, under the condition that the test 
error is excluded, the law obtained by the test experiment is 
consistent with the theoretical calculation results, and the 
optimized flexible plunger rate can effectively improve the 
fluid production of the well to a certain extent. 

7. Conclusion 
(1) Considering the well condition parameters and the 

structure parameters of the pump comprehensively, the 
motion model of the flexible plunger of the pump was 
established with the filling coefficient of the pump as the main 
optimization objective, and the optimized rate curve of the 
flexible plunger was found. 

(2) When other factors are not considered, the theoretical 
analysis and calculation show that the pump efficiency under 
the optimized flexible rate condition is improved, and the 
pump efficiency is 3.7% higher than that before optimization. 
The simulation model was established to analyze the inlet 
flow rate and pump efficiency of the pump before and after 
optimization. It can be seen that the mass flow rate of the inlet 
fluid increased within a single swabbing cycle of the flexible 
rate curve after optimization, and the pump efficiency 
increased by 4.9%. 

(3) The test results of the pumping unit test system show 
that liquid production after the flexible rate optimization is 
higher than that before the optimization, with the maximum 
increase of 4.1%, which is consistent with the results of 
theoretical analysis. 

(4) The optimized flexible plunger rate can effectively 
improve the pump efficiency and liquid production, and the 
conclusions can provide certain guidance for the flexible 
operation control strategy of the pumping system. 

References 
[1] DOU Shuping. Analysis of the application effect of the flexible 

control system of the pumping unit [J].Chemical Engineering 
& Equipment, 2016 (9) : 157-158. 

[2] HU Songhua, BAI Cunan. Research and application of flexible 
drag control technology of pumping unit [J]. Petroleum 
Geology & Oilfield Development in Daqing, 2016, 25(S1): 73-
74, 89, 118. 

[3] DING Qiao，ZHANG Min. Analysis of soft start and running 
characteristics of optimal control technology of oil pumping 
unit [J]. Journal of Beijing Institute of Petrochemical 
Technology, 2014, 22 (1): 12-15. 

[4] CHEN Jiancheng. Research on flexible control intelligent 
optimization technique of beam pump [D]. Beijing: China 
University of Petroleum ( Beijing), 2016. 

[5] YUAN Yue. Study on the optimization of system efficiency of 
low yield wells in Yu Shu Lin Oil Field[D]. Northeast 
Petroleum University, 2017. 

[6] ZHAO Xuanmin. Experimental design method [M]. Beijing: 
Science Press, 2005. 

[7] LIU Chao.Study on the Mechanism of Energy Saving 
Operation of Pumping Speed [D]. College of Petroleum 
Engineering China University of Petroleum (East China), 2016. 

[8] DI Minyan, YANG Haibin, LI Hanzhou, et al, Analysis of 
factors affecting pumping efficiency of Jiangsu Oilfield pumps 
[J].Complex Hydrocarbon Reservoirs, 2009, 2 (2): 68-71. 

[9] GAO Ping. The system design and analysis of small diameter 
pump [D].Xi ’an: Xi ’an Shiyou University, 2013. 

[10] YU Mmaoqian. Research on model of pump’s working 
performance [D].Dongying: China University of Petroleum 
( Huadong), 2013. 

[11] LI Q, YIN X D. The Research on Calculation Method of Pump 
Efficiency [J]. Advanced Materials Research, 2012, 503/504: 
968-971. 

[12] WU Jianjun, QI Yaoguang,LIU Xinfu,et al.Simulation of pump 
valve motion law based on Simulink [J].China Petroleum 
Machinery,2011,39 ( 1) : 32-35. 

[13] ZHANG Qi. Principle and design of oil production engineering 
[M]. Dongying: China University of Petroleum Press, 2000.