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Development of Sensors Systems for the Validation of Mathematical Models
for Sucker Rod Pumps
I. C. Bastos, Federal University of Alfenas; L. Mayr, Consultant
Copyright 2017, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Latin America and Caribbean Petroleum Engineering Conference held in Buenos Aires, Argentina, 18-19 May 2017.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents
of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect
any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written
consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may
not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
In order to extract the oil from reservoirs which have reached the end of the natural flow, the use of an
artificial lift system is necessary. The mechanical pumping system accounts for about 90% of all artificial
lift systems in the world. This kind of pump has a highly complex mechanical design and serves as a test
for evaluating the developed mathematical model and the construction of special measuring equipments
for future analysis systems. This work includes the construction and performance testing of an electronic
force sensor installed at the Pitman (rod) and an acceleration sensor installed on the Walking Beam. The
design and development of these sensors are discussed from the basic including the process of selection and
configuration of strain gauges for the signal conditioning for use in harsh environments with interferences
during an necessary continuous data transfer. After the acquisition of data in real time, an analysis of the
mechanical pumping system using the developed mathematical model and the measured data is performed.
The validation of this model is performed by comparison of force and position (angle) values of the
measurement and the simulation. The entire system was implemented in software and hardware, and the
results are evaluated in field tests in Gänserndorf, Austria.
Most current diagnostic techniques for sucker rod pumping are based on the load measurements imposed
on the whole system. The dynamometer is an example for an instrument for such an application and is
applied on the polished rod. Its function is to measure simultaneously the load and motion (position) of the
polished rod during the operation of the rod pumping system (surface dynamometer card). As a first step in
this work, a force measurement is developed and applied on the pitman of the sucker rod pumping system.
The advantage is due to security issues (non-hazardous location at a distance from the well output). This
electronic device can be operated in this area without any problem and it also can provide online data. [3]. A
further step is related to the construction of an acceleration sensor to provide the position of each step of the
mechanical pumping operation. The Figure 1 shows how the sensors were installed in the mechanical pump
system. After data collection, a comparison of the measured and calculated data is performed validating
the developed mathematical model. The data collected as Force and Acceleration are part of a complete
analysis of the mechanical pump system to optimize its energy efficiency.
Figure 1—Mechanical assembly of the acceleration sensor and force Sensor
Force Transducer
Force Transducer with Strain Gauge Measuring System.
Force transducers are maintenance-free and can even be installed in places where access is difficult. In this
application, a linear strain gauge is applied on the pitman in the sucker rod pump to measure the force on
the system. In accordance with the movement of the rod string (upstroke and downstroke), a mechanical
deformation occurs on the material. This sensor transduces small amounts of mechanical spatial variation in
equivalent amounts of variations in electrical resistance. The force can be calculated through equation (1),
where ΔR/R is the variation of the resistance, EY is Young's modulus and K the factor of the strain gauge.
The variation of electrical resistance is correlated linearly with the force applied to the force sensor [1,2].
Experimentally, the force curve as a function of (ΔR/R) is a straight line with slope determined empirically
that depends on the physical characteristics of the extensometer and the material where it is mounted on. For
the study, a sucker rod from steel is used. High safety margins in mechanical layout make signal conditioning
difficult due to very small amounts of resistance variation.
Signal Conditioning and Adjusment of Sensor Force
To measure such small changes in resistance, strain gauges are used in a half Wheatstone bridge with a
voltage excitation source (Fig. 2). In this application, the two active strain gauges (120Ω) also compensate
temperature effects (resistance variation caused by thermal expansion). As it is shown in Fig. 2, the variation
of the electrical resistance provides a linear voltage variation - Uα (potential difference between point 1 and
2). To complete the Wheatstone bridge, two passive resistances (120Ω) are added (R4 and R3) to the system.
Figure 2—Linear strain gauge for the force measurement. A wheatstone half bridge can
be presented being one strain gauge also responsible to compensate then temperature.
As there is really a very small change in total signal due to the material where the deformation is measured,
a precision amplifier circuit was developed (Fig.3). The maximal input voltage variation is about ± 50mV.
Due to problems that might occur in the field, there are two stages of amplification, which allow two
possibilities to obtain the output signal. The first stage amplifier has an amplification factor about 200
(Output1) and the second one (output 2) has an amplification factor of 5 (connected directly to the output
1). A difference amplifier configuration is applied in both stages of the circuit. In the first test, just the first
stage of the amplifier is used (factor 200 – output 1). The error margins of the circuit are approximately 1%.
An offset is also added to provide a fine-tuning of the output. This offset of 2.5 V provides the output signal
corresponding to the stretch and compression of the strain gauge.
Figure 3—Mechanical assembly of the circuit. The whole system is adapted to endure field conditions.
The circuit has been supplied with 5V. The excitation voltage of the Wheatstone bridge is 2,5V being
regulated by an integrated circuit of type LM4040A. This component has an improved precision micro
power shunt voltage reference with multiple reverse breakdown voltages. Capacitors as filter components
and protection for all input signal also are included in the circuit.
The difference amplification is done by MCP6V27 (SMD type - Surface-Mount Device). Due to the
small changes of the signal, this integrated circuit has to exhibit low offset that reduces the error at the
measurement system. Fig. 3 shows the electronic circuit, which is mounted on the sucker rod pumping
system. As the system is applied outside in the field, the mechanical part like connectors, box and soldering
of the components are to be considered, too, because of climate conditions and the vibration of the pumping
system (mechanical movement). As can be observed, the electronic force sensor was installed in the pitman
of a mechanical pump system located in Ganserndorf, Austria (Figure 4). The pump used is the conventional
type of manufacturer Lufkin code C-640D-365-168. Figure 5 (Circuit Schematic) shows in details all the
information about the components used to realize the amplification circuit.
Figure 4—Assembly of the Electronic Force Sensor
Figure 5—Circuit schematic of the amplifier
Therefore, the measurement system includes a transducer capable of measuring mechanical deformations
of the material through a change in resistance (extensometer) and a precision amplifier circuit. In addition,
another sensor is used to indicate the position of the pump (acceleration sensor) and data acquisition
equipment is responsible for obtaining data online from a real pumping system. The data collected as force
and acceleration are part of a system analysis and in this case it is responsible for validating the mathematical
model of the surface pump.
Performance of Signal Conditioning and Adjustment of Sensor Force
In order to verify the developed force sensor, a simulation of the system to analyze of the all data is done.
Figure 6 shows the force measured on the pitman (sucker rod pumping system) through the use of the
Strain Gages and the amplifier circuit. A comparison between the surface dynamometer card provided by
the company and the calculated is also done. Beyond that, the comparison between the measured torque
and the calculated toque are done. All these calculatons will be demonstrated by section - Verification of
the mathematical model [4,5].
Figure 6—The calculated force on the pitman of the sucker rod pumping system. The force is based on
the measured data from the strain gauges, half bridge Wheatstone and the developed amplifier circuit.
In order to obtain the position of the sucker rod pumping system according to the downstroke and upstroke
movement, an acceleration sensor is developed. The sensor provides the x, y and z coordinates system being
that for 1 g (9.8m /s2) has a 3.3 Volts in the circuit output. The Figure 7 shows the developed circuit ready
to be installed on the pumping system.
Figure 7—Mechanical assembly of the acceleration sensor. The whole
system is adapted to endure the conditions of the external field.
In this case, the acceleration sensor is used to provide the position of the pump. With these data,
it is possible to compare the calculated kinematics model though the measured data. Figure 8 explains
installation of the sensor and also how the angle can be calculated. The calculation has been done through
simple geometry considerations. Figure 9 shows the comparison between calculated angle and measured
angle from the sucker rod pumping system [3].
Figure 8—Mechanical assembly of the acceleration sensor. The whole
system is adapted to endure the conditions of the external field.
Figure 9—Comparison between angle calculated and angle measured.
In order to verify if the mathematical model developed fits the original sucker rod pumping system we
compare the measured data to data obtained from the calculated model. As already demonstrated by the
Figure 8 and Figure 9, the angle ζ by the angle α (crank angle) is compared to the measured data and the
calculated model. It can be seen that due to some interferences on the measurement, there is a small error
between the curves. After this first proof, it is possible to find the polished rod position by the crank angle
(α) as shown by Figure 10.
Figure 10—Position of the Polished Rod x Angle Alpha (Crank Angle).
By the force on pitman already demonstrated by Figure 6, it is possible to calculate the torque on the
crank (Equation 2). Where the force is F [kN] and r [m] is the length of the crank. The torque is depicted
in Figure 11.
Figure 11—Simulation of the torque versus crank angle.
For final evaluation of the mathematical model developed, a comparison between mechanical power
calculated (Pmech = ω × τ) and the electrical power (measured on site) has been done. We observe that the
both values fit with the measurement system also taking motor efficiency into consideration. As can be seen
in figure 12, both curves adjust, proving the mathematical model and the proposed sensing.
Figure 12—Simulation of the crank torque and crank angle based on the measured data.
The most popular artificial lift system for extracting oil from underground reservoirs after the free- flowing
period traditionally is the sucker rod pump. Such a pump equips 90% of all the wells with an artificial lift
system. The sucker rod pump is a very complex mechanical system and it has been selected as a demanding
task for system analysis. This work describes the first step for improving the system performance. Initially
sensors are developed in order to obtain continuous monitoring of data that is essential for the analysis of
the entire system. These sensors can be used for efficiency analysis since they provide values such as the
amount of load and the position during its operation. In addition, these sensors can be used as a basis for
other measurements since they provide standardized signals, ie, any data acquisition system can be used.
To verify the funcionaliy of the system, a mathematical model is developed and used to compare the
measured and calculated data. By figure 12, we can observe a phase delay of power (due to an error by
measuring the current on site - a filter was inserted at the acquisition system) as well as changes in the
curve between 240° till 280° (angle alpha). This change is caused by the variable frequency device trying
to compensate the power, increasing the frequency. The whole system has been implemented in software/
hardware and the results are evaluated in field tests.
Acknowledgement to the National Council of Scientific and Technologic Development - CNPq for the
financial suport.
Author Unknown, Pratical Strain Gauge Measurements, E-130 © Agilent Technologies 1999.
Strain Gauge Measurement - A Tutorial, Application Note 078, National Instruments, Publish
Date: Sep 28, 2012 | 1117 Ratings | 4.08 out of 5.
Economides, Michael J., Hill Daniel, Petroleum Production Systems, 1993, Prentice Hall PTR,
NJ 07632. ISBN 013658683.
Author Unknown, Pratical Strain Gage Measurements, E-130 © Agilent Technologies, 1999.
Strain Gauge Measurement - A Tutorial, Application Note 078, National Instruments, Publish
Date: Sep 2012.
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