Method and apparatus for measuring pumping rod position and other aspects of a pumping system by use of an accelerometer

An oil well pumping unit has a walking beam which raises and lowers a rod connected to a downhole pump. To perform well analysis, it is desirable to know the position of the rod during the stroke. An accelerometer is mounted on the pumping system unit to move in conjunction with the rod. An output signal from the accelerometer is digitized and provided to a portable computer. The computer processes the digitized accelerometer signal to integrate it to first produce a velocity data set and second produce a position data set. Operations are carried out to modify the signal and produce a position trace with stroke markers to indicate positions of the rod during its cyclical operation.

FIELD OF THE INVENTION 
The present invention pertains, in general, to instrumentation for oil 
field equipment and in particular to the determination of pumping rod 
position and other physical aspects for a reciprocating pumping system. 
BACKGROUND OF THE INVENTION 
In most oil wells, the pumping is carried out by use of a reciprocating 
downhole pump that is supported by a pumping rod which extends from the 
pump to the earth's surface where it is connected to a reciprocating 
walking beam. The beam is provided with a counter balance weight to offset 
the weight of the rod, the pump and the fluid column. There are many 
variable factors involved in the operation for pumping equipment of this 
type. Various types of instrumentation have been developed to monitor the 
pumping operation and measure the parameters of such operation. Once such 
measurements have been made, it is often possible to make adjustments and 
optimizations to improve the pumping efficiency of the well. For some 
measurements it is necessary to know the position of the rod in the stroke 
of the pumping operation. This measurement has heretofore been made in a 
number of ways. One technique has been to use a spring-loaded rotating 
potentiometer connected to the rod or beam by a string or cable so that 
the potentiometer rotates with the up and down motion of the rod or 
walking beam. This produces a changing resistance that is proportional to 
the position of the rod. However, mechanical equipment of this type is 
awkward, expensive and subject to easy breakage. The position of the rod 
can also be determined by mechanical position switches, but these are also 
subject to wear, environmental damage and calibration difficulties. 
An apparatus for measuring the position of a sucker-rod is described in 
U.S. Pat. No. 4,561,299 entitled "Apparatus for Detecting Changes in 
Inclination or Acceleration". 
An apparatus which utilizes an accelerometer to measure course length in a 
wellbore is described in U.S. Pat. No. 4,662,209 entitled "Course Length 
Measurement". This device, however, does not measure pump rod position. 
Thus, there exists a need for a method and a corresponding apparatus for 
determining the position of a pumping rod and to analyze other pumping 
system aspects during pumping operations in such a manner that is 
reliable, accurate, inexpensive, convenient and not significantly affected 
by wear and exposure. 
SUMMARY OF THE INVENTION 
The present invention, in one embodiment, is directed to a method and 
apparatus for determining the position of a rod used in a reciprocating 
pumping system wherein the rod extends downward into a borehole in the 
earth and is joined to a downhole pump which lifts fluid within the 
borehole to the surface of the earth. An accelerometer is mounted on the 
pumping system to move in conjunction with the rod. An output signal is 
generated from the accelerometer. This output signal is provided to a 
digitizer which translates the analog output signal of the accelerometer 
into a first set of digital samples. The first set of digital samples is 
integrated to produce a second set of digital samples. The second set of 
digital samples are then integrated to produce a third set of digital 
samples, which essentially correspond to positions of the rod in its 
reciprocating motion. 
In another aspect of the present invention, the third set of digital 
samples are normalized to a predetermined actual rod stroke to correct the 
determined rod stroke so that it corresponds to the true rod stroke. The 
determined rod stroke could be inaccurate due to errors in accelerometer 
calibration or sensitivity drift due to temperature or other variable 
factors. 
In another aspect of the present invention, an accelerometer is calibrated 
by measuring the output signal in a first upright position and 
sequentially in a second inverted position. These two output signals are 
then combined to produce a calibration factor for the accelerometer. 
In a still further aspect of the present invention, the output from an 
accelerometer mounted on a pumping system is displayed on the screen of a 
computer to indicate operation of the pumping system, including any 
anomalies in the operation such as unusual vibrations or pounding.

DETAILED DESCRIPTION OF THE INVENTION 
The present invention and its application is illustrated in FIG. 1. A 
pumping system includes a walking beam 12 that is driven by a motor 14 
through a belt and pulley assembly 15 and gearbox 16. The beam 12 is 
connected by cables 18, which are secured by cable clamps 20 to a carrier 
bar 22. A polished rod 24 is secured by a rod clamp 26 to the carrier bar 
22. A polished rod 24 is connected to a sucker rod 28 that extends 
downward in the borehole and is connected to a downhole pump 30. The rod 
28 is positioned within tubing 32 and casing 34. An accelerometer 40 is 
mounted between the rod clamp 26 and the carrier bar 22. However, it could 
be mounted at any position where movement corresponds to motion of the 
polished rod 24. 
In operation, the motor 14 drives the beam 12 in an up and down, 
reciprocating, fashion which in turn raises and lowers the rods 24 and 28 
so that the pump 30 lifts fluid through the tubing 32 upward to the 
surface. 
The accelerometer 40 is mounted on the polished rod 24 and connected 
through a electrical cable 42 to an electronics package 44. The output 
from the package 44 is connected through a ribbon cable 46 to a computer 
50 that includes a screen 52, keyboard 54 and a disk drive 58. 
The accelerometer 40 uses a sensor which is preferably a model 3021 
manufactured by IC Sensors, a company located in Milpitas, Calif. This is 
a piezoresistive accelerometer. It preferably has a range of .+-.2 g or 
.+-.5 g. 
The accelerometer 40 is shown in greater detail in FIG. 8. This device has 
a U-shape with an open slot such that the accelerometer 40 can be inserted 
onto the rod 24 without the need to remove the rod clamp 26. Accelerometer 
40 includes a high-strength steel body 112 which has an opening for 
receiving an accelerometer sensor 114 and is provided with an electrical 
socket 116 for receiving the cable 42. The sensor 114 is the model 3021 
noted above. Accelerometer 40 can be inserted on the rod 12 with either 
side up. The accelerometer 40, or just the accelerometer sensor 114 can be 
affixed to the rod 24 in any manner, including merely clamping it to the 
rod. The body 112 can further comprise or include a load cell for 
measuring the load on the rod 24. Such load information can be measured 
concurrently with the acceleration information. 
Referring to FIG. 2, the electronics package 44 includes an amplifier 43 
which receives the output signal of the accelerometer 40 through cable 42. 
The output from the amplifier 43 is provided to an analog-to-digital (A/D) 
converter 45 which produces digital samples corresponding to the output 
signal from the accelerometer 40 and transmits these digital samples 
through the ribbon cable 46 to the computer 50. 
The electronics package 44 further includes a clock 48 which provides clock 
signals to the analog-to-digital converter and to the computer 50 through 
a line 49 in the cable 46. The clock 48 provides a 1000 Hz clock signal to 
the converter 45 so that it takes samples of the accelerometer signal at 1 
millisecond intervals. The clock 48 further produces a signal every 50 
milliseconds which is transmitted through line 49 and produces an 
interrupt at the computer 50. The computer 50 accepts a sample of the 
accelerometer signal upon receipt of each interrupt. Therefore, the 
computer 50 receives samples of the accelerometer signal at 50 millisecond 
intervals. 
The computer 50 is preferably a Toshiba Model 1000SE. The processing of the 
output signal from the accelerometer 40 is described in FIG. 3. 
The operation of the computer 50 with the output signal of the 
accelerometer 40 for a selected embodiment is described as a series of 
operational steps in FIGS. 3, 4A-4D and 6. Various waveforms are 
illustrated in FIGS. 4A-4D. FIG. 4A shows the analog output signal of the 
accelerometer and the vertical scale is in millivolts per volt. In FIG. 
4B, the accelerometer output signal is illustrated with a vertical scale 
in inches per second per second. In FIG. 4C, there is shown a velocity 
waveform with a vertical scale in inches per second. In FIG. 4D, there is 
shown a waveform for rod position with the vertical scale in inches. 
Accelerometer 40 generates a varying output depending on the state of 
acceleration it experiences. This analog electrical signal is provided 
through the cable 42, amplified and converted to digital samples within 
the electronics package 44. The digital samples are then provided through 
the cable 46 to the computer 50. Within the computer 50, the steps 
described in FIG. 3 are carried out. In step 70, data is received for a 
time sufficient to ensure that at least two complete pump strokes (cycles) 
of acceleration data are collected. The analog accelerometer output signal 
is illustrated in FIG. 4A. This data has five cycles in a period of time 
just over 50 seconds. In step 72 the algebraic mean of the accelerometer 
signal shown in FIG. 4A is subtracted from the signal itself to 
substantially correct for DC offset in the signal. The acceleration 
information portion of the accelerometer output signal can be relatively 
small compared to the DC offset. If this DC offset is not removed, 
integration of the signal to produce velocity will generate a steep ramp 
in which the cyclic information is obscured. This is due to integrating a 
constant. The subtraction of the algebraic mean removes this constant of 
integration. The digitized and DC corrected accelerometer output signal is 
illustrated in FIG. 4B as a function of time. 
In step 74, the digital signals corresponding to the output of the 
accelerometer, as shown in FIG. 4B, are integrated to produce a second set 
of digital signals which essentially correspond to rod velocity. The set 
of integrated samples (second set of digital samples) for pump rod 
velocity are illustrated as a waveform in FIG. 4C. 
In step 76, all positive zero crossings are detected and counted. Next, in 
step 78 a determination is made if the count of positive going zero 
crossings exceeds three. If not, an error message is generated by 
operation in step 80. If the count exceeds three, entry is made to step 82 
wherein the slope of the peaks within the signal is determined. 
Following step 82, entry is made into step 84 for determination if the 
slope determined in step 82 equals or exceeds a predetermined value termed 
epsilon. A dotted line 83 intersects the peaks of the waveform. An 
illustration of the velocity signal with the line 83 is further shown in 
FIG. 6. In this FIGURE the integration from the signals shown in FIG. 4B 
includes a constant of integration which causes the waveform to be 
progressively increasing. This constant must be removed so that the 
waveform has a zero slope of the peaks, as shown in FIG. 4C. If the slope 
is greater than or equal to epsilon, entry is made to step 86 in which the 
acceleration data produced in step 72 is adjusted by the formula 
ACCEL(n)=ACCEL(n)-dx/dy. A preferred value for epsilon is 0.01%. The value 
dx/dy is a measure of the slope of the peaks, i.e. the slope of line 83. 
In step 86, the value of dx/dy, in incremental steps, is subtracted from 
each of the data points shown in the acceleration waveform in FIG. 4B 
until the value of dx/dy, the slope of the dotted line 83, is less than 
epsilon. After each adjustment to the acceleration signal shown in FIG. 
4B, that signal is integrated to produce the signal shown in FIG. 4C 
wherein the slope of line 83 is again determined. This process is repeated 
until the slope of the peaks become less than epsilon. 
If the slope value determined is not greater than or equal to epsilon, 
entry is made through the negative exit to step 88 in which the second set 
of digital samples are integrated between the first positive zero crossing 
and the last positive zero crossing. This produces essentially a position 
signal for the pump rod. See FIG. 4D. 
Following step 88, step 90 is performed to adjust the position data for 
zero position at each positive zero crossing for the second set of digital 
values, which set represents velocity. 
In step 92, following step 90, stroke markers 93 are set at positive zero 
crossings for the velocity signal set of data. The stroke markers 93 are 
also applied at the determined times to the broad position waveform shown 
in FIG. 4D and the acceleration waveform shown in FIG. 4B. The adjusted 
position data with stroke markers is shown in FIG. 4D. After step 92, step 
94 is carried out to calculate the stroke rate from the average time 
between positive zero crossings. The processing of this signal enters an 
exit after the completion of step 94. 
The signal shown in FIG. 4A has the vertical axis labeled in millivolts per 
volt. The signal produced at the output of the accelerometer 40 is an 
electrical signal which is typically measured in millivolts. The value 
indicated in FIG. 4A is produced by dividing the actual accelerometer 
output signal by the amplitude of the power supply voltage. This produces 
a signal which is independent of variations in the supply voltage provided 
to the system. 
Acceleration, velocity and position data for the polished rod can be used 
in a variety of ways to measure and evaluate the performance of the 
pumping system. The load on a polished rod during the pumping cycle is 
normally acquired in conjunction with the polished rod position. Such load 
information can be acquired by use of a load cell such as that disclosed 
in U.S. Pat. No. 4,932,253 issued Jun. 12, 1990 to McCoy. The torque on a 
pumping unit gear box can be determined if there is a knowledge of the 
polished rod load, as well as the polished rod position. A thorough 
analysis of the pumping system requires a knowledge of polished rod load 
and position to verify that the surface equipment is operating properly 
and that the rod string is properly loaded. Further, recent mathematical 
treatments of load and/or position/velocity allow the calculation of 
downhole pump loadings. This is described in a publication by Gibbs, S. 
G., "Predicting the Behavior of Sucker Rod Pumping Systems", J. Pet. Tech. 
(July 1963) 769-778; Trans., AIME, 228. A downhole pump card, produced as 
described in the article, is illustrated in FIG. 5B. The information 
disclosed in this figure further helps to determine pump performance, 
including standing valve, traveling valve and pump plunger operation. The 
first integration of acceleration produces velocity, which is used in the 
determination of the downhole pump loading, as shown in FIG. 5B. 
The waveforms shown in FIGS. 4A-4D, 5A and 5B are displayed on the display 
screen 52 of the computer 50, shown in FIG. 1. This allows the operator to 
see the signals which have been collected, and those which have been 
processed. 
In a prior technique, the load on a polished rod was acquired and displayed 
as a function of the polished rod position. This used mechanical test 
equipment in which the display of polished rod load versus polished rod 
position was produced by rotating a drum on which the load was scribed. To 
produce a display, such as shown in FIG. 5A, the load on the rod and the 
position of the rod must both be known. 
Referring now to FIGS. 5A and 5B, there are illustrated respectively a 
surface card and a downhole card each measuring rod load versus rod 
position. The information in FIG. 5A can be produced by measuring rod load 
(vertical scale) through use of commonly available load cells. The 
position information (horizontal scale) can be that produced in accordance 
with the present invention as set forth in FIG. 4D. The utilization of 
this information to produce the downhole card shown in FIG. 5B is 
described in the article by Gibbs noted above. 
One objective of the present system is to acquire acceleration data from an 
oil well pumping system during the pumping cycle for the purpose of 
determining polished rod position. The accuracy of the calculated polished 
rod position depends upon the accuracy of the accelerometer sensitivity 
factor, also referred to as a calibration factor. The sensitivity of the 
accelerometer varies with temperature. In field installations, the 
accelerometer is not always installed in exact alignment with the axis of 
the polished rod. This results in variation of the accelerometer data. 
Further, the gravitational field of the earth varies from one location to 
another. In a further aspect of the present invention, an actual 
measurement of the accelerometer sensitivity factor is performed at the 
well location in the field and the sensitivity factor is calculated for 
the system being used by performing the following steps. The accelerometer 
40, see FIG. 8, is placed in an upright position on the polished rod, as 
shown in FIG. 1, and the output signal is measured while the pumping unit 
is stopped. Next, the accelerometer 40 is removed and then replaced in an 
inverted position. The output signal from the accelerometer 40 is again 
measured while the pumping unit is stopped. In both the upright and 
inverted cases, the output of the accelerometer is transmitted through 
cable 42 to the electronics package 44 where the signal is digitized and 
then transferred through cable 46 to the computer 50. The output of the 
accelerometer is a dc signal measured in millivolts. The first measurement 
produces a reference value with +1 g applied acceleration and the second 
value measured is for -1 g applied acceleration. The difference in the 
signal outputs represents the sensitivity of the accelerometer 40 to a 2 g 
field. This is a highly accurate method of measuring the accelerometer 
sensitivity while at the same time automatically compensating for all of 
the variables pertaining to the pumping system and the location. It 
further calibrates the accelerometer to the particular electronics being 
utilized, as well as to the effects of temperature, gravitational field 
and any other factors affecting the accelerometer 40 output. 
As an example of the above calibration procedure, the first output of the 
accelerometer can be, for example, +10 millivolts for the +1 g field and 
-10 millivolts for a -1 g field (inverted). This is a 20 millivolt 
difference for a 2 g gravity difference, which results in a calibration 
factor of 10 millivolts per g. (20 millivolts.div.2 g=10 mv/g) This 
calibration factor is used to produce the data shown in FIG. 4B from that 
shown in FIG. 4A. 
The accelerometer 40, as shown, is physically removed to invert its 
position to produce the calibration factor. However, the accelerometer 
sensor can also be clamped to the rod 24, or an element having 
corresponding motion, such that the accelerometer sensor can be rotated in 
place in an inverted position. This reduces the effort need to remove the 
accelerometer and then replace it on the polished rod. 
Further procedure for making the calibration constant is to utilize a value 
normalized for the supply voltage, as described above for the signal shown 
in FIG. 4A. Using the above example for calibration, assuming an 8.0 volt 
supply voltage, the +1 g calibration signal would be 1.25 millivolts/volt 
and the -1 g field calibration signal would be -1.25 millivolts/volt. This 
would result in a calibration factor of 1.25 millivolts/volt per g. This 
calibration factor can be used directly to multiply the data in FIG. 4A to 
produce the data in FIG. 4B. 
A still further aspect of the present invention is the utilization of an 
accelerometer for the observation of pumping system performance as 
illustrated in FIGS. 7A and 7B. FIG. 7A represents the output signal from 
the accelerometer 40 for a pumping system, such as shown in FIG. 1, in 
which the operation is normal. This is indicated by the generally smooth 
acceleration curve. FIG. 7B is the output signal from the accelerometer 40 
for the same or similar pumping unit, but with improper operation. The 
signal in FIG. 7B includes abnormal vibrations indicated by the lines 102, 
104 and 106. These abnormal vibrations are essentially repeated in each of 
the cycles of the signal. Such vibrations can be generated by defective 
gear teeth, worn bearings, abnormal surface conditions, unit misalignment, 
abnormal downhole pump conditions, and downhole mechanical problems. These 
large acceleration spikes (lines 102, 104 and 106) in the acceleration 
signal indicate that severe shock loads occur at these times. FIGS. 7A and 
7B are displayed concurrently on the screen 52 of the computer 50 so the 
abnormalities can be readily determined. The signal in FIG. 7A can be 
recorded at a time when it is known that the pumping system is working 
well or it can be a representative signal for a pumping unit of the 
particular type which is to be examined. 
Although one embodiment of the invention has been illustrated in the 
accompanying drawings and described in the foregoing detailed description, 
it will be understood that the invention is not limited to the embodiment 
disclosed, but is capable of numerous rearrangements, modifications and 
substitutions without departing from the scope of the invention.