Note: Descriptions are shown in the official language in which they were submitted.
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METHODS AND APPARATUS TO DETERMINE PRODUCTION OF
DOWNHOLE PUMPS
FIELD OF THE DISCLOSURE
[0001] This disclosure relates generally to downhole pumps and, more
particularly, to
methods and apparatus to determine production of downhole pumps.
BACKGROUND
[0002] Downhole pumps are used to pump fluid from a formation by moving a
piston relative
to a bore. Clearance is provided between the piston and the bore to ensure
that downhole
debris does not negatively affect the performance of the downhole pump.
However, this
clearance allows for leakage between the piston and the bore. Further, in some
instances the
pump may not be completely full when pumping. As a result, pump fillage
affects the
amount of fluid produced by a pump.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] FIG. 1 shows a pumping unit including an example apparatus used to
determine the
production of a well in accordance with the teachings of this disclosure.
[0004] FIG. 2 shows an example surface dynamometer card that may be produced
in
accordance with the teachings of this disclosure.
[0005] FIG. 3 shows an example pump dynamometer card that can be produced in
accordance with the teachings of this disclosure.
[0006] FIG. 4 shows an example pump dynamometer card produced by a pumping
unit
having anchored tubing.
[0007] FIG. 5 shows an example pump dynamometer card produced by a pumping
unit
having unanchored tubing.
[0008] FIG. 6 shows an example pump dynamometer card produced by a pumping
unit in
which the pump is not full during the down stroke.
[0009] FIG. 7 is a flowchart representative of an example method of
determining a pump
fillage factor and which may be implemented with the example apparatus of FIG.
1.
[0010] FIG. 8 is a flowchart representative of an example method of
calculating pump intake
pressure and which may be implemented with the example apparatus of FIG. 1.
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[0011] FIG. 9 is a flowchart representative of an example method of
controlling a pumping
unit based on pump intake pressure and which may be implemented with the
example
apparatus of FIG. 1.
[0012] FIGS. 10A and 10B are a flowchart representative of an example method
of
determining production of a pumping unit and which may be implemented with the
example
apparatus of FIG. 1.
[0013] FIG. 11 is a processor platform to implement any of the example methods
of FIGS. 7,
8, 9 or 10A and 10B and/or the example apparatus of FIG. 1.
[0014] Certain examples are shown in the above-identified figures and
described in detail
below. In describing these examples, like or identical reference numbers are
used to identify
the same or similar elements. The figures are not necessarily to scale and
certain features and
certain views of the figures may be shown exaggerated in scale or in schematic
for clarity
and/or conciseness. Additionally, several examples have been described
throughout this
specification. Any features from any example may be included with, a
replacement for, or
otherwise combined with other features from other examples.
DETAILED DESCRIPTION
[0015] An oilfield downhole reciprocating pump (e.g., a rod pump) is often
considered to be
a positive displacement pump because a plunger or piston of a known diameter
travels a
known (or calculable) distance with each stroke. It is desired to use a pump
as a meter to
approximate the daily production from a well by relating the number of pump
strokes during
the day and the pump geometry to an inferred production quantity. In other
words, because
the displacement volume of the pump is known (or calculable), it is desired to
use the number
of strokes during a time period to infer a volume of liquid produced. However,
downhole oil
pumps do not perform as true positive displacement pumps because the pumps are
typically
designed with significant clearance between the piston and a barrel through
which the piston
reciprocates, resulting in leakage or slip.
[0016] In accordance with the teachings of this disclosure, information
associated with a
downhole reciprocating pump may be used to approximate production from a
corresponding
well. In general, production can be estimated based on the area of a pump and
the distance of
the pump stroke, which equates to an estimated displacement volume for each
stroke.
However, known production estimates do not take into account other factors
that may affect
the volume produced such as, for example, pump fillage and/or pump leakage.
The example
methods and apparatus disclosed herein may be used to more accurately estimate
production
by taking into account at least these two variables.
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[0017] Pump fillage refers to the amount of fluid in a barrel of the pump
(e.g., between the
piston and a bottom of the barrel). If the barrel of the pump is not
completely full when the
piston moves downward during the downstroke, then the volume of the liquid
pumped by the
piston in the upstroke is not the same as the displacement volume of the pump.
The methods
and apparatus disclosed herein may be used to determine a pump fillage factor
(e.g., a
fraction), which is useful for a number of rod pump control applications. For
example, a
pump fillage factor is a highly desirable process variable for rod pump speed
control and/or
rod pump on/off control. In variable speed rod pumping applications, the pump
speed may
be decreased when pump fillage factor is below a target value (e.g., a set
point, a threshold)
and increased when pump fillage factor is above the target value. For on/off
control
applications, the pump fillage factor can be monitored and when the pump
fillage factor falls
below a target value for a specified number of strokes, the pump can be
stopped and the well
can be left in idle to allow the well casing to be filled by the producing
formation. Therefore,
when pumping is resumed (at the end of idle time), sufficient fluid may be
present to fill the
pump. These strategies may be employed to reduce energy consumption per unit
of liquid
produced and reduce wear on pump system components, thereby lengthening the
life of a
pumping system.
[0018] Additionally, downhole pumps are designed with a clearance or gap
between the
piston and the barrel or tube within which the piston reciprocates. Therefore,
on the upstroke
(e.g., when a pressure difference across the piston exists), leakage occurs
between the pump
and the barrel. As a result, the volume of fluid actually pumped is less than
the predicted or
estimated volume. The example methods and apparatus disclosed herein may be
used to
determine a leakage proportionally constant that may be used to more
accurately predict the
volume of oil produce in each stroke. In some examples, the pump fillage
fraction or factor
is also used to determine the leakage proportionally constant. Therefore, the
example
methods and apparatus disclosed herein may be used to determine pump fillage
and leakage,
which can then be used to more accurately infer production. Specifically,
production from
the well may be inferred based on the number of strokes of the pumping unit,
the geometry of
the downhole pump, the example leakage proportionality constant and/or the
pump fillage
factor. A stroke refers to a complete cycle including an upstroke and a down
stroke.
[0019] Also, in most applications of a reciprocating rod pump, an operator or
owner may
desire to operate the well at or near "pumpoff," which is the point at which
the available
liquid in the wellbore is marginally adequate to fill the pump. In general,
operating a well
near pumpoff results in the lowest practical producing bottom hole pressure.
Also, inflow to
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the wellbore increases as bottom hole pressure declines. Therefore, operating
the well at or
near pumpoff generally results in maximum production from the well. However,
in some
instances, an operator may desire to operate a well at a specified wellbore
pressure other than
at pumpoff. This strategy may provide superior reservoir management because it
enables
lighter hydrocarbon components to remain in solution with the liquid phase as
the products
flow toward the wellbore. By maintaining the product in a liquid only phase,
the effective
permeability to liquids is increased. In some instances, this approach results
in higher overall
recovery of hydrocarbons (although in some instances the recovery may take a
longer period
of time). To operate a well at (or around) a specified downhole pressure value
(e.g., a set
point, a threshold), some method of measuring or estimating wellbore (pump
intake) pressure
is needed. Some instrumentation products are available to directly measure
these values.
However, these products are generally expensive and operationally complex to
install. The
example methods and apparatus disclosed herein provide a technique for
determining the
pressure difference across the pump using the pump fillage factor described
above. As a
result, the intake pressure of the pump can be determined and used to control
the speed of the
pump. The intake pressure of the pump may be used for rod pump speed control
and rod
pump on/off control. In other words, the pump speed may be decreased or
increased and/or
the pump may be stopped or started based on the intake pressure of the pump.
[0020] FIG. 1 shows an example pumping unit 100 that may be used to produce
oil from an
oil well 102. The pumping unit 100 includes a base 104, a Sampson post 106 and
a walking
beam 108. In the illustrated example, the pumping unit 100 includes a motor or
engine 110
that drives a belt and sheave system 112 to rotate a gear box 114 and, in
turn, rotate a crank
arm 116 and a counterweight 118. A pitman 120 is coupled between the crank arm
116 and
the walking beam 108 such that rotation of the crank arm 116 moves the pitman
120 and the
walking beam 108. As the walking beam 108 pivots about a pivot point and/or
saddle
bearing 122, the walking beam 108 moves a horse head 124 to provide
reciprocating
movement to a downhole pump 126 via a bridle 128, a polished rod 130, a tubing
string 132
and a rod string 134.
[0021] In the illustrated example, the reciprocating movement of the horse
head 124 moves a
piston 136 of the pump 126 within a barrel 138 (e.g., a bore, a casing, a
housing, etc.) of the
pump 126 to draw liquid from the surrounding formation 140 (labeled as F).
During an
upstroke of the piston 136, liquid is drawn into the bore 138 through a
stationary valve 142
(e.g., a lower valve) located at a bottom of the bore 138. The piston 136
includes a traveling
valve 144 (e.g., an upper valve) that is in the closed position. As such, the
piston 126 pushes
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the fluid in the tubing 132 above the piston 136 to the surface. During a
downstroke, the
traveling valve 144 of the piston 126 opens, which enables the fluid in the
barrel 138 to flow
through the valve 144 and into the tubing 138 above the piston 126. During
this time the
stationary valve 142 is closed. The piston 126 then moves upward during a
subsequent
upstroke to push the fluid in the tubing 132 toward the surface, and so forth.
[0022] To ensure that debris does not negatively impact production and/or
negatively impact
movement of the piston 136 relative to the bore 138, a clearance or gap is
provided between
the piston 136 and the bore 138. The clearance reduces the volume of fluid
produced by the
pump 126 during each stroke of the pumping unit 100.
[0023] To accurately determine the production from the pump 126, the pumping
unit 100
includes an example apparatus and/or rod pump controller 146. In this example,
data from
and/or associated with the pumping unit 100 is received by an input/output
(I/0) device 148
of the rod pump controller 146 and stored in a memory 150 that is accessible
by a processor
152. As disclosed in further detail herein, the processor 152 can perform
processes to
determine, for example, an example pump fillage factor (e.g., based on the
volume of fluid
contained in the pump 126), an intake pressure of the pump 126, an example
leakage
proportionality constant (e.g., in2/1b0, the volume of fluid leaked through
the pump 126 (e.g.,
in3) and/or the net fluid produced during a stroke of the pumping unit 100
and/or a given time
period. In some examples, the components 148, 150, 152 of the apparatus 146
are disposed
within a housing 147, which may be located at the site of the pumping unit
100. In other
examples the apparatus 146 may be located in a remote location (e.g., at a
base station or
control room).
[0024] Several techniques have been proposed to calculate inferred production
using a well
site controller that can count the pump strokes and measure the effectiveness
of the individual
strokes. However, these known methods are hindered by the need for an
independent
estimate or measurement of the amount of leakage that occurs during each
stroke. In U.S.
Patent Application Serial No. 13/187,330, filed July 20, 2011, incorporated
herein by
reference in its entirety, a technique is set forth that applies a principle
that has been derived
from laboratory pump tests and, in particular, that the leakage through a pump
is directly
proportional to the pressure difference across the pump (e.g., the difference
between the
pressure inside the barrel 138 and the pressure above the piston 136). The
pressure difference
across a pump is directly proportional to the load or tension on a sucker rod
string. A
traditional diagnostic tool used with reciprocating rod pumps is called the
dynamometer card,
which is a plot of load (e.g., force) versus position (e.g., linear
displacement) for a single
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stroke of a pumping unit. Two types of dynamometer cards are typically used.
The first type
of dynamometer card is the surface card, which is based upon measurements
taken at the
surface and displays polished rod load versus polished rod position. The
second type of
dynamometer card is referred to as the pump dynamometer card and is computed
using data
collected for the surface dynamometer card and a mathematical computation
process that
models the flexibility of the sucker rod string.
[0025] FIG. 2 shows an example surface dynamometer card 200 that can be
generated in
accordance with the teachings of this disclosure using data associated with
the vertical
displacement of the polished rod 130 versus time and data associated with
tension on the
polished rod 130 versus time. In some examples, the surface dynamometer card
200
represents a scenario in which the downhole pump 126 is operating normally
with adequate
liquid to pump. As shown in FIG. 2, the x-axis 202 corresponds to the position
of the
polished rod 130 and the y-axis 204 corresponds to the load on the polished
rod 130.
[0026] In the illustrated example of FIG. 2, reference number 206 (at point 1)
corresponds to
when the polished rod 130 begins its upward motion (e.g., upstroke) to begin
to lift a column
of fluid. Between reference numbers 206 and 208 (at point 2), the increase in
tension on the
polished rod 130 is shown as the polished rod 130 is stretched and the fluid
column is lifted.
Reference number 208 corresponds to when the pumping unit 100 is supporting
the weight of
the rod string 134 and the weight of the accelerating fluid column. Between
reference
numbers 208 and 210 (at point 3), force waves arrive at the surface as the
upstroke continues,
which causes the load on the polished rod 130 to fluctuate. Reference number
210
corresponds to when the polished rod 130 has reached its maximum upward
displacement.
Between reference numbers 210 and 212 (at point 4), the fluid load is
transferred from the
rod string 134 to the tubing string 132, which causes the tension in the
polished rod 130 to
decrease. Reference number 212 corresponds to when the load has substantially
and/or
completely transferred to the tubing string 132. Between reference numbers 212
and 206,
force waves reflect to the surface as the downstroke continues, which causes
irregular loading
on the polished rod 130 until the polished rod 130 reaches its lowest point
and begins another
stroke.
[0027] FIG. 3 shows an example pump dynamometer card 300 that can be generated
in
accordance with the teachings of this disclosure using data associated with
the position of the
polished rod 130 and the load on the polished rod 130. In some examples, the
pump
dynamometer card 300 is generated using data measured at the surface. As shown
in FIG. 3,
the x-axis 302 corresponds to the position of the downhole pump (e.g., the
position of the
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piston 136) and the y-axis 304 corresponds to the load on the downhole pump.
Points 1, 2, 3
and 4 from FIG. 2 are illustrated in FIG. 3. Using the pump card 300, the
pressure difference
across the pump 126 is proportional to the height (e.g., vertical extent) of
the pump card 300.
Therefore, the leakage through the pump 126 is directly proportional to the
height of the
pump card 300. Using the trapezoidal rule (or another similar technique) the
measured data
from a pumping unit stroke may be integrated to derive the area of the pump
card 300. The
total area of a pump dynamometer card represents the amount of work (e.g.,
force acting over
a distance) performed. Thus, the area of the pump dynamometer card 300
represents the
work performed by the pump 126.
[0028] Under ideal conditions (e.g., where the pump 126 is full and there is
no tubing
movement and/or leakage), if the discharge pressure (e.g., the pressure of the
fluid above the
piston 136) and the intake pressure of the pump 126 (e.g., the pressure of the
fluid below the
piston 136) are known or estimated, the area of the card 300 can be used to
determine the
ideal production fluid volume Vstroke using Equation 1 below.
Apc
Vstroke =
Equation 1
[0029] In Equation 1, Vstroke represents the ideal (e.g., no leakage) volume
of fluid produced
during a stroke (e.g., in3), Apc represents the area of a pump card (e.g., in-
lbf) for the stroke,
and AP represent the pressure across the piston 136 (e.g., the difference
between the pump
discharge pressure and the pump intake pressure) (e.g., in lbf/in2). However,
the relationship
set forth in Equation 1 can only be used for a full pump card in a well that
has anchored
tubing. In particular, in some instances the tubing 132 is anchored or secured
to prevent the
tubing 132 from moving and/or stretching during operation. If the tubing 132
is unanchored,
the tubing 132 may move and/or stretch during operation. As a result, the area
of the pump
card 300 may be affected.
[0030] For example, FIG. 4 shows an example ideal "full" pump dynamometer card
400 for a
well (e.g., the well 102) with anchored tubing. The x-axis 402 corresponds to
the position of
the downhole pump and the y-axis 404 corresponds to the load on the downhole
pump. As
illustrated in FIG. 4, the shape of the card 400 is substantially rectangular.
Even with the
irregularities that may exist, the ideal area Apo for a pump card can be
determined (e.g.,
approximated) using Equation 2 below.
APCI = (Smax Smin) X (Fmax ¨ Frnin)
Equation 2
[0031] In Equation 2, Apo represents the ideal area of the pump card (e.g.,
in/lbf), Smax
represents the maximum pump position (e.g., in), Smin represents the minimum
pump position
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(e.g., in), Fma,, represents the maximum pump load (e.g., lbf) and Fnmi
represents the minimum
pump load (e.g., lbf), which have been labeled in FIG. 4.
[0032] In some instances, as explained above, the tubing is not anchored or
secured. As a
result the tubing may stretch during operation, thereby affecting the area of
the pump card.
FIG. 5 shows an example ideal "full" pump dynamometer card 500 for a well
(e.g., the well
102) with unanchored tubing. The x-axis 502 corresponds to the position of the
downhole
pump and the y-axis 504 corresponds to the load on the downhole pump. As
illustrated in
FIG. 5, the pump card 500 is in the shape of a parallelogram. In particular,
the slopes of the
sides of the pump card 500 are less steep than the sides of the pump card 400,
for example.
The slopes of the sides of the pump card 500 reflect the stretching and
relaxation of the
tubing string as the fluid load is transferred from the sucker rods 134 (e.g.,
on the upstroke) to
the tubing 132 (e.g., on the downstroke). The slopes of the sides of the pump
card dF/ds may
be determined using Equation 3 below.
dF Atubing
¨ = E ¨
Equation 3
ds (12.0xL)
[0033] In Equation 3, dF/ds represents the slope of the sides of the pump card
(e.g., lbf/in), E
represents the modulus of elasticity of the tubing material (e.g., lbf/in2),
Atubmg represents the
cross-sectional area of the tubing (e.g., in2) and L represents the length of
the unanchored
tubing (e.g., ft). As illustrated in FIG. 5, the pump card 500 is not a
rectangle like the pump
card 400 in FIG. 4. As such, Equation 2 cannot be applied to accurately
measure the area of
the pump card 500. The ideal area Apc1 for a pump card associated with
unanchored tubing
may be determined using Equation 4 below.
APCI = [(Smax Smin) X (Fmax ¨ Fain)] ¨ ATM
Equation 4
[0034] In Equation 4, Alm represents the sum of the two triangular areas on
the sides of the
parallelogram (e.g., in-lbf), which can be determined using Equation 5 below.
[12.0x(Fmax¨ Fmin)2><L]
ATM = Equation 5
(ExAtubmg)
[0035] The value for Alm determined using Equation 5 can be used in Equation 4
to
determine the ideal area Apc1 of the pump card.
[0036] Another problem that exists and that may affect the production volume
is pump
fillage. FIG. 6 shows an example pump dynamometer card 600 for a well (e.g.,
the well 102)
with anchored tubing that is about %50 full. The x-axis 602 corresponds to the
position of
the downhole pump and the y-axis 604 corresponds to the load on the downhole
pump.
When the pump 126 is not full, the pump card 600 retraces itself during the
empty portion of
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the downstroke until the fluid is encountered by the piston 136. In other
words, during a
downstroke, the pump 126 should ideally be full of fluid. As such, the
pressure of the fluid
above and below the piston 136 is the same and, thus, the load on the pump 126
during the
downstroke is typically zero. However, if the pump 126 is not full of fluid,
then the piston
136 supports the column of fluid above the pump 126 as the piston 126 moves
downward
during the downstroke. Once the piston 136 encounters the fluid in the pump
126, the
pressure above and below the piston 136 stabilizes and, thus, the load on the
pump 126
moves to zero. As compared to FIG. 4, the pump card 400 in FIG. 4 includes a
larger area
than the pump card 600 in FIG. 6. The ideal area A1 of the pump card 600 may
be
determined using Equation 6 below.
API= {[(Smax ¨ Smin) X (Fmax ¨ Fmin)] ¨ ATM} X ri
Equation 6
[0037] In Equation 6, Alm represents the sum of the triangular areas (e.g., as
calculated using
Equation 5) andrirepresents a pump fillage factor (e.g., a fraction).
Therefore, Equation 6
combines the pump fillage aspect with the tubing movement aspect to accurately
determine
the area of a pump card. For wells that are anchored, the length of the
unanchored tubing L
in Equation 5 is zero, which causes the value of Alm in Equation 6 to be zero.
Equation 6 can
be rearranged to solve for the pump fillage factor 11, as shown in Equation 7
below.
Apc
11 = ___________________________________________________________________
Equation 7
([(Smax¨Smin)x(Fmax¨Fmin)1¨ATM}
[0038] In Equation 7, Apc represents the actual integrated card area (e.g., in-
lbf), which may
be determined using the trapezoidal rule, for example. Equation 7 provides a
means of
determining (e.g., estimating) pump fillage factor 11 using known parameters
(e.g., attributes)
of a tubing string and a pump dynamometer card. Therefore, an example method
or process
for determining the pump fillage factor 11 may include computing a surface
dynamometer
card (e.g., the surface dynamometer card 200), computing (e.g., calculating) a
pump
dynamometer card (e.g., the pump dynamometer card 600, which may be based on a
surface
dynamometer card), analyzing the pump dynamometer card for maximum and minimum
positions and maximum and minimum loads (Sma,, Sõ,õ, Fmax, Fõ,õ), integrating
the pump
dynamometer card to determine the true or actual area Apc, calculating the
triangular areas
Alm using Equation 5 (if the tubing is unanchored) (L, E and A are known from
the tubing
configuration) and calculating the pump fillage factor 11 using Equation 7.
This process may
be performed by the processor 152 of the rod pump controller 146, for example.
The pump
fillage factor 11 may be determined for each stroke of the pumping unit 100.
In some
examples, the pump fillage factor 11 may be monitored and may be used to
control the speed
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and/or on/off operations of the motor 110. For example, if the pump fillage
factor 11 falls
below a threshold or target value, the speed of the motor 110 may be
decreased. As a result,
there is relatively more time for the pump 126 to fill between strokes.
[0039] As disclosed herein, pump leakage occurs when there is a pressure
difference across
the pump 126. Therefore, any time a pump card shows a positive load on the
pump 126, a
pressure difference across the pump 126 is present. Additionally, the leakage
rate is
proportional to the pressure difference across the pump 126. Because a
pressure difference
across the pump is proportional to the load on the pump card, the leakage rate
is proportional
to the pump card load. The pump leaks on the upstroke because there is a
pressure difference
across the pump (e.g., as indicated by the load on the pump 126 during the
upstroke).
Additionally, the pump 126 may leak on the downstroke when fillage is less
than 100%,
because a pressure difference across the pump 126 exists when the pump 126 is
less than
100% full. Considering the fact that the discrete values used to calculate
pump dynamometer
cards are spaced equally in time, the volume of fluid leakage LKG can be
determined (e.g.,
approximated) using Equation 8 below.
LKG = CLKG X Apc X (2.0 ¨ TO Equation 8
[0040] In Equation 8, LKG represents the volume of fluid leaked through a pump
(e.g., in3)
and CLKG represents a leakage proportionality constant (e.g., in2/1b0. The
(2.0-1-1) term in
Equation 8 accounts for leakage on the downstroke. If the pump 126 is full
(e.g., the volume
of the bore 138 beneath the piston 136), then pump fillage factor 11 is 1.0,
and the (2.0-1-1) term
becomes 1Ø However if the pump 126 is less than full such as %50, the pump
fillage factor
11 is 0.5 and the (2.0-1-1) term becomes 1.5, which reflects the leakage
occurred during half of
the downstroke. Once the volume of leaked fluid LKG is known, net production
for a pump
stroke IPstroke can be determined using Equation 9 below.
IPstroke = Vstroke ¨ LKG Equation 9
[0041] Equations 1 and 8 may be combined into Equation 9 to produce Equation
10 below
for the net production of a pump stroke IPstroke=
IPstroke = APC{(T1p) [CLKG X (2.0 ¨ r011
Equation 10
[0042] In general, the pressure difference AP term in Equation 10 can be
problematic to
estimate from known or measured operational parameters. As disclosed herein,
the example
methods and apparatus consider that the pressure across the pump AP is
proportional to the
pump load. A relationship for determining an instantaneous pressure
measurement AP, may
be determined using Equation 11 below.
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= (F1)
A
Equation 11
Apump
[0043] In Equation 11, AP, represents the instantaneous pressure across a pump
(e.g., lbf/in2),
F, represents instantaneous pump force (e.g., lbf) and Apump represents a
cross-sectional area
of the pump (e.g., in2). To derive an average or mean force Favg on the pump
126 for a
complete or full stroke (e.g., an upstroke and a downstroke), the average
force Favg can be
determined used Equation 12 below.
Apc
Equation 12
Favg = [(Smax-Smin)x11]
[0044] Applying Equation 12 to Equation 11 leads to Equation 13 below.
Apc
APavg rA
Equation 13
- e-Tump x (Smax¨Smm)xi]
[0045] In Equation 13, AP,g represents the average pressure across the pump
during times
when leakage is occurring (e.g., lbf/in2). Substituting Equation 13 into
Equation 10 yields
Equation 14 below, which provides an accurate method of inferring (e.g.,
estimating) the net
production IPstroke from a single stroke of a pumping unit.
IPstroke = [Apump X (Smax ¨ Smin) X id ¨ [Apc X CLKG x (2.0 ¨ T)]
Equation 14
[0046] From Equation 14, production Pobserved for a series of strokes of the
pumping unit can
be estimated using Equation 15 below.
Pobserved = E{[Apump X (Smax ¨ Smin) X id ¨ [AFT X CLKG x (2.0 ¨11)]} Equation
15
[0047] In Equation 15, Pobserved represents the total observed production
during the series of
strokes (e.g., in3) and represents a summation of terms for all strokes during
the
observation period (e.g., for two strokes, eight strokes, etc.). Equation 15
can be rearranged
to solve for the leakage proportionality constant CLKG, which yields Equation
16 below.
vipumpx[E(Smax-Smm)xi]-Pobserved}
CLKG =
Equation 16
(E [A, x(2.o-i)]}
[0048] In some examples, a calibration process may be performed to derive the
leakage
proportionality constant CLKG. For example, a producing well may be coupled to
a dedicated
2-phase or 3-phase separator, which can measure liquid production from the
well over a time
period (e.g., 6 hours, 1 day, etc.) and/or for a certain number of strokes.
For example, a
separator 154 is illustrated in FIG. 1 that may separate oil from water and
gas and determine a
volume of produced oil. The processor 152 may measure required parameters,
calculate
pump dynamometer cards (e.g., for each of the stroke) and perform calculations
disclosed
herein to determine a value for the E(Smax ¨ Smin) X 11 term (e.g., a first
summation term)
and a value for the EApc X (2.0 ¨ TO term (e.g., a second summation term)
based on the
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strokes of the pumping unit during the calibration period. At the end of the
calibration
period, the observed total liquid (oil and water) production Pobserved and the
summation terms
(S max ¨ S min) X 11 and EApc X (2.0 ¨ TO may be used in Equation 16 to derive
a value for
the leakage proportionality constant CLKG. The value for the leakage
proportionality constant
CLKG can then be used to infer or determine production for a single stroke
(e.g., using
Equation 14) or for multiple strokes over a period of time (e.g., using
Equation 15). In other
words, given the leakage proportionality constant CLKG (which may be derived
using the
example process above or another means), the inferred production of an
individual stroke can
be determined using Equation 14 and values available from a downhole
dynamometer card.
The inferred production from individual strokes may be accumulated over a
period of time
(e.g., an hour, a day, a month, etc.), which may be determined using Equation
15.
[0049] Equation 13 above provides a means of determining or estimating the
pressure
difference AP across the pump 126 using known attributes of the pump 126 and a
pump
dynamometer card. Pump intake pressure PIP may be determined using Equation 17
below.
PIP = PDP ¨ APpump
Equation 17
[0050] In Equation 17, PIP represents the pump intake pressure (e.g.,
lbf/in2), PDP represents
pump discharge pressure (e.g., lbf/in2) and APpump represents the pressure
difference across
the pump (which can be determined using Equation 13). A number of methods can
be used
to determine (e.g., estimate) the pump discharge pressure PDP. The fluid
contained in the
production tubing can be treated as a flowing or as a static vertical column
of fluid. In some
examples, because the fluid flow is cyclic (e.g., reciprocating rod pump
systems only pump
during upstroke) and the flow rates are relatively low, the friction pressure
loss in the vertical
column is often ignored. However, the density changes in the fluid column
should be
considered. For example, an example process may include starting at the
surface with the
surface discharge pressure (e.g., measured via a sensor), and incrementally
calculating the
pressure down the tubing string 132 (FIG. 1). An example method or process may
include
(e.g., assuming fixed density within a section or discrete increment) (1)
obtaining estimates of
oil, water and gas production rates for a well; (2) obtaining or approximating
pressure,
volume and temperature (PVT) relationships of the liquid components over
reasonable
pressure and temperature ranges; (3) measuring or estimating surface discharge
pressure and
temperature; (4) using PVT characteristics, along with pressure and
temperature estimates to
calculate the density of the presumed oil, water and gas mixture at discharge
pressure and
temperature; (5) assuming the constant density over a discrete increment of
depth or pressure;
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(6) calculating or estimating the depth, pressure and temperature at the
bottom of the discrete
increment; (7) determining if the pump depth has been reached, using the
currently calculated
pressure as the pump discharge pressure; and (8) if the pump depth has not
been reached,
returning to step 4. In this example, the PVT relationships may be estimated
using oil and
gas gravity measurements, empirical correlations and/or estimates of pressure
and
temperatures, which may be stored in the memory 150, for example. Additionally
or
alternatively, a complex equation of state model may be used. In some
examples, a processor
(e.g., the processor 152) may estimate pump discharge pressure, estimate
pressure difference
across the pump at the end of each stroke (e.g., using Equation 13) and apply
Equation 17 to
derive an estimated pump intake pressure.
[0051] In some examples, the results of this example process may result in a
relatively noisy
pump intake pressure measurement (e.g., the pump intake pressure estimates may
vary from
stroke to stroke). In such an example, a damping function or low gain
proportional-integral-
derivative (PID) controller may be used, such that the processor can perform
either on/off or
variable speed control of the pumping system. In on/off control mode, for
example, the rod
pump controller 146 may stop the pump 126 (e.g., stop the motor 110) and place
the pumping
unit 100 into temporary idle time when the estimated pump intake pressure is
below the
pump intake pressure threshold for a specified number of strokes. In a
variable speed control
mode, for example, the rod pump controller 146 may decrease pump speed when
the
estimated pump intake pressure is below the threshold and increase pump speed
when the
estimated pump intake pressure is above the threshold.
[0052] While an example manner of implementing the apparatus 146 is
illustrated in FIG. 1,
one or more of the elements, processes and/or devices illustrated in FIG. 1
may be combined,
divided, re-arranged, omitted, eliminated and/or implemented in any other way.
Further, the
example I/0 device 148, the example memory 150, the example processor 152
and/or, more
generally, the example apparatus 146 of FIG. 1 may be implemented by hardware,
software,
firmware and/or any combination of hardware, software and/or firmware. Thus,
for example,
any of the example I/0 device 148, the example memory 150, the example
processor 152
and/or, more generally, the example apparatus 146 of FIG. 1 could be
implemented by one or
more analog or digital circuit(s), logic circuits, programmable processor(s),
application
specific integrated circuit(s) (ASIC(s)), programmable logic device(s)
(PLD(s)) and/or field
programmable logic device(s) (FPLD(s)). When reading any of the apparatus or
system
claims of this patent to cover a purely software and/or firmware
implementation, at least one
of the example I/0 device 148, the example memory 150 and/or the example
processor 152
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is/are hereby expressly defined to include a tangible computer readable
storage device or
storage disk such as a memory, a digital versatile disk (DVD), a compact disk
(CD), a Blu-
ray disk, etc. storing the software and/or firmware. Further still, the
example apparatus of
FIG. 1 may include one or more elements, processes and/or devices in addition
to, or instead
of, those illustrated in FIG. 1, and/or may include more than one of any or
all of the
illustrated elements, processes and devices.
[0053] Flowcharts representative of example methods for implementing the
apparatus 146 of
FIG. 1 are shown in FIGS. 7, 8, 9 and 10A and 10B. The methods of FIGS. 7, 8,
9 and 10A
and 10B may be implemented machine readable instructions that comprise a
program for
execution by a processor such as the processor 1112 shown in the example
processor
platform 1100 discussed below in connection with FIG. 11. The program may be
embodied
in software stored on a tangible computer readable storage medium such as a CD-
ROM, a
floppy disk, a hard drive, a digital versatile disk (DVD), a Blu-ray disk, or
a memory
associated with the processor 1112, but the entire program and/or parts
thereof could
alternatively be executed by a device other than the processor 1112 and/or
embodied in
firmware or dedicated hardware. Further, although the example methods are
described with
reference to the flowcharts illustrated in FIGS. 7, 8, 9 and 10A and 10B, many
other methods
of implementing the example apparatus 146 may alternatively be used. For
example, the
order of execution of the blocks may be changed, and/or some of the blocks
described may be
changed, eliminated, or combined.
[0054] As mentioned above, the example methods of FIGS. 7, 8, 9 and 10A and
10B may be
implemented using coded instructions (e.g., computer and/or machine readable
instructions)
stored on a tangible computer readable storage medium such as a hard disk
drive, a flash
memory, a read-only memory (ROM), a compact disk (CD), a digital versatile
disk (DVD), a
cache, a random-access memory (RAM) and/or any other storage device or storage
disk in
which information is stored for any duration (e.g., for extended time periods,
permanently,
for brief instances, for temporarily buffering, and/or for caching of the
information). As used
herein, the term tangible computer readable storage medium is expressly
defined to include
any type of computer readable storage device and/or storage disk and to
exclude propagating
signals and to exclude transmission media. As used herein, "tangible computer
readable
storage medium" and "tangible machine readable storage medium" are used
interchangeably.
Additionally or alternatively, the example methods of FIGS. 7, 8, 9 and 10A
and 10B may be
implemented using coded instructions (e.g., computer and/or machine readable
instructions)
stored on a non-transitory computer and/or machine readable medium such as a
hard disk
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drive, a flash memory, a read-only memory, a compact disk, a digital versatile
disk, a cache, a
random-access memory and/or any other storage device or storage disk in which
information
is stored for any duration (e.g., for extended time periods, permanently, for
brief instances,
for temporarily buffering, and/or for caching of the information). As used
herein, the term
non-transitory computer readable medium is expressly defined to include any
type of
computer readable storage device and/or storage disk and to exclude
propagating signals and
to exclude transmission media. As used herein, when the phrase "at least" is
used as the
transition term in a preamble of a claim, it is open-ended in the same manner
as the term
"comprising" is open ended.
[0055] FIG. 7 illustrates an example method 700 to calculate a pump fillage
factor (e.g.,
fraction) for a pumping unit. The example method 700 may be implemented by the
apparatus
146 (e.g., using the processor 152) of FIG. 1, for example, to calculate a
pump fillage factor
for the pump 126. The example method 700 includes computing a surface
dynamometer card
(block 702). As disclosed herein, a surface dynamometer card is based on
measurements
taken at the surface and displays polished rod load versus polished rod
position. FIG. 2
illustrates an example surface dynamometer card 200 that may be computed for
the example
pumping unit 100 of FIG. 1. The surface dynamometer card may be computed by
the
processor 152 of FIG. 1, for example.
[0056] The example method 700 includes computing a pump dynamometer card
(block 704).
As disclosed herein, a pump dynamometer card may be computed using data
collected for the
surface dynamometer card and a mathematical computation process that models
the
flexibility of the sucker rod string. FIGS. 3, 4, 5 and 6 illustrate example
pump dynamometer
cards that may be computed for the example pumping unit 100 of FIG. 1. The
pump
dynamometer card may be computed by the processor 152 of FIG. 1, for example.
[0057] The example method 700 includes determining a maximum pump position
Sn,a,, a
minimum pump position Sõ,õ, a maximum pump load Fmax and a minimum pump load
Fõ,õ
from the pump dynamometer card (block 706). The pump positions and loads may
be
determined by the processor 152 of FIG. 1, for example.
[0058] The example method 700 of FIG. 7 includes determining whether a tubing
(e.g.,
tubing string) of the pumping unit is anchored (bock 708). As disclosed
herein, if the tubing
of a pumping unit is unanchored, the tubing may flex and stretch during
operation. As a
result, the force on the pump may be relaxed at times. For example, FIG. 4
shows an
example pump dynamometer card 400 have a well having anchored tubing and a
FIG. 5
shows an example pump dynamometer 500 of a well having unanchored tubing. If
the tubing
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is anchored, the example method 700 includes calculating an ideal area Apo of
the pump
dynamometer card for an anchored tubing (block 710). The ideal area Apo may be
based on
the maximum pump position Smax, the minimum pump position S., the maximum pump
load Fmax and the minimum pump load Fniln. For example, the ideal area Apo may
be
calculated using Equation 2. If the tubing is unanchored, the example method
700 includes
calculating an ideal area Apo of the pump dynamometer card for unanchored
tubing (block
712). The ideal area may be based on the maximum pump position Snmx, the
minimum pump
position Snilõ, the maximum pump load Fmax and the minimum pump load Fõõõ, the
modulus
of elasticity E of the tubing material, the cross-sectional area of the tubing
A tubing and the
length L of the unanchored tubing. For example, the ideal area Apo of a pump
dynamometer
card for unanchored tubing may be calculated using Equation 4. The processor
152 of FIG. 1
may determine whether the tubing 136 is anchored or unanchored and may
calculate the ideal
area Apo of the pump dynamometer card using the Equation 4.
[0059] The example method 700 includes calculating a true area Apc of the pump
dynamometer card (block 714). The true area of the pump dynamometer card may
be
calculated using the trapezoidal rule, for example, or any other mathematical
formula. The
true area Apc of a pump dynamometer card may be calculated by the processor
152 of FIG. 1,
for example. The example method 700 includes determining a pump fillage factor
11 based on
the calculated ideal area Apo of the pump dynamometer card and the true area
Apc of the
pump dynamometer card (block 716). For example, the pump fillage factor 11 may
be
determined using Equation 7. The pump fillage factor 11 may be determined by
the processor
152 of FIG. 1, for example. The pump fillage factor 11 may be used to, among
other things,
determine intake pressure PIP of a pump and/or determine a leakage
proportionality constant
CLKG, which can then be used to infer production and/or control a pumping unit
more
efficiently. In some examples, the pump fillage factor can be used to control
the speed and/or
on/off operation of the pump. For example, the pump fillage factor can be
monitored and
when the pump fillage factor falls below a target value (e.g., for one stroke
or a specified
number of strokes), the pump can be stopped (or decreased in speed) and the
well can be left
in idle to allow the well casing to be filled by the producing formation.
Therefore, when
pumping is resumed (at the end of idle time), sufficient fluid may be present
to fill the pump.
[0060] FIG. 8 illustrates an example method 800 to calculate or determine
intake pressure of
a pump. The example method 800 may be implemented by the apparatus 146 (e.g.,
using the
processor 152) of FIG. 1, for example, to determine intake pressure PIP of the
pump 126.
The example method 800 includes determining a pump fillage factor 11 (block
802). The
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pump fillage factor 11 may be determined using the example method 700 of FIG.
7, which
may be implemented by the example apparatus 146 of FIG. 1. The example method
800
includes calculating an average force Favg on a pump during a time period when
leakage
occurs (block 804). The average force Favg may be based on, for example, an
area Apc of a
pump dynamometer card, a maximum position of the pump Smax, a minimum position
of the
pump Snam and/or the pump fillage factor ii. The area Apc of a pump
dynamometer card, the
maximum position of the pump Smax and the minimum position of the pump Snail,
are
explained in connection with the method 700 of FIG. 7. The average force Favg
may be
determined using Equation 12, which may be implemented by the processor 152 of
FIG. 1,
for example.
[0061] The example method 800 includes calculating an average pressure APavg
across the
pump during times when leakage occurs (block 806). The average pressure APavg
may be
determined using Equation 13, which may be implemented by the processor 152 of
FIG. 1,
for example. In Equation 13, the average pressure APavg is based on the true
area Apc of the
pump dynamometer card, the cross-sectional area Apump of the pump, the maximum
position
of the pump Smax, the minimum position of the pump Snam and the pump fillage
factor ii. The
example method 800 includes obtaining estimates of oil, water and gas
production rates for
the well (block 808). The estimates for the production rates may be obtained
by the
processor 152 of FIG. 1, for example. The rates may be based on measurements
from the
separator 154. In other examples, the rates may be determined based on
inferred production,
such as determined in connection with the method in FIGS. 10A and 10B and
disclosed in
further detail herein.
[0062] The example method 800 of FIG. 8 includes obtaining or approximating
pressure,
volume and temperature relationships of the liquid components over pressure
and
temperature ranges (block 810) (e.g., pressure and temperature ranges that are
appropriate for
the operating conditions of the well). The relationships may be obtained or
approximated by
the processor 152 of FIG. 1, for example. In some examples, the relationships
are stored on
the memory 150. The example method 800 includes measuring or estimating
surface
discharge pressure and temperature (block 812). For example, the processor 152
of FIG. 1
may receive measurements via the I/0 device 148 and determine a discharge
pressure and
temperature at the surface.
[0063] The example method 800 includes using pressure, volume and temperature
characteristics, along with the pressure and temperature
measurements/estimates, to calculate
the density of the presumed oil/water/gas mixture at the discharge pressure
and temperature
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(block 814). The density may be calculated by the processor 152 of FIG. 1, for
example.
The example method 800 includes assuming the constant density over a discrete
increment of
depth or pressure (block 816) and calculating the depth, pressure and
temperature at the
bottom of a discrete increment (block 818). The discrete increment may be any
increment
(e.g., 1 mm). The depth, pressure and temperature values may be calculated by
the processor
152 of FIG. 1, for example.
[0064] The example method 800 includes determining when a pump depth has been
reached
(block 820). In other words, the method 800 includes determining whether the
increment is
the last or bottom most increment of the well. If not, the example method 800
includes using
the pressure, volume and temperature characteristics to calculate the density
and calculating
the depth, pressure and temperature values at the bottom of the next discrete
increment
(blocks 814-818). This process may continue until the pump depth has been
reached. If the
pump depth has been reached, the method 800 includes using the currently
calculated
pressure as the pump discharged pressure (block 822) (e.g., the pressure value
calculated at
block 818) and calculating pump intake pressure based on the calculated
pressure difference
across the pump and the pump discharge pressure (block 824). The pump intake
pressure
may be calculated using Equation 17, which may be implemented by the processor
152 of
FIG. 1, for example.
[0065] FIG. 9 illustrates a flowchart representative of an example method 900
that may be
used to operate a pumping unit based on pump intake pressure. The example
method 900
may be implemented by the apparatus 146 (e.g., using processor 152) of FIG. 1,
for example,
to operate the pump 126 above or below a threshold intake pressure and/or
pressure range.
The example method 900 includes determining pump intake pressure (block 902),
which may
be determined using the example method 800 of FIG. 8. The example method 900
includes
comparing the pump intake pressure to a pump intake pressure threshold (block
904). The
pump intake pressure may be a range (e.g., having an upper limit and a lower
limit). The
pump intake pressure may be set by an operator. For example, the processor 152
of FIG. 1
may determine the intake pressure PIP of the pump 126 and compare the intake
pressure PIP
to a pump intake pressure threshold.
[0066] The example method 900 includes determining whether the pump intake
pressure is
within the pump intake pressure threshold (block 906). For example, the pump
intake
pressure may be higher than an allowed or threshold pump intake pressure. If
the pump
intake pressure is not within the pump intake pressure threshold, the example
method 900
includes starting or stopping the pump and/or changing the speed of the pump
(block 908).
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For example, the apparatus 146 of FIG. 1 may be used to control the motor 110
to increase or
decrease the speed of the motor 110. As disclosed herein, in some examples it
may be
desired for the pump to operate above a set intake pressure threshold, which
may enable
lighter hydrocarbons to remain in liquid phase, for example. The example
method 900
includes determining whether monitoring of the well is to continue (block
910). If
monitoring is to continue, the example method 900 may repeat. Otherwise, the
example
method 900 may end.
[0067] FIGS. 10A and 10B illustrate a flowchart representative of an example
method 1000
that may be used to infer production of an oil well. The example method 1000
may be
implemented by the apparatus 146 (e.g., using the processor 152) of FIG. 1,
for example, to
infer production of the well 102 by the pumping unit 100. The example method
1000
includes obtaining pump parameters or attributes such as a diameter of the
pump, a cross-
sectional area Apump of the pump, the modulus of elasticity E of the tubing
material and/or the
length L of any unanchored tubing (block 1002). The parameters or attributes
may be
obtained by the processor 152 of FIG. 1, for example. At block 1004, the
process of directly
measuring liquid production from a well (e.g., the well 102 of FIG. 1) for a
first
predetermined period of time and/or for a first predetermined number of
strokes begins
(block 1004). The liquid produced from the well (e.g., the well 102) is
directly measured for
one or more strokes of the pumping unit (e.g., the pumping unit 100) (block
1006). In some
examples, the liquid is directly measured using a well test separator (e.g.,
the separator 154 of
FIG. 1). The example method 1000 includes determining if the pumping unit has
completed
a stroke (block 1008). For example, the processor 152 may determine if the
pumping unit
100 has completed a stroke. In some examples, the processor 152 determines
that the
pumping unit 100 completes a stroke based on feedback received from a sensor
adjacent the
crank arm 116. If a stroke of the pumping unit has not been completed, the
method continues
to directly measure the liquid produced from the well (block 1006).
[0068] If the pumping unit has completed a stroke (determined at block 1008),
the example
method 1000 includes computing a pump dynamometer card based on, for example,
a
determined surface dynamometer card and/or data collected for the surface
dynamometer
card (block 1010). The pump dynamometer card may be computed by the processor
152 of
FIG. 1, for example. The example method 1000 includes determining a maximum
pump
position Snam, a minimum pump position Snam, a maximum pump load Fmax and a
minimum
pump load Fnam from the pump dynamometer card (block 1012). The pump positions
and
loads may be determined by the example processor 152 of FIG. 1, for example.
The
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example method 1000 includes determining an area Apc of the pump dynamometer
card
(block 1014). For example, the processor 152 may determine the area Apc of a
pump card
using the trapezoidal rule.
[0069] The example method 1000 includes determining a pump fillage factor 11
(block 1016).
The pump fillage factor 11 may be determined using the example method 700 of
FIG. 7. The
example method 1000 includes calculating a first summation value and a second
summation
value (block 1018) for the pump dynamometer cards of the stroke(s) that have
occurred
during the first predetermined time period and/or the first predetermined
number of strokes.
For example, the first summation value may be calculated using E(Smax ¨ Smin)
X ii for the
stroke(s) occurred during the first predetermined time period, and the second
summation
value may be calculated using EApc X (2.0 ¨ TO for the stroke(s) occurred
during the first
predetermined time period. The first and second summation values may be
determined by
the processor 152 of FIG. 1, for example.
[0070] The example method 1000 includes determining whether the first
predetermined time
period has elapsed and/or if the first predetermined number of strokes of the
pumping unit
has occurred (block 1020). For example, the processor 152 of FIG. 1 may
determine if the
first predetermined time period has elapsed and/or the first predetermined
number of strokes
has occurred. If the first predetermined time period has not elapsed and/or if
the
predetermined number of strokes has not occurred, the liquid produced from the
well
continues to be measured (block 1006).
[0071] If the first predetermined time period has elapsed and/or if the
predetermined number
of strokes has occurred, the example method 1000 includes determining total
liquid
production Pobserved during the first predetermined time period and/or for the
first
predetermined number of strokes (block 1022). The example method 1000 includes
determining a leakage proportionality constant CLKG (block 1024). The leakage
proportionality constant CLKG may be based on the pump parameters (e.g.,
obtained at block
1002), the total liquid production Pobserved during the first predetermined
time period and/or
during the first predetermined number of strokes (e.g., obtained at block
1022) and/or the first
summation value and the second summation value (e.g., obtained at block 1020).
For
example, the leakage proportionality constant CLKG may be determined using
Equation 16,
which may be implemented by the example processor 152 of FIG. 1.
[0072] The example method 1000, which continues in FIG. 10B, includes
determining (e.g.,
inferring) production of the pumping unit during normal operation and/or while
the pumping
unit is continuously operating for a second predetermined time period (block
1026). The
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second predetermined time period may be, for example, an hour, a day, a week,
a month, etc.
The example method 1000 includes determining whether the pumping unit has
completed a
stroke (block 1028) (e.g., a complete cycle including an upstroke and a
downstroke). If the
pumping unit has not completed a stroke, the method 1000 iteratively
determines if a stroke
has completed. If the pumping has completed a stroke (e.g., determined by the
processor
152), the example method 1000 includes computing a pump dynamometer card
(block 1030).
The pump dynamometer card may be based on, for example, a determined surface
dynamometer card. The pump dynamometer card may be computed by the processor
152 of
FIG. 1, for example.
[0073] The example method 1000 includes determining a maximum pump position
Sn,a,, a
minimum pump position Sõ,õ, a maximum pump load Fmax and a minimum pump load
Fõ,õ
from the pump dynamometer card (block 1032). The pump positions and loads may
be
determined by the example processor 152 of FIG. 1, for example. The example
method 1000
includes determining an area Apc of the pump dynamometer card (block 1034).
For example,
the processor 152 may determine the area Apc of a pump card using the
trapezoidal rule. The
example method 1000 includes determining a pump fillage factor 11 (block
1036). The pump
fillage factor 11 may be determined using the example method 700 of FIG. 7.
For example,
the processor 152 may determine the pump fillage factor 11 using Equation 7.
[0074] The example method 1000 includes determining inferred production of the
stroke of
the pumping unit (block 1038). The production of the pumping unit may be based
on the
pump parameters (e.g., obtained at block 1002), the pump fillage factor 11
(e.g., obtained at
block 1036) and/or the leakage proportionality constant CLKG (e.g., obtained
block 1024).
For example, the production IP stroke may be determined using Equation 14,
which may be
implemented by the processor 152 of FIG. 1. The example method 1000 includes
determining whether the second predetermined time period has elapsed and/or
the second
predetermined number of strokes has occurred (block 1040). If the second
predetermined
time period has not elapsed and/or the second predetermined number of strokes
has not
occurred, the example method 1000 continues to block 1028 where the method
1000
continues to determine whether the pumping unit has completed another stroke.
If the second
predetermined time period has elapsed and/or the second predetermined number
of strokes
has occurred, the example method 1000 includes summing the production from the
stroke(s)
(block 1042). The total production Pobserved of all the stroke(s) may be
determined using
Equation 15, for example. The total production Pobserved may be determined by
the processor
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152 of FIG. 1, for example. The example method 1000 may repeat itself as
desired.
Otherwise, the example method 1000 may end.
[0075] FIG. 11 is a block diagram of an example processor platform 1100
capable of
executing instructions to implement the methods of FIGS. 7, 8, 9 and 10A and
10B and/or to
implement the apparatus 146 of FIG. 1. The processor platform 1100 can be, for
example, a
server, a personal computer, a mobile device (e.g., a cell phone, a smart
phone, a tablet such
as an iPadTm), a personal digital assistant (PDA), an Internet appliance or
any other type of
computing device.
[0076] The processor platform 1100 of the illustrated example includes a
processor 1112.
The processor 1112 of the illustrated example is hardware. For example, the
processor 1112
can be implemented by one or more integrated circuits, logic circuits,
microprocessors or
controllers from any desired family or manufacturer.
[0077] The processor 1112 of the illustrated example includes a local memory
1113 (e.g., a
cache). The processor 1112 of the illustrated example is in communication with
a main
memory including a volatile memory 1114 and a non-volatile memory 1116 via a
bus 1118.
The volatile memory 1114 may be implemented by Synchronous Dynamic Random
Access
Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS Dynamic
Random Access Memory (RDRAM) and/or any other type of random access memory
device.
The non-volatile memory 1116 may be implemented by flash memory and/or any
other
desired type of memory device. Access to the main memory 1114, 1116 is
controlled by a
memory controller.
[0078] The processor platform 1100 of the illustrated example also includes an
interface
circuit 1120. The interface circuit 1120 may be implemented by any type of
interface
standard, such as an Ethernet interface, a universal serial bus (USB), and/or
a PCI express
interface.
[0079] In the illustrated example, one or more input devices 1122 are
connected to the
interface circuit 1120. The input device(s) 1122 permit(s) a user to enter
data and commands
into the processor 1112. The input device(s) can be implemented by, for
example, an audio
sensor, a microphone, a camera (still or video), a keyboard, a button, a
mouse, a touchscreen,
a track-pad, a trackball, isopoint and/or a voice recognition system.
[0080] One or more output devices 1124 are also connected to the interface
circuit 1120 of
the illustrated example. The output devices 1124 can be implemented, for
example, by
display devices (e.g., a light emitting diode (LED), an organic light emitting
diode (OLED), a
liquid crystal display, a cathode ray tube display (CRT), a touchscreen, a
tactile output
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device, a printer and/or speakers). The interface circuit 1120 of the
illustrated example, thus,
typically includes a graphics driver card, a graphics driver chip or a
graphics driver processor.
[0081] The interface circuit 1120 of the illustrated example also includes a
communication
device such as a transmitter, a receiver, a transceiver, a modem and/or
network interface card
to facilitate exchange of data with external machines (e.g., computing devices
of any kind)
via a network 1126 (e.g., an Ethernet connection, a digital subscriber line
(DSL), a telephone
line, coaxial cable, a cellular telephone system, etc.).
[0082] The processor platform 1100 of the illustrated example also includes
one or more
mass storage devices 1128 for storing software and/or data. Examples of such
mass storage
devices 1128 include floppy disk drives, hard drive disks, compact disk
drives, Blu-ray disk
drives, RAID systems, and digital versatile disk (DVD) drives.
[0083] Coded instructions 1132 to implement the methods of FIGS. 7, 8, 9 and
10A and 10B
may be stored in the mass storage device 1128, in the volatile memory 1114, in
the non-
volatile memory 1116, and/or on a removable tangible computer readable storage
medium
such as a CD or DVD.
[0084] From the foregoing, it will appreciated that the above disclosed
methods, apparatus
and articles of manufacture relate to determining the production of a downhole
reciprocating
pump by, for example, relating the work performed by a pumping unit on a
sucker rod string
to the work used to lift a single volumetric unit of fluid from the well.
Using this
relationship, the work performed by the pumping unit during a single stroke of
the pumping
unit can be used to estimate the amount of fluid produced during the stroke.
The estimated
production from each stroke can be summed over a period of time (e.g., hourly,
daily,
monthly, etc.) to infer, estimate and/or determine production estimate for the
pumping unit.
[0085] In at least some examples, a rod pump controller does not calculate the
downhole
pump card. Thus, the examples disclosed herein can be incorporated on a
computing
platform of moderate to low computational power. Using the examples disclosed
herein,
there is no need to analyze the downhole pump card to identify the net liquid
stroke, the fluid
load or other such parameters from the downhole card. In at least some
examples, a leakage
test is not performed because the leakage proportionality constant is
determined using
calculations associated with a well test. The examples disclosed herein can be
implemented
in a field controller.
[0086] An example method disclosed herein includes measuring an amount of
liquid
produced from a well by a pumping unit during a predetermined time period and
determining
first areas of first pump cards during the predetermined time period. The
example method
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includes summing the first areas and, based on the amount of liquid produced
and the
summed first areas, determining a leakage proportionality constant of a
downhole pump of
the pumping unit.
[0087] In some examples, the method also includes, while continuously
operating the
pumping unit, determining a second area of a second pump card. In some
examples, the
method also includes determining a net fluid produced during a stroke of the
pumping unit
based on the leakage proportionality constant and the second area. In some
examples,
measuring the amount of liquid produced includes measuring the liquid produced
at separator
conditions using a well test separator.
[0088] In some examples, determining the first areas of first pump cards
during the
predetermined time period includes using a rod pump controller to determine
the first areas.
In some examples, the method also includes, while continuously operating the
pumping unit
over a second predetermined time period, determining second areas of second
pump cards. In
some examples, the method also includes determining a net fluid produced
during the second
predetermined time period based on the proportionality constant and the second
areas. In
some examples, the leakage proportionality constant is determined further
based on a
pressure difference across the downhole pump of the pumping unit.
[0089] An example apparatus disclosed herein includes a housing for use with a
pumping
unit and a processor positioned in the housing. The processor is to determine
first areas of
first pump cards during a predetermined time period, sum the first areas and,
based on an
amount of liquid produced by a downhole pump of the pumping unit during the
predetermined time period from a well and the summed first areas, determine a
leakage
proportionality constant of the downhole pump.
[0090] In some examples, while continuously operating the pumping unit, the
processor is to
determine a second area of a second pump card. In some examples, the processor
is to
determine a net fluid produced during a stroke of the pumping unit based on
the leakage
proportionality constant and the second area. In some examples, the apparatus
includes a rod
pump controller. In some examples, while continuously operating the pumping
unit over a
second predetermined time period, the processor is to determine second areas
of second pump
cards. In some examples, the processor is to determine a net fluid produced
during the
second predetermined time period based on the proportionality constant and the
second areas.
In some examples, the processor is to determine the leakage proportionality
constant further
based on a pressure difference across the downhole pump of the pumping unit.
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[0091] Another example method disclosed herein includes measuring a first
amount of liquid
produced from a well by a pump during a first stroke of the pump, computing a
first pump
card based on the first stroke, determining a first area of the first pump
card and determining
a leakage proportionality constant of the pump based on the first amount of
liquid produced
and the first area. The example method also includes computing a second pump
card based
on a second stroke of the pump, determining a second area of the second pump
card and
determining a second amount of liquid produced by the pump during the second
stroke based
on the leakage proportionality constant and the second area.
[0092] In some examples, the method includes determining a first pump fillage
factor for the
pump during the first stroke. In such an example, the leakage proportionality
constant is
further based on the first pump fillage factor. In some such examples, the
method includes
determining an ideal area of the first pump card. The first pump fillage
factor is based on a
ratio of the determined first area of the first pump card and the ideal area
of the first pump
card. In some examples, the method includes determining whether a tubing of
the pump is
anchored. In some examples, if the tubing is not anchored, the ideal area of
the first pump
card is based on a modulus of elasticity of a material of the tubing, a cross-
sectional area of
the pump and a length of the unanchored tubing.
[0093] In some examples, method includes determining a second pump fillage
factor for the
pump during the second stroke. In such an example, the second amount of liquid
produced is
further based on the second pump fillage factor.
[0094] In some examples, the method includes determining a pressure difference
across the
pump during the first stroke based on the first pump fillage factor. In such
an example, the
leakage proportionality constant is determined further based on the pressure
difference across
the pump.
[0095] In some examples, the first amount of liquid produced is measured using
a separator.
In some examples, the method includes computing a third pump card based on a
third stroke
of the pump, determining a third area of the third pump card, determining a
third amount of
liquid produced by the pump during the third stroke based on the leakage
proportionality
constant and the third area and summing the second amount and third amount to
determine a
net fluid produced by the pump during the second and third strokes.
[0096] Another example apparatus disclosed herein includes a housing to be
used with a
pumping unit having a downhole pump and a processor disposed in the housing.
The
processor of the example apparatus is to determine a first area of a first
pump card based on a
first stroke of the pump, determine a leakage proportionality constant of the
pump based on a
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first amount of liquid produced by the pump during the first stroke and the
first area,
determine a second area of a second pump card based on a second stroke of the
pump and
determine a second amount of liquid produced by the pump during the second
stroke based
on the leakage proportionality constant and the second area.
[0097] In some examples, the apparatus includes a separator. The separator is
to measure the
first amount of liquid produced by the pump during the first stroke. In some
examples, the
processor is to determine a first pump fillage factor for the pump during for
the first stroke.
In such an example, the leakage proportionality constant is further based on
the first pump
fillage factor. In some such examples, the processor is to determine a second
pump fillage
factor for the pump during the second stroke. In such an example, the second
amount of fluid
produced is further based on the second pump fillage factor. In some such
examples, the
processor is to determine an intake pressure of the pump during the second
stroke based on
the second pump fillage factor. In some examples, the apparatus includes a
motor to drive
the pump. In such an example, the processor is to control a speed of the motor
based on the
intake pressure of the pump.
[0098] Disclosed herein is an example tangible machine readable storage device
having
instructions that, when executed, cause a machine to at least compute a first
pump card based
on a first stroke of a downhole pump, determine a first area of the first pump
card and
determine a leakage proportionality constant of the pump based on a first
amount of liquid
produced by the pump during the first stroke and the first area. The
instructions are also to
cause the machine to compute a second pump card based on a second stroke of
the pump and
determine a second amount of fluid produced by the pump during the second
stroke based on
the leakage proportionality constant and the second area.
[0099] In some examples, the instructions, when executed, further cause the
machine to
determine a first pump fillage factor for the pump during the first stroke. In
such an example,
the leakage proportionality constant is further based on the first pump
fillage factor. In some
examples, the instructions, when executed, further cause the machine to
determine a second
pump fillage factor for the pump during the second stroke. In such an example,
the second
amount of liquid produced is further based on the second pump fillage factor.
In some
examples, the instructions, when executed, further cause the machine to
determine an ideal
area of the second pump card. In such an example, the second pump fillage
factor is based on
a ratio of the determined second area of the second pump card and the ideal
area of the
second pump card. In some such examples, the instructions, when executed,
further cause the
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machine to determine a pressure difference across the pump during the second
stroke based
on the second pump fillage factor.
[00100] Although certain example methods, apparatus and articles of
manufacture
have been disclosed herein, the scope of coverage of this patent is not
limited thereto. On the
contrary, this patent covers all methods, apparatus and articles of
manufacture fairly falling
within the scope of the claims of this patent.
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