Apparatus for analysis and control of a reciprocating pump system by determination of a pump card
View Patent ↗An instrumentation system for assessing operation of a reciprocating pump system which produces hydrocarbons from a non-vertical or a vertical wellbore. The instrumentation system periodically produces a downhole pump card as a function of a directly or indirectly measured surface card and a friction law function from a wave equation which describes the linear vibrations in a long slender rod. A control signal or command signal is generated based on characteristics of the downhole pump card for controlling the pumping system. It also generates a pump and well analysis report that is useful for a pump operation and determination of its condition.
1. An instrumentation system for assessing operation of a reciprocating pump system producing hydrocarbons from a non-vertical wellbore which extends from the surface into the earth, the system comprising,
a data gathering system which provides signals representative of surface operating characteristics of the pumping system, and characteristics of said non-vertical wellbore,
a processor which receives said operating characteristics with said characteristics of said non-vertical wellbore and generates a surface card representative of surface polished rod load, as a function of surface polished rod position, with
said processor determining a friction law function based on said characteristics of said non-vertical wellbore, and with
said processor periodically generating a downhole pump card as a function of said surface card and said friction law function for a wave equation which describes the linear vibrations in a long slender rod,
wherein,
said wave equation for a deviated well is of the form,
∂
2
u
(
x
,
t
)
∂
t
=
v
2
∂
2
u
(
x
,
t
)
∂
x
2
-
c
∂
u
(
x
,
t
)
∂
t
-
C
(
x
)
+
g
(
x
)
in
which
C
(
x
)
=
δ
μ
(
x
)
[
Q
(
x
)
+
T
(
x
)
∂
u
(
x
,
t
)
∂
x
]
δ
=
∂
u
(
x
,
t
)
/
∂
t
∂
u
(
x
,
t
)
/
∂
t
where C(x) represents rod on tubing drag force, and
where
v=velocity of sound in steel in feet/second;
c=damping coefficient, 1/second;
t=time in seconds;
x=distance of a point on the unrestrained rod measured from the polished rod in feet;
u(x,t)=displacement from the equilibrium position of the sucker rod in feet at the time t, and
g(x)=weight of pump rod pump assembly in the x direction,
and where
μ(x), Q(x) and T(x) are determined by mathematical modeling of a rod string in said wellbore.
2. The system of claim 1 wherein,
said processor includes pump card analysis software which produces a control signal for controlling said pump.
3. The system of claim 1 wherein,
said pump card analysis software produces a control signal to turn off a drive motor of said pump if a pump card indicator is recognized requiring pump shut off.
4. The system of claim 1 wherein,
said pump card analysis software produces a control signal to control a variable speed of the pump if a pump card indicator is recognized which indicates that varying the speed of the pump enhances pump operation.
5. An instrumentation system for assessing operation of a reciprocating pump system producing hydrocarbons from a wellbore which extends from the surface into the earth, the system comprising,
a data gathering system which receives said characteristics of said wellbore and includes a processor which generates a surface card representative of surface polished rod load as a function of surface polished rod position,
said processor determining a friction law function for said wellbore,
said processor periodically generating a downhole pump card of said surface card as a function of said surface card and said friction law factor for a wave equation which describes the vibrations of a long slender rod, said wave equation being of the form,
∂
2
u
(
x
,
t
)
∂
t
=
v
2
∂
2
u
(
x
,
t
)
∂
x
2
-
c
∂
u
(
x
,
t
)
∂
t
-
C
(
x
)
+
g
(
x
)
in
which
C
(
x
)
=
δ
μ
(
x
)
[
Q
(
x
)
+
T
(
x
)
∂
u
(
x
,
t
)
∂
x
]
δ
=
∂
u
(
x
,
t
)
/
∂
t
∂
u
(
x
,
t
)
/
∂
t
where C(x) represents rod on tubing drag force, and
where
v=velocity of sound in steel in feet/second;
c=damping coefficient, 1/second;
t=time in seconds;
x=distance of a point on the unrestrained rod measured from the polished rod in feet;
u(x,t)=displacement from the equilibrium position of the sucker rod in feet at the time t, and
g(x)=weight of pump rod pump assembly in the x direction,
and where
μ(x), Q(x) and T(x) are determined by mathematical modeling of a rod string in said wellbore.
6. The system of claim 5 wherein
said wellbore is substantially vertical and said friction law factor represents the friction characteristic of a rod in a vertical wellbore.
7. The system of claim 5 wherein
said wellbore is non-vertical and rod friction law factor represents the friction characteristic of a rod in a non-vertical wellbore.
8. The system of claim 5 wherein,
said processor includes pump card analysis software which produces a control signal for controlling said pump.
9. The system of claim 5 wherein,
said pump card analysis software produces a control signal to turn off a drive motor of said pump if a pump card indicator is recognized requiring pump shut off.
10. The system of claim 5 wherein,
said pump card analysis software produces a control signal to control a variable speed of the pump if a pump card indicator is recognized which indicates that varying the speed of the pump enhances pump operation.
11. The system of claim 8 wherein,
said control signal is applied via either a hardwire or a wireless arrangement to said pump.
12. The system of claim 8 wherein,
said pump card analysis software generates a summary report of pump card characteristics, the system further comprising
a data transfer module which sends said summary report to a remote location from said pump system.
13. The system of claim 8 wherein,
said processor is geographically remote from said rod reciprocating pump and is arranged and designed to receive said characteristics wirelessly from said data gathering system, and
said processor is arranged and designed to send said control signal wirelessly to said pump.