Nodal Analysis and Natural Flow
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Transcript of Nodal Analysis and Natural Flow
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Mauricio G. Prado The University of Tulsa
Flow in Production System
Compressed Fluids in the
Reservoir
Porous Media
Perforations
Production String
Downhole Equipment
Restrictions
Surface Flowline
Surface Equipment
Restrictions
Final
Destination
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Mauricio G. Prado The University of Tulsa
Reservoir
PressureIndividual
Components
Mommentum
Mass and
Energy
balance
Final
Pressure
rP
Driving Force for Production
Energy Difference
Energy
Use
cPfP
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Mauricio G. Prado The University of Tulsa
Pr
Pr
q
Ps
Pt
Pf
Pc
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Mauricio G. Prado The University of Tulsa
Path of produced fluids
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Mauricio G. Prado The University of Tulsa
Flow in Production System
Compressed Fluids in the Reservoir
Production String
Downhole Equipment
Restrictions
Surface Flowline
Surface Equipment
Restrictions
Final
Destination
Porous Media
Perforations
Flow in Porous Media
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Mauricio G. Prado The University of Tulsa
Flow in Production System
Compressed Fluids in the Reservoir
Production
Separator
Porous Media
Perforations
Production String
Downhole Equipment
Restrictions
Surface Flowline
Surface Equipment
Restrictions
Pressure changes in Pipes and Equipment
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Mauricio G. Prado The University of Tulsa
For this system to be in equilibrium we must have:
Production Flowrate
src PPP = For single phase incompressible fluids, the pressure drop
in each of the components is function of the flowrate.
( )qPP cc = So the equilibrium equation becomes.
src PPqP = )(
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Mauricio G. Prado The University of Tulsa
We can see that the equilibrium equation is an equation which the independent variable is the flowrate. The flowrate solution for this equation is the equilibrium flowrate of the system
Production Flowrate
eq
src PPqP = )(
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Mauricio G. Prado The University of Tulsa
We also know that for a certain single phase incompressible fluid, the pressure drop in each component is also function of the properties of the component. For instance the pressure drop in the reservoir is function of the productivity index and pressure drop in pipes is function for instance of pipe diameter, inclination angle and roughness.
Production Flowrate
src PPqP = )()( PropertiesComponentsqq ee =
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Mauricio G. Prado The University of Tulsa
Components Performance
9Single Phase Incompressible Flow
C-1 C-2 C-3 C-n
1P 2P 3P nP
( )c cP P q = Individual ComponentsAnalysis
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Mauricio G. Prado The University of Tulsa
For compressible fluids or for multiphase flow, the fluid properties are a strong function of the pressure level in the component.
The pressure drop in each component is then not only function of the flowrate, but also of the a pressure reference on the component.
Production Flowrate
( )PqPP cc ,= So the equilibrium equation becomes.
src PPPqP = ),(
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Mauricio G. Prado The University of Tulsa
For instance when calculating the pressure available downstream of a pipeline segment, the pressure drop in the segment is function of the flowrates but also of the pressure at the entrance of the pipe segment.
When calculating the pressure required upstream of a pipeline segment, the pressure drop in the segment is function of the flowrates but also of the pressure at the exit of the pipe segment
Production Flowrate
( )upstreamcc PqPP ,=q upstreamP
downstreamPq
( )downstreamcc PqPP ,=
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Mauricio G. Prado The University of Tulsa
It is obvious then, that the pressure downstream of a component can not be calculate without knowing the behavior of the upstream components.
Also the pressure upstream of a component can not be calculated without knowing the behavior of the downstream components.
The major difference between single and two phase flow problems is that the componenst interact with each other in two phase flow conditions.
Production Flowrate
( )upstreamcc PqPP ,=q upstreamP
downstreamPq
( )downstreamcc PqPP ,=
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Mauricio G. Prado The University of Tulsa
Components Performance9Multiphase Flow
C-1 C-2 C-3 C-n
1P 2P 3P nP
Individual Components
Analysis
Nodal Analysis),( PqPc
1P 2P 3P
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Individual components analysis is adequate
when components dont interact with each other. In two phase flow, the pressure drop function not
only of the flowrates but also of the pressure level on the component.
This creates an interdependence between each component.
Individual component analysis is no longer applicable.
A new tool is necessary Nodal Analysis
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
System Composed of
Interacting Components
rP sP
( ) PqPc ,
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
sPrP InflowSectionOutflow
Section
Node
( ) PqPc ,
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
rP InflowSection
),()( PqPPqPIS
crinode =
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
rP InflowSection
inodeP
),()( PqPPqPIS
crinode =
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
The inflow pressure at the node represents the pressure that the inflow section can deliver the flowrate q at the node
),()( PqPPqPIS
crinode =
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
sPOutflow
Section
),()( PqPPqPOS
csonode +=
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
sPOutflow
SectiononodeP
),()( PqPPqPOS
csonode +=
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
The outflow pressure at the node represents the pressure that the outflow section requires to produce the flowrate q up to the separator
),()( PqPPqPOS
csonode +=
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
The equilibrium point is the point at which the inflow section is capable of delivering the flowrate at a pressure enough for the outflow section to flow the fluids up to the separator
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
( ) ( )i onode nodeP q P q=
eqComponents performance are included
only in the part of the System where the component is located
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Mauricio G. Prado The University of Tulsa
Nodal Analysis - Example
Production String
Production Separator
Reservoir
Flowline
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Mauricio G. Prado The University of Tulsa
Nodal Analysis - Example
Production String
Production Separator
Reservoir
Flowline
Node = Perforations
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Inflow
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Flow rate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
rP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Inflow
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Flow ra te (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
rP
( )resP q
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Inflow
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Flowrate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
rP
( )resP q
iwfP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Outflow
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Flow ra te (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
sepP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Outflow
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P
r
e
s
s
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(
p
s
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sepP
( )lineP q
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Outflow
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Flowrate (bpd)
P
r
e
s
s
u
r
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(
p
s
i
)
sepP
( )lineP q
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Outflow
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Flow ra te (bpd)
P
r
e
s
s
u
r
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(
p
s
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)
sepP
owhP
( )tubingP q
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Outflow
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Flowrate (bpd)
P
r
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s
s
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(
p
s
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sepP
owhP
( )tubingP q
owfP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example
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P
r
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p
s
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iwfP
owfP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example
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P
r
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s
u
r
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(
p
s
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)
iwfP
owfP
eq
wfP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis - Example
Production String
Production Separator
Reservoir
Flowline
Node = Wellhead
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Wellhead
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Flow ra te (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
iwhP
owhP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis - Example
Production String
Production Separator
Reservoir
Flowline
Node = Separator
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Separator
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Flow ra te (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
isepP
sepP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis - Example
Production String
Production Separator
Reservoir
Flowline
Node = Reservoir Boundary
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Mauricio G. Prado The University of Tulsa
Nodal Analysis Example - Reservoir
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Flow ra te (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
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orP
rP
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Mauricio G. Prado The University of Tulsa
Nodal Analysis
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Flowrate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
g
)
Preservoiri
Preservoiro
Pperforationsi
Pperforationso
Pw ellheadi
Pw ellheadoPseparatori
Pseparatoro
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Mauricio G. Prado The University of Tulsa
Stable and Unstable Conditions
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Mauricio G. Prado The University of Tulsa
Stability Generally speaking, mechanical equilibrium is defined as a condition
where the summation of forces acting on a body equal to zero. This means that a body in equilibrium has no acceleration.
The equilibrium can be stable, unstable or indifferent. Stable equilibrium is a condition where after a small disturbance, the
system will return to the original equilibrium position Unstable equilibrium is a condition where after a small disturbance, the
system will move away from the original equilibrium position Indifferent equilibrium is a condition where after a small disturbance,
the system will not move since the points around the original equilibrium condition are also equilibrium points.
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Mauricio G. Prado The University of Tulsa
Stability For a well, we understand equilibrium as the steady state
condition. The equilibrium flowrate is a flowrate where the IPR and OPR
meet. This equilibrium can also be stable, unstable or indifferent. The nodal analysis is a very powerful tool to determine steady
state equilibrium conditions. We can clearly see that determination of stability conditions
requires an analysis of the behavior of the system after a disturbance.
This analysis requires determination of the performance of the system for points that are not in equilibrium and as a consequence are NOT in steady state.
This is a transient problem and the steady state nodal analysis tool is very limited of fully describing the phenomena.
Nonetheless, an unsteady analysis of the problem can lead us to stability criteria that may be used to check the stability of the equilibrium flowrate determined by Nodal Analysis.
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Mauricio G. Prado The University of Tulsa
Stability Imagine that we have a closed completion
system as shown. During transient conditions that normally
occur after a disturbance, mass and momentum balance equations are still valid.
In order to investigate the stability, lets examine the case of a single phase incompressible fluid being produced.
If we assume that the fluid is incompressible, the flowrate coming from the reservoir needs to be equal to the flowrate going into the tubing string.
The dynamic Inflow bottonhole flowing pressure needs to be equal to the dynamic outflow bottonhole flowing pressure.
The steady state nodal analysis assume that the fluids are not accelerating and the flow is steady state.
rP
eq
whP
wfP
eq
J
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Mauricio G. Prado The University of Tulsa
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Flowrate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
iwfP
owfP
Stable and Unstable Conditions
owf
iwf PP > owfiwf PP
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Mauricio G. Prado The University of Tulsa
Stability Imagine that during a transient
phenomena (for instance due to fluctuations on wellhead pressure) the flowrate in the system becomes smaller than the equilibrium steady state value.
If you observe on the steady state nodal analysis graph you will see that for this condition, the inflow pressure is higher than the outflow pressure
How is this possible ? What is the bottomhole flowing pressure during the transient that follows a disturbance ?
rP
eqq
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Mauricio G. Prado The University of Tulsa
Stability The solution is as follows. During the transient disturbance,
the true bottonhole flowing pressure is between the steady state inflow and the outflow values.
This difference in pressure (true values compared to the steady state values is going to cause the fluids to accelerate !!! (changes in time transient !!!)
rP
eqq
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Mauricio G. Prado The University of Tulsa
Stability For the reservoir, since the true
bottomhole pressure is smaller than the steady state value, the flowrate is going to increase.
For the tubing, since the bottomholepressure is greater than the steady state value, the system will also accelerate and the flowrate is going to increase as well.
This transient coupling between reservoir and system is going to promote an increase with time of the flowrate through the system. rP
eqq
Time
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Mauricio G. Prado The University of Tulsa
Stability A similar analysis can be made
when the fluctuations cause the flowrate to be bigger then the equilibrium value.
rP
eqq >
whP
wfPJ
eqq >
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Mauricio G. Prado The University of Tulsa
0
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Flowrate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
iwfP
owfP
Stable and Unstable Conditions
owf
iwf PP
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Mauricio G. Prado The University of Tulsa
Stability
In this case the true bottonhole flowing pressure is again in between the steady state values for the IPR and OPR.
For the reservoir, since the true bottomholepressure is greater than the steady state value, the flowrate is going to decrease.
For the tubing, since the bottomhole pressure is smaller than the steady state value, the system will also accelerate and the flowrate is going to decrease.
This transient coupling between reservoir and system is going to promote an decrease with time of the flowrate through the system.
rP
eqq >
whP
wfPJ
eqq >
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Mauricio G. Prado The University of Tulsa
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Flowrate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
iwfP
owfP
Stable and Unstable Conditions
owf
iwf PP
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Mauricio G. Prado The University of Tulsa
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Flowrate (bpd)
P
r
e
s
s
u
r
e
(
p
s
i
)
iwfP
owfP
Stable and Unstable Conditions
owf
iwf PP
whP
wfPJ
eqq >
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Mauricio G. Prado The University of Tulsa
0
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Flowrate (bpd)
P
r
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s
u
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e
(
p
s
i
)
iwfP
owfP
Stable and Unstable Conditions
Stable Production Equilibrium Point
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Mauricio G. Prado The University of Tulsa
Stability In some cases, due to the nature of two
phase flow phenomena, two equilbriumpoints may be possible.
rP
eqq >
whP
wfPJ
eqq >
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Mauricio G. Prado The University of Tulsa
Stable and Unstable Conditions
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P
r
e
s
s
u
r
e
(
p
s
i
)
iw fP
owfP
A
B
Stable?
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Mauricio G. Prado The University of Tulsa
Stability What can you say about the equilibrium
conditions for point B ?
rP
eqq >
whP
wfPJ
eqq >
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Mauricio G. Prado The University of Tulsa
Stable and Unstable Conditions
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Flowrate (bpd)
P
r
e
s
s
u
r
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p
s
i
)
iwfP
owfP
B
owf
iwf PP < owfiwf PP >
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Mauricio G. Prado The University of Tulsa
Stability Again, during the disturbance, the true
bottonhole flowing pressure is between the steady state IPR and OPR values.
When the flowrate is smaller then the equilibrium point, the true bottonholepressure is greater than the steady state IPR value.
This will cause the reservoir flowrate to decrease.
When the flowrate is smaller then the equilibrium point, the true bottonholepressure is smaller then the steady state OPR value and this will cause the flowrate in the tubing to decrease.
What will happen ?rP
whP
wfPJ
eqq
eqq >
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Mauricio G. Prado The University of Tulsa
Stable and Unstable Conditions
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P
r
e
s
s
u
r
e
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p
s
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iwfP
owfP
B
owf
iwf PP >
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Mauricio G. Prado The University of Tulsa
Stability Point B is an unstable operating point. If the flowrate is suddenly decreased from
the equilibrium point, the well will die. If the flowrate is suddenly increased from
the equilibrium point, the well is going to produce the next stable flowrate value.
rP
whP
wfPJ
eqq