Nodal Analysis
Wathik Mohammed Alhashimi, P.Eng.
Nodal Analysis
➢ Nodal Analysis Concept,
➢ Reservoir/well pressure loss,
➢ Inflow performance curve,
➢ Outflow performance curve,
➢ System graph,
➢ Solution node.
Nodal Systems - (Systems Analysis)
Nodal analysis:- Application of systems analysis to complete well system.
Reservoir Outer boundary
String (restrictions)
Sand face
Perforations
Downhole Safety Valves
Completion Section
Surface Choke
Flowline
Tubing Intake
Tubing
Separator.
Use
1. Well inflow performance.
2. Downhole multipurpose flow conduit performance (vertical or directional conduit performance).
3. Surface performance (choke, horizontal or inclined flow performance & separator).
Performance of naturally flowing/artificial lift well.
Changes Effect
1. Separator pressure.
2. Flowline size.
3. Surface choke size.
4. Tubing size.
Effect of changes in one component of system
Effect on entire system .
Whether or not well limited in its production rate by reservoir’s
ability to give up fluids or by producing system.
System Pressure Losses
• Fluid flows from reservoir to stock tank due to pressure
gradients within the system.
• Total pressure drop (Reservoir to Separator) = sum of
individual pressure drops through four segments:
o Reservoir,
o Completion,
o Wellbore,
o Flowline.
• Calculate pressure drop for each segments,
• Flow rate upstream/downstream pressure,
• Physical properties of segment.
• Flow rate (unknown) try to find.
• How to calculate flow rate, knowing reservoir &
separator pressures? = Question of Nodal Analysis.
• Known
• Reservoir pressure separator pressure
• Physical properties of each segment,
• What flow rate at which well produce?
How to determine the right flow rate?
Known:❖ Separator pressure
❖ Average reservoir pressure.
Start in reservoir at average reservoir pressure (pr)
Assume a flow rate.
1. Calculate pressure just beyond completion (p wfs )
2. Calculate pressure drop across completion,&
bottomhole pressure (p wf.) –Pressure valid for assumed
flow rate.
Or
1. start at separator at (p sep) and
2. Calculate pressure drop in flowline - wellhead pressure
(pwh)
3. Calculate pwf. (Pressure valid assumed flow rate).
If two calculated bottomhole pressures not same, then
assumed rate wrong.
“Nodal” analysis :- have to choose a point or “node” in system
at which to evaluate pressure - ( in this case wellbore bottom)
Point = Solution Point or Solution Node.
Outflow Performance Curve
• Outflow curve” or “Tubing performance curve”.
curve”.
• Until considering reservoir behavior, this curve a tells almost
nothing about rate at which the well produces.
3500
Flowing bottomhole pressure, psi
• Assume separator close to wellhead (ignore pressure drop
through flowline).
• At low flow rate,(200 STB/D??),flowing bottomhole pressure
=1500 psi (??).
• Increase flow rate without changing surface pressure (need
to raise flowing bottomhole pressure).
• (At extremely low flow rates, bottomhole pressure falls with
increasing flow rate).
• Bottomhole pressure for a shut-in well filled with oil is
actually higher than the bottomhole pressure for a well
flowing a mixture of oil and gas at low rates.
• Curve :- “Outflow curve” or “Tubing performance
Outflow (Tubing) Curve
3000
2500
2000
1500
1000
500
0
0
500
1000
1500
2000
2500
3000
Production rate, STB/D
3500
4000
4500
Intake Curve from Combined Flowline & Tubing Multiphase Flow Horizontal Flow Curves
Alternate Solution
Wellhead pressures used for an alternate solution
Practical oil field problem
➢ Horizontal flowline incorporated into system.
➢ Constant separator pressure expected,
➢ Flow rate changes, wellhead pressure increases a, tubing intake pressure increases.
➢ Wellhead pressure changes with each flowrate.
1. Assume a flow rate
2. Find the wellhead pressure by using a horizontal multiphase flow correlation,
3. Using that wellhead pressure, find the tubing intake pressure.
System Graph
Inflow curve :- relationship between bottomhole pressure
and flow rate for reservoir.
Outflow curve :-relationship between bottomhole pressure
and flow rate for wellbore.
Plotting two curves :- “System graph”.
Intersection of inflow curve and outflow curve :- unique flow
rate at which well produces for a specified set of reservoir &
wellbore properties.
Intersection Point :- unique bottomhole pressure at which
this rate occurs.
(A different point chosen as solution node; shapes of curves
would have been different).
Y-coordinate :- intersection of inflow & outflow curves would
have given pressure at new solution node.
Flow rate at which curves intersect, however, same no matter
where solution node is taken.
(Calculated intersection points may differ slightly because of
numerical errors).
“System graph”.
Solution Node At Wellhead
Solution node at wellhead?
Known
Separator pressure
Average reservoir pressure.
Start in reservoir at (pr)
Assume a flow rate.
Calculate (pwfs )
Calculate pressure drop across completion & p wf.
Calculate the pressure drop up wellbore to find p wh.
(Pressure valid for assumed flow rate).
Or,
Start psep,
Calculate pressure drop in flowline to find, p wh.
(Pressure valid for assumed flow rate).
Plotting inflow and outflow curves for a range of assumed
rates :- solution flow rate & d wellhead pressure to be
obtained from intersection of curves.
System Graph - Wellhead Node
Inflow curve : Relationship between pressure at solution
node and flow rate into node.
Solution node at wellhead:- Inflow curve represents
combined performance of reservoir & tubing system.
Outflow curve :- relationship between pressure at solution
node & flow rate out of node.
Solution node taken at wellhead; outflow curve horizontal
(Wellhead pressure fixed at 500 psi in input data).
Intersection of curves gives flow rate (2050 STB/D) &
wellhead pressure (500 psi).
(Slight discrepancy between this value and the 2111 STB/D
calculated using a bottomhole node not be of concern).
Inflow Performance Curve
“Inflow curve” or “reservoir curve”.
curve” or the “reservoir curve”.
Until pressure drop within the wellbore known , curve tells
very little about rate at which well produces for a given
wellhead pressure.
3500
Inflow (Reservoir) Curve
Flowing bottomhole pressure, psi
Assume well completed open hole (neither damaged nor
stimulated. Pressure drop across completion = zero.
Ignore wellbore & flowline.
If flow rate = 0,
pwf = average reservoir pressure, p r.
As increase the flow rate, pressure drop in reservoir
segment increases - pwf to decrease.
Plot flowing bottomhole pressure as a function of flow rate
Result a curve intersecting y-axis at initial reservoir
pressure,& intersecting x-axis at maximum rate well would
produce if opened to atmosphere at perforations=“inflow
3000
2500
2000
1500
1000
500
0
0
500
1000
1500
2000
2500
3000
Production rate, STB/D
3500
4000
4500
Inflow Performance Curves
Well’s Good Test Data
Reservoir Capability.
IPR (Inflow Performance Relationship)
1. Straight line (constant PI - Productivity Index denoted “J”).
2. Curve which shows that the PI decreasing with rate (gas wells).
3. Combination of 1 and 2.
• Constant PI :- single phase liquid flow above
bubble point pressure.
• Curved line shows PI decreasing below the
bubble point pressure because of two phase
flow conditions in the reservoir (liquid plus
gas).
Inflow Performance Curves.
Simplest case:-constant wellhead pressure assumed.
Curve constructed (assuming flow rates and determine corresponding flowing bottomhole intake pressure for a set tubing size,
GOR, wellhead pressure, depth and fluid properties).
Any number of vertical multiphase flow correlations used (e.g., Hagedorn and Brown, Orkiszewski, Duns and Ros & Beggs &
Brill)
Software allow these individual curves to be generated directly with computer as opposed to referring to the thick volumes of
pre-generated curves.
Future Inflow Performance Curves.
Tubing Intake Curve in Combination with IPR Curve.
Horizontal Flow Curves
• Practical oil field problem:- horizontal flowline incorporated into system.
• Constant separator pressure expected,
• Flow rate changes, wellhead pressure increases a, tubing intake pressure increases.
• Wellhead pressure changes with each flowrate.
• Assume a flow rate,
• Find the wellhead pressure by using a horizontal multiphase flow correlation,
• and then, using that wellhead pressure, find the tubing intake pressure.
• Wellhead pressures plotted on same graph (Figure 6-4),
• Wellhead pressures used for an alternate solution (Figure 6-5).
Practice case
Simple Producing System.
Three phases
1. Flow through porous medium.
2. Flow through vertical or directional conduit.
3. Flow through horizontal pipe.
pressure losses in system from the reservoir to separator.
Location of Various Nodes.
Nodes for Simple Producing System
• Node classified as a functional node when a pressure differential exists across it and pressure or flow rate response
represented by mathematical/physical function.
• Node 1 :- separator pressure (regulated at a constant value:- gas sales lines pressure or gas compressor suction pressure. ).
• Pressure at node 1B constant at 0 psig.
• Separator pressure held constant at the higher of the two pressures needed to flow single phase gas from node 1 to node 1A or
to flow single phase liquid from node 1 to node 1B.
• Assumed that the separator pressure constant for any flow rate, designated as node 1.
Notice :- two pressures that not a function of flow rate (Pr at node 8 and PSEP at node 1).
• Trial and error solution to total system problem started at node 1 (PSEP), or at node 8 (Pr) or both nodes 1 and 8 if and
intermediate node such as 3 or 6 is selected as solution node.
• Once solution node selected, pressure drops or gains from starting point added until the solution node reached.
• Following four examples show this procedure for four possible nodes shown in Figure 6-9.
• Although all nodes are not shown, the same node numbers are maintained as in Figure 6-8.
• Note: Pr can be a function of flow rate or drainage distribution in the reservoir.
• However, for the flow rates investigated in this section, Pr is assumed to be constant.
Problem:- Using Node 8 to Find the Flow Rate Possible
(Node 8 = Pr) - Given data:
Flowing oil well
Separator pressure: 100 psi
Flow line: 2", 3000 ft long
WOR: 0
Depth: 5000 ft mid perf.
GOR: 400 scf/B
Pr: 2200 psi
IPR: PI = 1.0 B/D psi
(assume constant)
Tubing size: 2-3/8"
Find the oil flow rate using node 8 as the solution point?
Procedure:
1. Select flow rates for a trial-and-error procedure: Assume flow rates of 200, 400, 600, 800, 1000 and 1500 B/D.
2. For each rate, start at PSEP = 100 and add all the pressure losses until reaching Pr at node 8.
Losses DP3-1 + DP6-3 + DP8-6 or loss in surface flow line + loss in tubing string + loss in porous medium.
Losses for assumed rates :Table.
3. Plot the created pressure vs flow rate :- system performance from separator to Pr.
4. Plot Pr at the given 2200 psi .
5. Intersection of reservoir pressure line and system performance line gives presided flow rate (900 BOPD).
Thank you