Nodal Analysis by Donald Tambunan AKA Dairi Aka Asuteles

Introduction to Nodal Analysis

Introduction to Nodal Analysis Instructional Objectives

1. Explain the concept of Nodal Analysis.2. List 4 segments in the reservoir/well system where pressure

loss occurs.3. Define the following terms: inflow performance curve,

outflow performance curve, system graph, solution node.

Presenter

Presentation Notes

Upon completion of this section, the student should be able to: 1.Explain the concept of Nodal Analysis. 2.List the four major segments between the reservoir and the separator where pressure loss occurs. 3.Give definitions for each of the following terms: Inflow performance curve Tubing performance curve System graph Solution node

Pressure Losses in Well System

ΔP1 = Pr - Pwfs = Loss in reservoir

ΔP2 = Pwfs - Pwf = Loss across completion

ΔP3 = Pwf - Pwh = Loss in tubing

ΔP4 = Pwh - Psep = Loss in flowline

Pr PePwfsPwf

ΔP1 = (Pr - Pwfs )ΔP2 = (Pwfs - Pwf )

ΔP3 = Pwf - Pwh

ΔP4 = (Pwh - Psep )

Psep

Sales lineGas

LiquidStock tank

ΔPT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh

Presenter

Presentation Notes

Fluid flows from the reservoir to the stock tank because of the pressure gradients within the system. The total pressure drop from the reservoir to the separator is the sum of the individual pressure drops through four different segments: in the reservoir, across the completion, up the wellbore, and through the flowline. It is relatively straightforward to calculate the pressure drop for each of these segments, if we know the flow rate and either the upstream or downstream pressure, and the physical properties of the segment. But we do not know the flow rate - that is what we are trying to find. How do we calculate the flow rate, knowing the reservoir and separator pressures? This is the central question of Nodal Analysis. Given the reservoir pressure and the separator pressure, along with the physical properties of each segment, what is the flow rate at which the well will produce?

Nodal Analysis





Pr PePwfsPwf


ΔP3 = Pwf - Pwh


Psep

Sales lineGas

LiquidStock tank



Pwh

Presenter

Presentation Notes

How do we determine the right flow rate? We know the separator pressure and the average reservoir pressure. We start in the reservoir at the average reservoir pressure, pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure pwf. This pressure is valid only for the assumed flow rate. Or, we may start at the separator at psep, and calculate the pressure drop in the flowline to find the wellhead pressure, pwh. Then we can calculate the bottomhole pressure pwf. Again, this pressure is valid only for the assumed flow rate. The two calculated bottomhole pressures will probably not be the same. If not, then the assumed rate is wrong. “Nodal” analysis refers to the fact that we have to choose a point or “node” in the system at which we evaluate the pressure - in this case, the bottom of the wellbore. This point is referred to as the solution point or solution node.

Inflow Performance Curve

0

500

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1500

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3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flow

ing

botto

mho

le p

ress

ure,

psi

Inflow (Reservoir) Curve

Presenter

Presentation Notes

Lets assume that the well is completed open hole, and that the well is neither damaged nor stimulated. In this case, the pressure drop across the completion is zero. For the moment, we ignore the wellbore and the flowline. If the flow rate is 0, the bottomhole pressure pwf will be the same as the average reservoir pressure, pr. As we increase the flow rate, the pressure drop in the reservoir segment increases - causing the bottomhole pressure pwf to decrease. When we graph the flowing bottomhole pressure as a function of flow rate, the result is a curve intersecting the y-axis at the initial reservoir pressure, and intersecting the x-axis at the maximum rate the well would produce if opened to the atmosphere at the perforations. This curve is usually referred to as the “inflow curve” or the “reservoir curve”. Until we take into account the pressure drop within the wellbore, this curve tells us very little about the rate at which the well will produce for a given wellhead pressure.

Outflow Performance Curve

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500

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0 500 1000 1500 2000 2500 3000 3500 4000 4500


Flow

ing

botto

mho

le p

ress

ure,

psi

Outflow (Tubing) Curve

Presenter

Presentation Notes

Now let’s assume that the separator is so close to the wellhead that we may ignore the pressure drop through the flowline. At some low flow rate, perhaps 200 STB/D, the flowing bottomhole pressure may be 1500 psi. In order to increase the flow rate without changing the surface pressure, we have to raise the flowing bottomhole pressure. (At extremely low flow rates, the bottomhole pressure actually falls with increasing flow rate. This is a real phenomenon, and we will address it at some length later in the course. For now, note that the 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.) This curve is usually referred to as the “outflow curve” or the “tubing performance curve”. Until we take into account the reservoir behavior, this curve also tells us almost nothing about the rate at which the well will produce.

System Graph

0

500

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0 500 1000 1500 2000 2500 3000 3500 4000 4500


Flow

ing

botto

mho

le p

ress

ure,

psi

Inflow (Reservoir) CurveOutflow (Tubing) Curve

2111 STB/D

1957.1 psi

Presenter

Presentation Notes

The inflow curve describes the relationship between the bottomhole pressure and the flow rate for the reservoir. The outflow curve describes the relationship between the bottomhole pressure and flow rate for the wellbore. When we graph these two curves on the same graph, we refer to this as the “system graph”. The intersection of the inflow curve and the outflow curve gives the one unique flow rate at which the well will produce for a specified set of reservoir and wellbore properties. The point of intersection will also give the unique bottomhole pressure at which this rate will occur. If we had chosen a different point as our solution node, the shapes of the curves would have been different. The y-coordinate of the intersection of the inflow and outflow curves would have given the pressure at the new solution node. The flow rate at which the curves intersect, however, will be the same no matter where the solution node is taken. Calculated intersection points may differ slightly because of numerical errors.

Solution Node At Wellhead

Pr PePwfsPwf


ΔP3 = Pwf - Pwh


Psep

Sales lineGas

LiquidStock tank


Pwh






Presenter

Presentation Notes

What if we take the solution node at the wellhead? Again, we know the separator pressure and the average reservoir pressure. As with the bottomhole node, we start in the reservoir at the average reservoir pressure, pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure pwf. Finally, we calculate the pressure drop up the wellbore to find the wellhead pressure pwh. This pressure is valid only for the assumed flow rate. Or, we may start at the separator at psep, and calculate the pressure drop in the flowline to find the wellhead pressure, pwh. Again, this pressure is valid only for the assumed flow rate. Graphing inflow and outflow curves for a range of assumed rates allows the solution flow rate and wellhead pressure to be obtained from the intersection of the curves.

System Graph - Wellhead Node

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Flow

ing

wel

lhea

d pr

essu

re, p

si

Inflow CurveOutflow Curve

2050 STB/D

500 psi

Presenter

Presentation Notes

In general, the inflow curve describes the relationship between the pressure at the solution node and the flow rate into the node. For this case, with the solution node at the wellhead, the inflow curve represents the combined performance of the reservoir and tubing system. The outflow curve describes the relationship between the pressure at the solution node and flow rate out of the node. Here, with the solution node taken at the wellhead, the outflow curve is horizontal - we have fixed the wellhead pressure at 500 psi in our input data. The intersection of the curves gives the flow rate (2050 STB/D) and the wellhead pressure (500 psi). The slight discrepancy between this value and the 2111 STB/D calculated using a bottomhole node should not be of concern.

Nodal Analysis : Uses

• Estimation of Reservoir Parameters e.gSkin

Permeability

Reservoir Pressure

Note : Non unique solutions unless only one unknown

• Evaluation of Potential Stimulation Treatments Primarily through reduction in skin

Parameter sensitivity studies are important

Nodal AnalysisTwo Main Components

• Inflow Performance Curve/Relationship (IPR)

Oil or Gas Flowrate vs Bottomhole Flowing Pressure

Ordinate Origin = Reservoir Pressure (Δp = 0 q = 0)

Abscissa Intercept = Absolute Open Flow Potential

(Δp = pr q = Max)

• Outflow Curve (Tubing Intake)

Function of Hydrostatic, Friction & Acceleration Components

Curves Shifted by Wellhead Pressure & Artificial Lift

• Intercept of Curves Gives FBHP (psi) & Flowrate

Nodal Analysis

Inflow Operating Point

OutflowPressure PWF

Operating Flowrate

Flowrate (stb/d)

Pres

sure

at N

ode

Reservoir Pressure

• Fluid Properties• Oil

– Viscosity, Gas oil Ratio, Bubble Point– Formation Volume Factor, Density

• Gas– Viscosity, Z Factor, Compressibility– Density

• Inflow Correlation Used e.g. Oil - Darcy, Vogel, Gas - Jones, Darcy• Well Geometry i.e. Vertical or Horizontal• Formation Properties

• Reservoir Pressure • Permeability• Skin (Includes deviation, perforation, damage etc)• Net Pay Height

The Inflow Performance Relationship Dependent On:

Outflow

Flowrate

Pres

sure

at N

ode

5 0 -1 -3

SKIN

Inflow(IPR)

qo α

1/ ln re +S rw

Note : Log effect

10

Effect of Skin on IPR

Effect of Pressure Depletion on IPR

Outflow

Flowrate

Pres

sure

at N

ode

8 04

Oil Recovery (% STOIIP)

12

Reservoir with no pressure support

Inflow

• Fluid Properties• Oil

• Viscosity, Gas oil Ratio, Bubble Point• Formation Volume Factor, Density

• Gas• Viscosity, Z Factor, Compressibility• Density

• Outflow Correlation Used e.g. Oil - Duns & Ross, Gas - Gray• Friction• Completion Properties

• Tubing Size • Tubing Restrictions• Tubing Roughness

The Outflow Performance Relationship Dependent On:

Effect of Tubing Size on Outflow

Inflow(IPR)

Outflow

Flowrate (stb/d)

Pres

sure

at N

ode

For a Tubing Restricted Well

2 3/8”

2 7/8”4 1/2”3 1/2”

Solution Procedures for Oil wells

Node location 1. separator3. Pwh6. Pwf8. Pr

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1

6

3

Solution at bottom of the well


8

1

6

3

Step by step solution procedure

• (1) Assume several rates and construct the IPR curve • (2) Assume several flow rates and obtain the required well

head pressures necessary to move the fluids through the horizontal flowline to the separator

• (3) Using the same assumed flowrate as step 2 and the corresponding Pwh determine Pwf

• (4) Plot IPR curve and and Pwf from step 3

• ___ __ ___ _____________ ___ __ __________ __ ________

• _____ __________ ___________ ______

_____ ______

Klik om het opmaakprofiel van de modeltekstte bewerkenTweede niveauDerde niveauVierde niveau

Vijfde niveau

Assumed rate,b/d

Pwf for constantJ, psi

Pwf for Vogel,psi

200 2000 2000400 1800 1800600 1600 1590800 1400 13501000 1200 10671500 700

Pressure 100 psi

Leng

ht, 1

000f

t

Pwh

Assumed rate,b/d

Pwh (requiredhoriz), psi

200 2000400 1800600 1600800 14001000 12001500 700

Pwf

Pressure 100 psi

Depth, 1000 ft

Assumed rate,b/d

Pwh horiz, Psi

Tubing intake(node outflow),

psi200 115 750400 140 880600 180 1030800 230 12251000 275 13701500 420 1840

Rate (Vogel)

Rate (linear)

Solution at top of the well


8

1

6

3


(1) Assume several flowrates as before(2) Start with the separator pressure and find the

required wellhead pressures to move the fluids horizontally

(3) Using the same asumed flow rates and starting from Pr find the corresponding Pwf for the reservoir to produce these rates

(4) Using the flowing pressures obtained in 3 determine the permissible wellhead pressure for these flowrates

(5) plot the wellhead pressures of step 2 vs wellhead pressures of step 4 to obtain the flowrate

• ___ __ ___ _____________ ___ __ __________ __ ________

• _____ __________ ___________ ______

_____ ______

Klik om het opmaakprofiel van de modeltekstte bewerkenTweede niveauDerde niveauVierde niveau

Vijfde niveau

Assumed rate,b/d

Pwf for constantJ, psi

Pwf for Vogel,psi

200 2000 2000400 1800 1800600 1600 1590800 1400 13501000 1200 10671500 700

Pressure 100 psi

Leng

ht, 1

000f

t

Pwh

Pwh

Pressure 100 psi

Depth, 1000 ft

Rate (linear)

Rate (Vogel)

Solution node at the separator


8

1

6

3


(1) Assume various flowrates(2) Start with the other end position at Pr and determine the

flowing borttom hole pressures necessary for the well to produce the assumed flowrates

(3) Start with the Pwf values of step 2 as tubing intake pressure and find Pwh

(4) Starting with Pwh of step 3 find the corresponding permissible separator pressures for each rate

(5) Plot the separator pressure vs rate drawing the constant separator pressure

Nodal Analysis by Donald Tambunan AKA Dairi Aka Asuteles

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