Introduction to NODAL Analysis

April 2003

Instructor: Felipe Montoya

Objective

The objective of this course is to give the engineer the basic tools and knowledge of Nodal Analysis for him/her to understand its benefits, usefulness and limitations and help him/her apply it to his/her work for production optimization.

Outline

• Explain the concept of Nodal Analysis.• List the four major segments between the reservoir and the

separator where pressure loss occurs.• Give definitions for each of the following terms:

– Inflow performance curve– Tubing Intake curve– System graph– Solution node

• Benefits of NODAL Analysis

Agenda

1. The concept of Nodal Analysis2. Segments in the reservoir/well system where

pressure loss occurs3. Fluid Properties4. Solution node5. Inflow performance curve6. Outflow performance curve7. System graph

Pressure Losses in Well System

P1 = Pr - Pwfs = Loss in reservoir

P2 = Pwfs - Pwf = Loss across completion

P3 = Pwf - Pwh = Loss in tubing

P4 = Pwh - Psep = Loss in flowline

Pr PePwfsPwf

P1 = (Pr - Pwfs)

P2 = (Pwfs - Pwf)

P3 = Pwf - Pwh

P4 = (Pwh - Psep)

Psep

Sales lineGas

Liquid

Stock tank

PT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh

Nodal Analysis

P1 = Pr - Pwfs = Loss in reservoir

P2 = Pwfs - Pwf = Loss across completion

P3 = Pwf - Pwh = Loss in tubing

P4 = Pwh - Psep = Loss in flowline

Pr PePwfsPwf

P1 = (Pr - Pwfs)

P2 = (Pwfs - Pwf)

P3 = Pwf - Pwh

P4 = (Pwh - Psep)

Psep

Sales lineGas

LiquidStock tank

PT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh

Inflow Performance Curve

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flo

win

g b

ott

om

ho

le p

ress

ure

, p

si Inflow (Reservoir) Curve

Tubing Intake Curve

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flo

win

g b

ott

om

ho

le p

ressu

re,

psi

Tubing Curve

System Graph

2111 STB/D

1957.1 psi

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flo

win

g b

ott

om

ho

le p

ress

ure

, p

si

Inflow (Reservoir) Curve

Tubing Curve

Solution Node At Wellhead

P1 = Pr - Pwfs = Loss in reservoir

P2 = Pwfs - Pwf = Loss across completion

P3 = Pwf - Pwh = Loss in tubing

P4 = Pwh - Psep = Loss in flowline

Pr PePwfsPwf

P1 = (Pr - Pwfs)

P2 = (Pwfs - Pwf)

P3 = Pwf - Pwh

P4 = (Pwh - Psep)

Psep

Sales lineGas

Liquid

Stock tank

PT = Pr - Psep = Total pressure loss

Adapted from Mach et al, SPE 8025, 1979.

Pwh

Fluid Physical Properties• Oil Properties

– Oil in the absence of gas in solution is called dead oil. The physical properties of dead oil are a function of the API gravity of the oil, pressure and temperature. The API gravity of oil is defined as:

5.131F60@SpGr

5.141gravity API

o

– With gas in solution, oil properties also depend on gas solubility. Gas solubility is normally represented by Rs.

• Gas Solubility:– Gas solubility is defined as

the volume of gas dissolved in one stock tank barrel of oil at a fixed pressure and temperature.

– There are several correlations for gas solubility such as:

• Standing

• Lassater

• and others …

Fluid Physical Properties

2.1

T00091.0

API0125.0

gs 10

10x

18

p

STB

scfR

• Formation Volume Factor (o):– Is the volume in barrels occupied by one stock tank barrel

of oil with the dissolved gas at any elevated pressure and temperature. It measures the volumetric shrinkage of oil from the reservoir to surface conditions.

– There are different correlations for calculating the formation volume factor. They are empirical and based on oil from different areas. The Standing correlation was developed for California crude and can be written as follows:

o = 0.972+0.000147 x F1.175

Fluid Physical Properties

T25.1RF

5.0

o

gS

Example

Required

Formation volume at 200o F of a bubble point liquid having a gas/oil ratio of 350 CFB, a gas gravity of 0.75, and a tank oil gravity of 30o API

Procedure

Starting at the left side of the chart, proceed horizontally along the 350 CFB line to a gas gravity of 0.75 . From this point, drop vertically to the 30o API line. Proceed horizontally from the tank oil gravity scale to the 200o F line. The required formation volume is found to be 1.22 barrel per barrel of tank oil.

Properties of natural mixtures of hydrocarbon gas and liquids, formation volume of bubble-point liquids after Standing.

Copyright 1952

Chevron Research Company

Reprinted by Permission

Graphical Form of Standing’s Correlation, Bo

• Standing’s or any other correlation for formation volume factor cannot be used above the bubble point pressure Pb. Above the bubble point:

Fluid Physical Properties

bo PPCobo e

Where Pb and Bob are calculated from Standing’s or Lassater’s correlation using Rs=Rp, Rp being the produced GOR. The parameter Co is not a constant and can be calculated by Trube’s correlation as follows:

5

gso 10 x P

API61.12180,1T2.17R5433,1C

Properties of Natural Hydrocarbon Mixtures of Gas and Liquid Bubble Point Pressure

Example:

RequiredBubble point pressure at 200oF of a liquid having a gas-oil ratio of 350 CFB, a gas gravity of 0.75, and a tank oil gravity of 30o API.Procedure:Starting at the left side of the chart, proceed horizontally along the 350o CFB line to a gas gravity of 0.75. From this point drop vertically to the 30o API line. Proceed horizontally from the tank oil gravity scale to the 200o F line. The required pressure is found to be 1930 PSIA.

Bubble Point Pressure -

- Pounds p

er square

inch

Abso

lute

Graphical Form of Standing’s Correlation, Pb

• The fluid viscosity of reservoir oil containing solution gas decreases with pressure up to the bubble point pressure

Oil Viscosity

Oil Viscosity

• In the absence of lab data the Beal correlation is used.

Rate of increase of oil viscosity above bubble-point pressure. After Beal.

Dead Oil Viscosity

Abs

olu

te V

isco

sity

of

Gas

-Fre

e O

il (c

p)

Oil Gravity o API at 60oF and Atmospheric PressureDead oil viscosity at reservoir temperature and

atmospheric pressure. After Beal.

Gas Viscosity• Carr, Kobayashi and Burrows presented a correlation for

estimating natural gas viscosity as a function of gas gravity, pressure and temperature

Gas Deviation Factor

• Variable used in calculating the gas density and gas formation volume factor.

• To determine this parameter, the law of corresponding states is used:– This law states that at the same reduced pressure

and reduced temperature, all hydrocarbon gases have the same gas deviation factor.

Gas Deviation Factor

As a function of Ppr and Tpr, After Standing and Katz

Inflow Performance Relationship

Inflow Performance Relationship

Inflow Performance is the ability of the reservoir to deliver oil or gas through the formation and is described by the pressure / rate response of the reservoir. The IPR depends on reservoir parameters and reservoir fluid characteristics.

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Production rate, STB/D

Flo

win

g b

ott

om

ho

le p

ress

ure

, p

si Inflow (Reservoir) Curve

Inflow Performance Relationship

Inflow Performance Relationship

Progressive deterioration of IPR’s as depletion proceeds with time.

Reservoir Conditions:

Original Pressure = 2150 psi

Bubble Point = 2150 psi

Crude oil PVT. Characteristics

and relative permeability

Characteristics from Ref. 7

Well spacing = 20 acres

Well radius - 0.33 footCumulative recover,

percent of original

oil in place

Producing rate, bopd

Bo

tto

m h

ole

we

ll p

ress

ure

, p

si

o oBr

rs

e

wln .

0 75

7.08 x 10-3 kh (Pr - Pwf)qo =

Inflow Performance Relationship

For single phase oil or liquids, the IPR shown below is stated by Darcy’s law for radial flow as follows:

Productivity Index (PI)

On the IPR curve the PI is defined as the negative inverse of the slope of the line:

For PI calculations, q = surface production of fluids, and Pr-Pwf = reservoir pressure drawdown.

q = qmax when Pwf = 0

APws

Pwf

00 q B

TAN = = J = PIOBOA

Productivity Index (PI)

The Productivity Index of a well is defined as the total liquid production per day per psi of pressure drawdown.

or, PI = J = , BPD/psi(qo + qw)

(Pr - Pwf)

Example Problem No.1

• For the following oil-well data, calculate:a) The absolute open flow potential, AOF and draw the IPR curveb) Calculate the Productivity Index

Permeability, Ko = 30 mD Pay thickness, h = 40 ft Avg reservoir pressure, Pr = 3,000 psi Reservoir Temperature, T = 200o F Well Spacing, A = 160 Acres (43,560 ft2/acre) OH size, D = 12 ¼” Formation Volume factor, o = 1.2 bbl/stb Oil viscosity, o = 0.8 cp Assume skin, St = 0 and no turbulence

1. Drainage radius = A x 43,560 , ft = 1,490 ft

2. Applying Darcy’s law , qo = 26,550 = 3,672 bopd

7.23

3. PI = = 1.22 bopd/psi

Answers to Example Problem No.1

BPD/psi qo

(Pr - Pwf)

Darcy Equation for Gas Wells

gtw

eg

wfrgg

DqSr

rTZ

PPhkEq

75.0ln

03.7 224

Skin factor

• The Skin Factor (St) is a constant which relates the pressure drop in the skin to the flow rate and transmissibility of the formation. Thus:

Kh

q

PS

oo

skint 2.141

wfwfskin PPP '

Skin Factor – graphical representation

Pr

P’wf

Pwf

rw

rd

Positive skin ~ Damaged wellbore or Reduced wellbore radius

......, soturbpppdt SSSSSSS

Skin factor

St = total skin effect, (+ damaged; - stimulated)Sd = skin effect due to formation damage (+)Spp = skin due to partial penetration (+)Sp = skin effect due to perforation (+)Sturb = Dq, skin effect due to turbulence (+)So = skin effect due to slanting of well (-)Ss = skin effect due to stimulation (generally -)