Nodal analysis

1
Production Optimization
using nodal analysis
Introduction
2Production Optimization - Introduction
The nodal systems analysis approach is a very flexible method
that can be used to improve the performance of many well
systems.
The nodal systems analysis approach may be used to analyze
many producing oil and gas well problems. The procedure can
be applied to both flowing and artificial
Introduction

2
The nodal systems analysis schematic model
Introduction
To apply the systems analysis procedure to a well, it is
necessary to be able to calculate the pressure drop that will
occur in all the system components listed in Fig. 1-l.
These pressure drops depend not only on flow rate, but on
the size and other characteristics of the components.
Unless accurate methods can be found to calculate these
pressure drops, the systems analysis can produce
erroneous results
Introduction

3
Kermit Brown, p. 88, Fig. 4.2
Pressure drop that will occur in all the system
Introduction
The procedure consists
of selecting a division
point or node in the well
and dividing the system
at this point.
The locations of the
most commonly used
nodes are shown in
Fig. 1-2.
Introduction

4
Once the node is selected,
the node pressure is
calculated from both
directions starting at the
fixed pressures.
Therefore, a plot of node
pressure versus flow rate
will produce two curves,
the intersection of which
will give the conditions
satisfying requirements
Introduction
The effect of a change in any of the components can be analyzed by
recalculating the node pressure versus flow rate using the new
characteristics of the component
The procedure can be further illustrated by considering the simple
producing system shown in Fig. 1-4 and selecting the wellhead as the
node.
Introduction

5
The effect on the flow capacity of changing the tubing size is
illustrated in Fig. 1-5, and the effect of a change in flowline size is
shown in Fig. 1-6.
Introduction
The effect of a change in tubing size on the total system producing
capacity when pwf, is the node pressure is illustrated in Fig. 1-7.
Introduction

6
If too much pressure drop occurs in one component or module, there
may be insufficient pressure drop remaining for efficient performance of
the other modules. This is illustrated in Fig. 1-8 for a system in which
the tubing is too small.
Introduction
A case in which the well
performance is controlled
by the inflow is shown in
Fig. 1-9. In this case, the
exces-sive pressure drop
could be caused by
formation damage or
inadequate perforations.
Introduction

7
A qualitative example of selecting the optimum tubing size for a well
that is producing both gas and liquids is shown in Fig. 1-10 and I-11.
Introduction
an example of determining the optimum gas injection rate
for a well on gas lift is illustrated in Fig. 1-12 and 1-13.
Introduction

8
a different inflow curve would exist for each perforating
density. This is illustrated qualitatively in Fig. 1-14 and Fig.
1-15
Introduction
Introduction

9
A suggested procedure for applying NODAL Analysis is
given as follows :
• Determine which components in the system can be
changed. Changes are limited in some cases by
previous decisions. For example, once a certain hole
size is drilled, the casing size and, therefore, the tubing
size is limited
• Select one component to be optimized
• Select the node location that will best emphasize the
effect of the change in the selected component. This is
not critical because the same overall result will be
predicted regardless of the node location
Introduction
• Develop expressions for the inflow and outflow.
• Obtain required data to calculate pressure drop versus
rate for all the components. This may require more data
than is available, which may necessitate performing the
analysis over possible ranges of conditions
• Determine the effect of changing the characteristics of
the selected component by plotting inflow versus outflow
and reading the intersection.
• Repeat the procedure for each component that is to be
optimized.
Introduction

10
The nodal systems analysis approach may be used to :
1. Selecting tubing size.
2. Selecting flowline size.
3. Gravel pack design.
4. Surface choke sizing.
5. Subsurface safety valve sizing.
6. Analyzing an existing system for abnormal flow re-strictions.
7. Artificial lift design.
8. Well stimulation evaluation.
9. Determining the effect of compression on gas well performance.
10.Analyzing effects of perforating density.
11.Predicting the effect of depletion on producing ca-pacity.
12.Allocating injection gas among gas lift wells.
13.Analyzing a multiwell producing system.
14.Relating field performance to time
Introduction
End of slide

1
Predicting Current and Future IPR’s
2Production Optimization – Predicting IPR
Reservoir Performance
One of the most important components in the total well system is the
reservoir. Unless accurate predictions can be made as to what will
flow into the borehole from the reservoir, the performance of the
system cannot be analyzed.
The flow from the reservoir into the well has been called "inflow
performance" by Gilbert' and a plot of producing rate versus bottomhole
flowing pressure is called an "inflow performance relationship" or IPR.

2
WELL PERFORMANCE EQUATIONS
To calculate the pressure drop occurring in a reservoir, an equation that
expresses the energy or pressure losses due to viscous shear or friction
forces as a function of velocity or flow rate is required. Although the form
of the equation can be quite different for various types of fluids, the basic
equation on which all of the various forms are based is Darcy's law.
In 1856, while performing experiments for the design of sand filter beds
for water purification, Henry Darcy proposed an equation relating
apparent fluid velocity to pressure drop across the filter bed. Although
the experiments were performed with flow only in the downward vertical
direction, the expression is also valid for horizontal flow, which is of most
interest in the petroleum industry.
Darcy's Law
Darcy's sand filters were of constant cross-sectional area, so the equation
did not account for changes in velocity with location. Written in differential
form, Darcy's law is:
or in terms of volumetric flow rate q

3
I. Linear Flow
For linear flow, that is for constant area flow, the equation may be integrated
to give the pressure drop occurring over some length L:
If it is assumed that k, µ and q are independent of pressure, or that they can
be evaluated at the average pressure in the system, the equation becomes

4
Integration gives:
where C is a unit conversion factor. The correct value for C is 1.0
for Darcy Units and 1.127 x 10-' for Field Units (See Table 2-1).

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Oil flow

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Gas flow
Darcy's law can be used to calculate the flow into a well where the fluid
is converging radially into a relatively small hole.
Referring to the flow geometry illustrated in Figure 2-2, the cross-sectional
area open to the flow at any radius is A = 2π r h.
Radial Flow

7
Oil flow
For field units, became :
Gas flow
For field units, became :

8
PREDICTING PRESENT TIME IPR'S FOR OIL WELLS
The factors affecting the inflow performance for oil wells were discussed
qualitatively in the previous section. If all of the variables in the inflow equations
could be calculated, the equations resulting from integration of Darcy's law could
be used to quantify the IPR.
Unfortunately, sufficient information rarely exists to accomplish this and, therefore,
empirical methods must be used to predict the inflow rate for a well
Several of the most widely used empirical methods for predicting an IPR for a well
are presented in this section. Most of these methods require at least one
stabilized test on a well, and some require several tests in which pwf test and
qtest were measured.
Methods to account for the effects of drawdown only are first presented, that is,
pR is assumed constant. Modification of the methods for depletion will then be
discussed
Vogel Method
Vogel reported the results of a study in which he used a
mathematical reservoir model to calculate the IPR for oil wells
producing from saturated reservoirs.
The study deal with several hypothetical reservoirs including those
with widely differing oil characteristics, relative per-meability
characteristics, well spacing and skin factors.
The final equation for Vogel's method was based on calculations
made for 21 reservoir conditions.
Although the method was proposed for saturated, dissolved gasdrive
reservoirs only, it has been found to apply for any reservoir in which
gas saturation increases as pressure is decreased

9
Vogel's original method did not account for the effects of a non-zero
skin factor, but a later modification by Standing extended the method
for application to damaged or stimulated wells.
The Vogel method was developed by using the reservoir model
proposed by Weller' to generate IPR's for a wide range of conditions.
He then replotted the IPR's as reduced or dimensionless pressure
versus dimension-less flow rate.
It was found that the general shape of the di-mensionless IPR was
similar for all of the conditions studied. Examples of these plots from
the original paper are illustrated in the next Figures
Vogel Method
Vogel’s dimensionless IPR
Vogel Method

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Vogel Method
Vogel Method

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Vogel arrived at the following relationship between dimensionless
flow rate and dimensionless pressure :
Vogel Method
The dimensionless IPR for a well with a constant productivity index
can be calculated from
Vogel pointed out that in most applications of his method the error in
the predicted inflow rate should be less than 10%, but could increase
to 20% during the final stages of depletion
Vogel Method

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In the original paper by Vogel, only cases in which the reservoir was
saturated were considered. The method can be applied to undersaturated
reservoirs by applying Vogel's equation only for values of Pwf < Pb,
Application of Vogel Method-Zero Skin Factor
Vogel Method
a. Saturated Reservoirs.
b. Undersaturated Reservoirs.
Application of Vogel Method- non Zero Skin Factor
(Standing Modification)
Vogel Method
The method for generating an IPR presented by Vogel did not
consider an absolute permeability change in the reservoir. Standing6
proposed a procedure to modify Vogel's method to account for either
damage or stimulation around the wellbore.
The degree of permeability alteration can be expressed in terms of a
Productivity Ratio PR or Flow Efficiency FE, where:

13
Undersaturated Reservoirs with FE ≠ 1.
Standing's modification of Vogel's method to be used when the flow
efficiency is not equal to one may also be applied to undersaturated
reservoirs.
Vogel Method
Application of Vogel Method- non Zero Skin Factor
(Standing Modification)
Fetkovich proposed a method for calculating the inflow
performance for oil wells using the same type of equation
that has been used for analyzing gas wells for many
years.
The procedure was verified by analyzing isochronal and
flow-after-flow tests conducted in reservoirs with
permeabilities ranging from 6 md to greater than 1000 md.
Pressure conditions in the reservoirs ranged from highly
undersaturated to saturated at initial pressure and to a
partially depleted field with a gas saturation above the
critical.
In all cases, oil-well back-pressure curves were found to
follow the same general form as that used to express the
inflow relationship for a gas well. That is:
Fetkovich Method

14
That is:
Fetkovich Method
The value of n ranged from 0.568 to 1.000 for the 40 field tests analyzed by
Fetkovich. The applicability of Equation to oil well analysis was justified by
writing Darcy's equation as:
Fetkovich Method
For an undersaturated reservoir, the integral is evaluated over two regions as:

15
Three types of tests are commonly used for gas-well testing to determine C
and n. These tests can also be used for oil wells and will be described in this
section. The type of test to choose depends on the stabilization time of the
well, which is a function of the reservoir
Fetkovich Method
1. Flow-After-Flow Testing
A flow-after-flow test begins with the well shut in so that the pressure in
the entire drainage area is equal to pR. The well is placed on production
at a constant rate until the flowing wellbore pressure becomes constant.
The test may also be conducted using a decreasing rate sequence.
The idealized behavior of production rate and wellbore pressure with time is
shown in Figure.
Fetkovich Method

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2. Isochronal Testing
If the time required for the well to stabilize on each choke size or
producing rate is excessive, an isochronal or equal time test is
preferred.
The values of PR
2 - Pwf
2 determined at the specific time periods are
plotted versus qo and n is obtained from the slope of the line. To
determine a value for C, one test must be a stabilized test. The
coefficient C is then calculated from the stabilized test.
The idealized behavior of producing rate and pressure as a function
of time is shown in Figure.
Fetkovich Method
Fetkovich Method

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3. Modified Isochronal Testing
If the shut-in time required for the pressure to build back up to PR
between flow periods is excessive, the isochronal test may be
modified. The modification consists of shutting the well in between
each flow period for a period of time equal to the producing time
Fetkovich Method
1. Horizontal Wells
IPR Construction for Special Cases
The productivity index for a horizontal well in which permeability
difference in the vertical and horizontal directions is small was described
by Giger, et al as:

18
2. Waterflood Wells
It can be assumed that the IPR will be linear for values of pwf > pb. For
pwf < pb, Vogel's equation may be used to account for the effect of gas
saturation developing around the wellbore when pwf is below pb.
IPR Construction for Special Cases
PREDICTING FUTURE IPR's FOR OIL WELLS
As the pressure in an oil reservoir declines from depletion, the ability of
the reservoir to transport oil will also decline. This is caused from the
decrease in the pressure function as relative permeability to oil is
decreased due to increasing gas saturation.
Standing Method
Standing" published a procedure that can be used to predict the
decline in the value of qo (max) as gas saturation in the reservoir
increases from depletion.

19
Once the value of qo (max) or J has been adjusted, future IPR's can
be generated from
Fetkovich Method
The method proposed by Fetkovich to construct future IPR's consists
of adjusting the flow coefficient C in his Equation for changes in ƒ(PR).
He assumed that f( PR) was a linear function of PR, and, therefore, the
value of C can be adjusted as
Future IPR's can thus be generated from

20
Combining Vogel and Fetkovich
The method proposed by Fetkovich for adjusting C can also be
used to adjust qo(max) if a value for the exponent n is assumed.
The expressions for qo(max)P and qo(max)F can be expressed
using the Fetkovich equation as:
If a value of n equal to one is assumed, then:
PREDICTING PRESENT TIME IPR's FOR GAS WELLS
Darcy's equation for radial gas flow including permeability alteration
and turbulence may be expressed as follows:

21
This definition of B includes the assumption that re is much greater than
rw. The effects of turbulence can also be accounted for by including an
exponent in the pressure term of previous Equation.
This results in the familiar back-pressure form of the equation.
Use of the Back Pressure Equation
Jones, Blount and Glaze Method
The method of plotting test data, which was proposed by Jones, et
al., can be applied to gas-well testing to determine real or present
time inflow performance relationships. The analysis procedure allows
determination of turbulence or non-Darcy effects on completion
efficiency irrespective of skin effect and laminar flow.

22
Predicting Future IPR's for Gas Wells
As reservoir pressure declines from depletion in a gas reservoir, the
change in the IPR is not as significant as it is for an oil reservoir.
If no changes are made in re S or h, the values of C, or A and B can be
adjusted for reservoir pressure changes as follows:
where the subscript P refers to present or real time and the subscript F refers
to some future time.

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END OF SLIDE

1
Inflow and Outflow Performance Curve
2Production Optimization – Inflow and outflow Performance curve
Tujuan:
Menggabungkan kinerja dari berbagai komponen sumur minyak
dan gas dalam sistem produksi untuk menentukan laju produksi
dan menentukan suatu sistem produksi yang optimal.
Sistem Produksi:
Dalam pendekatan analisa nodal ini, sistem produksi meliputi
reservoir (aliran dari reservoir ke sandface), perforasi, gravel
pack, screen, tubing, downhole safety valves, choke, pipa
permukaan dan separator.

2
Skema Sistem Produksi
Posisi “Node” dalam Analisa Nodal

3
Analisa Nodal di Dasar Sumur
Posisi “node” di dasar sumur adalah yang paling umum digunakan
dalam analysis nodal.
Sistem dibagi menjadi dua bagian, reservoir dan sistem pipa (sumur
dan permukaan).
Analisa Nodal di Dasar Sumur (Lanjutan)
Bagian reservoir dalam hal ini
meliputi aliran fluida dari reservoir
ke sand-face, aliran melalui
perforasi, gravel pack dan screen.

4
Sistem pipa dalam hal ini
meliputi aliran fluida dari
dasar sumur ke wellhead
(melalui tubing string dan
downhole valves) atau ke
separator (melalui pipa
permukaan dan chokes).
Kinerja dari setiap sistem dievaluasi pada “node” yang sama dalam
bentuk hubungan antara tekanan pada “node” dan laju alir. Untuk
“node” di dasar sumur, hubungannya adalah antara tekanan alir dasar
sumur (pwf) dan laju alir (q).
Konsep dari analisa nodal ini adalah pada “node”, yang merupakan titik
temu antara dua atau lebih sistem yang berbeda, kinerja dari sistem
yang bertemu di “node” itu haruslah sama.
Kinerja reservoir dalam bentuk hubungan antara tekanan dan laju alir
disebut dengan “Inflow Performance Relationship” (IPR). Sedangkan
kinerja sistem pipa disebut “Outflow Pressures”.
Satu kurva IPR dibuat pada satu harga tekanan reservoir rata-rata.

5
Kermit Brown, p. 91, Fig. 4.9a
Pemilihan “node” di dasar
sumur digunakan untuk
melihat pengaruh dari
penurunan tekanan
reservoir terhadap laju
produksi. Hal ini berguna
dalam peramalan
produksi.

6
Analisa Nodal di Wellhead
Sistem dibagi menjadi dua
bagian, reservoir+tubing
strings dan
flowline+separator.
Analisa Nodal di Wellhead (Lanjutan)
Flowline dan separator.

7
Reservoir dan tubing strings.
Untuk berbagai laju produksi, dihitung tekanan wellhead yang
diperlukan untuk mengalirkan fluida dari wellhead ke separator. Dari
langkah ini kita mendapatkan “node” tekanan outlow.
Menggunakan laju produksi yang sama, dengan tekanan reservoir rata-
rata yang tertentu hitung tekanan alir dasar sumur, kemudian tentukan
tekanan di wellhead dengan mengurangi tekan alir dasar sumur dengan
kehilangan tekanan di tubing strings. Prosedur ini menghasilkan “node”
tekanan inflow.
Laju produksi untuk kombinasi dua sistem tersebut diperoleh dari
perpotongan dua kurva tekanan outflow dan inflow.

8
Kermit Brown, p. 93, Fig. 4.15b
Pemilihan “node” di wellhead adalah untuk mengetahui pengaruh dari
perubahan flowline terhadap produksi.

9
Analisa Nodal di Separator
Analisa Nodal di Separator (Lanjutan)

10
Sumur A memperlihatkan bahwa
peningkatan produksi akan terjadi
cukup besar apabila tekanan
separatornya rendah. Tetapi sumur
D menunjukkan tidak ada
perubahan produksi yang cukup
berarti dengan perubahan tekanan
separator.

11
Analisa Nodal di Reservoir
Analisa Nodal di Reservoir (Lanjutan)

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END OF SLIDE

Nodal analysis

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Nodal analysis