02 Theoretical Basis Continue

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TẬP ĐOÀN DẦU KHÍ VIỆT NAM TRƯỜNG ĐẠI HỌC DẦU KHÍ VIỆT NAM

THEORETICAL BASIS(continue)

Lecturer : MSc Luong Hai LinhEmail : [email protected] : +84 1234 081 666


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Production engineeringMSc Luong Hai Linh 2

Content

Darcy’s law

Flow regimes

Skin effect

Nodal analysis

Inflow performance relationship (IPR)


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Production engineeringMSc Luong Hai Linh

The linear IPR for a reservoir that presents some skin effectis then:

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Skin effect


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Skin effect


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The flow efficiency coefficient is defined as the ratiobetween the drawdown with no skin effect to the drawdownwith skin:

= −

= 1

141,2ℎ

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Skin effect


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Skin effect- saturated reservoir


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For a saturated IPR we have:

= 1 (1 ) (1) − = 1 (2)

Or:

= 1 1 (1 ) 1

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The value of J is:

= = (3)From (1)we have:

= ( + ) − − (4)From (2): − = (5)(3),(4),(5), we have:

= + − (6)

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(2),(6) we have:

= 2 1 1

The value of is: = 2 1 1

= 2(1 )(1 )

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For

to be zero we have:

0 = 2(1 )(1 ) = 22 2

The value of FE can not be higher than this critical value

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For Vogel the maximum value of FE is 1,125



Nodal analysis

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Individual components analysis is adequate whencomponents don’t interact with each other

In two phase flow, pressure drop is function not only offlowrates but also of pressure level at the component

This creates an interdependence between each componentIndividual component analysis is no longer applicable

A new tool is necessary- Nodal analys is

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Nodal analysis


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Nodal analysis

= ∆( , )

The inflow pressure at the node represents the pressurethe inflow section can deliver the flowrate q at the node



Nodal analysis

= ∆( , )

The outflow pressure at the node represents the pressurethe outflow section requires to produce the flowrate q up to

the separator.


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Nodal analysis


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Nodal analysis


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Nodal analysis


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Nodal analysis


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Nodal analysis

d l l


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Nodal analysis

d l l


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Nodal analysis

N d l l i


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Example:

Perform a Nodal analysis for the following well:

- IPR: Vogel with = 5000 / and = 4500 - Separator pressure = 450 psig

- The pressure drop at the flowline, and production string isgiven in the following table

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Nodal analysis

N d l l i


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Nodal analysis

Nod l n l sis


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Nodal analysis

Nodal analysis


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Nodal analysis

Nodal analysis stability


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If the system is disturbed from the equilibrium point, it will

readjust itself to restore equilibrium

If an unstable system is disturbed, it will readjust itself to bea stable point

This is a transient problem and the steady state nodalanalysis tool is very limited for explaining this phenomena

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Nodal analysis-stability



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As a consequence, for the situation illustrated, the transient

coupling between the tubing and the reservoir will generatethe driving force to promote equilibrium

For any small disturbances in the system, the reservoir and

tubing will interact to bring the production back toequilibrium point



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Two equilibrium points


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Two equilibrium points

Stable and unstable conditions


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Point B is an unstable operating point

If the flowrate is decreased from the equilibrium point, thewell is going to die

If the flowrates is increased from the equilibrium point, the

well is going to produce the next stable flowrate valueThis is a very important and common phenomenon in thefield

A well with this IPR~OPR behavior can not produce thestable flowrate without some help




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Point B represents a barrier that the well needs to

overcome in order to produce under stable conditions. Thisis usually accomplished by inducing flow in the well

If this well dies it can not be put into production simply byopening the choke or valves

If the well has an artificial lift installed it can be put intoproduction by using the lift system to help the wellovercome the unstable point B. After that if artificial lift is not

required you can leave the well under natural flowIf we don’t have an artificial lift system installed we can:rock the well, nitrogen injection, swab, etc



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END OF CHAPTER 2

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02 Theoretical Basis Continue