Chapter 3 Inflow Performance (1)

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I nflow Performance



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I nflow Performance

Contents Contents 1.1. Introduction Introduction

2.2. The Radial F low Equation The Radial F low Equation

3.3. Straight L ine I nf low PerformanceStraight L ine I nf low PerformanceRelationship Relationship

4.4. Vogel I nf low Performance Relationship Vogel I nf low Performance Relationship

5.5.

Other I nf low Performance Relationship Other I nf low Performance Relationship

6.6. Establishing the Well ' s IPR Establishing the Well ' s IPR

7.7. Use of the I nflow PerformanceUse of the I nflow Performance

Relationship Relationship



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I nflow Performance

1. INTRODUCTION1. INTRODUCTION



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I nflow Performance

The rate at which fluid will flow towards the

wellbore depends upon

The nature of the fluid,

The type of reservoir rock and theDriving force.

This is driving force is not the reservoir

pressure but the difference in pressure betweenthe reservoir and the wellbore, and is called

The Drawdown (PDD

)



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I nflow Performance

The Inflow

Performance

Relationship (IPR)

quantifies the

flow-rate from

a well as a

function of the

drawdown.



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I nflow Performance

2. THE RADIA L2. THE RADIA L

FLOW EQUATION FLOW EQUATION



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I nflow Performance

Consider radial inflow into a well as depicted in

the Figure.

The change in pressure profile and the pressure

at the outer boundary (pe) depend on the initial

and boundary conditions imposed.



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I nflow Performance

Three different f1ow conditions can be

distinguished:

Transient flowSemi Steady State flow

Steady State flow



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I nflow Performance

Transient f low Trans ient f low

This condition is only applicable for a relatively

short period after some pressure disturbance

has been created in the reservoir.

Transient flow conditions are applied to the

analysis of well tests.



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I nflow Performance

Sem i Steady State f low Sem i Steady State f low

This condition is applicable to reservoir which

has been producing for a sufficient period of

time so that the effect of the outer boundary has

been felt.

It is considered that

the well is surrounded

at its outer boundary

by a solid "brick wall

which prevents flow of

fluids into the radial cell (Figure). re = drainage radiusrw = well bore radius



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I nflow Performance

Steady State f low Steady State f low

This condition applies to a well draining a cell

which has a completely open outer boundary.

It is assumed that, for:

q A constant

production rate,

q Fluid withdrawal

from the cell willbe exactly

balanced by fluid

entry across the open boundary.



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I nflow Performance

This condition is appropriate when pressure is

being maintained in the reservoir due to either:

Ø Natural water influx, orØ The injection of displacing fluid.



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I nflow Performance



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I nflow Performance

Radial inf low equat ion fo rRadial inf low equat ion for

steady state flow steady state flow

Assuming that the reservoir is homogeneous

in all reservoir parameters, Darcy's law for the

radial flow of a single phase fluid can beexpressed as:

Where: k = Permeability

A = Flow area

! = Viscosity



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I nflow Performance

More realistically, for a well located in a

reservoir containing other wells, the radius fromwhich liquid is being

drained is known and

is called the

drainage radius r e.

The inflow equation for Steady State flow may

be written;



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I nflow Performance

The radial flow model is therefore adapted to

express the drawdown in terms of the average

reservoir pressure P.

This value would be obtained if the producing

field was shut in until the pressure in the

reservoir had equalize, and the average

reservoir pressure is found by analyzing

individual well shut-in bottom hole pressures.



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I nflow Performance

3. STRA IGHT 3. STRA IGHT - - LINELINE

INFLOW PERFORMANCEINFLOW PERFORMANCE

RELATIONSHIP RELATIONSHIP



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I nflow Performance

When we consider the parameters in the

equation for the Productivity Index the followingcomments can be made:

Ø h, r e and r w are constant.

Ø k, ! and Bo are pressure dependent.

The criteria is the flowing bottom hole pressurewith respect to the phase envelope of the fluidconsidered.

For single phase flow, which occurs when theflowing pressure is above the bubble pointpressure, these parameters can be consideredconstant (independent of pressure).



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I nflow Performance

Under the above conditions the Productivity

Index (J) is constant and is called "PI".

The equation q = PI x Pdd describes a straight

line.



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I nflow Performance

4. VOGEL INFLOW4. VOGEL INFLOW

PERFORMANCEPERFORMANCE

RELATIONSHIPRELATIONSHIP



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I nflow Performance

When the flowing bottomhole pressure is belowthe bubble point pressure, two phase liquid and

gas flow occurs in the reservoir and the linear

relationship defined above is no longer valid.

When the pressure declines below Pb.

The permeability decrease,

Oil formation volume factor will decrease,The viscosity will increase.



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I nflow Performance

This type of behavior has been observed in

solution gas drive reservoirs, as depletionprecedes the productivity of a typical welldecrease.

Under these conditions,

a plot of flowing bottomhole pressure againstproduction rate resultsin a curved, rather than

a straight line and thereis a progressivedeterioration in the inflowperformance relationships as the reservoir isdepleted.



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I nflow Performance

The inflow performance relationships shown in

the previous Figure may be redefined as nodimensional IPR's.

This is done by

expressing the bottomhole flowing pressure

as a fraction of the

maximum shut-in

pressure, and the

relevant flow rate as

a fraction of the maximum production rate for

that curve, at very similar throughout most of

the producing life of the reservoir.



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I nflow Performance

It is shown that non-dimensional IPR's apply tomany different reservoirs.

Exceptions are wells with:

qLarge positive skins,

q High viscosity crudes, and

q Very high rate producers.

Because of the similar nature of the non-

dimensional IPR's, it is possible to group theminto one representative curve which closely

approximates them all.



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I nflow Performance

The curve giving the best fit to the non-dimensional IPR's shown above is called the

reference IPR curve, or the Vogel IPR.



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I nflow Performance

The equation of the reference curve is:

If q/q max is plotted against pWf / p, the referencecurve will result.

Having established the maximum possible flow

rate and the reservoir pressure, plotting q

against pwf will give the actual inflow

performance relationship for a particular well.



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I nflow Performance

For comparison to the Vogel IPR, therelationship for a straight line (PI) IPR would

be;



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I nflow Performance

5. OTHER INFLOW5. OTHER INFLOW

PERFORMANCEPERFORMANCE

RELATIONSHIPS RELATIONSHIPS



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I nflow Performance

5.1 IPR or reservoirs with static pressures5.1 IPR or reservoirs with static pressures

above bubble point pressureabove bubble point pressure

5.2 Gas Well5.2 Gas Well IPR's IPR's



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I nflow Performance

5.1 IPR or reservoirs w ith s tat ic p ressu res5.1 IPR or reservoirs w ith s tat ic p ressu resabove bubble point pressure above bubble point pressure

The IPR's described in the previous sections

dealt with either above or below bubble pointconditions.

It is more realistic to define an IPR which is valid

for both conditions.



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I nflow Performance

Above Pb the IPR will respond linear and whenthe Pwf is below Pb a curved IPR will occur.



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I nflow Performance

The solution for Pwf < Pb is then:

Where J* is the Productivity Index for the

straight line part of the IPR.



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I nflow Performance

5.2 Gas Well5.2 Gas Well IPR's IPR's

The IPR's described in the previous sections are

applicable to oil wells only.

In gas wells, fluid velocity around the well bore

is much higher than that found in oil wells.

Due to this high velocity, turbulent flow will

occur resulting in an additional pressure drop.

In addition the gas viscosity and

compressibility are highly dependent on

pressure and temperature.



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I nflow Performance

The resulting non-linear IPR of gas wells is

often expressed as:

Where Q = the pressure drop due to laminar

(Darcy) flow and

bQ2 = the pressure drop due to inertial

turbulent (non-Darcy) flow.

The constants a, and b can be derived from

known reservoir and gas properties.



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I nflow Performance

6. ESTABLISHING6. ESTABLISHING

THE WELL'S IPR THE WELL'S IPR



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I nflow Performance

The inflow performance

relationship for a given

well has to be

established by

a well test.

In theory, oneproduction rate with

corresponding bottom

hole pressure and the

shut-in pressure willdefine the inflow

performance

relationship.



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I nflow Performance

In practice a number of flow rates may be taken

to confirm the well performance.

If a sample of formation fluid is taken and

analyzed to establish the bubble point pressure,

it will be possible to decide whether to use the

straight line, the Vogel or the Vogel / Glass

inflow performance relation hit.



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I nflow Performance

During well testing, it should not be necessaryto draw the well bore pressure down very low in

order to establish the maximum inflow potential

of the well, the IPR may be used to establish

this value.

In the case that the formations being tested are

friable, unconsolidated sands, it is unwise to

apply a high drawdown for a fear of collapsingthe formation and getting no test data at all.



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I nflow Performance

7. USE OF THE INFLOW7. USE OF THE INFLOW

PERFORMANCEPERFORMANCERELATIONSHIP RELATIONSHIP



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I nflow Performance

The inflow performance relationship is useful asa tool to monitor well performance and predict

the stimulation and artificial lift to requirements

of a number of wells.

The IPR for a well must be known in order to

size the well tubular correctly.



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I nflow Performance

Based on interpolation between wells, if the

initial IPR for a well is lower than expected in aparticular part of the reservoir, it may then be

suspected that the formation has been badly

damaged during the drilling and completion

phase.

Mapping the IPR's across the field may highlight

this situation.

When well bore damage is confirmed by a build-

up survey the well may require stimulation.



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I nflow Performance

Even with stimulation, the inflow performance

of a well will decline with falling reservoirpressure.

Plotting this decline

will indicateapproximately when

the wells will have to

be artificially lifted in

order to maintain therequired off take rate

from the field.

Chapter 3 Inflow Performance (1)

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