Well Test

Notes

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Basic Petroleum EngineeringSchlumberger

Well Testing

Well TestingFlow Regimes

Basic EquationWell Testing

Drawdown TestBuild up Test

IPR TestSummary

© JJ Consulting 1997

Notes

The pressure wave is likened to a wave in a pool after a stone has been dropped into it. At the earliest time the wellbore and zones close to it are influencing the response, at later time it is the reservoir boundaries.

The idea is very simple but gives a lot of information about the reservoir in spite of the simple measurement of pressure and time.

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Well Testing Theory

A well test is conducted by making a sudden change in flowrate and then measuring the changes in the pressure with respect to time.

The pressure wave travels out into the reservoir “seeing” deeper as time goes on.

0Shut in

Time, t

rate

QBo

ttom

hol

ePr

essu

re P

0

0

Time, t

Producing

Notes

The flow in the wellbore/casing/tubing of oil will take a number of forms. The flow starts as single phase, as gas comes out of solution the flow regime changes first to bubble flow, small gas bubbles in the oil. The other states may or may not happen in the tubing depending on the pressures and gas oil ratio.

Slug and Plug flow are not very efficient as they lose energy as they tumble.

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Flow In the well

The actual flow regime depends on a number of factors, such as gas-oil-ratio and pressures.

1 10 102 103

1

10

102

10-1

BUBBLE FLOW

PLUG FLOWSLUG FLOW

MIST FLOW

REGION IIIREGION II

REGION I

GAS VELOCITY

TRA

NSI

TIO

N

LIQ

UID

VE

LO

CIT

Y

FLOW REGIMES

Notes

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Flow in the formation

Flow form a reservoir into a borehole is normally radial

Well bore

It flows from the surrounding reservoir into the borehole, equally on all sides

This model is used to compute flow rates and pressure distributions

The idea of radial flow seems obvious as the fluid is coming from all directions in the reservoir.

Notes

Other forms of flow are possible near the wellbore. An induced or natural fracture will cause the flow to be linear, not radial. However as the pressure/flow moves further out into the reservoir the flow is moving radially to reach the fracture.

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Types of flow

Linear Flow

Bi-Linear Flow

Radial Flow

Notes

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Radial Flow Model

This is the model for flow in the ideal caseConstant pressure at the boundary, Pi

Reservoir thickness, hReservoir radius re

Wellbore radius is rwPwf, is the flowing pressure

i

rw

rre

PPWF Pih

Assuming radial flow and knowing some parameters, Pwf, Pi, rw, h, re. the pressure at any point in the reservoir, P, can be described in terms of known or measured quantities.

Notes

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Flow States

The transient period is also known as infinite acting radial flow

All tests have some time in this region hence this is the zone normally analysed.

Time

Pre

ssure

Transientperiod

Transition

Pseudo-SteadyState

The pressure time graph is roughly split into three regions. The final region is when the reservoir reaches its steady state. As this is unknown, it could have arrived at the reservoir limits, or a fault or the pressure disturbance created by a nearby well, this region cannot be easily described.

The transition is equally ill defined. However in the transient period radial flow can be assumed and hence the problem analysed.

Notes

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Basic Equation

This equation in “oilfield units” is

Note this is only valid if:

•The pressure gradients are small

•Viscosity is constant

•Fluid flow is single phase

•Darcy (non turbulent) flow exists

•Constant flow rate

•Small compressibility

∆p = pi − pwf = 162. 6qBµkh

logkt

φ µCtr

w2

− 3. 23

Note the units used determine the constant.

The solution to the proposed model, assuming radial flow gives this equation. It is simply the pressure versus the log of time. If a plot is made of these two the radial flow period should, from this equation, appear as a straight line with a slope of 162.6qBµ/kh. In this everything else but the permeability k, are known, hence this can be determined.

The solution assumes some “starting” and “boundary” conditions, which work well for liquids. Gas is different, it has a high compressibility, and the equation has to be modified.

Notes

The measurements in the well test are simply pressure and time, with a constant, known, flowrate.

The build up test is the one normally used because the flowrate (in the reservoir) is constant. In a drawdown test it is often difficult to keep a constant rate.

Mathematical analysis produces the required answers.

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Well Testing RequirementsThe objective of a well test is to obtain detailed information about the reservoir

the parameters sought are

Permeability

Formation pressure

Skin factor

productivity ratio

reservoir geometry

There are two possibilities

• Drawdown test

the well goes from shut in to flowing

The pressure drops from the shut in to flowing

• Build-up test

The well goes from flowing to shut in.

pressure increases towards the reservoir pressure

Notes

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Drawdown test

0Shut in

Time, t

rate

QB

otto

m h

ole

Pre

ssur

e P

0

0

Time, t

Producing

A drawdown test, as the name suggests, starts shut - in and is the opened to flow. The pressure drops with time.

The production rate is controlled on surface with a choke.

Notes

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Drawdown Test equations

The Transient equation becomes the following equation with the flowing pressure a function of the time during the flow period.

pwf = p i −162.6qµB

khlog t( ) + c[ ]

The equation is the one seen previously, Pwf is the well flowing pressure which is measured. Pi is the initial pressure of the reservoir just prior to flow.

Notes

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Drawdown Test Plot

Time, t.1 1 10

Pre

ssur

e, P

wf recorded data

straight line, slope = m

The standard method of analysing a drawdown test is to plot the pressure on a linear scale against the time on a logarithmic scale.

A straight is drawn through the later time points when the flow is assumed to be radial, the slope is

The reservoir parameters can then be obtained.

m =162.6qµB

kh-

The pressure v log time plot should give a straight line when the well is at radial flow. The slope is computed and hence the permeability calculated. Note the slope is negative as the pressure is decreasing.

Notes

The zone around the wellbore is susceptible to damage from a number of sources. The net result is a zone of poor permeability close to the borehole. Perforating guns are made to fire deep in an effort to bypass this region.

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Damaged Zone

The zone immediately surrounding the wellbore can be damaged for several reasons

• clay materials in the formation swollen by the drilling fluids

• emulsions between the drilling fluid and the reservoir oil

• drilling mud particles clogging pore channels

• precipates forming from incompatible drilling and formation waters

• crushing of the rock by the drilling process

This causes a zone of pressure loss called the "skin".

Notes

The Skin Factor is an important number in reservoir planning. A high positive skin will mean that some form of stimulation is required to improve the situation.

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Skin Factor

The skin factor, S is given a positive sign for a damaged formation and a negative sign for an improved one.

The positive sign reflects the additional resistance to fluid flow, the negative the improvement in flow.

The amount of skin can be calculated from well tests

Improvements can be made by techniques such as fracturing or acidising or both.

Notes

The damaged zone has the effect of creating a pressure drop around the wellbore. The Skin is thus added to the basic equation as an additional pressure term.

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Pressure -Damaged Zone

Pressure Distribution with Skin

Pressure distribution without skin

Damaged zone

Pwf

Kres

Kdamaged zone

Kres > Kdamaged zone

Pressure

∆p skin

Notes

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Build up test

time, t

Pre

ssur

e P

w

Pwf, ∆t = 0

∆t

Flow period

constant rate

A common form of the pressure versus time curve for a build up test.

The well is flowed for a (known) period of time, t at a constant rate and the shut in.The pressure starts to rise.

tp

The build up test is the opposite of a drawdown test, here the well is closed in and the pressure increases. In order to analyse this type of test the production time has to be known.

Notes

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Build up test equations

This test is slightly more complex than the drawdown test to analyse mathematically.

It is assumed there are two periods of “flow” one with a flowrate of q and the other of -q.

The equation becomes:

pws = pi +162.6qµB

khlog

tp + ∆t

∆t

The reservoir is still “flowing” as it builds up to its static pressure. The equation used is called the Horner equation and uses the production time is the time part of the equation. In all other respects it is the same as the equation for the drawdown test.

Notes

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Horner plot

skin and wellborestorage effect

extrapolated to Pr

Pre

ssur

e

Horner Time function110102103104

time, t

Slope = m

The Horner time function is

where tp is the production time

∆t the time of the test, ie since shut in.

t p + ∆t

∆t

This plot is analysed in exactly the same manner as that for a drawdown. The slope in the radial flow section is taken and the permeability computed.

Notes

A major problem in build up tests is wellbore storage. If it is large it may mask the radial flow portion of the plot and hence make the test unusable.

Downhole shut-in, for example using a DST tool limits the effect. If there is tubing in the well a special tool has to be used.

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Wellbore Storage

Wellbore storage happens because when the well is shut in on surface it continues to flow downhole as the fluid in the column is compressible.

The effect is greatest when the well contains released gas.

Conventional well tests are run for a long time to overcome this effect.A better solution is to shut in downhole limiting the problem to a small volume.

Gas comingout ofSolution

SinglePhase Flow

Notes

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Wellbore Storage Equations

The wellbore storage is given by

In a well with a single phase fluid

therefore

If ∆p is plotted against ∆t on a linear scale the wellbore storage will show up at early time as a straight line with the slope that is a function of C.

C = ∆V∆p

∆V =qB0

24∆t

C =qB0

24∆t∆p

m =qB0

24C

The wellbore storage is simple to compute. The plot of ∆p v ∆t gives a straight line which will deviate at the end of wellbore storage.

Notes

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Definitions-production

Drawdown Pressurefor fluid flow a pressure difference must exist between the reservoir and the well bore

Drawdown = Pi - Pwf

Productivity IndexThe productivity index, J, is the ratio between the production rate, q, and the pressure drawdown

J = q / ( Pi - Pwf)

The drawdown pressure is fixed by the operator and depends on the tubing and the fluid flowing. The Productivity Index is a measure of how good a well is. It is measured in barrels/psi.

Notes

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Inflow Performance Relation

This shows the relationship between the production rate, q, and the flowing pressure.

It is determined by flowing the well at a number of rates and measuring the pressures.

Flow rate

Pwf

Pwf = Pi

This is an idealised curve for a liquid only.

The slope of this curve is the Productivity Index

0

This plot is used to compute the productivity index. The flow rate does not increase continuously with reducing pressure, it will reach a maximum value. The PI is computed in the straight portion of the graph.

Notes

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IPR test procedure

P1

P2

P3

P4

Bott

om

Hole

Pre

ssur

e

Time

Time

Wel

lhea

d F

low

rate

QT1

QT2

QT3

QT4

The test used to compute the PI is often part of a standard well test. The well is flowed at a number of different rates and the steady pressures measured. These values are used to make the plot .

Notes

The derivative plot is a very useful construction as it will give valuable information unseen on other plots. This is usually the first plot made in a modern well test to ensure all the objectives have been met, radial flow and flow barriers or other information have been acquired. In some complex cases a theoretical plot of the expected reservoir is made first. It is then compared to the actual results to better analyse the test.

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Derivative Plots

A method of identifying the straight line is to use not only the pressure and time but the derivative of the pressure as well

The straight line portion of radial flow appears as a horizontal straight line on a log-log derivative plot

In addition to identifying radial flow the derivative identifies reservoir geometry and some parameters.

The derivative for each situation is unique although the pressure profile may look identical.

The analysis of this these curves is called

Type curve analysis

Notes

There a very large number of possible geometry's and hence shapes for these plots. Some, although showing widely different properties are similar and have to be dealt with carefully. There is always enough difference for a full interpretation.

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Derivative Plot Uses

The plots show the different shapes of the pressure derivative curve with changing reservoir properties or geometry.

Using model libraries a more precise picture of the reservoir is obtained.

Notes

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Well test summary

Analysis of well tests for reservoir properties is done when the test has reached radial flow

Radial flow is occurring when there is a straight line on the plot of pressure versus a logarithmic time function

The straight line portion of the curve may be masked by early time effect

- skin and wellbore storage late time effects

- the pressure wave reaches a heterogeneity in the reservoir. This could be a fault, the reservoir boundary

Specialised analysis using MDH and Horner plots gives the required properties of the well and reservoir.

Well Test

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