well testing 1

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Well TestingModule #1: Introduction

Shahab Gerami, PhD

1


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Well Testing

Basic theory and current techniques for well testing

Introduction Review of basic fluid and rock properties

Basic definitions and concepts

Well Test Objectives

Components of Well Test Models

Characteristics of Inverse Solution

Mathematical Treatment of Reservoir Engineering Problems Fundamental of Fluid Flow in Porous Media

Flow Tests

Pressure Drawdown Test

Multi Rate Flow Testing

Effect of Wellbore Condition

Build up tests Derivative Analysis

Fractured Wells

Naturally Fractured Reservoirs

Gas Well Testing

Test Design and Implementation


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References

John Lee, Well Testing (1982)

C. S. Matthews and D. G. Russell, Pressure Buildup and Flow Test in Wells(1967)

Robert Earlougher, Advances in Well Test Analysis (1977)

Canadian Energy Resources Conservation Board, Theory and Practice of theTesting of Gas Wells (1975)

Roland Horn, Modern Well Test Analysis (1995)

Selected papers from SPE journals and symposium proceedings


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Well TestingBasic theory and current techniques for well testing

Introduction

Review of basic fluid and rock properties

Basic definitions and concepts

Well test objectives

Reservoir management

Reservoir description

Decline curve analysis

Types of tests Drawdown test

Buildup test

Falloff test

Interference tests

Primary reservoir characteristics

Components of well test models

Direct & inverse solutions Input-system-response

Characteristics of inverse solution

Importance of analytical models

Mathematical treatment of reservoir engineering problems


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Economic Study and

Decision Making for the

Field Development

Reservoir

Information

Production Forecast

Field Data (i) Well test data

(ii) Production data

Predictive Models

(forward solution)

Production

Analysis Models(backward solution)

(i) Well test models

(ii) Material balance models

(iii) Decline curve analysis

0

50

100

150

200

250

300

350

0 100 200 300 400 500 6 00 700 800

Time (day)

Rate(MSCFD)

0

50

100

150

200

250

300

350

Pressure(psia)

Gas rate Wellbore pressure

Importance of Production Data Analysis

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Review of Basic Rock And Fluid Properties

The units of B are bbl/STB for oil and

water, and ft3/scf for gas


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This is the value of the oil viscosity at RESERVOIR

CONDITIONS. It is a very strong function of reservoir temperature,

oil gravityandsolution gas-oil ratio.

Below the bubble point pressure, the amount of gas dissolved in

the oil increases as the pressure is increased. This causes the in-situ oil viscosity to decrease significantly. Above the bubble point

pressure, oil viscosity increases minimally with increasing

pressure.


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The pressure difference between overburden and internal pore pressure isreferred to as the effective overburden pressure. During pressure depletion

operations, the internal pore pressure decreases and, therefore, the effective

overburden pressure increases. This increase causes the following effects:

The bulk volume of the reservoir rock is reduced.

Sand grains within the pore spaces expand.


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Basic Definition & Concepts

Test:Measurement of (i) Rate, (ii) Time, and (iii) Pressure in controlled conditions.

Homogeneous formation:Formation with rock properties that do not change withlocation in the reservoir. This ideal never actually occurs, but many formations are

close enough to this situation that they can be considered homogeneous. Most of the

models used for pressure-transient analysis assume the reservoir is homogeneous.

Heterogeneous formation:Formation with rock properties changing with location in

the reservoir. Some naturally fractured reservoirs are heterogeneous formations.

Isotropic formation:A type of formation whose rock properties are the same in all

directions. Although this never actually occurs, fluid flow in rocks approximates this

situation closely enough to consider certain formations isotropic.

Anisotropic formation:A formation with directionally dependent properties. Themost common directionally dependent properties are permeability and stress. Most

formations have vertical to horizontal permeability anisotropy with vertical

permeability being much less (often an order of magnitude less) than horizontal

permeability.


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Basic Definitions & Concepts

Initial reservoir pressure: Reservoir pressure before any production

Average reservoir pressure: The pressure that would be obtained if all fluidmotion ceases in a given volume of reservoir. It also is the pressure to which a wellwill ultimately rise if shut in for an infinite period.

Flowing pressure: The pressure determined at the formation face during theflowing periods of a well test.

Static pressure:The pressure measured in a well after the well has been closed infor a period of time, often after 24 or 72 hours. When a reservoir is first discovered,the static pressure equals the initial pressure. After production begins, the staticpressure approaches the average reservoir pressure.

Drainage area: If a well is flowed until boundary-dominated flow has been reached,a certain area will experience a pressure drop. This area is called the Drainage

Area of a well. The boundaries of a wells drainage area could be physicalboundaries, such as faults, or no-flow boundaries from nearby producing wells.

Partial Penetration: When a well does not fully penetrate the formation, or theperforations do not open up the whole formation, the reservoir fluid has to flowvertically and the flow lines converge near the wellbore.


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Net Pay: This is the thickness of the formation that contributes to the flow of fluids. It is

determined from logs or core, and can be different from the gross pay or the perforated

interval. In the case of inclined wellbores in dipping formations, the net payis measured

perpendicular to the angle of dip. Several examples of net pay are shown below.

Basic Definitions & Concepts


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The Objectives of Well Test

Reservoir evaluation Deliverability (conductivity; kh)

Design of well spacing

Number of wells

Wellbore stimulation

Properties (initial reservoir pressure ) Potential energy of the reservoir Size (reservoir limits)

Closed or open (with aquifer support) reservoir boundaries

Near well conditions (skin, storage and turbulence)

Reservoir management

Monitoring performance and well conditions

Reservoir description Fault, Barriers

Estimation of bulk reservoir properties

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Types of Test

Type of tests is governed by the test objective.

Transient tests which are relatively short term tests are used to define

reservoir characteristics.

Drawdown Test

Buildup Test

Injection Test Falloff Test

Interference Test

Drill Stem Test

Stabilized tests which are relatively long duration tests are used to define

long term production performance.

Reservoir limit test

AOF (single point and multi point)

IPR (Inflow Performance Relationship)

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Types of Test-Drawdown Test

Conditions An static, stable and shut-in is opened to flow .

flow rate is supposed to be constant (for using

traditional analysis).

Objective

To obtain average permeability of thereservoir rock within the drainage area of the

well

To assess the degree of damage or stimulation

To obtain pore volume of the reservoir

To detect reservoir inhomoginiety within the

drainage area of the well.

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Types of Test-Buildup Test

Conditions

A well which is already flowing (ideally constant

rate) is shut-in

Downhole pressure measured as the pressure

builds up

Objective To obtain average permeability of the reservoir

rock within the drainage area of the well

To assess the degree of damage or stimulation

To obtain initial reservoir pressure during the

transient state To obtain the average reservoir pressure over the

drainage area of the well during pseudo-steady

state

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Types of Test-Injection Test

Conditions

An injection test is conceptually identical to a

drawdown test, except flow is into the well rather

than out of it.

Objective

Injection well testing has its application in water

flooding, pressure maintenance by water or gas

injection, gas recycling and EOR operations.

In most cases the objective of the injection test is

the same as those of production test (k,S,Pavg). Determination of reservoir heterogeneity and

front tracing.

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Types of Test-Fall off Test

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A pressure falloff test is usually proceeded by an injectivity test of a long

duration. Injection then is stopped while recording the pressure. Thus, the

pressure falloff test is similar to the pressure buildup test.

As with injection test, falloff test, interpretation is more difficult if the

injected fluid is different from the original reservoir fluid.


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Types of Test

Falloff Test:

A pressure falloff test is usually proceeded by an injectivity test of a long

duration. Injection then is stopped while recording the pressure. Thus, thepressure falloff test is similar to the pressure buildup test.

Interference Test:

In an interference test one well is produced and pressure is observed in a

different wells.

To test reservoir continuity To detect directional permeability and other major reservoir heterogeneity

Determination of reservoir volume

Drill Stem Test (DST):

It is a test commonly used to test a newly drilled well (since it can only be

carried out while a rig is over the hole. In a DST, the well is opened to flow by a valve at the base of the test tool, and

reservoir fluid flows up the drill string.

Analysis of the DST requires the special techniques, since the flow rate is not

constant as the fluid rises in the drill string.

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Primary reservoir characteristics

Types of fluids in the reservoir

Incompressible fluids

Slightly compressible fluids

Compressible fluids

Flow regimes

Steady-state flow

Unsteady-state flow Pseudosteady-state flow

Reservoir geometry

Radial flow

Linear flow

Spherical and hemispherical flow Number of flowing fluids in the reservoir.

Single-phase flow (oil, water, or gas)

Two-phase flow (oilwater, oilgas, or gaswater)

Three-phase flow (oil, water, and gas)

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Flow Regimes

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Reservoir Flow Geometry

Hemisph erical f lowSpherical f low

Radial f low

Linear flow

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Components of Well Test Models

Well

Reservoir

Boundaries

Direction (Vertical, Horizontal)Storage (Constant, Changing)

Completion (Damaged, Fractured and Acidized)

HomogeneousHeterogeneous

Composite

Multilayer

Dual porosity

Flow boundaries (No flow, Constant pressure, infinite)

Geometrical boundaries (Circular, Rectangular)29


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Direct versus Inverse Solutions

Input system+ Output (?)

Direct solution

Inverse solution

Input System (?)+ Output

Example of a simple systemActual measurement compared

to the system

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Inverse Solution Compared to Actual System

Inverse solution can be used for theidentification of system characteristics

Inverse solution can result in grossly

erroneous answers

Whereas the mathematics is correct, the

utility of the results derived from this

mathematically process is questionable.


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Characteristic of Inverse Solution

Non-unique solution (the inverse

solution has its limitation)

A good looking history match is not a

good enough answer

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Input-System-Response

Reservoir

Mechanism

Mathematical Model

Input Perturbation Output Response

Model Input Model Output

Well test interpretation is essentially an inverseproblem and in general is better

suited to analytical solution.


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The objective of well test analysis is to describe an unknown system S ( well +

reservoir) by indirect measurement ( Oa pressure response to Ia change of rate).

I f A l i l M d l


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Importance of Analytical Models

Focus on the main issues

Create a conceptual analysis Pattern recognition and better understanding

Judgment( cause and effect)

Consistency checks

Groups that control response

Newton'slawofcooling

0@0

0

tTT

dt

dTVcTThA

p

t

Vc

hATTTT

pexp0

T

)(tT


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Mathematical Treatment of Reservoir

Engineering Problems

In the development and application well testing analysis techniques,the preliminary aim is to come up with some practical methodswhich will enable the engineer in gathering accurate informationabout some physical reservoir parameters that play an importantrole on fluid flow dynamics in porous media.

A properly developed mathematical formulation is a critical facet ofthe methodology that will be used in interpretation.

Although the mathematics involved is relatively simple and

straightforward, a good understanding of the mathematical basistogether with the physical laws that control the dynamics of fluid flowis essential.


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Mathematical Treatment of Reservoir

Engineering Problems

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Physical model

Simplifying assumptions

Mathematical model

Choosing an appropriate element

Governing equation Mass balance

Momentum balance (Darcys law)

Equation of state

Initial and Boundary conditions

Infinite acting

Finite acting

Solutions

Application


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rw re

pw

Physical model

Simplifying assumptions

Single phase fluid flow

Fluid has a small compressibilityDarcys law applies

Flow is radial towards the wellbore

Rock and fluid properties are constant

1-D Radial Steady State Flow

pe

q

A bilit i i


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Average permeability in a region

Not

Permeability at a fixed radius

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Drainage area: The reservoir area or volume drained by the well.

Mathematical model Steady State Radial Flow


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Mathematical model Steady State, Radial Flow

Choosing an appropriate element

Governing equation

0OutputInput

0 rrr

vAvA

r

pkv

Darcys law

)(expbb

ppc

Equation of state

0

rrr r

pkA

r

pkA

01

r

pr

rr

k

....

r

dr

dpkA

dr

d

dr

dpkA

dr

dpkA

rrrr

Mass balance


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01

r

pr

rr

pr

rr

k

01

r

pr

rr

pr

r

p

pr

p

V

Vpc

11

01

r

pr

rr

pr

r

p

pr

0

2

r

pr

rr

pcr

0

r

pr

r

Negligible

01

2

2

r

p

rr

p

Governing equation

or


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Initial condition

wi rrtpp ,0,

wfr pp w

er pp

e

Boundary conditions

Solution

21 )ln( CrCp 1C

dr

dpr

)ln(

1

w

e

we

r

rppC )ln(

)ln(2 w

w

e

we

w r

r

rpppC


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)ln(

)ln(

)(w

w

e

we

wr

r

r

r

ppprp

Solution

r

r

r

pp

dr

dp

w

e

we 1

)ln(

wrdr

dphkrq 2

)ln(

2

w

e

we

r

r

pphkq

r

A i #1


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Assignment#1

Considering the flow of a slightly compressible oil (co) in a

constant cross section homogeneous porous medium with constantporosity, permeability and no initial water saturation (Swi=0) (see

the below figure)

1. Derive the governing equation (hydraulic diffusivity equation) for

one dimensional linear flow (X-direction)?

2. Obtain the solution to the above governing equation subjected tothe following conditions

Steady state flow

Constant pressure (pL) at X=L

Constant pressure (p0) at X=0

pLp0

q

well testing 1

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