Well Test Analysis

1

PCB 3013Well Test Analysis

Instructor:Prof. Dr. Mustafa Onur

Schlumberger Professorial ChairSchlumberger Professorial Chair

September 2013 Semester – PE Department UTP09 September -13 December 2013

Assistants (GAs) for the Course:• Mohamed Ali Hamid• Azeb Demisi Habte

General• Instructor: Mustafa Onur• Office: 16.03.04• Office Hours:

– Wednesday 9:00-11:00 am.

2

– Friday 9:00-11:00 am

• Phone: (05) 368-7099• E-mail: mustafa.onur@petronas.com.my• Course notes, handouts, homework, and test

solutions will be available at e-learning system.• HWs will be graded by the GAs.

AssessmentAssessment• Final Exam 40%• Course work 60%

Course work:» Test 1 (23 October 2013, 4-6 pm) 20%» Test 2 (11 December 2013, 4-6 pm) 20%» Assignment(5-10) 20%

Total 60%

General Remarks

• On each exam, you will be responsible forall material covered to that point in thecourse.

• The date of the final is fixed. It is possible,but unlikely that the times of the otherexams will be changed.

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General Remarks– There will be no makeup of tests. If you

miss a test, you will receive a zero on theexam. unless (i) you notify me prior to theexam that you will miss it and (ii) have amedical excuse that is supported by app yletter from a medical doctor.

– You cannot pass this course withouttaking the final exam.

– The University policy on attendance andcheating will be enforced.

Weekly Timetable

Course outlineWks Date Chapters Remarks

1-3 9 Sept. – 23 Sept. 1. Introduction & fundamental s (basic methodology , data and equation)

3-5 23 Sept – 07 Oct. 2. Drawdown , Buildup , Interference Tests

5-7 07 Oct. – 24 Oct. 3. Semilog and Type Curve Matching TEST 1

Mid -Semester Break (24-27 October)

7-9 28 Oct. -11 Nov. Superposition in Space (Linear Discountunities)

9-11 11 Nov. - 25 Nov.Superposition in Time (Buildup and Multi rate Testing)

11-13 25 Nov. – 09 Dec. Gas Well Testing

13-14 09 Dec. – 13 Dec.Other well tests and new advances (wire Line Formation Testing and complex well and reservoir systems

TEST 2

Study Week (14-18 December) and Exam Week (19-29 December)

References• Horne, R.N. (1995), Modern Well Test Analysis, Petroway

• L.P. Dake (1981), Fundamentals of Reservoir Engineering (Chapters 5-8).

• R. C. Eourlougher (1977), Advances in Well Test Analysis, SPE Monograph No. 5.Monograph No. 5.

• J. Lee, (1982), Well Testing, SPE, New York.• D. Bourdet (2002), Well Test Analysis: The Use of Advanced

Interpretation Models, Elsevier Science. • Kuchuk, F., Onur, M, Hollaender, F. (2010). Pressure Transient

Formation and Well Testing: Convolution, Deconvolution and Nonlinear Estimation, Elsevier, 2010.

• Medhat M. Kamal (Editor) (2009). SPE Monograph, Volume 23, Transient Well Testing,

Well Test Analysis

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Course Learning Outcomes

• Fundamental knowledge on well testing and its methodology.

• Knowledge of basic theory and physics

At the end of this course, the students will be equippedwith:

(including mathematical equations) describing pressure transient fluid flow in porous media and its applications.

• Basic knowledge on conventional and modern pressure transient analysis methods.

• Information needed on well test design to improve the students’ quantitative capabilities in solving reservoir engineering problems.

Introduction to Pressure Transient Test (PTT)

Instructional Objectives1. List 4 objectives of pressure transient

testing.

2. Understand the basic methodology of PTT interpretation and analysis

3. Define testing variables.

4. Be familiar with various fluid and rock properties of reservoir systems.

What Is A Pressure Transient Test?

• A pressure transient test is a field experiment, that is like any experiment, partially controlled.

• It cannot be repeated under the same conditions, but can be rerun using the results from earlier test (experiments)test (experiments).

• There are many ways to interpret pressure transient test data; There are many models with a set of parameters that may match the observed data, but there is only one correct and more than a few probable answers.

(Source: Kuchuk, Onur, Hollaender, 2010; Pressure Transient Formation and Well Testing)

What Is A PTT…?• A tool for well and reservoir evaluation and

characterization

– Investigates a much larger volume of the reservoir than cores or logsese o t a co es o ogs

– Provides estimate of porosity, permeability under in-situ conditions

– Provides estimates of near-wellbore condition– Provides estimates of distances to boundaries

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Primary Objective of PTT• is to obtain the productivity of a well and

properties of the formation from downhole and/or surface pressure and flow-rate measurements.

• The formation and reservoir information obtained from pressure transient measurements are essential (Why)– They reflect the in-situ dynamic

properties of the reservoir under realistic production/injection conditions.

How Is A PTT Conducted?

q

qq = 0

t

t

p

0

Some Definitions

The rate change at the surface or subsurface creates pressure diffusion (transient) in porous, but permeable formations. The pressure diffuses away from the wellboreThe pressure diffuses away from the wellbore deep into formation and contains (brings) information about the properties and characteristics of the reservoir.This process is traditionally called pressure transient well testing.

Pressure Diffusion Process-Limited Entry Well

Probe

Dual packer interval

t = 0.05 hour t = 0. 5 hour

Well Test Analysis

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Some Definitions (Cont’d)

• Drill Stem Testing (DST) is also part of pressure transient testing.

• Pressure transient tests are also d t d ith Wi li F ticonducted with Wireline Formation

Testers (WFT). Such tests are called wireline formation pressure transient tests.

• DSTs and WFTs are usually run in exploration and appraisal wells.

Well Testing vs. Formation Testing

• A well test may last from several days toseveral weeks and even months, and henceprovide information on reservoir over a largescale. Large volumes are produced/injected.

Both are subsets of PTT.

• On the other hand, WFTs refer to small scaletests with low flow rate and short duration (e.g.,from a few minutes to a few hours).

Both obey the same law of physics and cantheoretically be interpreted in the same way, butnote their scales are different.

Wireline Formation Testing Interval Pressure Transient Testing (IPTT)(MDT†)

Vertical 2 Vertical 2

Vertical 1

† Trade mark of Schlumberger.

SinkHorizontal

Vertical 110.3

2.3 ftDual-Packer 6.4

14.4Vertical 1

3.2

Allows determination of vertical continuityand horizontal and vertical permeability

Well Test Analysis

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IPTT

Vertical 2

Vertical 1

er 1

2

Probe 2

Probe 1

Dual-Packer zo1

zo2Vertical 1

hw

er 2

er 3

zo1

zo2

IPTT - Wireline Formation Testing • It provides dynamic in-situ information about discrete

permeability distribution (kh and kv) along thewellbore in the medium scale (1 foot to 100 ft).

• Identify and test possible barriers andIdentify and test possible barriers andfaults/fractures in the vertical directions (or in generalalong the wellbore axis).

• Provides information on the scale of a simulationgrid.

• Cost effective and no production to surface.

“Slug” and DST Tests DST Response

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Primary Objective of PTT• When pressure transient test data are

incorporated into with geoscience data such as geophysical, geological, core, log, etc., it considerably improves reservoir characterization.

• Particularly, when the long-term production data are not available for undeveloped reservoirs, it is necessary to complement the volumetric estimate of oil or gas in-place with long duration well tests to estimate well productivity and reservoir size before the optimization of the field development.

A Note on Scale

μm

H2O molecules

Earth to sun

mm cm m

Well Tests

core sample

Visible light

Well Logs

WFTs

10-10 10-7 10-6 10-5 10-4 10-3 1011107

Earth diameter

10-2 10-1 100 101 102 103

deepest sediment

wellbore diameter

pore sizes

vugs

Microscopic scale(Navier stokes and Poiseuille Equation)

Macroscopic scale(Darcy’s equation and continuum approach)

A Note on Scale… Reservoir Characterization

• It is a process of building (or coming up with) a reservoir simulation model including spatial variability of rock/fluid properties and boundaries that inegrates and satisfies allboundaries that inegrates and satisfies all sources of data available (static and dynamic data) to reduce gelogical uncertainties in performance predictions.

• The purpose is to define a well/reservoir model that honors both static and dynamic knowledge about the well/reservoir system.

Well Test Analysis

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Tools for Reservoir Characterization• Well/Formation/Reservoir Evaluation:

– Core Analysis/Petrophysics– Wireline Well Logs– Production Logging (Flowmeter)– Pressure Transient Formation and Well– Pressure Transient Formation and Well

Testing– Measurement While Drilling (MWD)– Borehole Geophysics

• Siesmics (2D, 3D, or even 4D)• Geostatistics (stochastic modeling)• Upscaling and Numerical Reservoir Simulation

Reservoir Characterization

Scale

Source: Tiab

Numerical Reservoir Simulation

F i PorositFacies Porosity

PermSw

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Numerical Reservoir SimulationReservoir Management Process

GeologicalData/Model

Geophysical Data/Model

Geochemical Data/Model

PetrophysicalData/Model

GeomechnanicalData/Model

FluidData/Model

Drilling

ProductionLogging Model

Tracer

Well TestModel

Integration

static data dynamic data

TracerModel

ProductionData

g

Well/Reservoir Model

upscaling

Numerical Simulation Model

Calibrated Simulation Model

Performance Prediction

history matching

Well Performance

Well Performance

Source: Gringarten (2007)

Well Performance/Production Optimization

Source: Gringarten (2007)

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Role of PTT in Reservoir Characterization

• PTT belongs to the dynamic part of the characterization process.

• The contribution of pressure transient testing is the well test interpretation model.

• This model is part of well and reservoir performance predictions.

How Is A PT Test Conducted?qq = 0

t

q

t

t

p

0

PTT Applications

• Exploration

• Reservoir engineeringg g

• Production engineering

PTT Objectives

• Define reservoir limits

• Estimate average drainage area pressure

• Characterize reservoir

• Diagnose productivity problems

• Evaluate stimulation treatment effectiveness

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Types of PTTq

Single-Well Multi-Well

Productivity Testing• The primary purpose of well testing is the

determination of the Productivity Index and the average reservoir pressure

– Used for designing tubulars and artificial lift systems.

Productivity Index• Productivity Index is a measure of the well's

ability to produce fluids under an imposed reservoir pressure drop.

J Productivity Index, STB/d/psi

Average pressure in drainage area, psia

Bottomhole flowing pressure, psia

Production rate, STB/day

( )wf

q tJ

p p=

−

( )tp( )tpwf

( )tq

Productivity Index• Function of many parameters

– Transmissibility, kh/μ– Storativity, φcth

“Ski ” d– “Skin” damage, s– Drainage area of the well, A– Reservoir and well geometry

Can we determine individual values of theseparameters?

Well Test Analysis

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Productivity Tests Productivity Tests[ ] scwfwfsc q

JppppJq 1−=⇒−=

Is Well A or B more productive?

Why is Well C exhibiting a curvedy gbehavior instead of straight-line?

Productivity Tests[ ] scwfwfsc q

JppppJq 1−=⇒−=

Is Well A or B more productive?

Why is Well C exhibiting a curvedy gbehavior instead of straight-line?

Oil Well Productivity Index• Single-phase flow of oil and partially

penetrating well (hp) in a homogeneous-isotropic system with thickness h:

kh1/ 2

2

( )141.2 4ln

wf

pA w p

khq p pB A hs s

e C r hγ

μ= −

⎡ ⎤⎛ ⎞⎢ ⎥+ +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

J

What could be the reason(s) for the well producing less?Is it due to skin, limited entry, or low permeability?

Well Test Analysis

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Gas Well Productivity Index• Single-phase flow of gas and limited entry

well (hp) in a homogeneous-isotropic system with thickness h:

What could be the reason(s) for the gas well producing less? Is non-Darcy flow significant?

J

( )

2 21/ 2

2

( )1422 4ln

wf

pA w w

khq p pT z A hs s Dq

e C r hγ

μ= −

⎡ ⎤⎛ ⎞⎢ ⎥+ + +⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

Limitations of Productivity Testing• Assumes stabilized flow conditions (steady state

or pseudo-steady state flow regimes to be discussed later).

• It does not allow us to determine individual values of parameters (kh, skin, limited entry skin, non-Darcy term, etc.)

• So, we need (actually transient) tests that allow individual values of parameters.

Skin Effect Skin EvaluationVertical well with gravel pack

Prior to acid operation

After acidizing

Well Test Analysis

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Skin EvaluationVertical well with gravel pack

1000 4300 6300

Drawdown Testing

Rat

eq,

STB

/D

q=0

q > 0

Bot

tom

-hol

e pr

essu

re, p

wf,

psi

q

time

time

t1

t1

Buildup Testing

Rat

eq,

STB

/D

q =0

q > 0

Bot

tom

-hol

e pr

essu

re p

wf,

psi

q

time

time

t1

t1

drawdown

buildup

Injection/Falloff Testing

Well Test Analysis

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Variable Rate Testing “Slug” and DST Tests

DST Response Multi-Well Testing

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Vertical Interference Testing

Allows determination of vertical continuity and horizontaland vertical permeability information.

Wireline Formation Testing (MDT†)

Vertical 2 Vertical 2

Vertical 1

† Trade mark of Schlumberger.

SinkHorizontal

Vertical 110.3

2.3 ftDual-Packer 6.4

14.4Vertical 1

3.2

Wireline Formation Testing (MDT†)

Vertical 2

Vertical 1

Layer 1

Layer 2

† Trade mark of Schlumberger.

Dual-Packer 6.4

14.4

3.2

aye

Layer 3

Wireline Formation Testing (MDT†)

h

Probelw

kh

kv

† Trade mark of Schlumberger.

Dual-Packer

h

zw

zo

θw

Well Test Analysis

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Summary on PTT Types…• In summary, a basic pressure transient

test consists of a production/injection rate change, during which the wellbore pressure is measured in general the d h l ddownhole, and

• Production is monitored (measured directly or in directly) either at the wellbore or surface, a subsequent buildup/falloff period during which the wellbore pressure is usually measured downhole.

Basic Steps of PTT Interpretation

• It involves three basic steps:

– Step 1: Model Identification– Step 2: Estimation of model parameters – Step 3: Validation of results

Interpretation Methodology of PTTs

• During a well test, a transient response is created by a temporary and controlled change in production rate.

• Then, the response (pressure, temperature and/or flow rate at bottom hole) of the well/reservoir system to changing production (or injection) is monitored.

• The response is, to a greater or lesser degree, characteristic of the properties of the well/reservoir sytsem and thus it is possible in many cases to infer well/reservoir parameters from the observed response.

Interpretation Methodology… • A Constant-Rate Drawdown-Buildup Sequence:

Rat

e, q

q > 0

RB

otto

m-h

ole

pres

sure

, pw

f, ps

i

q = 0

time

time

t1

t1

drawdown

buildup

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Interpretation Methodology…• Is to identify the “appropriate” interpretation model(s)

and obtain “reasonable” estimates of the formation (or reservoir) parameters of interest from indirect measurements of pressure and rate data.

• These estimates are defined in terms of a• These estimates are defined in terms of a mathematical well/reservoir model, derived based on simplified assumptions, yet from physical principles (conservation laws) governing the behavior of the system under observation.

• All monitored pressure transients in porous media are governed by some form of the diffusivity equationwith appropriate initial and boundary conditions.

Interpretation Methodology…• Pressure transient interpretation sequence is

applications of inverse/forward(direct) problems:

Real system ( S )I (rate-time)

O (observed pressure vs time)

Real system ( S )

Model (k, φ, s, etc)I (rate-time)

OM (model pressure vs time)

O ≈ OM

Matching

Forward and Inverse Problems• Inferring an interpretation model from an observed

response (or signal) is an application of inverseproblem.

• Once model is identified, estimating model parameter is application of both forward andparameter is application of both forward and inverse problems, depending on the estimation method used.

• Therefore, a mathematical (analytical/or numerical) model is required to estimate the model parameters from observed data. There are variety of models developed for pressure transient analysis.

STEP 1: Model Identification• Find a model SM which behaves in the same way

as the real system S given the input and output.

I S O OM should show thesame features of O

Inverse problemwith a non-uniquesolution

I SM OM

same features of O

To reduce non-uniqueness:-More test data: pressure/rate-Checking procedure on model-Consistency with geology, geophysics, petropyhsics, etc.

Well Test Analysis

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STEP 1: Model Identification…• Tools for Model Identification

– Pressure-Derivative signal based on superposition time

– Pressure-Derivative signal based onPressure Derivative signal based on deconvolution

• To reduce non-uniqueness:– More test data: pressure/rate– Checking procedure on model– Consistency with geology, geophysics,

petropyhsics, etc.

STEP 1: Model Identification…

(Taken from Schlumberger Modern Reservoir Testing book)

STEP 1: Model Identification…

(Taken from Schlumberger Modern Reservoir Testing book)

(a) Well (near sealing fault)producing in homogeneous-isotropic reservoir

(b) Well producing in a naturally fractured reservoir system.

STEP 2: Model Parameter Estimation• Adjust the parameters of the MODEL SM so that

OM matches O “quite well.”

I S OI S O

I SM OM

O ≈ OM

Direct or Inverse problem depending on the method as well as quality and span of the test data.

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STEP 2: MP Estimation…• Tools for Model P. Estimation

– Straight line methods (semilog, Cartesian plots, etc.)

– Type-curve matching based on Pressure and/or Pressure-Derivative responses

– Non-linear regresion• To reduce non-uniqueness:

– Calculated parameters should be very similar independent of the method (or tool) used.

STEP 2: MP Estimation…

Δp'

, p

si

102

Pressure change

Closed reservoir model

Time (h)

Δp

and

10-1

10-4 10-3 10-2 10-1 100 101 102

100

101

Infinite actingreservoir

model

ttest = 3 h.

Reservoir boundary has no effecton the responses

STEP 3: Validation of Results• Verify the consistency of the interpretation model

by:– matching with test observed data (log-log,

Horner, simulation)– matching results from other well testsatc g esu ts o ot e e tests– matching with other knowledge (geology,

petrophysics, cores, fluids, completion)– common sense (range of plausible parameter

values).– Inspect confidence intervals, correlation

coefficients, RMS errors if non-linear regression is used.

PTT Interpretation (Outer Loop)

(Source: Kuchuk, Onur, Hollaender, 2010)

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PTT Interpretation (Inner Loop)

(Source: Kuchuk, Onur, Hollaender, 2010)

PTT Interpretation ModelsNear WellboreEffects

Reservoir Behavior

Boundary Effects

Wellborestorage Infinite actingHomogeneous

SkinFractures

Limited Entry

Horizontal/slanted well

Early times

No-flow

Constantpressure

Leaky

Late timesMiddle times

Heterogeneous2-PorosityLayeredComposite

Remarks on Reducing Uncertainty in PTT

• We should always resort to other independent sources of information (geoscience data, drilling, logs, cores).

We should carefully design tests by taking into• We should carefully design tests by taking into consideration of flow rate history to be applied, accuracy and resolution of pressure gauges.

• Perform sensitivity studies prior to testing by performing forward runs with the appropriate model(s) for the system under consideration.

Pressure-Derivative

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Pressure-Derivative (P-D)• It was introduced in 1980 by Bourdet et. al

and has become a standard tool in PTT Interpretation since then.

• It helps identifying the appropriate model for the system under consideration and flow regimes.

• It also helps reducing non-uniquess in parameter estimation when it is used together with pressure.

• It magnifies the changes in pressure data so it is useful for diagnostic purposes.

Pressure-Derivative• It is defined as the rate of pressure change with

respect to natural logarithm of time.

( ) ( ) dtdp

tdt

tppdt

tdtppd

tdpdp wfwfiwfi −=

−=

−=

Δ=′Δ

))((ln

))((ln

)(

Why is it based on logarithm of time?What is the unit of pressure-derivative?

Pressure-Derivative-Example 1

102

Δp'

, p

si

Circular no-flowreservoir

10-4 10-3 10-2 10-1 100 101 10210-1

100

101

Time (h)

Δp

andΔ

Pressure-derivative

Pressure-Derivative-Example 2

ndΔ

p' ,

psi

102

103

1.0=ω

Δp

Time (h)

Δp

an

10-1

100

101

10-4 10-3 10-2 10-1 100 101 102

Naturally fractured reservoir (Warren-Root, λ =10-7)

01.0=ω

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Some Remarks on P-D• Unlike pressure, pressure-derivative is not

measured and has to computed by numerical differentiation of the measure pressured data with respect to time.

• Differentiation amplifies the noise in pressure• Differentiation amplifies the noise in pressure data. This often causes pressure-derivative data to oscillate wildly and complicate model identification and parameter estimation.

• To eliminate the oscillatory behavior, we often apply smoothing methods to pressure derivative.

P-D Computation• It is computed by numerical differentiation of

the measure pressured data with respect to time.

ΔpΔpj+1

t

Δpj

Δpj-1

lntj-1 lntj lntj+1

( ) ( )( ) ( )

( )( ) ( )

( )( ) ( )

2

11 11

1 1 1 1

11

1

1

1 1

ln /ln /

ln / ln / ln / ln /

ln /

ln / ln /

jj j jj j

j j j j j j j j

j j

j j j j

j j

j

t t tt t

t t t t t t t t

t t

p

pt t

pp

t

t

t

+−

−+

+ − − + −

+−

+ − +

′Δ − Δ Δ

Δ

= +

+

Bourdet method (2nd degree polynomial through successive three points)

P-D Computation…• Differentiation amplifies the noise in pressure

data. This often causes pressure-derivative data to oscillate wildly and complicate model identification and parameter estimation.Suppose we have equally spaced pressure dataSuppose we have equally spaced pressure data, containing uncorrelated noise with zero mean and constant standard deviation σp, and are using Bourdet method to generate pressure-derivative, then we can show that std. of noise in pressure derivative is:

1

ln constant < 1j

j

tL

t −

⎛ ⎞= =⎜ ⎟⎜ ⎟

⎝ ⎠

12d pL

σ σ=

Noise in derivative data will also be correlated, though noise in pressure is not, see SPE 71579

Effect of Noise on P-D

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A Catalogue of P-D: Flow RegimesLog-Log Plot

70.6 constan for radial ft lowh

qpk h

μ′Δ = = ⇒

PTT : A Signal Analysis-CR DD Log-log plot(Flow regime identification)

Specialized St. LineAnalysis (e.g., MDH)

PTT : A Signal Analysis-CR BU Log-log plot(Flow regime identification)

Horner Plot

A Summary of Straight Line Methods

Source: Gringarten (SPE 102079)

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Interpration of PTTs

• We attempt to recognize specific flow regimes exhibited (on log-log plot) thatregimes exhibited (on log log plot) that dominate the data behavior to identify the appropriate interpretation model.

Various Flow Regimes

Various Flow Regimes…

H (IARF) High conductivity fractureHomogeneous (IARF) High conductivity fracture

2-Porosity or Multilayer Composite or Multiphase Fluid

Various Flow Regimes…

Source: Gringarten (SPE 102079)

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Various Flow Regimes…

Source: Gringarten (SPE 102079)

History of PTT AnalysisDate Analysis Method Emphasis Identification Verification

50s Straight lines Homogeneous reservoir

Poor None

70s Pressure Type Curves

Near wellbore effects, 2-

porosity, fractured wells

Fair (limited) Fair to good

80 P H V d V d

Modified from Gringarten (SPE 102079)

80s Pressure Derivatives

Heterogoneous reservoirs and

boundaries

Very good Very good

90s Non-linear Regression

Computerizedanalysis, variable

rate tests, multilayer reservoirs

Very good Much better

00s Deconvolution Computerized analysis, enhance

radius of investigation

Much better Same as Derivative