Temperature Modelling and Real-time Flow Rate Allocation in Wells with Advanced Completion ...

210 Pages·2010·7.67 MB·English

Temperature Modelling and Real-time Flow Rate Allocation in Wells with
Advanced Completion

Khafiz Muradov
Submitted for the degree of Doctor of Philosophy

Heriot-Watt University
Institute of Petroleum Engineering
November 2010

The copyright in this thesis is owned by the author. Any quotation from the
thesis or use of any of the information contained in it must acknowledge
this thesis as the source of the quotation or information.
Abstract
The ability of advanced wells for downhole monitoring and zonal, fluid production
control in real time allows well control decisions to be implemented that optimize
current production and long-term recovery. Real-time monitoring of the downhole
pressure and temperature is a common practice. Interpretation of the consequent data
flow to locate influxes and quantify distributed as well as zonal, flow performance is an
important step towards a comprehensive well and field control strategy.
Temperature measurements have the potential to be as informative as pressure
measurements in reflecting the reservoir’s and the well’s production performance.
However, currently available tools are not applicable to inverse temperature modeling in
advanced completions.
The theoretical underpinning for a temperature data interpretation workflow is
provided in this thesis. Novel temperature models for steady state multiphase flow in
both wells with advanced completions and in the reservoirs are presented. This thesis
will show that they accurately reproduce the results of rigorous numerical simulators.
A group of direct methods for the quantitative interpretation of downhole pressure
and temperature measurements is proposed. The resulting workflow is capable of
providing both flow rate and phase composition profiles along the length of an
advanced well. Further, it is shown that a group of mathematical optimization
algorithms and a recursive filter can be used for the downhole multiphase soft-metering
in real-time.
The basis for the Temperature Transient Analysis has been formed for horizontal,
liquid producing wells. This task was treated as a multidimensional, heat transfer
problem. Both an asymptotic, early time, solution and an accurate, integral solution are
derived. The asymptotic, analytical solution is tested against a scientific, numerical
simulation software. The applicability and practical importance of the solution is
discussed.
The resulting rate allocation methodology has been tested on synthetic and real well
data. The examples illustrate how the comprehensive workflow proposed in this thesis
for the flow rate allocation in advanced wells can be practically applied.
Acknowledgements
It is a pleasure to thank those who made this thesis possible.
I owe my deepest gratitude to my supervisor Prof. David Davies for his patience,
guidance, and immense help with the research work presented here.
I am grateful to Profs Ken Sorbie and Michael Golan for their time and valuable
comments given during the thesis examination and correction phase.
I am heartily thankful to my colleagues: Faisal Al-Khelaiwi, Ivan Grebenkin, Yousef
Rafiei, Andrei Ryazanov, David Olowoleru, Andrei Scherbakov, Drs Vasily Birchenko,
Fajhan Al-Mutairi, Yang Qing, Oleksandr Ivakhnenko and George Aggrey for their
ideas, fruitful discussions and moral support throughout the study.
I thank the sponsors of the “Added Value from Intelligent Field & Well system
Technology'' JIP at Heriot-Watt University for the financial support and feedback. I am
especially grateful to Vidar Alstad, Line Skarsholt, Hugh Rees and Laurent Maho for
their comments and data provided for the research.
I gratefully acknowledge the Heriot-Watt University staff for continuous support
throughout this study.
I thank my wife, parents, and friends who were far, but remained close. I am deeply
indebted to my friends Ivan Valko and Dr. Alexander Abramov who helped me to start
this research project and continuously supported during its completion.
ACADEMIC REGISTRY
Research Thesis Submission

Name: Khafiz Muradov
School/PGI: Institute of Petroleum Engineering
Version: (i.e. First, Final Degree Sought PhD in Petroleum Engineering
Resubmission, Final) (Award and
Subject area)

Declaration

In accordance with the appropriate regulations I hereby submit my thesis and I declare that:

1) the thesis embodies the results of my own work and has been composed by myself
2) where appropriate, I have made acknowledgement of the work of others and have made reference to
work carried out in collaboration with other persons
3) the thesis is the correct version of the thesis for submission and is the same version as any electronic
versions submitted*.
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available for loan or photocopying and be available via the Institutional Repository, subject to such
conditions as the Librarian may require
5) I understand that as a student of the University I am required to abide by the Regulations of the
University and to conform to its discipline.

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Submitted By (name in capitals): KHAFIZ MURADOV

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Updated February 2008, November 2008, February 2009
Table of Contents
Abstract............................................................................................................................ii
Acknowledgements.........................................................................................................iii
Declaration Statement...................................................................................................iv
Table of Contents............................................................................................................v
Nomenclature.................................................................................................................ix
Abbreviations.................................................................................................................xi
Notations........................................................................................................................xii
Subscripts.......................................................................................................................xii
Publications by the Candidate....................................................................................xiii
Chapter 1: Introduction and Background...................................................................1
1.1 Introduction and Motivation.................................................................................1
1.2 Literature Review..................................................................................................2
1.2.1 Wells Equipped with Advanced Completions..............................................2
1.2.2 Monitoring in Intelligent Wells.....................................................................4
1.2.3 Fibre Optics Well Measurement (FOWM)...................................................6
1.2.4 Thermometry in Wellbores.........................................................................10
1.2.5 Temperature Modelling in Wellbores.........................................................16
1.2.6 Reservoir Temperature Modelling..............................................................22
1.2.7 Multiphase Soft-Sensing.............................................................................26
1.3 Thesis Outline.....................................................................................................29
Chapter 2: Calculation of Temperature Distribution in Wellbores of Advanced
Wells...............................................................................................................................30
2.1 Introduction.........................................................................................................30
2.2 Determination of Advanced Well Completion Components for Temperature
Calculation...................................................................................................................30
2.3 Construction of Temperature Model for Well Interval where Tubing and
Annulus are not Hydraulically Connected...................................................................31
2.3.1 Mass Balance Equation...............................................................................33
2.3.2 Total Energy Balance Equation..................................................................33
2.3.3 Derivation of Temperature Model for Well Interval without a
Tubing/Annulus Hydraulic Connection...................................................................33
2.3.4 Joule-Thomson Coefficient.........................................................................36
2.3.5 Solution: Temperature Model for the Well Interval...................................36
v
2.4 Heat Transfer and Inflow Fluid’s Temperature Calculations.............................38
2.4.1 Heat Transfer within Wellbore....................................................................38
2.4.2 Correlations Used for Convective Heat Transfer Coefficients Calculation40
2.4.3 Reservoir Performance................................................................................41
2.5 Temperature Calculation Downstream of a Flow Device...................................41
2.6 Calculation Algorithm.........................................................................................42
2.7 Case Studies........................................................................................................44
2.7.1 Case 1: Three-Zone Intelligent Producer with Non-Linear Geometry.......44
2.7.2 Case 2: Three-Zone Horizontal Intelligent Production Well......................48
2.8.1 Simulators...................................................................................................53
2.8.2 Conclusions from the Evaluation of Available Temperature Modelling
Tools 57
2.9 Summary and Conclusions..................................................................................58
Chapter 3: Reservoir Temperature Calculation for Steady State Flow Conditions
.........................................................................................................................................60
3.1 Introduction.........................................................................................................60
3.2 Calculation of Sandface Temperature.................................................................60
3.2.1 Problem Formulation..................................................................................61
3.2.2 Description of Heat Losses to the Surrounding Formation for Semi-steady
Heat Flow Regime....................................................................................................62
3.2.3 Sandface Temperature for Horizontal Well – General Solution for Liquid
Flow 66
3.2.4 Sandface Temperature for Horizontal Well – Asymptotic Solution for
Liquid Flow..............................................................................................................68
3.2.5 General Asymptotic View and Solution for Other Cases...........................69
3.2.6 Derivation of Temperature Change across the Reservoir Containing
Flowing Fluids..........................................................................................................71
3.2.7 Inclined Wells and Gas-Liquid Semi-steady State Flow............................73
3.3. Summary and Conclusions..............................................................................74
Chapter 4: Zonal Rate Allocation in Intelligent Wells..............................................75
4.1 Introduction.........................................................................................................75
4.2 Soft-Sensing of Zonal Rates in an Intelligent Well...............................................76
4.2.1 Problem Description and Models Applied......................................................76
4.2.2 Methods Used..................................................................................................78
4.2.3 Data Cleansing.................................................................................................81
v i
4.2.4 Example Cases.................................................................................................82
4.3 Rate Profiling.........................................................................................................93
4.3.1 Production Logging Data Analysis in a Well Prior to Completion.................95
4.3.2 Completed Well, One Phase Production.........................................................97
4.3.3 Completed Well, Two Phase Production.........................................................99
4.3.4 Additional Sources of Information................................................................101
4.3.5 ICD Inflow and Annular Flow Monitoring...................................................103
4.4 Discussion on the Robustness of the Presented Inverse Problem Solutions........104
4.5 Summary and Conclusions..................................................................................107
Chapter 5: Temperature Transient Analysis in a Horizontal, Liquid Producing
Well...............................................................................................................................109
5.1 Introduction..........................................................................................................109
5.2 Problem Description and Assumptions Made.....................................................110
5.2.1 Conditions......................................................................................................110
5.2.2 Assumptions..................................................................................................112
5.2.3 Dividing the problem into three....................................................................114
5.3 Analysis of Available Solutions for Closely Related (to the Sub-Problem 2.2)
Problems....................................................................................................................116
5.3.1 Description of Closely Related Problems and Their Adaptation to Our Case
................................................................................................................................116
5.3.2 Description of the Testing Model..................................................................127
5.3.3 Comparison and Discussion..........................................................................131
5.4 Asymptotic Analytical Solution and its Limitations...........................................135
5.4.1 Solution Derivations......................................................................................135
5.4.2 Complete Solution for the Liquid Producing Horizontal Well Temperature
Response during Draw-Down................................................................................155
5.5 Application of our Solution and its Practical Importance...................................158
5.5.1 Flow Conditions for the Temperature Transient Analysis............................158
5.5.2 Considerations on the Required Measurement System Capacity..................159
5.5.3 Discussion on the Basic Workflow for Temperature Transient Analysis.....162
5.5.4 Real Well Analysis Example.........................................................................164
5.6 Summary and Conclusions..................................................................................169
Chapter 6: Summary, Conclusions, Recommendations..........................................171
6.1 Summary and Conclusions................................................................................171
6.2 Recommendations for Further Study................................................................174
vi i
Bibliography................................................................................................................117059
Appendix A..................................................................................................................189
Appendix B..................................................................................................................119954

vi ii
Nomenclature
a volume element area
A reservoir area
b defined by equation B-10
c defined by equation B-11
C compressibility
C discharge coefficient
D
Cp mass heat capacity at constant pressure
C multiplier to exclude tubing temperature
position
C tubing-annular heat transfer coefficient, divided by annular rate
Uat
D hydraulic diameter
f heat flow
f Moody friction factor
Moody
g gravity acceleration constant
G observation error covariance matrix
H, h reservoir thickness
U heat transfer coefficient of a medium
h enthalpy of phase j per unit mass
j
h latent (transformation) enthalpy
lat
I unitary matrix
J Jacobian
k permeability
K thermal conductivity
~
K defined by equation B-12
K’ modified (specifically averaged) Joule-Thomson coefficient
JT
K Joule-Thomson coefficient
JT
L distance from well to reservoir boundary
N number of measurements
n unit vector in z direction
z
p pressure
q volumetric flow rate
Q heat flux per unit area
heat
q* defined by equation B-13
q’ defined by equation 191
R, r radius
R measurement covariance matrix
Ridc ideal gas constant
Rs solubility (in-situ)
s Laplace variable
S saturation (fraction)
T temperature
(cid:2)
T vertically averaged temperature
t time
U overall heat transfer coefficient
v velocity
V volume
(cid:2) Fourier variable
w mass flow rate
w’ mass inflow rate per unit well length
Y full reservoir distance
ix
y volume fraction of phase j
j
z z-factor (in the EOS)
(cid:2) correction term
(cid:3) thermal expansion coefficient
denominator, used to evaluate effect of interaction with
(cid:4) adjacent layers
(cid:5) fraction of casing area open for fluid inflow
(cid:5) unitary diagonal matrix ((cid:2) =1 if i=j; (cid:2) =0 if i!=j)
ij ij ij
(cid:6) roughness
(cid:6) measurement error
(cid:7) Heaviside step-function
(cid:7) nozzle efficiency
N
(cid:8) angle of well inclination from horizontal axis
(cid:9) damping parameter
(cid:10) dynamic viscosity
(cid:11) number of moles of a substance
(cid:12) density
(cid:13) temperature change T-Ti
(cid:14) porosity (fraction)
(cid:15) gas quality
x