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ISBN 10: 1593702310
ISBN 13: 978-1593702311
Author: George Stewart
Petroleum engineers face the daily challenges of designing and testing wells. Finding the right technical data guide for conducting these tasks can be daunting, and so renowned petroleum engineer George Stewart has written the comprehensive volume Well Test Design & Analysis, filled with advanced information unparalleled on a variety of wellbore topics. From ascertaining accurate reservoir descriptions, to the intricacies of designing a horizontal well program, the author covers every topic in detail. The volume includes a CD containing chapters 16 – 20.
Table of contents:
Chapter 1. Pressure Transient Analysis in Drawdown and Buildup
Background to Transient Pressure Analysis
Introduction
Development of pressure testing.
Exploration well testing.
Radial Flow Theory..
The basic flow equations..
Fluid of constant compressibility
Further development of the accumulation term.
Linearization of the radial flow equation..
Initial and boundary conditions
Dimensionless form of the diffusivity equation
The line source analytical solution in an infinite reservoir.
Wellbore damage and improvement effects
Analytical solution for the case of a bounded circular reservoir.
Analytical solution for a constant pressure outer boundary
SPE field units..
The depth of investigation and radius of drainage.
The dynamics of reservoir pressure response.
Pressure Drawdown Testing..
Introduction
Pressure drawdown analysis in infinite-acting reservoirs.
The Principle of Superposition.
Introduction
Multiple-well situations
Variable rate situations
Pressure Build-up Testing.
Introduction
Pressure buildup test analysis during the infinite-acting period.
After production..
Determination of reservoir parameters
Impulse test in a tight reservoir..
Peaceman probe radius..
Transient productivity index, Jt.
Notes……..
Chapter 2. Wellbore Storage and Type Curve Matching
Wellbore Storage..
Introduction
Liquid-filled wellbore
Early time behavior of a well with storage
Practical use of the wellbore storage calculation
Solutions to the diffusivity equation in Laplace space.
The Stehfest algorithm
Well with storage and skin
Type Curve Matching
Introduction
Log-log type curve
Type curve based on t₁/CD…
Type Curve Matching using the Pressure Derivative.
Derivative analysis
Middle time region (MTR) derivative match
t₁/CD type curve including the derivative
Finite wellbore radius solution.
Analysis of Buildup Responses-The Producing Time Effect..
Equivalent drawdown time..
Desuperposition
Nonideal Wellbore Storage..
Introduction
Gas phase redistribution.
Empirical models of nonideal wellbore storage
Rising liquid level..
Downhole shut-in tools..
Falling liquid level in water injection wells
Numerical wellbore simulator.
Well Cleanup and Changing Skin
Theory
Field examples..
Notes.
Chapter 3. Semi-Infinite System Late Transient Analysis
Introduction to Fault Detection..
Drawdown Analysis in the Case of a Single Linear Discontinuity.
Hemiradial flow
Build-up Analysis in the Case of a Single No-flow Boundary
Perturbed radial cylindrical buildup..
Radius of investigation in build-up testing
..
Reservoirs with Multiple No-flow Boundaries
Elementary Fault Systems..
Constant Rate Drawdown Theory for Semi-infinite Systems.
Analysis Methods for Constant Rate Drawdown (CRD) Tests.
t/L, derivative type curve…
Constant Rate Build-up (CRB) Theory for Semi-infinite Systems.
Optimum form of build-up derivative presentation
Field Examples..
North Sea example-Oseberg Field
Partially Communicating Faults ( PCFs).
Introduction
Active well response
Linear composite system
Finite element method (FEM) numerical simulation of a PCF
Observation well response.
Linear composite system
Homogeneous system
PCF in a channel reservoir.
Pulse testing
Notes…
Chapter 4. Well in a Bounded Drainage Area
Reservoir Limit Testing.
Introduction
Average reservoir pressure.
Dietz semi-steady-state shape factors
Full analytical solution..
Semi-steady-state depletion and reservoir limit testing.
Analysis of a reservoir limit test
Pressure Build-up Analysis in Bounded Systems
Introduction
Conditions for applicability of Horner analysis
Determination of the skin factor.
Matthews, Brons, and Hazebroek (MBH) method
Extended drawdown test with intermittent buildups
Reservoir monitoring
Concept of Synthetic Flowing Time
Single well in a closed compartment
Multiple well situations.
Synthetic test problem..
Developed Reservoir Effects -Slider’s Method
Introduction
North Sea field example
Libyan field example
Determination of average pressure p
Interference testing
Notes.
Chapter 5. Variable Rate Well Test Analysis
Introduction
Step Rate Flow Schedule.
General superposition formula for step rate flow schedule.
Infinite-acting Radial-cylindrical Flow..
Drawdown theory
Drawdown superposition time function
Variable rate drawdown (VRD) semilog plot
Simplified variable rate analysis.
Build-up theory
Evaluation of the skin factor S.
Analysis of a Variable Surface Rate Buildup Using Drawdown Type Curve.
Introduction
Synthetic afterflow deconvolution
Generalized Superposition Methods
Derivative diagnostic and type curve matching
Desuperposition and the Role of the Extrapolated Pressure
Time Transformation for Variable Properties.
Superposition with a non-Darcy skin effect
Superposition Theory for Linear Flow
Linear flow (root of time) derivative..
Variable Rate Extended Drawdown Testing.
Bounded system behavior.
Approximate deconvolution.
Effect of build-up periods..
Filtering for material balance studies
Pseudopressure and pseudotime transformation..
Field example of an extended draw-down test
Further synthetic example
Permanent downhole gauges (PDGs).
Afterflow Measurement and Convolution.
Introduction
Field example of afterflow convolution
Slug Testing, Closed Chamber Testing, and Pumping Well Buildups
Slug testing
Slug test analytical solution
Build-up analysis following variable rate drawdown.
Integral method for the slug test flow period
Russian field example
Multiple slug test periods.
Application to coal bed methane.
Closed chamber test
Stress-dependent permeability
Notes…
Chapter 6. Channel Sands and Parallel Faults
Introduction
Parallel Boundary Systems
Constant rate drawdown (CRD) in a semi-infinite system.
Constant rate buildup (CRB)
Related systems..
Offset well positions
Linear flow derivative
Bounded Rectangle
Constant rate drawdown
..
Synthetic example
Semi-steady-state depletion..
Constant Rate Buildup in a Closed Rectangle..
Build-up theory for rectangular systems.
Desuperposition analysis
Use of the semi-infinite-acting time in build-up analysis.
Matthews, Brons, and Hazebroek (MBH) method
Detection of a closed system
Amplified treatment of the extrapolated pressure.
Depletion in a Channel System
Fluvial Systems
Sequence stratigraphy..
Bilinear flow
Geostatistics
Constant-Pressure Boundary.
Well Test Design..
Notes.
Chapter 7. Constant Pressure Boundaries
Constant-pressure Upper or Lower Boundary
Introduction
Theory
General derivative-type curve for a limited entry
Steady-state productivity
Depth of investigation with a constant-pressure boundary.
Analysis of the drawdown behavior
The effect of wellbore storage
Miller-Dyes-Hutchison (MDH) Method
Determination of reservoir
pressure.
Infinite-acting radial flow…
Field Examples..
Single Vertical Constant-pressure Boundary
Non-intersecting vertical fracture..
Notes….
Chapter 8. Vertically Fractured Wells
Introduction
Uniform Flux and Infinite Conductivity Fractures.
Introduction
Linear flow theory
Constant rate solution-uniform flux case
Constant rate solution-infinite conductivity case
Linear Flow Theory
Pseudoradial flow
Semi-steady-state (SSS) productivity index.
Effect of wellbore storage
Type Curve Analysis
Effect of fracture face skin
Semilog analysis
Analysis of Build-up or Fall-off Tests
Specialized plots for buildup
Desuperposition..
Generalized superposition plot.
Automatic matching or nonlinear parameter estimation.
Iranian field example of an acidized well.
North Sea field example
Limited height fracture.
Finite Conductivity Hydraulic Fractures
Finite conductivity fracture p, function.
Bilinear flow regime..
Pseudolinear flow..
Pseudoradial flow
Type curve matching.
Permeability from prefracture test
Transient and SSS production.
Layered systems
Bilinear Flow with Fracture Face Skin and Well-bore Storage.
Pseudolinear flow..
Nonintersecting (Distant) Fracture.
Notes.
Chapter 9. Dual Porosity Systems
Introduction
Models of Dual Porosity Systems.
Radial diffusivity equation for the fracture system
Dimensionless groups.
Material balance equation for the matrix system..
Pseudo-semi-steady-state analysis
Dimensionless interporosity flow parameter
Warren and root PSSS dual porosity model
Transient interporosity flow model
Two-layer systems
General Solution to the Double Porosity Diffusivity Equation
Wellbore storage and skin…
Model Pressure Responses
Behavior of the PSSS dual porosity model.
Behavior of the transient dual porosity model
Effect of wellbore storage and skin
Analysis Methods.
Constant rate drawdown-semilog plot
Constant rate buildup (CRB) analysis.
Well test analysis for dual porosity systems
Automatic matching
Fracture Network Theory.
Iranian Field Examples
Well Q-18.
Well X-33T1
Radial Composite Behavior
Notes..
Chapter 10. Limited Entry and Double Permeability Systems
Well with Limited Entry or Partial Penetration
Introduction
Drawdown behavior of partially penetrating wells
Effects of Wellbore Storage..
Analysis of early time response using type curve matching.
Analytical solution.
Derivative type curve match
Determination of vertical permeability
Negative skin case
Spherical flow theory..
Double Permeability Model
Introduction
Limiting form of the dual permeability model
Aquifer support
Double permeability behavior
Analytical Solutions in Laplace Space.
Case II-Only One Layer Perforated
Case II-Fundamental (constant-rate) active layer response.
Well test interpretation
Murchison field..
Vertical Interference Testing
Observation layer response
Effect of wellbore storage
Vertical Interference Testing Field Data.
CDA Type Curve
Simulation of vertical interference tests.
Field examples ..
Conclusions
Shale Lens Model
Notes.
Chapter 11. Radial Composite Systems
Radial Composite Systems
Introduction
Fundamental response
Derivative type curves..
Build-up behavior..
Aquifer influx
Gas block and liquid condensate dropout.
Unfavorable displacement situations
Negative skin situation
Geological setting for the radial composite model
Formation damage as a radial composite.
Radial Composite with a Closed Outer Boundary
Thermally Induced Fracturing (TIF)..
Introduction
Rock mechanics of thermal fracturing.
Simplified model of equilibrium fracture half length
Interpretation of pressure injection and fall-off tests
Step-rate test (SRT)
Fall-off Tests in Water Injection Wells-Effect of Saturation Profile
Displacement theory
Determination of mobility profiles.
Determination of flood front radius, rff
Average pressure of inner region.
Fall-off Tests in Gas Injection Wells
Notes…
Chapter 12. Horizontal Wells
Introduction
Flow Regimes.
Vertical radial flow.
Effect of anisotropy
Anisotropic parallel boundary solution
Fractured well solution
Horizontal pseudo-radial flow.
General Solution for a Horizontal Well
Derivative type curve..
Acidized horizontal wells
Strip source solution
Evaluation of the Green’s function solution
Pseudo-radial flow regime skin factor
Vertical lateral boundaries
Analysis Methods Based on Specialist Plots
Early time analysis-infinite-acting radial flow
Derivative analysis..
Hemiradial vertical flow
Intermediate time analysis-linear flow regime.
Late time analysis-horizontal pseudo-radial flow
Build-up analysis
Transient Deliverability.
Constant-pressure Boundary
.
Layered Commingled Systems.
Theory of a near-horizontal well penetrating several layers..
Synthetic example
Horizontal multilateral wells
Effect of Lateral Boundaries.
Closed systems
Dietz shape factors (CA)
Highly Deviated (Slant) Wells
Hydraulically Fractured Horizontal Wells.
Sinusoidal Wells
Radial Composite Behavior
Notes.
Chapter 13. Gas Well Testing
Theory of Gas Well Testing..
Introduction
Linearization of the radial flow equation for a real gas.
Constant-rate inner boundary condition.
Detection of depletion..
Analysis Methods..
Constant Rate Drawdown (CRD) analysis..
Gas well field units.
Constant rate buildup (CRB) analysis.
Real gas pseudo-time ta..
Wellbore Storage in Gas Wells..
Application of Agarwal pseudo-time transformation
Very low permeability reservoirs.
Determination of rate-dependent skin coefficient D.
Gas Reservoir Limit Testing.
Behavior of a closed gas reservoir..
Pseudo-time based on average pressure
Reservoir limit test..
Variable (step) rate case
Semi-steady-state gas well deliverability
Simulated extended drawdown.
Analytic simulation option.
Step-rate Transient (SRT) Test.
Methodology and test objectives.
Variable rate drawdown (VRD) plot for gas wells
Prediction of the SSS deliverability of development wells
North Sea gas well test field example.
Design of Step-rate Tests…
Isochronal Testing and its Limitations.
Reserves Proven by a Gas Well Test
Notes.
Chapter 14. Automatic Model Matching
Introduction
Structure of fundamental (CSFR) PD functions or models.
Interpretation methodology…
Storage and interrogation of tabulated dimensionless responses
Real-time Convolution
Introduction
Ideal wellbore storage and skin
Nonideal wellbore storage
Time-dependent skin and wellbore storage coefficient.
Application to gas wells.
Automatic Matching
Nonlinear regression
Model selection
Selection of data points..
Advantages and disadvantages of nonlinear regression
Production Analysis: Prediction of Production Decline
Transient deliverability
Fractured well example..
Fetkovich approximation
Semi-steady-state depletion..
Closed system p, functions
iv
Notes …
Chapter 15. Two Cell Compartmentalized Systems
Extended Drawdown Behavior.
Period of negligible support……
Time to reach total system semi-steady-state..
Dimensionless form of the material balance support
Superposition of material balance effect in a closed system
Late time drawdown derivative type curve.
Analysis methods on the Cartesian graph.
Extended Build-up Behavior…
Derivative diagnostic.
Exponential approach region.
Analysis of transient and semi-infinite-acting period
Build-up analysis by desuperposition..
Build-up derivative type curve.
Synthetic Example
Total System Productivity Index
Effect of a Poor Cement Bond
Reservoir Engineering Aspects of Compartmentalization.
Field Examples..
Further Field Examples
Katnook field..
Middle East carbonate..
Notes.
The following chapters are on the accompanying CD-ROM.
Chapter 16. Well Test Design
Introduction
Background to test design
Permeability estimate
Review of seismic data..
Decision to Test or Not.
Objectives of the Test.
General objectives
Skin cleanup
Enhanced objectives
Obtaining a permeability estimate
Completion design..
Forecasting of development well deliverability.
Estimation of accessible hydrocarbon
Tubing diameter selection
Design Criteria
Based on the depth of investigation
Based on the duration of the wellbore storage effect.
Wireline shut-in tools (SITs)
Based on the removal of tidal effects
Low-permeability systems
Incorporation of production logging
Role of Simulation in Test Design.
Application of a nodal analysis package..
Role of analytical well test simulation
Gauge selection and location.
Permanent downhole gauges.
Special Considerations for Gas Wells.
Classification of gas reservoirs.
Step-rate test design.
Design calculations related to wellbore storage
Role of analytical simulation
Rate control
Problem of well cleanup
Turner critical velocity
Example gas well test design
Estimation of reserves.
First gas well field example..
Second gas well field example
Fractured wells
Limitation on test rate due to environmental considerations
Wellhead temperature constraints
Compositional simulation
Extremely high permeability
Testing of the completion.
Testing of gas condensate wells.
Modern DST Testing Systems
Separator selection..
Multiphase flow measurement
Fluid disposal
Notes.
Chapter 17. Multiphase Flow
Introduction
Linearization of the Continuity Equation
Steady-state two-phase pseudopressure
Radius of drainage
Pseudopressure integrals
Diffusivity Equation in Terms Of Two-Phase Pseudopressure
Two-phase compressibility and pseudotime.
Two-phase material balance.
Analytical Solutions to the Linearized System
Case where the reservoir pressure is above the dew point.
Analytical solutions in terms of two-phase pseudopressure
Comparison with numerical simulation results.
Gas condensate well test methodology
Reservoir pressure below the dew point
Generation with a Pressure-dependent Viscosity Compressibility Product..
Sampling in Gas Condensate Systems.
Theory of Perrine and Martin
Steady-state pseudopressure for solution gas drive.
Transient flow in solution gas drive
Semi-steady-state depletion..
Build-up analysis in solution gas drive.
Case Studies..
Arun field.
Cupiagua field..
North Rankine field.
Britannia field
Non-Darcy Flow in Gas Condensate Well Tests.
Raghavan et al. Field Examples
Numerical Simulation of Gas Condensate Well Tests.
Barrios and Osorio studies..
Role of compositional modeling
Notes..
Chapter 18. Numerical Well Testing
Numerical Techniques..
Introduction
The finite element method..
Interaction of Geological Modeling and Well Test Interpretation
Introduction
Heriot-Watt fluvial reservoir project
Geoskin concept……
Geological Object Framework.
Introduction
Captain horizontal well
Dual permeability with a horizontal well.
Nonintersecting fracture situations
Shale lens problem.
Stacked channels
Makassar Strait deepwater fields..
EPS derivative fingerprint library
Multiple fault example..
Compartmentalized field example
Conditional Simulation..
Interference Testing.
Introduction
Dual permeability situations
Vertical sealing faults with windows.
Conclusions..
Notes.
Chapter 19. Layered Well Testing
Introduction
Direct measurement of layer pressures
Well testing objectives.
Integration of well test interpretation and core analysis.
Commingled systems with horizontal wells
Multilayer Convolution Algorithm.
Prediction of layer flow rates for a specified wellbore pressure history.
Two-Layer Situations….
Transient crossflow during buildup
Early shut-in time rate transient
Two-layer case studies
Unequal initial pressure
Incremental layer workover case..
Transient step-rate test (TSRT).
Partially Bounded System.
Constant total rate drawdown.
Regime 1: Both layers infinite-acting
Regime 2: Depletion of the bounded layer 1.
Regime 4: Layer 2 producing alone..
Draw-down type curve
Buildup…
Derivative diagnostics.
Three-layer Synthetic Problem.
Dual Profile Build-up Test (DPBT)..
Basic form of DPBT..
Reservoir monitoring and automatic matching
DPBT with NGWFT dual packer complement
Transient Step-Rate Test…
Communicating Layers.
Introduction
Pseudo-semi-steady-state (PSSS) crossflow model
Embedded lens of high permeability-Geoskin.
Finite element numerical modelling.
Crossflow index
Braided fluvial systems
Development of crossflow modelling using partial productivity indices.
Design and simulation of workover treatments
Synergistic Interpretation of Layered Well Tests
Integration of core analysis data
Effective flowing interval
Upscaling core and log permeability data
Natural fracturing
Hydraulic Flow Units (HFUs).
Introduction
Fundamental theory.
Hydraulic unit zonation process
Field examples from clastic reservoirs
Permeability prediction from core and log data.
Siberian field example..
Alternative lumped parameter approach..
Distributed Pressure Surveys..
Notes.
Chapter 20. Deconvolution in PTA
Introduction
Convolution of a Variable Rate Response
Iseger Algorithm..
Numerical Laplace Transformation
Step Rate Schedules
Deconvolution of a Variable Rate Response
Application of Deconvolution
Determination of reservoir volume
Further Simulated Test Problems
Gas well testing….
Application to Wireline Formation Testing.
Mini-DST.
Depth of Investigation..
Real-time Deconvolution
Permanent Downhole Gauge (PDG) Data.
Build-up Analysis
Partial Datasets.
Synthetic deconvolution.
Two-Cell Compartmentalized Systems
Gas Well Testing.
Shell field example
Notes….
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