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stewart g well test design analysis 2011

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Textbook in PDF format 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. Foreword by Roland N. Horne Foreword by Bernard J. Duroc-Danner Pressure Transient Analysis in Drawdown and Buildup Background to Transient Pressure Analysis 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 Pressure drawdown analysis in infinite-acting reservoirs The Principle of Superposition Multiple-well situations Variable rate situations Pressure Build-up Testing 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 Wellbore Storage and Type Curve Matching Wellbore Storage 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 Log–log type curve Type curve based on tD/CD Type Curve Matching using the Pressure Derivative Derivative analysis Middle time region (MTR) derivative match tD/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 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 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 tD/L2D 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) 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 Well in a Bounded Drainage Area Reservoir Limit Testing 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 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 North Sea field example Libyan field example Determination of average pressure p Interference testing Notes Variable Rate Well Test Analysis 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 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 Pemanent downhole gauges (PDGs) Afterflow Measurement and Convolution 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 Channel Sands and Parallel Faults 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 Constant Pressure Boundaries Constant-pressure Upper or Lower Boundary 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 Vertically Fractured Wells Uniform Flux and Infinite Conductivity Fractures 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 pDfunction 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 Dual Porosity Systems 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 racture Network Theory ranian Field Examples Well Q Well X-33T Radial Composite Behavior Notes Limited Entry and Double Permeability Systems Well with Limited Entry or Partial Penetration Drawdown behavior of partially penetrating wells ffects 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 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 CDλType Curve Simulation of vertical interference tests Field examples Conclusions Shale Lens Model Notes Radial Composite Systems Radial Composite Systems 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) 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 Horizontal Wells 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 Gas Well Testing Theory of Gas Well Testing 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 Automatic Model Matching Structure of fundamental (CSFR) pD functions or models Interpretation methodology Storage and interrogation of tabulated dimensionless responses Real-time Convolution 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 pDfunctions Notes 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 Well Test Design 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 Multiphase Flow 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 Numerical Well Testing Numerical Techniques The finite element method Interaction of Geological Modeling and Well Test Interpretation Heriot-Watt fluvial reservoir project Geoskin concept Geological Object Framework 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 Dual permeability situations Vertical sealing faults with windows Conclusions Notes Layered Well Testing 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 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 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) 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 Deconvolution in PTA 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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