Pressure Transient Testing

John LeePeterson Chair and Professor of Petroleum Engineering

Texas & U.

John . RollinsSenior Technical Consultant

International 8usiness Machines .

John . SpiveyPrincipal Reservoir Engineer

Schlumberger

Henry L. Doherty Memorial Fund of AIMESociety of Petroleum Engineers

Richardson, Texas2003

SPE Textbook Series Textbook Series of the Society of Petroleum Engineers was established in 1972 action of the SPEBoard of Directors. Th Series is intended to ensure availability of high-quality textbooks for use inundergraduate courses in areas clearly identified as being within the petroleum engineering field. Th workis directed the Society's Books Committee, n of the more than 40 Society-wide standing committees.Members of the Books Committee provide technical evaluation of the book. Below is listing of those who

n most closely involved in the final preparation of this book.

Book EditorsShah abir, ChevronTexaco Corp., HoustonFikri Kuchuk, Schlumberger, Dubai, UAE

Books Committee (2003)Waldo J. Borel, Devon Energy Production . LP, Youngsville, Louisiana, ChairmanBernt s. Aadnoy, Stavanger U. CoHege, StavangerJamal1. Azar, U. ofTulsa, TulsaRonald . Behrens, ChevronTexaco Corp., San Ramon, CalifomiaAli Ghalambor, U. of Louisiana-Lafayette, Lafayette, LouisianaJim Johnstone, Contek Solutions LLC, ln, Texas

n . Kouba, ChevronTexaco Corp., Houstonill Landrum, ConocoPhillips, HoustonEric . Maidla, Noble Engineering & Development Ltd., Sugar Land, TexasErik Skaugen, Stavanger U. CoHege, StavangerSaHy . Thomas, ConocoPhillips, Houston

Copyright 2003 the Society of Petroleum Engineers Inc.Printed in the United States of America. rights reserved.This book, or n part thereof, cannot reproduced in an formwithout written consent of the publisher.

ISBN 1-55563-099-5

Pressure Transient TestingSPE Textbook SeriesDedicationJohn LeeJonh RollinsJohn SpiveyIntroductionAcknowledgmentsContentsChapter 1. Fundamentals of Fluid Flow in Porous Media1.1 Overview1.2 Derivation of the Diffusivity Equation1.2.1 Fundamental Physical Principles1.2.2 Diffusivity Equation for Radial, Simgle-Phase Flow of a Liquid With Small, Constant Compressibility1.2.3 Diffusivity Equation for Radial, Single-Phase Flow of a Gas1.2.4 Diffusivity Equation for Radial, Multiphase Flow

1.3 Initial and Boundarcy Conditions1.3.1 Initial Condition1.3.2 Outer-Bourdary Conditions1.3.3 Inner-Boundary Conditions

1.4 Dimensionless Groups1.4.1 Radial Flow-Constant-Rate Production1.4.2 Radial Flow-Constant-Pressure Production1.4.3 Linear Flow-Constant-Rate Production-General Case1.4.4 Linear Flow-Constant-Rate Production-Hydraulically Fractured Wells

1.5 Solutions to the Diffusivity Equation1.5.1 Transient Radial Flow, Constant-Rate Production From a Line-Source Well1.5.2 Pseudosteady-State Flow, Constant-Rate Production From a Cylindrical-Source Well in Closed Reservoir1.5.3 Steady-Stante Flow, Constant-Rate Production From a Cylindrical-Source Well in a Reservoir with Constant-Pressure Outer Boundaries1.5.4 Transient Linear Flow, Constant-Rate Production From a Hydraulically Fractured Well

1.6 Superposition in Space1.6.1 Multiple Wells1.6.2 Method of Images

1.7 Superposition in Time1.7.1 Modeling Variable-Rate History1.7.2 Modeling Pressure-Buildup Tests

1.8 Deconvolution1.8.1 Rate-Normalization Methods1.8.2 Laplace Transform Deconvolution

1.9 Chapter Summary1.10 Discussion Questions

Chapter 2. Introduction to Flow and Buildup-Test Analysis: Slightly Compressible Fluids2.1 Overview2.2 Analysis of Flow Tests2.2.1 Constant-Rate Flow Tests2.2.2 Variable-Rate Testing With Smoothly Changing Rates2.2.3 Flow Tests With Discrete Rate Changes

2.3 Analysis of Pressure-Buildup Tests2.3.1 Builup Tests With Constant-Rate Production Before2.3.2 Buildup Tests Preceded by Two Different Flow Rates2.3.3 Buildup Tests Preceded by (n-1) Different Flow Rates

2.4 Complications in Actual Tests2.4.1 Radius-of-Investigation Concept2.4.2 Time Regions on Tests Plots2.4.3 Wellbore-Storage Effects2.4.4 Damage and Stimulation Analysis2.4.5 Effect of Incompletely Perforated Interval2.4.6 Effect of Deviated Hole

2.5 Analysis of Late-Time Data in Flow and Buildup Tests2.5.1 Estimating Drainage-Area Pressure2.5.2 Estimating Distance to Boundaries2.5.3 Estimating PV From Flow Tests

2.6 Analyzing Well Tests With Multiphase Flow2.7 Chapter Summary

Chapter 3. Introduction to Flow and Buildup-Test Analysis: Slightly Compressible Fluids3.1 Overview3.2 Pseudopressure and Pseudotime Analysis

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