Well test analysis for multilayered reservoirs with formation crossflow

Well test analysis for multilayered reservoirs with formation crossflow

Well Test Analysis for Multilayered Reservoirs with Formation Crossflow introduces the fundamentals of well test analysis of a multilayered reservoir with formation crossflow. The effects of reservoir parameters on wellbore pressure and flow rate are examined, as is a proper method that has been est...

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Detalles Bibliográficos
Otros Autores: Gao, Chengtai, author (author), Sun, Hedong, author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Cambridge, MA : Elsevier [2017]
Edición:First edition
Materias:
Oil wells > Testing.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009630315906719
Tabla de Contenidos:
  • Front Cover
  • Well Test Analysis for Multilayered Reservoirs with Formation Crossflow
  • Copyright
  • Contents
  • About the Author
  • Acknowledgment
  • Introduction
  • Chapter 1: Semipermeable Wall Model of a Multilayer Reservoir with Crossflow
  • 1.1. Introduction
  • 1.2. Semipermeable Wall Model and Fundamental Differential Equations-Oil Reservoir
  • 1.2.1. Semipermeable Wall Model of a Multilayer Oil Reservoir
  • 1.2.2. Fundamental Differential Equations of a Multilayer Oil Reservoir
  • 1.3. Semipermeable Wall Model and Fundamental Differential Equations-Gas Reservoir
  • 1.3.1. Semipermeable Wall Model of a Multilayer Gas Reservoir
  • 1.3.2. Fundamental Differential Equations of a Multilayer Gas Reservoir
  • 1.3.3. Linearization of the Differential Equations of a Multilayer Gas Reservoir
  • 1.4. Crossflow Behavior for Incompressible Flow
  • 1.4.1. Crossflow Caused by Different Boundary Pressures
  • 1.4.2. Crossflow Caused by Permeability Change
  • 1.5. Summary
  • Chapter 2: Single-Phase Fluid Flow in a Two-Layer Reservoir with Significant Crossflow
  • 2.1. Introduction
  • 2.2. Pressure Drawdown and Buildup Behavior When Both Layers Are Completed at a Single Well
  • 2.2.1. Basis Solution for a Single Layer
  • 2.2.2. Assumptions and the Flow Problem of a Layered Reservoir
  • 2.2.3. Numerical Solution
  • 2.2.4. Theory and Analytical Approximations
  • 2.2.5. Summary
  • 2.3. Crossflow Behavior in a Partially Perforated Two-Layer Reservoir
  • 2.3.1. Flow Nature of the Transient Test of a Partially Perforated Well in a Two-Layer Reservoir with Crossflow
  • 2.3.2. Estimation of Reservoir Parameters Using Drawdown Tests
  • 2.3.2.1. A Method for Evaluating Reservoir Parameters
  • 2.3.2.2. The Treatment of the Skin Factor
  • 2.3.3. Summary
  • 2.4. Maximum Effective Hole Mathematical Model and Analytical Solution for a Two-Layer Reservoir.
  • 2.4.1. Maximum Effective Hole-Diameter
  • 2.4.2. Analytical Solution When Both Layers Are Completed with Crossflow
  • 2.4.3. Analytical Solution for a Two-Layer Crossflow Reservoir Perforated Partially with Crossflow
  • 2.4.4. Analytical Solution of a Commingled Reservoir When All Layers Are Completed
  • 2.4.5. A Comparison of a Two-Layer Commingled Reservoir and Crossflow Reservoir
  • 2.4.6. Summary
  • Chapter 3: Pressure Transients and Crossflow Caused by Diffusivities in Multilayer Reservoirs
  • 3.1. Assumption and the Flow Problem
  • 3.2. Approximate Analytic Solutions
  • 3.3. Numerical Solutions for Cases with n=3 and n=5
  • 3.4. Numerical Solutions and Comparison with Theory
  • 3.4.1. Three-Layer Cases
  • 3.4.1.1. Behavior of Wellbore Pressure
  • 3.4.1.2. Behavior of the Flow Rate
  • 3.4.1.3. The kh-Weighted Pressure for the Drawdown Cases
  • 3.4.1.4. Similarity of Area Crossflow Rates
  • 3.4.1.5. Distribution of the Area Crossflow Rates with Time
  • 3.4.1.6. Behavior of Crossflow Velocity
  • 3.4.2. Five-Layer Cases
  • 3.4.2.1. Behavior of Wellbore Pressure
  • 3.4.2.2. Behavior of Area Crossflow Rates
  • 3.5. Analytical Solution of the Three-Layer Reservoir
  • 3.5.1. Assumption and the Flow Problem
  • 3.5.2. Derivation of Solutions for Pressure and Rate
  • 3.6. Summary
  • Chapter 4: Crossflow Behavior and the Determination Reservoir Parameters by Drawdown Tests in Multilayer Reservoirs
  • 4.1. Assumption and Mathematical Expression of the Problem
  • 4.2. The Unsteady Flow Behavior in Drawdown and Buildup Tests When Partial Layers Produce with Crossflow
  • 4.2.1. Behavior of Wellbore Pressure
  • 4.2.2. Behavior of the Area Crossflow Rate
  • 4.2.3. Behavior of Function g(tD)
  • 4.2.4. Behavior of Function g-ln(2dei)
  • 4.3. New Drawdown Test
  • 4.4. Summary.
  • Chapter 5: Determination of Total Productivity by a Constant Wellbore Pressure Flow Test and the Crossflow Behavior in Mu ...
  • 5.1. Assumption and Approximate Theoretical Solution of the Problem
  • 5.2. Numerical Results and Comparison with the Approximation Theory
  • 5.2.1. Flow Rate of Each Layer Changes with Time
  • 5.2.2. kh-Weighted Pressure Changes with Time
  • 5.2.3. Distributions of Pressure Difference Changes with Time
  • 5.2.4. Distributions of Area Crossflow
  • 5.2.5. The Peak Value of qci Changes with Time
  • 5.3. Exact Solution of a Two-Layer Reservoir with Crossflow Under a Constant Pressure Condition
  • 5.3.1. Model Description
  • 5.3.2. Derivation of Solutions for Pressure and Rate
  • 5.3.3. Numerical Inversion of the Laplace Transform and Discussion of Results
  • 5.4. Summary
  • Chapter 6: Determination of Individual Layer Properties by Layer-by-Layer Well Tests in Multilayer Reservoirs with Crossflow
  • 6.1. Assumptions and Mathematical Model
  • 6.2. Approximate Solution of Unsteady Flow in a Three-Layered Reservoir and Its Extension
  • 6.2.1. Approximation Solution for the Short Time Period
  • 6.2.2. Approximation Solution for the Early Transition Period
  • 6.2.3. Approximation Solution for the Long Time Period
  • 6.2.4. Determination of Semipermeability
  • 6.2.4.1. Determine Semipermeability by Steady Wellbore Pressure Differences
  • 6.2.4.2. Determine Semipermeability by the Crosspoint of Two Straight Lines
  • 6.2.5. Buildup Case
  • 6.2.6. Extension to n-Layered Reservoirs
  • 6.3. Discussion of Simulation Results
  • 6.4. Interpretation Theory
  • 6.4.1. The Interpretation of a Drawdown Curve
  • 6.4.2. The Interpretation of Buildup Curves
  • 6.4.3. Extension to n-Layered Reservoirs
  • 6.5. Summary
  • Chapter 7: Determination of Parameters for Individual Layers by Transient Well Tests in Multilayer Reservoirs
  • 7.1. Introduction.
  • 7.2. Approximation Solution of Unsteady-Flow and Crossflow Behavior Caused by Skin Factors
  • 7.2.1. Assumptions and Three Flow Periods
  • 7.2.2. Approximation Solution for the Short Time Period
  • 7.2.3. Approximation Solution for the Long Time Period
  • 7.2.4. Buildup Case
  • 7.2.5. Crossflow Behavior and Comparison of the Simulation Results with the Approximation Theory
  • 7.3. Determination of Parameters for Individual Layers by a Series of Transient Tests
  • 7.3.1. Two-Layer Case, Drawdown Period
  • 7.3.2. Two-Layer Case, Buildup Period
  • 7.3.3. Example1
  • 7.3.4. n-Layer Case
  • 7.3.5. Example2
  • 7.4. Determination of Semipermeabilities by Steady Rates
  • 7.5. Summary
  • Chapter 8: Interpretation Theory for Vertical Interference Testing Across a Low-Permeability Zone
  • 8.1. Introduction
  • 8.2. Model Description
  • 8.3. The Interpretation Theory When q(t) is Known
  • 8.3.1. Case for Known Function f(pw1,pw2)
  • 8.3.2. Case for Unknown Function f(pw1,pw2)
  • 8.3.3. Case for f=αD(pwD1-pwD2)
  • 8.3.4. Case k=0
  • 8.4. The Interpretation Theory When the Well Produces with a Constant Surface Rate
  • 8.4.1. Case for Known Function f(pw1, pw2)
  • 8.4.2. Case for Unknown Function f(pw1, pw2)
  • 8.4.3. Case for f=αD(pwD1-pwD2)
  • 8.4.4. Case for k=0
  • 8.4.5. Limiting Behavior for f=αD(pwD1-pwD2)
  • 8.4.6. Buildup Case
  • 8.4.7. The Determination of Initial Values for Nonlinear Parameter Estimation
  • 8.5. The Influence of Different Parameters on Drawdown Curves
  • 8.5.1. The Influence of the Linear Leakage Rate on Wellbore Pressure
  • 8.5.2. The Influence of Storativity of the Low-Permeability Layer on Wellbore Pressure
  • 8.5.3. The Influence of Wellbore Storage on Wellbore Pressure
  • 8.5.4. The Influence of Semipermeability on Wellbore Pressure
  • 8.5.5. The Influence of Skin Factor on Wellbore Pressure.
  • 8.5.6. The Influence of w1 on Wellbore Pressure
  • 8.5.7. The Influence of Leakage Rates on Wellbore Pressure
  • 8.6. Summary
  • Chapter 9: Unsteady Crossflow Model for Leaky Vertical Interference Testing Across a Low-Permeability Zone
  • 9.1. Introduction
  • 9.2. Model Description
  • 9.3. Relationships of Different Models
  • 9.4. Solution of the Problem
  • 9.4.1. Leakage Function is Known or Has a Linear Form
  • 9.4.2. Leakage Function f is a Nonlinear Unknown Function
  • 9.4.3. Limiting Behavior for f=αD(pwD1-pwD2)
  • 9.4.3.1. Early Time Period
  • 9.4.3.2. Short Time Period
  • 9.4.3.3. Long Time Period
  • 9.5. Interpretation Method of Parameters
  • 9.5.1. Steps of Interpretation
  • 9.5.2. Example of Interpretation
  • 9.6. Comparison of Different Models
  • 9.7. Summary
  • Chapter 10: Material Balance Equation of Multilayer Gas Reservoir
  • 10.1. Material Balance of Two-Layer Gas Reservoir
  • 10.1.1. Physical Model
  • 10.1.2. Mathematical Model of a Two-Layer Gas Reservoir Without Crossflow
  • 10.1.3. Mathematical Model of a Two-Layer Gas Reservoir with Crossflow
  • 10.1.4. p/Z Curve of a Two-Layer Gas Reservoir
  • 10.1.4.1. p/Z Curve of a Two-Layer Gas Reservoir Without Crossflow
  • 10.1.4.2. p/Z Curve of a Two-Layer Gas Reservoir with Crossflow
  • Early Time Period
  • Long Time Period
  • 10.1.5. Influencing Factor Analysis of Reserve Estimation
  • 10.1.5.1. The Effect of an Interlayer Heterogeneity on Dynamic Reserve Estimation
  • 10.1.5.2. The Effect of Crossflow on Dynamic Reserve Estimation
  • 10.1.5.3. The Effect of the Permeability on Reserve Estimation
  • 10.1.6. Method of Improving the Ratio of Dynamic Reserve to OGIP
  • 10.1.6.1. Well Stimulation for Formation with Low Permeability
  • 10.1.6.2. Reduce the Production Output
  • 10.1.6.3. Single-Layer Production for Layer with Low Permeability.
  • 10.2. Reserve Estimation of a Two-Layer Commingled Gas Well.

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