Sin t

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Paper Results from Averaging Model for
Cuttings Transport in Horizontal
Drilling Authors Salazar-Mendoza, R. (IMP),
and A. García-Gutiérrez (IIE). Session
Drilling Tuesday September 12, 2006
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• Table of Contents

• Introduction

• Model Description

• Methodology

• Results

• Conclusions

Acknowledgements
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• Introduction

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• Introduction...

Factors affecting drill cuttings transport
The pressure gradient is considered the most
important parameter in a solid-liquid flow

• Velocity
• Drill Cuttings volume fractions
• Drill Cuttings Density
• Fluid Density
• Fluid Viscosity

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• Introduction...

There are three main flow patterns for
solid-liquid flow (Doron and Barnea, 1996) 1)
Fully suspended flow 2) Flow with a moving bed
3) Flow with a stationary bed
Photographies from Iyoho (1980)
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• Model Description

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• Methodology

Point Equations Fully suspended flow
Point Equations Stationary Bed
The Method of Volume Averaging (Whitaker, 1999)
Porous Medium Averaging Model ?-region
Two-Fluid Averaging Model ?-region
Closures
Closures
Condition of Local Mechanical Equilibrium
Two-Regions Averaging Model Flow with a
stationary bed
Numerical Solution
Comparation with Exp. Data
One-equation Averaging Model ?-region
Stress in the boundary ?-?
Conclusions
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• Point equations

Interfacial Boundary Condition
Initial Conditions
Boundary Conditions
Interfacial Jump Conditions
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• The Method of Volume Averaging

-Superficial average
-Intrinsic average
-Volume fraction
-Relation
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• The Method of Volume Averaging...

-Spatial averaging theorem and the general
transport theorem (Gray and Lee, 1977)
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• Two-Fluid Averaging Model for w-region

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• Closures

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• Condition of Local Mechanical Equilibrium

This mean that the fully suspended flow can be
characterized by a single velocity
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• One-Equation Averaging Model for w-region

where
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• Porous Medium Averaging Model for ?-region

Derived by Ochoa-Tapia and Whitaker (1995)
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• Closures

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• Final Formulation of the Two-Regions Averaging
  Model for Cutting Transport in Horizontal Drilling

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• Numerical Solution

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• Results

Case 1.-Fully suspended flow
Case 2.-Flow with a stationary bed
Case 3.-Flow with a moving bed
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• Results Case 1

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• Results Case 2

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• Results Case 2

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• Results Case 3

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• Results for Cases 2 and 3

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• Results for Cases 2 and 3

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• Conclusions

• In this work, the process of cutting transport
  for the three main flow patterns was analyzed 1)
  fully suspended flow, 2) flow with a stationary
  bed, and 3) flow with a moving bed.
• The numerical results and their comparison with
  experimental data and theoretical results show
  that 1) the model for a fully suspended flow is
  not adequate for simulating a flow with a moving
  bed nor a flow with a stationary bed, 2) the
  models for a flow with a stationary bed and a
  flow with moving bed allow to obtain the
  theoretical flow pattern transition, as a
  function of total volume fraction, which depends
  on the maximum packing at the bottom of the pipe,
  3) the results for the dimensionless pressure
  gradient, obtained for a flow with a stationary
  bed and a flow with a moving bed, are in
  agreement with experimental data and theoretical
  results reported in the literature

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• Acknowledgements

The authors wish to thank the financial support
provided by the Instituto Mexicano del Petróleo
(IMP), the Consejo Nacional de Ciencia y
Tecnología (CONACyT), and the Secretaría de
Educación Pública (SEP) of México.