Robello Samuel Dmitry F. Baldenko Fedor D. Baldenko

POSITIVE DISPLACEMENT MOTORSTheory and Applications

A SigmaQuadrant Engineering Publication

PositiveDisplacement MotorsTheory and Applications

PositiveDisplacement MotorsTheory and Applications

Robello Samuel Dmitry F. Baldenko

Fedor D. Baldenko

A Sigmaquadrant Engineering PublicationHouston/Beijing/Chennai/Moscow

σ

iv

DISCLAIMERWhile the authors and the publisher have used their best efforts in preparing and producing the book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by marketing or sales representatives or in print or online sales and marketing materials. The advice and strategies contained herein are the opinions of the authors and may not be suitable for your situation. You should consult with the proper professional where appropriate. Neither the publisher nor the authors shall be held liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or any other damage.

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Positive Displacement Motors – Theory and Applications

Copyright © 2015 by Sigmaquadrant LLC, Houston, Texas. All rights reserved. No part of his publication may be reproduced or transmitted in any form without the prior written permission of the publisher.HOUSTON, TX:Sigmaquadrant.com11306 Dawnheath drCypress, TX 77433

Director: Dorothy SamuelManaging Editor: Dorothy SamuelProduction Editor: Hubert DanielSenior Design Editor: Kryon Publishing Services (P) Ltd.

Library of Congress Cataloging-in-Publication DataSamuel, Robello.Positive Displacement Motors – Theory and Applications / Robello Samuel.p. cm.Ies bibliographical references and index.ISBN: 978-0-9906836-0-510 9 8 7 6 5 4 3 2 1

1. Positive Displacement Motors—Equipment and supplies. 2. Oil well drilling—Equipment and supplies. 3. Oil well drilling. 4. Gas well drilling. I. Title.Printed in the United States of AmericaPrinted on acid-free paper.

Text design and composition by: Kryon Publishing Services (P) Ltd., Chennai, India. www.kryonpublishing.com

“Great engineering minds march off the maps, Mediocre engineering minds stay within the boundary,

Small engineering minds never draw the line”

— Ollebor Leumas

Contents

viii Preface

ix Acknowledgments

x About the Authors

chapter 1 1 General Introduction

chapter 2 39 Downhole Drilling Motors

chapter 3 55 Motor Components

chapter 4 71 Geometrical Description

chapter 5 117 Kinematical Description and Operation

chapter 6 165 Design and Motor Operation

chapter 7 207 Contact Line, Wear, Leakage, and Losses

chapter 8 259 Motor Bottomhole Assembly

chapter 9 293 Motor Operating Parameters

chapter 10 347 Pneumatic Motor

chapter 11 393 Advances

409 Bibliography

421 Index

Preface

This book provides detailed theory and working princi-ples of positive displacement motors based on Moineau principle. Our aims are to (1) emphasize the basic prin-ciple involved in the operation; (2) instill theory in the operation of the motor; (3) explain the application with reference to drilling framework; and (4) provide the advancement in this area in the recent years. The text is intended for designers, practical field personals, and drilling engineers. It can also be used as a supple-ment book for downhole drilling tools study and other advanced drilling courses. The mathematics, science, and engineering presented provides in depth under-standing of this simple machine but complex intricate geometry. Undoubtedly, analytical and geometrical treatment provided gives a systematic approach for the use under downhole conditions. More advanced treatment with mathematical rigor is also interspersed throughout the book wherever needed and justified. Numerous problems and supplementary problems are given at the end of each chapter so as to give more understanding of the theory presented.

Painstaking efforts have been taken to present usable material; however, errors are sometimes inevitable. We encourage readers to send their suggestions and comments toward the improvement of this book. They can download the errata sheets from the site sigmaquadrant.com.

Authors

Acknowledgments

We thank Kryon Publishing Services (P) Ltd. who helped us with the copyediting and proofreading of this book. We thank Saravanan Boopathy who devel-oped to put together the cover image for this book. We would also like to thank Dr. Hubert (Kannan) Daniel of John Hopkins University and Balaji Srinivasan of Kryon Publishing Services, Chennai for helping us at various stages of the book. Every possible effort has been taken to acknowledge and give appropriate credits in using the copyrighted materials. Should there be any omis-sion, we sincerely apologize for the mistake and suitable corrections will be made at the first possible update.

We would like to dedicate this piece of work to our fellow drilling engineers, technicians, field hands, designers, and manufacturers who have worked on this amazing piece of tool.

About the Authors

Dr. Robello Samuel is a Chief Technical Advisor and Halliburton Technology Fellow with Halliburton since 1998. He helps to lead well engineering applications and is responsible for research in new drilling tech-nologies. He makes decisions and recom-mendations that are authoritative and have far- reaching impact on research and scien-tific activities of the company and he serves

as a corporate resource, providing technical direction and advice to management in long-range planning for new or projected areas of drilling. He has more than 30 years of multi-disciplinary experi-ence in oil and gas operations, management, consulting, software development, and teaching. His special areas of oilfield expertise include onshore and offshore well engineering, cost estimating, and drilling supervision.

Dr. Samuel has written or coauthored more than 150 journal articles, conference papers, and technical articles and is regarded as one of the world’s most influential contributors to advancement of research and practice in drilling engineering. He has given sev-eral graduate seminars at various universities and keynote speeches at forums and conferences. Dr. Samuel has been the recipient of numerous awards including the SPE Regional Drilling Engineering Award and the “CEO for A Day (Halliburton)” award. He presently serves as a review chairman on several journals and professional committees. He has been on the faculty of various universities and holds an adjunct professor appointment (concurrently) for the past 12 years, at the University of Houston and Texas Tech University in Lubbock.

xiAbout the Authors

Dr. Samuel, a Society of Petroleum Engineer Distinguished Lec-turer, holds B.S. and M.S. degrees in mechanical engineering from the University of Madurai and College of Engineering, Guindy. He also holds M.S. and Ph.D. degrees in Petroleum Engineering from Tulsa University.

Dr. Samuel’s unique blend of skills as a field engineer, researcher, and instructor has helped him author 10 drilling books and a forth-coming book “Drilling Engineering Optimization.” He can be reached via e-mail at robellos@hotmail.com or phone at (832) 275-8810.

Dr. Dmitry F. Baldenko, doctor of technical sciences, is an active member of the Russian Academy of Natural Sciences. He graduated from Moscow Oil Institute named after Gubkin (now Russian State University of Oil and Gas) with specialty in “Machinery and Equipment of Oil and Gas Fields.”

From 1957 to 1969, D. Baldenko was a lead designer for production of rodless pumps

and participated in the creation of single-screw submersible pumps for oil production and water lifting and other oilfield machineries. Since 1969, D. Baldenko has been working for the Russian Scien-tific Research Institute of Drilling Techniques (VNIIBT). As a chief designer of screw-type hydraulic machinery, he was directly involved in design, testing, and implementation of multi-stage positive dis-placement motors (PDMs). As one of the inventors of Russian PDM, D. Baldenko established initial contacts between Russian and western companies to promote this technology in the western markets.

He was the first to propose and demonstrate the advantages of multi-lobe progressive cavity pumps, as well as a scheme of sub-mersible hydraulic drive screw pumping unit for oil production.

Dr. Dmitry Baldenko authored 200 scientific publications, including 12 books and reviews in the area of drilling and oilfield technology and is the owner of more than 250 Russian and foreign patents for invention.

About the Authors

Dr. Fedor D. Baldenko, in 1980, graduated from the Moscow Institute of Petrochemical and Gas Industry named after Gubkin with spe-cialty “Machinery and Equipment of Oil and Gas Fields” and is constantly working in this institution (now Russian State University of Oil and Gas).

As an associate professor of the oil and gas industry machinery and equipment depart-

ment, F. Baldenko gives courses on “Machinery and equipment for drilling oil and gas wells”, “Installation and operation of drilling and oilfield equipment” and “Hydraulic machines and compres-sors.” He conducts research in the field of operation of single-screw hydraulic machines, theory cycloidal gearing, geometry optimi-zation of screw working bodies, modeling of dynamic systems of drilling, and oilfield machinery.

F. Baldenko has authored 120 scientific publications, including 8 monographs and reviews in the area of drilling and oilfield equip-ment. He is also the author of more than 50 patents for invention.

xii

General IntroductionSelection of proper downhole motor is important in designing the bottomhole assembly (BHA) with mud motors. Improper designs may lead to costly problems such as wellbore crookedness, improper build rate, and string failures. One of the components in the BHA is a downhole motor. Before going through in detail about the working principle, position of the motor in the BHA, and operating param-eters few basic terms need to be understood. This chapter outlines the basic terms involved in the wellpath and motor design.

PUMPS AND MOTORS

A hydraulic pump converts mechanical power into hydraulic power. The input of mechanical power into the pump is the product of the angular velocity of the pump and torque, whereas the output hydraulic power is equal to the volumetric flowrate and the pres-sure drop across the pump as shown in Fig. 1.1.

Hydraulic motors can be broadly classified as shown in the chart (Fig. 1.2).

Hydraulic motors are used to turn hydraulic power into rotary motion and they can be classified as

•  Gear motors•  Vane motors•  Gerotor motors

1C H A P T E R

Motor Components 65

Figure 3.8 Rotor cross-section.

As the number of lobes increase the speed decreases and torque increases.

Universal Joint

Eccentric rotation of the rotor is converted to concentric rotation by the use of a universal joint or a flexible joint, and an adjustable universal drive shaft is shown in Fig. 3.9.

Adjustable Bent Housing

It is an option to provide wide range of build rates with the motor. Different manufacturers provide different adjustment settings.

Bearing Assembly and Drive Shaft

The axial load is transmitted to the bit through the thrust bearing assembly. The drive shaft rotation is made smooth by radial bearings.

Positive Displacement Motors98

5 Stationary Circle

(n + 1)r

6 Rolling Circle

4 Power Section Axisy

x

1 2 3 7

e

r

∆x1

ru

2πr

δ2

Figure 4.20 Formation of the conjugate profile with interference.The chart description is as follows: 1 – shortened cycloid, 2 – offset cycloid, 3 – equidistant,

4 – motor axis, 5 – stationary circle, 6 – rolling circle, 7 – resulting position rack.

a 2

h

12

a 1

D 1

hh*

* D 2*

D2D

1

Figure 4.21 Shrinkage profile of stator.1 - the nominal profile, 2 - the actual profile.

Positive Displacement Motors166

III. Calculation of axial forces IV. Calculation of rotor and the motor output rotor V. Calculation of rotor section VI. General design of components VII. Calculation of deflection layout

The details of the design in the respective categories are explained in detail.

I. Calculation of the geometric parameters of the power section (rotor and stator)

1. Outer diameter of the motor stator D (Fig. 6.1) To provide the necessary clearance (gap between the borehole

wall and the motor stator) that can be calculated using the simple equation: D = (0.8 -> 0.9) Dh (6.1)

2. Pitch circle diameter of the stator

Dc = D – 2(εM + εp) (6.2)

Figure 6.1 Outer diameter of the motor stator.

Dc εp εM

p o

D

e

p s

Positive Displacement Motors336

0

200

400

600

800

1000

1200

1400

1600

Flow Rate (gpm)

Impa

ct F

orce

(lbf

)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

TFA

(in2 )WOB 30 kips

WOB 50 kips

WOB 70 kips

No Motor

No Motor

WOB 30 kips

WOB 70 kips

WOB 50 kips

Motor Config:0.5

0 100 200 300 400 500 600 700 800

Figure 9.20 Impact force vs flow rate.

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,0000

10

20

30

40

50

60

WOB (lbf)

RO

P (

ft/h

r)

1/2

2/3

3/44/5

5/66/7

7/8

Figure 9.21 ROP vs WOB.

Positive Displacement Motors398

The resultant force acting at the contact point is given by

Fn = π ρL S d pd

eNss

s( ) i ∆ 22

2 22

2+

(11.4)

where i = winding or configuration ratio

i = nn + 1

n = number of rotor lobes of the motor (winding number)

Because of the contact forces, the piezoelectric material under-goes strain as shown in Fig. 11.5 for a 3:2 lobe motor. The number of piezoelectric material embedded in the motor will also be a function of the number of lobes in the power section of the motor.

*

**

**

*

PiezoelectricMaterial

Figure 11.5 Piezoelectric material placements for 3:2 lobe motor.

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• Horizontal Drilling Engineering - Theory Methods and Application Robello Samuel, Dali Gao

• Drilling Operations - Cost and Risk Management Prosper Aideyan

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Drilling Operations: Cost and Risk ManagementP

rosp

er A

ideyan

A SigmaQuadrant

Engineering Publication

Cost and Risk Management Drilling Operations:

Prosper Aideyan A SigmaQuadrant Engineering

Publication

www.Sigmaquadrant.com

ISBN: 978-0-9906836-0-5

A comprehensive and valuable book

written by a team of outstanding

experts in this tool and published

through SigmaQuadrant publishing.

The Positive Displacement Motors

covers the full spectrum of topics in

terms of analysis and design of the

downhole mud motor that serves

the workhorse of the downhole drill-

ing system for several decades. This

book presents functional, operational

and technical aspects of positive

displacement motor. It provides a

platform ideal to seasoned engi-

neer, experienced researcher and

other professionals involved in the

drilling operations as it offers real

insight into this simple but complex

machine. It highlights the background

and development of this tool

• Provides details of the design

• Offers operational guidelines of

this tool

• Emphasizes technology selection

and innovation in the offing

• Incorporates practical operating

envelop

Dr. Robello Samuel has been a Chief

Technical Advisor and Technology

Fellow (Drilling Engineering) working

with Halliburton since 1998 in Houston.

He is currently a research and engi-

neering lead for well engineering applications and

responsible for research and scientific activities

for new drilling technologies. In his present role

he also conceives and develops creative/inno-

vative technology and drilling solutions critical

to the company’s success. He has more than 30

years of multi-disciplinary experience in domestic

and international oil/gas drilling operations. He

has been an adjunct Professor at the University

of Houston for the past 12 years teaching. He has

published more than 150 technical papers, reports

and 10 books. He started his career working on

rigs as a drilling engineer. He holds BS and MS

degrees in mechanical engineering, as well as MS

and PhD degrees in petroleum engineering.

Dr. Dmitry F. Baldenko, graduated from

Moscow Oil Institute (now Russian State

University of Oil and Gas) with specialty

in “Machinery and Equipment of Oil and

Gas Fields.” From 1957 to 1969, he was

a lead designer for production of rodless pumps

and involved in the development of single-screw

submersible pumps. Since 1969, he has been work-

ing for the Russian Scientific Research Institute of

Drilling Techniques (VNIIBT). As a chief designer

he was directly involved in design, testing and

implementation of multi-stage positive displace-

ment downhole motors (PDM). He authored 200

scientific publications, including 12 books and

holds more than 250 Russian and foreign patents.

Dr. Fedor D. Baldenko, graduated from

the Moscow Institute of Petrochemical

and Gas Industry with specialty

“Machinery and equipment of oil and

gas fields” and is currently working in

this institution (now Russian State University of Oil

and Gas). As an Associate Professor at the O&G

machinery and equipment department he teaches

several course and conducts research in the field

of hydraulic machines, theory cycloidal gearing,

optimization of screw working bodies, modeling

of dynamic systems of drilling and oilfield machin-

ery. He has 120 scientific publications, including

8 monographs and holds more than 50 patents for

invention.

Robello Samuel

Dmitry F. Baldenko

Fedor D. Baldenko

About the Authors

POSITIVE DISPLACEMENT

MOTORSTheory and Applicati

ons

A SigmaQuadrant Engineering Publication

POSITIVE DISPLA

CEMEN

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TORS

Positive

Displacement

Motors - Theory and

Applications by Robello Samuel

Drilling

Engineering

Optimization

by Robello Samuel and

J.J. Azar

OTHER UPCOMING TITLE FROM

SIGMAQUADRANT

THIS BOOK is a practical guide to generate risk barriers required to manage risks and cost

during well operations. Chapter 1 describes the basic principle of risk management (risk

identification, risk assessment, risk barrier creation, and monitoring). This book covers drilling

optimization and major drilling operations; non-productive time events such as hole cleaning,

casing wear, lost circulation, wellbore stability, well control and so on; and providing barriers

to the risk events. These barriers are sometimes presented in a table or “bow-tie” form for

clarity. This book also covers useful drilling calculations during well planning and operations

as well as continuous improvement opportunities for well cost management (e.g., wellbore

trajectory optimization, hole size optimization, casing running optimization, optimization of

time to break circulation, wellbore monitoring during flow check, after cementing and so on.

Prosper Aideyan, P.E. holds a B.S. in

Chemical Engineering from Louisiana

Tech University and an M.Eng. in

Petroleum Engineering from

The University of Houston. He has

over 10 years of multi-disciplinary

experience in well planning and

design, well operations, and process

safety with major oil and gas

companies.

He is very passionate about

continuous improvement and

optimization including but not limited

to equipment design and re-design,

process and procedural improvement,

and process parameters optimization.

His book on Drilling Operations: Cost

and Risk Management is based on his

experience from various successful

drilling engineering and operations

improvement projects he has worked

on during the course of his career.

Prosper Aideyan is a registered

Professional Engineer in the State of

Texas, USA.

ABOUT THE AUTHOR

9 780990 683629

ISBN 978-0-9906836-2-9

ISBN: 978-0-9906836-2-9

POSITIVE DISPLACEMENT MOTORS - Theory and Applications

DR

ILLING

EN

GIN

EE

RIN

G O

PTIM

IZATIO

N

sigmaquadrant.comuadrant

501 SOLVED

PROBLEM

S AND

CALCULATION

S FOR D

RILLING

OPERATIO

NS

501Solved Problems

and CALCULATIONS for

DRILLING OPERATIONS

ROBELLO SAMUEL

A SigmaQuadrant Engineering Publication

uadrant

Dr. Robello Samuel is a Chief Technical Advisor and Technology

Fellow with Halliburton. He is currently a research and engineering

lead for well engineering applications and responsible for research

and scienti� c activities for new drilling technologies. He has

more than 30 years of multi-disciplinary experience in domestic

and international oil/gas drilling and completion operations,

management, consulting, software development and teaching.

He is also an adjunct Professor at the University of Houston and

Texas Tech University, Lubbock for the past 10 years. Dr. Samuel,

a SPE Distinguished Lecturer, holds B.S. and M.S. (mechanical

engineering) degrees from University of Madurai and College of

Engineering, Guindy, Anna University (Chennai), M.S. and Ph.D.

(petroleum engineering) degrees from Tulsa University. He is also

the author of nine bestselling drilling engineering books.

This book is an expanded and corrected version of the author’s

“Formulas and Calculation for Drilling Operations – Edition 1”

book. It is the most comprehensive practical handbook with

calculations and solved problems for drilling operations. The

central premise of this book is easy to use step-by-step calculations

which can be used by students, lecturers, drilling engineers,

consultants, software programmers, operational managers, and

researchers. Apart from a basic introductory chapter giving a brief

treatment of calculations on rig math, this book consists entirely of

problems and solutions on focused topics encountered in drilling

operations. 501 solved Problems and calculations will help you

to connect relevant engineering theories associated with drilling

operations and quickly identify the parameters in� uencing the

operations.

ABOUT THE AUTHOR

ISBN-13: 978-0-9906836-1-2

ABOUT THE BOOK

501Solved

Problems

and CALCULATIONS for

DRILLING OPERATIONS

ROBELLO SAMUEL

A SigmaQuadrant Engineering Publication

uadrant

Horizontal Drilling Engineering - Theory, Methods and Applications

ISBN-13: 978-0615837703

Positive Displacement Motors - Theory and Applications

ISBN-13: 978-0990683605

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A SigmaQuadrant Engineering Publication

Houston/Beijing/ChennaiPUBLISHED:

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D CALCULATION

S FOR DRILLIN

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ISBN: 978-0-9906836-0-5

A comprehensive and valuable book written by a team of outstanding experts in this tool and published through SigmaQuadrant publishing. The Positive Displacement Motors covers the full spectrum of topics in terms of analysis and design of the downhole mud motor that serves the workhorse of the downhole drill-ing system for several decades. This book presents functional, operational and technical aspects of positive displacement motor. It provides a platform ideal to seasoned engi-neer, experienced researcher and other professionals involved in the drilling operations as it offers real insight into this simple but complex machine. It highlights the background and development of this tool

• Provides details of the design

• Offers operational guidelines of this tool

• Emphasizes technology selection and innovation in the offing

• Incorporates practical operating envelop

Dr. Robello Samuel has been a Chief Technical Advisor and Technology Fellow (Drilling Engineering) working with Halliburton since 1998 in Houston. He is currently a research and engi-

neering lead for well engineering applications and responsible for research and scientific activities for new drilling technologies. In his present role he also conceives and develops creative/inno-vative technology and drilling solutions critical to the company’s success. He has more than 30 years of multi-disciplinary experience in domestic and international oil/gas drilling operations. He has been an adjunct Professor at the University of Houston for the past 12 years teaching. He has published more than 150 technical papers, reports and 10 books. He started his career working on rigs as a drilling engineer. He holds BS and MS degrees in mechanical engineering, as well as MS and PhD degrees in petroleum engineering.

Dr. Dmitry F. Baldenko, graduated from Moscow Oil Institute (now Russian State University of Oil and Gas) with specialty in “Machinery and Equipment of Oil and Gas Fields.” From 1957 to 1969, he was

a lead designer for production of rodless pumps and involved in the development of single-screw submersible pumps. Since 1969, he has been work-ing for the Russian Scientific Research Institute of Drilling Techniques (VNIIBT). As a chief designer he was directly involved in design, testing and implementation of multi-stage positive displace-ment downhole motors (PDM). He authored 200 scientific publications, including 12 books and holds more than 250 Russian and foreign patents.

Dr. Fedor D. Baldenko, graduated from the Moscow Institute of Petrochemical and Gas Industry with specialty “Machinery and equipment of oil and gas fields” and is currently working in

this institution (now Russian State University of Oil and Gas). As an Associate Professor at the O&G machinery and equipment department he teaches several course and conducts research in the field of hydraulic machines, theory cycloidal gearing, optimization of screw working bodies, modeling of dynamic systems of drilling and oilfield machin-ery. He has 120 scientific publications, including 8 monographs and holds more than 50 patents for invention.

About the Authors

POSITIVE D

ISPLACEM

ENT M

OTO

RS