Contents

Cover

Half Title page

Title page

Copyright page

Preface

Notation

Chapter 1: Main Results and Development Lines of Hydro-Aeromechanics of Drilling Processes

Chapter 2: Basic Problems of Hydro-Aeromechanics in Drilling Processes

Chapter 3: Multiphase Media in Drilling Processes

Chapter 4: Hydro-Aeromechanic Equations of Drilling Processes

4.1 Mass Conservation Equation

4.2 Momentum (Motion) Equation

4.3 Thermodynamic Equations Of State

4.4 Rheological Equations of State

4.5 Equation of Concentrations

4.6 Formulation of Hydro-Aeromechanical Problems For Drilling Processes

Chapter 5: Hydrostatics of Single-Phase Fluids and Two-Phase Mixtures in Gravity Field

5.1 Hydrostatics of Single-Phase Fluids

5.2 Hydrostatics of Incompressible Fluid at τw = 0

5.3 Hydrostatics of Single-Phase Compressible Fluid (Gas) at τw = 0

5.4 Hydrostatics of Slightly Compressible Fluid at τw = 0

5.5 Hydrostatics of A Fluid with Dynamic Shear Stress (τ0 ≠ 0)

5.6 Hydrostatics of Two-Phase Fluids

Chapter 6: Stationary Flow of Fluids in Elements of The Well Circulation System

6.1 Equations For Stationary Flows of Homogeneous Incompressible Fluids

6.2 Calculation of Pressure in Laminar Flows of Viscous Incompressible Fluids in Circular Slots, Pipes, and Annular Channels

6.3 Calculation of Pressure in Laminar Flows of Viscous-Plastic Fluids in Circular Slots, Pipes, and Annular Channels

6.4 Calculation of Pressure in Laminar Flows of Power Incompressible Fluids in Slots, Pipes, and Annular Channels

6.5 Calculation of Pressure in Turbulent Flows in Pipes and Annular Channels

6.6 Transition of Laminar Flow of Viscous, Viscous-Plastic, and Power Fluids Into Turbulent One

6.7 Calculation of Pressure in Flows in Eccentric Annulus: Formation of Stagnation Zones

6.8 Effect of Internal Pipe Rotation on Pressure in Annulus

6.9 Pressure Drop in Local Resistances of Circulation System

Chapter 7: Equilibrium and Motion of Rigid Particles in Fluid, Gas, and Gas—Liquid Mixture

7.1 Washing of The Well Bottom

7.2 Levitation of Rigid Particles in Fluid, Gas, and Gas—Liquid Mixture Flows

7.3 Flow Rates of Fluid, Gas, and Gas—Liquid Mixture Needed For Removal of Cutting From Well Bore

7.4 Calculation of Ball Drop Time in Descending Flow of Washing Fluid in A Column of Pipes

7.5 Hydraulic Calculation of Circular System in Drilling with Incompressible Fluid Washing

Chapter 8: Stationary Flow of Gas and Gas-Cutting Mixture in Elements of Well Circulation System

8.1 Pressure Distribution in Ascending Flow of Gas and Gas-Cutting Mixture in Annular Channel of A Well

8.2 Pressure Distribution in Descending Flow of Gas in Pipes

8.3 Pressure Losses in Bit Heads and Pipe Joints

8.4 Calculation Procedure of Pump Capacity and Compressor Pressure in Drilling with Blasting

Chapter 9: Stationary Flows of Gas—Liquid Mixtures in A Well

9.1 Equations of Gas—Liquid Mixture Flow

9.2 Laminar Ascending Flow of Gas—Liquid Mixtures in Pipes and Annular Channels

9.3 Calculation of Pressure in Pipes and Annular Space in Ascending Vertical Turbulent Flows of Gas—Liquid Mixtures

9.4 Pressure Drop in Bit Heads in Flow of Gas—Liquid Mixture

9.5 Pressure Drop in Turbo-Drills

9.6 Calculation of Pressure in Pipes in Descending Vertical Turbulent Flow of Gas—Liquid Mixture

9.7 Method of Calculation of Delivery and Pressure of Pumps and Compressors in Drilling with Aerated Fluid Washing

9.8 Effect of Gas Solubility in Fluid on Pressure of Mixture in Well

Chapter 10: Nonstationary Flows of Single-Phase Fluids in A Well

10.1 Equations of Nonstationary Single-Phase Flows

10.2 Nonstationary Flows of Incompressible Fluid in Round Trip Operations

10.3 Hydrodynamic Pressure in Round Trip Operation in A Well Filled By Viscous Fluid

10.4 Hydrodynamic Pressure Generating in Drill-Stem Descent in A Well Filled By Viscous-Plastic Fluid

10.5 Examples of Pressure Calculation in Round Trip Operations

10.6 Nonstationary Fluid Flow in A Well As Wave Process

10.7 Pressure Calculation in Deterioration of The Safety Bypass

10.8 Calculation of Pressure in Recovery of Circulation in A Well

10.9 Calculation of Pressure in A Well in Setting of A Ball Cage on A Seat (Thrust Ring) in Drill-Stem

10.10 Calculation of Pressure in Round Trip of Drill-Stem As Wave Process

Chapter 11: Flows of Formation Fluids and Rock Solids

11.1 Basic Equations of Formation Fluid and Rock Solid Flows

11.2 Stationary Laminar Flows of Incompressible and Compressible Fluids and Gases

11.3 Nonstationary Laminar Flows of Incompressible and Compressible Fluids and Gases

11.4 Flows of Formation Fluids and Rock Solids in Regimes Different From Laminar

Chapter 12: Nonstationary Flows of Gas—Liquid Mixtures in Well-Formation System

12.1 Estimation of Bottom-Hole Decompression in Removal of Gas Bench From A Well

12.2 Recognition of The Gas Outburst and Selection of Regimes of Its Liquidation

12.3 Calculation of Amount, Density, and Delivery of Fluid Needed To Kill Open Gas Blowout

12.4 Calculation of Pressure at The Well Mouth in Blowout Killing By Direct Pumping of Killing Fluid in The Well

Chapter 13: Nonstationary Flows of Fluid Mixtures in Well-Formation System: Calculation of Fluid-Gas Blowout Killing

Chapter 14: Distribution of Concentration and Pressure in Displacement of Newtonian and Viscous-Plastic Fluids From Circular Pipes and Annular Channels: Hydraulic Calculation of Cementation Regime

14.1 Main Reasons of Incomplete Displacement of Fluids

14.2 Distribution of Concentrations in Displacement of One Fluid By Another Fluid

14.3 Taking Into Account Needed Displacement Completeness in Calculation of Cementing

14.4 Method of Hydraulic Calculation of Cementation Regimes with Regard To Given Concentration in Channel Cross Section

14.5 Calculation of Single-Stage Well Cementation: Method and Calculation of Cementation with Foam-Cement Slurry

Chapter 15: Sedimentation of Rigid Phase in Drilling Fluid After Deadlock of Mixing

15.1 One-Dimensional Equation For Hydraulic Pressure in Sedimentation of Rigid Phase of Suspension

15.2 Lowering of Hydraulic Pressure in Well After Deadlock of Solution Circulation

Chapter 16: Experimental Determination of Rheological Characteristics

16.1 Determination of Rheological Characteristics with Rotary Viscometer

16.2 Determination of Rheological Characteristics with Capillary Viscometer

16.3 Determination of Rheological Characteristics of Rock Solids

16.4 Examples of Applications of Rheological Characteristics

References

Author Index

Subject Index

About the Authors

APPLIED HYDRO-AEROMECHANICS IN OIL AND GAS DRILLING

Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Leonov, Eugeniy G., 1935-
Applied hydroaeromechanics in oil and gas drilling / Eugeniy G. Leonov, Valeriy I. Isaev ; translated from Russian into English by Sinaiski E.G.
p. cm.
“Text is based on lectures held by authors in Moscow State Gubkin University of Oil & Gas”-Pref.
Includes index.
ISBN 978-0-470-48756-3 (cloth)
1. Oil well drilling. 2. Gas well drilling. 3. Hydraulics. I. Isaev, Valeriy I., 1940- II. Title.
TN871.2.L42 2010
622’.3381-dc22

2009018426

PREFACE

At the basis of majority technological operations of oil and gas well drilling lie hydro-aeromechanical processes. Currently, drilling is practically impossible without circulation of drilling and plugging fluids. Actually, removal of cutting from the well, application of turbo drills and jet bits, lowering of casing strings and casing cementing, control of circulation loss and reservoir fluid showings, investigation of lost circulations, and production horizon zones do not make a complete list of operations that go hand in hand with hydro-aeromechanical processes.

Hydro-aeromechanics in drilling is a special branch in oil technology in which flows of circulating and plugging fluids, skeleton, and bed fluid in well drilling are considered and described. Designing, planning, optimization, and realization of drilling schemes would have been impossible without data made available by this branch.

A rapid rise in the number and depth of wells in the last few years has attracted enhanced attention to hydro-aeromechanical problems in drilling. With scientists joining forces, some problems were successfully solved. On the basis of these developments, the hydro-aeromechanical theory underlying the main technological operations of well drilling has been systematically presented in this book. The text is based on lectures given at the Moscow State Gubkin University of Oil and Gas.

EUGENIY G. LEONOV
VALERIY I. ISAEV

Moscow, Russia
September 2009

NOTATION

a	parameter; aeration flow factor; degree of cement slurry aeration
ai	empirical factor
ar	degree of grouting mortar aeration
	minimal aeration degree of the grouting mortar
as	sound velocity of gas
a	acceleration vector
A	pressure drop per pipe unit length
	Archimedes number
Arcr	critical Archimedes number
bi	empirical factor
Bi	constant for viscous (viscous-plastic) fluid
c	sound velocity
C	empirical constant
C	filtration resistance factor.
Ci	constant for viscous fluid
Cw	resistance factor of a rigid particle
d	pipe diameter
dax	diameter of the pipe axis in annular channel
dbb	diameter of the borehole bottom
dd	diameter of the drill pipe
ddc	external diameter of the drill collar
dex	external diameter of the well pipe
dexdp	external diameter of the drill pipe
dexdc	external diameter of the drill collar
dexj	external diameter of the joint
dh	hydraulic diameter
din	internal diameter of well pipe
dindc	internal diameter of the drill collar
dinw	internal diameter of the well
dm	maximal diameter of the joint or the coupling; diameter of motor body
dp	particle diameter; equivalent diameter of a rigid (cutting) particle; maximal diameter of cutting particles to be removed; pipe diameter
dt	diameter of tubing
dT	diameter of turbo drill
dw	well diameter
d/dt	total derivative
Dc	contour diameter
e	eccentricity
et	gearing eccentricity
E	elastic modulus of fluid (water and mud solution)
E′	elastic modulus of the pipeline material
E′	modulus of elasticity
Ei	integral exponential function
F	vector of mass force, gravity force, external force
Fas	area of well annular space cross section
	Froude number
	Froude number
	Froude number
Frg	Froude number for gas flow
g	gravity acceleration
g	effective gravity acceleration
G	shear modulus; particle weight
H	depth
h0	height of the cement box
h1	distance from the bottom to lower boundary of the bench
	critical height at which happens outburst of fluid from the well
h(t)	height of the gas bench
H	well depth; cylinder height; slot height
H	gap width
H	formation thickness
H	drilling depth
H*	height of the clean cement slurry
Hfc	fall of foam-cement slurry column level
Hr	occurence depth of bed roof with maximal bed pressure gradient
	Hedström number
i	parameter of the equation (9.6.5)
i,j,k	basis (unit) vectors of Cartesian coordinate system
k	parameter of the power fluid
k	adiabatic index
k,n	empirical factors characterizing leakage of a turbo drill
k	roughness
k	consistence parameter; permeability factor
k	Karman universal constant
k	Rittinger constant
k	permeability factor; permeability factor of rigid phase skeleton
k	vector of mixture momentum
k′	correction factor for thixotrope solution
ka	abnormality factor
kav	average value of permeability factor of rigid phase skeleton
kc	compressibility factor
keq	equivalent roughness of the drill pipe in an uncased annular space
kf	filtration factor
kf	permeability factor
kh	hinderness factor
hpc	factor of piezo-conductivity
kr	absolute equivalent roughness; reserve factor
ks	safety factor
ksol	solubility factor
K	safety factor
l	distance from the wall surface.
l	length
l	length of the drill stem
l	section length of drill pipe
lcem	length of the section to be cemented
lf	see Fig. 12.4b
lm	motor length
lsh	depth of the showing formation
lsh	length of the pipe between joints and couplings; length of turbo drill
Lt	depth of reservoir top bedding with maximal reservoir pressure gradient depth of the bottom from the mouth
	vector of phase displacement in time Δt
L	channel length; well depth
Lt	depth of reservoir top bedding with maximal reservoir pressure gradient
m	mass
m	pump operating efficiency
mn	mass flow rate through a single head
M	moment; torque at the engine shaft
M	point at time t
M′	point at time t + Δt
	dimensionless torque
	moment of the motor rotor
Mp	down-hole motor moment sufficient to crush rock solid
Mp	turbo-drill moment needed for rock fracture
Mtr	reference data of the turbo-drill shaft moment
Mtr	turbo-drill shaft moment in the regime of maximal power
n	consistence parameter
n	rotation frequency of the motor rotor
n	number of joints and couplings; number of pumps
n	parameter of the power fluid
njoint	number of joints
n	normal vector
N	power
N	hydraulic power delivered to the bit
N	number of phases, components; number of pump strokes
p	pressure
p(z)	current pressure
p*	pressure at which changes the flow regime
po	normal pressure, initial pressure
pab	absolute pressure; absorption pressure
pal	allowed pressure of the drill pump
pap	pressure in the ascending pipe
papcv	pressure in the ascending pipe of closed well
pam	pressure at the well mouth in the annulus
pas	pressure in annular space
pasd	difference of pressures in the annular space
pat	atmospheric pressure
pcp	counter-pressure
par	pressure averaged over the depth
pb	pressures at the bean
pbh	bottom-hole pressure
pbean	pressure at the bean
pbit	pressure in the bit
pbitbs	pressure in the drill string before bit
pbaitds	pressure in drillstem before bit
pbm	minimal pressure expected at the bottom
pbot	bottom hole pressure
pbp	bursting pressure of the casing column
pc	pressure in the orifice
pc	circuit pressure
pcm	pressure at the column mouth
pcp	counter-pressure
pcr	critical pressure
pdcds	pressure in the drillstem before weighted drill string
pdp	pressure at the entrance into DP
pdptdas	pressure in the annular space at junction of DC and TD
pdpdcas	pressure in the annular space at junction of DP and DC
pdsb	pressure in the drillstem before the bit (pdsb = pbot + Δpb)
pdstd	pressure in the drillstem before the turbo-drill
pend	end pressure
pex	excess pressure; pressure at the slot counter
pf	formation pressure; pressure at formation contour
pfl	hydraulic pressures of pure fluid
pgtc	expected pressure indicated in geotechnical conditions
ph	absorption pressure (hydraulic fracturing pressure)
ph	hydraulic pressures of solution
phf	reservoir hydraulic fracture pressure
phf	hydraulic fracturing pressure
phyd	hydrostatic pressure of a solution without regard for cutting
phyd	hydrostatic pressure of a solution with regard to cutting
pib	pressure at the tth bean inlet
pib	pressure at the bean when the top of gas bench reaches the well mouth
pin	pressure in the slot orifice
pinit	initial pressure of pumping
pk	pressure on the slot contour
pl	pressure in lower part of the drill-stem
plp	pressure at lower cross section in descending flow
pm	pressure at the well-head (well mouth)
pm	manometer pressure
pnom	nominal component of the stress vector
pov	overpressure
pnn	normal component of the stress vector
pnτ	tangential component of the stress vector
pp	pressure in a pipe
pper	permissible pressure
ppump	pump pressure
ppl,Pp2	absorption or hydrofracturing pressure
ppd	difference of pressures in pipes
pr	reservoir (pore) pressure
ps	pressure in sonic flow
psbl,Psb2	pressures in showing beds; formation pressures
psat	saturation pressure
pst	pipe strength; pressure opposite formation most disposed to absorption less friction losses
pt	pressures at the pipe top
pu	pressures in upper part of the drill stem
pw	pressure of fluid column in well
pwm	pressure at the well mouth.
p	dimensionless pressure
p	stress vector
pn	stress vector to a surface with normal n
prr, , pzz	normal stresses
pr,p,pz	stress vectors of surface force in cylindrical coordinates
	tangential stress components
Δp	pressure drop
Δpan	pressure drop in annular channel with zero eccentricity
	friction along annular space length
Δpbit	losses in water courses of the bit; pressure drop in drill bit
Δpbot	pressure drop on the bottom
Δpbr	pressure drop on the motor rotor at braking operation regime
Δpcr	critical pressure drop
Δpdhm	losses in the down-hole motor (turbo drill)
Δpfr	friction loss
Δphp	difference between hydrostatic pressures of fluid columns in the annular space and pipe
Δphyd	hydrostatic pressure of fluid column
Δpin	inertial component of pressure drop
Δpjoint	pressure drop in the joint
Δplas	pressure drop owing to local resistances in annular space
Δplj	pressure drop owing to local losses from joints in the annular space
Δplock	pressure loss from locks in annular space
ΔpTlp	pressure drop owing to losses in local resistances inside pipes
Δplrp	pressure drop owing to local resistances in pipes
Δpisb	pressure drop owing to losses in surface binding
ΔpM	pressure increase in resistance
	pressure drop owing to friction along pipe length
ΔpTr	pressure reserve in the drill bit
Δpsb	pressure loss in the surface bending
ΔpT	pressure drop in turbulent flow
Δptd	pressure drop in turbo drill
q	dimensionless mass flow rate
qas	flow rate in the annulus
qfd	flow rate of the fluid displaced
qp	flow rate in pipe
qpd	pump delivery
Q	flow rate
Qo	volume flow rate of gas (air) at normal conditions
Q1	flow rate of fluid displaced by rigid phase
Qas	flow rate of fluid in the annular space
Qc	volume flow rate of cement slurry
Qcr	critical delivery
Qcut	volumetric flow rate of cuttings
QG	gas flow rate
Qk	killing fluid delivery
Ql	flow rate (leakage) of washing fluid through the seal of turbo-drill shaft
Qp	pump delivery
Qpd	pump delivery
Qpnd	pump nominal delivery
Qtd	fluid flow rate in the turbo drill
Qwb	flow rate of fluid in the wellbore
r	radius; pipe radius; radial coordinate
ro	radius of initial circle
rc	formation circuit radius; external boundary of reservoir
rex	external radius
rin	internal radius
rw	well radius
r, ,z	cylindrical coordinates
R	gas constant; pipe radius
R	resultant force acting on a particle
Re	Reynolds number
Re*	Reynolds number of viscous-plastic flow
Reas	Reynolds number in the annular space
Recr	critical Reynolds number
	critical Reynolds number calculated with particle velocity up
Recr1	first critical Reynolds number
Recr2	second critical Reynolds number
Rep	Reynolds number of fluid flow in a pipe
Res	Reynolds number of the soaring particle
S	surface element; surface area; cylinder lateral surface; pipe area
S	downhole pressure increase (safety margin)
Sav	saving of the oil-well cement
Sas	annular space cross-section area
Si	area of annular space; part of pipe area occupied by t-th phase
Ski	areas of sectors
Sn	normal cross section; normal cross-section area
Sp	area of casing
Ssi	sector area
St	area of tubing cross section
ΔS	surface element
	Saint Venant number
Seas	Saint Venant number for annular space
Secr	critical Saint Venant number
Sep	Saint Venant number for pipe
	Strouhal number
t	time
tblow	time counted from the beginning of well blowing
tc	instant of time of pump disconnection beginning
tf	inflow time
tL	time at which the upper boundary of the bench arrives the well mouth
	time of pump start; time of gate valve closure; time of pumping needed to displace mixture column from the well
tr	recovery time
Δt	time step
Δtpd	time interval of pump disconnecting
T	temperature
T	absolute temperature
T	time of ball drop
Tav	temperature averaged over the depth
Tbot	temperature at the well bottom
Tm	temperature at the well mouth
Tk	time of blowout killing
	temperature averaged over well depth
	Taylor number
Tacr	critical Taylor number
uds	velocity in round trip operation of the drill stem
up(t)	velocity of pipe motion
v	mean velocity
v*	dynamic velocity
vas	mean velocity of fluid in hole annulus
vav	average velocity
vb	velocity of fluid flow in washing holes of the bit
vc	velocity of particle centre.
vcr	critical velocity
vcut	velocity of cutting
vd	mechanical rate of drilling
vdwf	velocity of the lower bench boundary displaced by washing fluid
vf	fluid velocity
vg	gas velocity
vk	minimal velocity of fluid lift in hole clearance providing cutting removal
vM	mechanical drilling rate
vp	average velocity of a rigid particle
vr	relative velocity of a rigid particle
vs	levitate velocity of a particle; velocity of particle start
vsed	sedimentation velocity
V	volume of space, of system part
V	specific volume
Vas	annular space volume of the well
Vcem	cementing volume
Vdr, Vdrf	volume of driving fluid
Vds	internal volume of the drill stem
Vflush	volume of the flushing fluid
VG	Volume of gas in cement slurry
Vi	volume of ith phase
Vp	volume of casing
Vs	volume of the weighted solution
Vsh	volume of the driving fluid
Vw	well volume
δV	specific volume increment
w	velocity vector
wi	velocity vector of ith phase in the mixture
WL	velocity of laminar flow
Wmax	maximal flow velocity
Wx, Wy	components of the flow velocity in Cartesian coordinates
WT	velocity of turbulent flow
Wn	normal component of fluid velocity
Wr, , Wz	velocity components in cylindrical coordinates
Wz	velocity component directed along pipe z axis
Wr	resistance force acting on a particle
W	velocity vector
z	coordinate along pipe axis; current well depth with reference point at the well mouth
	over-compressibility factor averaged over well depth
	coordinates of washing, flushing, driving fluids and grouting mortar
Zt	number of rotor teeth
Zh	coordinate of the absorptive formation
	analog of consolidation factor
α	angle of inclination; zenith angle
α	angle between z axis and the direction of gravity force
α	correction factor for velocity of turbulent flow
α	hydraulic resistance factor of surface element
αap, αbh, αsw, αks	resistance factors of surface elemets listed in Table 6.1
βo	compressibility factor
β(Se)	dimensionless parameter
γ	shear; relative displacement of fluid layer
γ	shear rate
γc	mean shear rate
γw	shear rate gradient at a wall
δ = di/dc	dimensionless parameter
	dimensionless tension of rotor in braking operation regime
	dimensionless tension
δo	dimensionless parameter
δL	thickness of the laminar sublayer
Δ	discriminant
Δadm	admissible error
	relative roughness
	relative accuracy of calculation
	analog of porosity factor in soil mechanics
	compression curve
	deformation rate
	relative deformation
ζ	dimensionless parameter; dimensionless variable
η	plastic viscosity factor
η	aeration mass factor; mass factor reflecting the cutting existence; plastic viscosity factor
θ	dead-loss (static) shear stress
θ1	shear stress; dead-load shear stress
λ	hydraulic resistance factor
λas	hydraulic friction resistance factor in annular space
λc	hydraulic resistance factor
λcr	critical resistance factor
λm	resistance factor of a mixture
λt	resistance moment factor
λp	hydraulic friction resistance factor in pipes
Λi	constant for viscous fluid
μ	dynamic viscosity factor
μ	empirical flow rate factor
μ	discharge factor
μ	correction flow rate factor
μeff	apparent viscosity factor
μfr	friction factor
ζ	dimensionless parameter; dimensionless variable; resistance factor
ζ	resistance factor
	dimensionless parameter
ζs	vector of surface force
ρ	density
ρo	initial density; gas density at normal pressure
ρch	density of the chaser
ρcs	density of the cement slurry
ρcut	density of the cutting
ρf	density of fluid
ρflush	density of the flushing fluid
ρwash	density of the washing fluid
ρg	density of gas
ρgtj	expected density in geological-technical job
ρi	density of ith phase
ρk	killing fluid density
ρm	mixture density
ρp	density of a particle; density of cutting particles
ρper	permissible density of fluid
ρs	kill mud density
ρw	density of water
ρws	density of weighted solution
ρwf	washing fluid density
δρ	density increment
σ	normal stress
σ	root-mean-square deviation
σ	diaphragm ultimate strength
Δσ	surface element
	mean velocity
τ	friction stress; tangential stress
τw	dynamic shear stress
τc	mean stress in fluid
τn	normal stress
τw	friction stress at a wall
	volume concentration
	volume content of ith phase; volume concentration of ith phase
	average concentration
	total area of hydromonitor bit heads; area of nozzles; area of the head cross section
	total area of all bit head cross sections
	force density vector
χ	mass concentration; piezo-conductivity factor
,	angles of annular space sectors
ω	angular velocity
	divergence

ACRONYMS

DC	drill collar
DP	drill pipe
TD	turbodrill
AS	annular space
TJ	tool joint
TJAS	tool joint in annular space
DS	drill string
SL	sludge (cutting)
DM	downhole motor

CHAPTER 1

MAIN RESULTS AND DEVELOPMENT LINES OF HYDRO-AEROMECHANICS OF DRILLING PROCESSES

Intensive investigation of forms and laws of fluid flow in wells began in 1901 when in the United States application of the mechanical rotary drilling with washing, the so-called rotary drilling, was found on Spindletop field in Texas state. In 1911, for the first time in Russia's Suruchan region several wells were bored by rotary method with washing of well bottom by mud solution. After nationalization of the oil industry, the rotary boring began to develop quickly.

With steady increase in well depth and complexity of mine geological conditions, widespread use of jet drilling bit and downhole motors resulted in the washing and plugging back in hydro-aeromechanical well-bed system becoming more costly and power intensive. Since under real hydro-aeromechanical system it is understood that the whole set of well elements and uncovered beds connected with each other in a unified technological set have a complex structure, it is necessary to build a mathematical model of this system. The model was developed in two directions: the description of main hydro-aeromechanical properties of separate elements and the structure of the system as a whole.

Investigation of basic element properties is aimed at finding correlations between pressure, flow rate, and time through relations of theoretical hydro-aeromechanics and applied hydraulics. Let us point out the most significant results of hydro-aeromechanics in drilling.

Rheological equations formulated for viscous fluids by Newton in 1685 (Krilow, 1936), for viscous-plastic media by Shvedoff in 1889 (Reiner, 1960) and Bingham in 1916 (Bingham, 1922), and for pseudo-plastic media by Ostwald in 1924 (Reiner, 1960) are of profound importance in solving problems of drilling hydro-aeromechanics. With the help of these equations, formulas were obtained for pressure distribution in stationary laminar flow of viscous (Poiseuille, 1840, 1841; Stokes, 1845, 1850, 1901), viscous-plastic (Buckingham, 1921), and pseudoplastic (Rabinowitch, 1929; Mooney, 1931) fluids in circular pipes. Solutions have also been obtained for flows in concentric circular channels of viscous (Lamb, 1945), viscous-plastic (Volarovich and Gutkin, 1946), and pseudoplastic (Fredrickson and Bird, 1958) fluids.

On the basis of Bukingham and Volarovich and Gutkin formulas for the flow of viscous-plastic fluids in circular and concentric circular pipes, Grodde (1960) applied convenient graphic method to calculate pressure drop.

Schelkachev (1931) considered laminar stationary flow of viscous fluid in eccentric circular channel and obtained formula for pressure distribution. McLean et al. (1967) gave a general scheme for approximate calculation of pressure distribution in laminar flow of rheologic stationary fluid in concentric circular channel with cross section replaced by conventional sections of concentric channels with independent flows.

The stability of laminar flows of viscous fluid in circular pipes was experimentally investigated by Reynolds during 1876-1883 (Reynolds, 1883). He established transition criterion from laminar to turbulent flow. Hedström (1952) characterized the loss of viscous-plastic fluid laminar flow stability by Reynolds and Saint Venant numbers.

On the basis of boundary layer theory developed by Prandtl during 1904-1925 (Prandtl and Tietjens, 1929, 1931) for turbulent flow of viscous fluid in pipes with smooth and rough walls, Altshul (Altshul and Kiselev, 1975) obtained dependences for hydraulic resistance factors.

In developing the theory of multistage turbine, Shumilov (1943) gave formula for pressure drop in turbo-drill. To derive the pressure change in local resistances of circulation system, Herrick (1932) used the equivalent length method. Shumilov (1943) applied Borda-Karno formula for locks and Torricelli formula for drill bit orifice when determining pressure drop. Laminar flow of viscous fluid around a sphere was considered by Stokes (1845). Experimental investigations of flows around rigid spherical particles in a wide range of Reynolds numbers were generalized in the form of Rayleigh curve. Shischenko and Baklanov (1933) investigated conditions of stability and flow of mud solution around particles.

Targ (1951) found pressure distribution in laminar stationary flow of viscous fluid in an axially symmetric circular channel, one of the wall of which moves with constant velocity. Gukasov (1976) considered laminar flow of viscous-plastic fluid in concentric circular channel with movable internal wall.

Basic hydrodynamic equations for multiphase fluids using empirical relations for concentrations and hydraulic resistance factor were derived by Teletov (1958). On this basis were obtained pressure distributions in pipes and circular channels in well washing by aerated fluid or gas blowdown.

A fundamental contribution to solving the problem of nonstationary flows in hydraulic systems with regard to compressibility of fluids and elasticity of walls was made by Zhukowski (1899-1921), who developed the theory of one-dimensional nonstationary flow of viscous fluid to solve many problems (Zhukowski, 1948).

In connection with problems of oil- and gas-field development in works of Pavlowski (1922), Leibenson (1934), Schelkachev (1990), Charniy (1963), Muskat (1963), and many others, the flow of reservoir fluid in porous medium has been extensively studied to solve problems with opening up of productive buildup and problems with drilling.

Along with the investigation of hydro-aeromechanic properties of system elements, methods to investigate well-bed system as a whole have also been developed. In doing so, there have been established correlations between elements of the system needed to simultaneously solve all equations characterizing separate elements. For exampfe, Herrick (1932) had considered a problem on feed and pressure of drilling pump for circulation of washing fluid and Shazov (1938) devised a scheme of procedure in choosing number and parameters of cementing aggregates for one-step well plugging. Mirzadjanzadeh and his collaborators (Mirzadjanzadeh, 1959) developed a method for analyzing hydro-aerodynamic processes with the help of stochastic and adaptive training models.

Shischenko and Baklanov (1933) were first to systematically outline a number of washing fluid hydraulic problems. Many aspects of hydro-aeromechanics of drilling processes were considered in monographs (Gukasov, 1976; Gukasov and Kochnev, 1991; Goins and Sheffield, 1983; Esman, 1982; Mezshlumov, 1976; Mezshlumov and Makurin, 1967; Mirzadjanzadeh, 1959; Mirzadjanzadeh and Entov, 1985; Shischenko et al., 1976; Macovei, 1982; and others), handbooks (Mittelman, 1963; Filatov, 1973; Gabolde and Nguyen, 1991; and others) and the periodic literature.

At present, there has been a tendency to develop systems approach to drilling hydro-aeromechanics chiefly in building well-bed system models both simplified and more complex ones demanding application of various mathematical methods with regard to designing, building, and operation of wells.

CHAPTER 2

BASIC PROBLEMS OF HYDRO-AEROMECHANICS IN DRILLING PROCESSES

Hydro-aeromechanic processes in drilling occur in the well-bed system consisting in the simplest case of two parts: circulation system of the well along which fluid, gas, or their mixture including rigid particles flow and one or several opened up bed formations.

In general, the hydro-aeromechanic program of well-bed operation would be engineered when distributions of the following parameters are determined and reconciled: (1) flow rates; (2) pressures; (3) densities; (4) stresses; (5) concentrations; (6) temperatures; (7) geometric sizes of system elements (length, diameter, and spatial arrangement of each circulation system including level depth, radius, and thickness of beds); (8) characteristics of compressors and pumps, cementing units, and mixers (deliveries and pumps); (9) strength characteristics of system elements; (10) characteristics of the lifting mechanism of the drilling rig (velocities and accelerations in round trips); (11) characteristics of downhole motors (pressure drops at different flow rates of the flushing fluid); and (12) granulometric compositions of the cutting drilled and carried out from the well.

Distributions 1-6 are connected with each other by common hydro-aeromechanic equations in the region of distributions 7-12 taking place in drilling. The description of hydro-aeromechanic processes of drilling reduces to finding relations connecting distributions listed in 1-12.

Depending on the goal of technological operation, any distribution from 1 to 12 can be sought or given in the form of technical, technological, economic, or ecological restrictions. In designing and handling hydro-aeromechanic program or its parts, it is required to get distributions or separate values of some of them as functions of flow rate and pressure at given values of the rest.

Figure 2.1 presents a list of main processes 1.1-1.3 and 2.1-2.5 and problems 1.1.1-1.3.3 and 2.1.1-2.5.1 associated with them, which usually happen to be considered in drilling. In order to solve them, it is necessary to investigate distributions 1-12 for stationary and nonstationary flows in well-bed system elements. When solving a concrete problem, one finds one or more distributions among 1-12 so that they would not contradict the rest of them.

For example, let us consider in more detail a distribution of pressure in underground part of the circulation system, which happens to be often determined in carrying out hydro-mechanical process of drilling with fluid washing. Figure 2.2 shows the sought pressure distribution (diagram) in circulation system of a vertical well in boring with washing of incompressible fluid at a given arrangement of the drill pipe string (the arrows show directions of the circulation). The pressure in the diagram is determined under the following conditions:

In a variety of problems, the expected pressure depends on the characteristics of items 1-12. In performing calculations, it is not necessary to find the whole pressure distribution (diagram). For example, in the absence of weak or showing beds, it is enough to determine the pressure only in the ascending pipe, which should not exceed permissible pressure in the pump. In the process considered, other distributions 1-12 are not mentioned, but it is meant that they satisfy the diagram in Fig. 2.2. And yet the existence of such distributions should be kept in mind, and they must be taken into account when solving concrete problems.

From what has been said, it follows that the basis of all hydrodynamic calculations consists of the facility to find pressure distributions in circulation system elements of the well. In order to calculate pressure distribution and to build pressure diagram, one should be able to determine pressure drop both in concrete circulation system elements and in given cross section of the well element.