SPE

Society of Petroleum Engineel'S

SPE 15950
Analysis of Air Drilling Circulating Systems With Application to
Air Volume Requirement Estimation
by D.S. Wolcott, EDCON, and M.P. Sharma, U. of Wyoming
SPE Members

Copyright 1986. Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Eastern Regional Meeting held in Columbus, Ohio. November 12-14, 1986.
This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the
author(s). Contents of the paper, as presented, have not been reviewed by the SOCiety of Petroleum Engineers and are subject to correction by the
author(s). The material, as presented. does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers
presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is
restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of
where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL.

ABSTRACT
Air drilling uses air or gas as the
circulating medium. Because there are so many
variables involved in air or gas drilling no one
general method has been developed to predict the
appropriate volumetric requirements for field use.
In an attempt to alleviate this problem a
computational model has been designed and
developed which can analyze the pressure drop
contributions for the complete air drilling
system. This will facilitate the optimization of
the air or gas pressure and volume requirements.
The model is capable of analyzing the effects of
variations in flow rate, sandpipe pressure,
cutting size distribution, and loading.
Studies conducted using the computational
model includes an analysis of several methods for
determining pressure drop due to the solids phase.
The results from these studies were compared with
Two of the
Industry Field Experience Data.
methods indicated good agreement with the data.

drilling techniques are rendered inoperative.

Air drilling is very useful in minim~zing
formation damage to potential producing zones.
It is clear that there are many economic
incentives to develop a method which will
accurately determine the standpipe pressures and
air flowrates required to lift drilled cuttings
up the wellbore annulus. This method should
prove useful and accurate for various drill ing
environments that may be encountered.
There
are
many
difficulties
in
mathemati ca lly mode 11 i ng gas-parti cl e flows.
Because of these difficulties studies conducted
in the past have made assumptions which simplify
the approach but lose accurate predictive
capabil ities.
The primary difficulty which
arises is the fact that the friction,
hydrostatic effects, and heat flows are not
easily described in a two phase environment.
This paper presents a computational model
which can analyze the behavior of the
air-drilling circulation system, and can be used
to estimate the minimum flow rates and pump
pressure
for
varying
drilling
rates.
Incorporated in the computational model is an
opt i on to cons i der the effects of ve 1oc i ty and
temperature non-equilibrium between the gas and
solid phases and the heat flow contribution from
the formation, using a combination of momentum
and energy coupl i ng. Thi s computati ona 1 model
can
be
applied
to
any
isothermal
or
non-isothermal one dimensional flow of oas
solids suspension. The model offers variations
in air flow rate, standpipe pressure, cutting
size distribution, loading, and therefore can be
used for sizing of surface equipment in the
designing stages of an air drilling operation.

INTRODUCTION
Air is the ultlmate low-density drilling
fluid which enhances the generation of fractures
at the formation and bit interface. This is
accomplished because the hydrostatic pressure
created by the column of air at the bottom of the
hole is less than would be created by conventional
mud systems.
The use of lower hydrostati c
pressure allows the rock at the bit surface to be
easily crushed and the chips to explode off the
bottom and be introduced into the air stream,
thereby increasing the penetration rate.
Optimal results and greatest economy from air
drilling techniques depend on several factors.
r~ature competent formations that produce 1ittle or
nr formation fluids provide the best results.
Also drilling should be limited to geologic areas
~/here reservoir pore pressures are low or not
lurge enough or prolific enough that dry air dust

LITERATURE REVIEW
There have been severa' industry accepted
methods
developed
for
predicting
volume
requirements in air or gas drilling techniques.

Rpfr;'-ences and illustrations at end of paper.

271

2 ANALYSIS OF AIR DRILLING.CIRCULATING SYSTH1S WITH APPLICATION TO AIR VOLUME!REQUIRH1ENT ESTIMATION SPE 15950
One of the first and still most widely used
approaches to volume determination using air as
the dri 11 i ng medi um was developed by R. R. Angel
(1).
He assumed that the drilled solids and
circulating medium formed a homogeneous mixture,
in other words there was no slip between the
twophases. Angel appl i ed the Weymouth equation
for vertical-flow which included the effects of
solids being transported up the annulus, resulting
in what is known as Angel's Equation.
Angel in his works for the first time
incorporated drilling rate as a parameter and made
an attempt at correcting for downhole temperature
changes. He did however assume that there was no
slip between the solid phase and the gaseous
phase. This was later proven to be an invalid
assumption. Also his work neglected particle wall
resistance.
In shallow quarry drilling, 3000 ft/min
downhole annular velocity proved satisfactory (1)
in transporting particles to the surface. It was
assumed then that this value could be used to
calculate basic circulation requirements. This
assumption is not considered reliable because
formations, drill speed, and bit selection change
the particulate shape and size to such an extent
that it cannot be considered valid. It was shown
by Gray (2) that 3000 ft/min at the surface would
lift no more than a 0.2 in. particle.
In the same year that Angel presented his
work, 1954, Gray (2) experimentally determined
turbulent flow drag coefficients for cuttings
normally encountered in drilling operations. He
studied
characteristically
flat
particles
(limestones and shales) and angular to sub-rounded
particles (sandstones). He established a drag
coefficient of 1.40 for flat particles and 0.85
for angular to sub-rounded particles.
In 1967 Sapre and Schoeppel (3) developed a
mathematical model which considered gas-wall and
solid-wall frictional effects and slip of the
so 1i d pha se in the gaseous medi um. They based
their analysis of slip on Newton's equation and
combining with the mass flow rate equation
developed an equation that gives the minimum mass
of gas required to lift a single solid particle of
a given diameter.
In 1973 Capes and Nakamura (4) studied
vertical pneumatic conveying in a 3.0 inch
diameter riser.
By using a series of
quick-closing valves they found that the particle
slip velocity was often greater than the
The frictional
calculated terminal velocity.
pressure losses in the riser were also determined
and their correlation will be studied in this
paper.
In 1976 Sharma and Crowe (5) incorporated in
their analysis of gas-particle flows the concept
of regarding the particle phase as a source of
momentum and energy to the gaseous phase. They
analyzed the flow metering of gas-particle
suspension in a venturi, illustrating the
applicability of this computational scheme using
conservative variables.
In 1980 Makado and Ikoku (6) working under
contract for the DOE experimentally determined the
solids friction factors and minimum volumetric
requirements in air or gas drilling. Their work
included an in-depth study of the solids friction
factors created by flowing sands, limestones or
shales up the wellbore annulus. Makado and Ikoku
based their mathematical formulation on the
Con<:prv;,tion of Mompntum pouation This eouation

is used for flow down the drill pipe and up the

annulus, the difference being that gas and 501i0
flows are considered in the annulus and only g~s
flows are considered in the drill pipe. This
method did not incorporate considerations for
particle size variations and it assumed a
setvalue for the temperature gradient. A'so an
area of critical 1ift above the drill collars
was not considered.
Makado and Ikoku's
correlation for frictional pressure drop due to
solids (sandstone) is studied in this paper.
In 1983 Sharma and Chowdhry (7) developed a
model
for
drilled
cutting
computational
transport in air drilling operations. Their
model used a total pressure drop approach
resulting from effects due to particle drag,
friction, and hydrostatic head.
The model
predicted the pressure drop due to particle drag
based on the number of particles in each cell.
To determine the particle number they assumed
that there was no slip between the particle and
the gas phases.
Wolcott (8) modified Sharma and Chowdhry
(7) method for pressure drop calculations and
deve loped a model fo r air vo 1ume requ i rement
calculations and compared other methods.
THEORETICAL ANALYSIS
The drilling interval is divided into
computational cells as shown in Figure 1. The
basic assumptions made in this analysis are:
1) The flow is in steady state.
2) The physical properties of the fluid are
constant across the computational cell.
3) The annulus, drill pipe, and collars are
concent ri c.
4) The inner and outer pipes are not rotating.
5) The solids are present as a dilute phase, so
that particle to particle interaction can be
neglected.
PRESSURE DROP INSIDE THE DRILL PIPE:
The pressure drop between two points in the
drill pipe can be evaluated by using Bernoulii's
principle:

The subscripts 1 and 2 represent the upper

and lower elevation of the control volume
respectively. In small computational cells of
constant area the change in velocity will not be
significant.
This can be shown by the
understandi ng that the flow rate changes very
little in a computational cell with small
pressure and tempurature changes. The velocity
which is dependent on the flowrate and area will
not change appreciably, therefore:
~P=f1-P2=(Y2-y,)~+Hlo

where

PRESSURE DROP ACROSS THE BIT:

The pressure drop across a drill bit in air
or gas drilling can be calculated from equation
i'n .. n"," i'lo.. th ..ollnh rhokp<: Fo~ ",<I; ",t,,,,t;",.
272

(2)

D. S. Wolcott & M. P. Sharma

SPE 15950

The general conservation of energy equation

for the control volume is written as

frictionless flow of gas through an orifice, the

gas flow is given by (9):
,K+I

Q:

.1/2

1555CAnPI 2Bs ~[(!i)"Ij(_ (!i)-K-] II

_GT91 K 1 PI
PI

(4)

(9)

I
I

This equation is in oil field units, where:

Q = gas flow rate, (mcf/day)
C
discharge coefficient
G
specific gravity of gas
T1
temperature above the bit (R)
pi
pressure above the bit (psia)
P2
pressure below the bit (psia)
A
total area of the nozzles
R specific heat ratio

The L'lE term is the "source" term for the energy

equati8n due to the presence of the particulate
phase. The "work-done" term is assumed to be
zero because no shaft work is done. The above
equation becomes,

v2

The discharge coefficient C accounts for the

fact that the minimum area of the flow stream will
be somewhat less than the area of the nozzles.
Solving this equation for the terms containing P2 '
since Q is a constant value, yields:

V A

92 92

erh.,+~+y,1=f1VgA.rh,+-iL+
- 2 go ~J I l L go
L

Y~+Q+IlEp
U

The Q term represents the heat fl ow from the

surrounding formation into the wellbore annulus.

(5)

Transformation of Variables
Considering the portions of equations
(6), (8), and (10) that are concerned with a
one-dimensional gas flow field, that is, the
wall friction, particle momentum, and particle
energy "source" terms are excluded for the
moment, and defining new variables X,Y and Z as:

This equation can now be solved for P using an

interative technique such as the secant~ethod.

X=f9v9A.

PRESSURE DROP IN THE WELLBORE ANNULUS:

In the following analysis the principles of
mass-conservation,
momentum-conservation
and
energy-conservation are applied to the one
dimensional flow of a particle laden gas up the
drilling annulus. The drilling interval is still
divided into computational cells as shown in
Figure 1.
The mass conservation equation for the
computational cell can be written as:

(11)

finally solving for Vg gives (8) (in X , Y, and Z)

(12)

where
C:

(6)

(.I$..:.!)
"K-l

b = (K~I)V

This equation simply states that the net mass flow

into the control volume (computational cell) and
the net mass flow out of the control volume are
equal.
The momentum-conservation principle can be
stated as: The net external force acting on the
fluid within the prescribed control volume equals
the time rate of change of momentum of the fluid
within the control volume plus the net rate of
momentum flux or transport out of the control
volume(10). For steady flow

+J~A.y

(13)

The correct sign to be used in equation 12 is

the negative sign, which can be shown by the
second law of thermodynamics. The conservative
variables X,Y and Z are used to provide an
expression for gas velocity V. Recombining
equations with the wall friAion, particle
momentum, and particle energy "source" terms,
the new equations can be written as:

'Sox,

(14)

(15)

(7)

(16)

Particle Velocity
The veloclty with which a solid particle
freely falls through a fluid will increase until
the accelerating force (gravity), is equal to
the resisting forces. The resisting forces are
buoyancy due to the fluid displaced by the
particle, friction due to the relative motion of
the particle through the fluid and any residual
acceleration.
When the gravitational and
resisting forces become equal the solid falls at
a constant maximum or terminal velocity. This
equation can be written as,

For purposes which will be discussed later

this equation is transformed into a more
convenient form.
PA

I'

f11

V'j~ A,

+ --- -

go

.
t.M - dF. - F.
P

(8)

For mathematical simpl ification the momentum

source term due to the particulate phase is called
L'lM.

v,: <Idp9(i'p- 1',)

IL - !_____________________--=-=::--_______________ 3 CD ~
273

(17)

4 ANALYSIS OF AIR DRILLING CIRCULATING SYSTEMS WITH APPLICATION TO AIR VOLUME REQUIREt1ENT ESTIMATION SPE 15950

The velocity of the particle for the cell can be

determined by the relation

heat transfer coefficient for the

gas
outside diameter of the annulus
(ft)
temperature of the formation

(18)

In practice, a somewhat greater velocity is

required. Any carrier fluid velocity in excess of
Vt will theoretically result in solids transport,
bat would result in a higher than necessary
pressure gradient.
An accepted velocity for
defining the minimum transport velocity, in a
practical sense, is twice the terminal velocity

Integrating equation (26) yields an expression

for the downstream temperature of the gas
(29)

where the interval Atg is estimated by

(11)

Drag Force Term

The term; na 1 velocity concept can used to
describe the pressure drop contribution due to
drag forces on the solid particles. When a solid
particle is transported vertically by an air
stream there will be, for most practical purposes,
a difference in velocity.
(19)
v, v9 - vP
The slip causes drag forces on the particles,
resulting in a loss of momentum in the gas phase.
The drag force acting on a single particle is
given by
(20)

6 ' c.ylv g
19

(30)

The heat transfer coefficient for the gas (Htc),

which controls the heat transfer to and from the
~as, is a functi on of the gas Reynolds number
(Reg) and gas Prandtl number (Pr). For gas flow
in concentric piping the heat transfer
coefficient is represented reasonably well by
Htc = 0.0000755 *Reg* Pr/d h
(31)
The energr source term due to the particles is
given by 7)

The total number of particles in a computational

cell is given by

(32)

(21)

The total drag force due to all particles present

in the computational cell can be written as,
(22)

Gas Friction Term

The force due to friction is equal to the
shear stress
acting on the pipe surface
multiplied by the total circumferencial area of
the inner and outer pipe
OF, ='1: I1(D, - Dpl Oil

shear is commonly defined as,

'I: =fg(f~ v?)
"go '

where

the specific internal energy

e
the specific heat capacity of the
Cpp
particle material
The change in particle temperature is
obtained from the energy equati on for a
particle, which is
(33)

(23)

where htc is the film heat transfer coefficient

for a pCarticle. The above equation can be
simplified to

(24)

In terms of pressure
6P,

21,

f</,f

(D,- Dpi9c

(34)

(25)
or,

Heat Transfer Terms:

The change in gas temperature is obtained
from the energy equation for gas, which is

dT.

Cit = '1:0

(26)

Integrating equation (33) yields an expression

for the downstream temperature of the particle
T.,

The above equation can be simplified to

"

(27)

(35)

(Tg- Tp l

=To-. '"'"

(T - T l e-(t.tp "!to)
91

(36)

P,

where the time interval

~tp

is estimated by

t.tp t.y/vp

(37)

or,
(28)

Nusselt number (Nu). which controls the

heat transfer to and from the particle, is a
function of the particle Reynolds number (Rep)
and gas Prandtl number (Pr). For a spheri ca 1
c:.h;\np

274

thp Nllc;c;p 1 t nllmhpr i c; rpn .. o"ontorl'

D. S. Wolcott & M. P. Sharma

SPE 15950

B)

reasonably by (6).
Nu = 2.0 0.6

It

Rep

It

Calculate new pressure, P2

(38)

Pr

(43)

This section has presented the equations that

are used to model the downhole air drilling
circulation system. The application of these
equations in the computational
model, to
determine the minimum flowrate and evaluate the
total system pressure drop, will be discussed in
the next section.

Repeat steps A through B until the total

depth of the drill pipe has been reached.
D) Calculate pressure drop across the bit using
equation (5).
This equation is iteratively solved for P
using the secant method. The pressure P tha~
is determined from this equation is the bottom
hole pressure.

C)

THE COMPUTATIONAL MODEL

The computational algorithm of the model
is discussed below.
The computational scheme
solves the flow field in a step-wise fashion.
To begin, a set of initial drill ing conditions
should be known:
1) Type or fluid (air or gas) to be used.
2) Standpipe pressure.
3) Rate of Penetration.
4) Atmospheric temperature and formation
temperature gradient.
5) Hole, collar, and pipe diameters.
6) Diameter of nozzles to be used.
7) Inside diameters of pipe and collars.
8) Collar length.
9) Type and characteristics of formations
being drilled.
10) The initial air or gas requirements
estimated low so that the drilling
program will not be overdesigned.
Once these values have been entered into the
computer program they represent the starting
values at the top of the drill pipe.
The
computational model divides the drilling interval
into
a pre-determined
integer number of
computational cells.

E) Calculate the following parameters for the

initial gas and sol id flows in the Ivell bore
annulus.
1)
2)
3)
4)

Gas density, P at P and T .

Gas Flow rate,gQ, ustng equQtion (39).
Conservative variables, Xl' Y1 , Zl using
equa t i on (11).
Calculate the mass flow rate of solids, Mp

1'\ RaP
F)

a = 14.7" 144.0" 0STO" T,

~

3)

Temperature of gas, Tg2 , using equation

(29).
4) Reynolds number of gas, Reg.
5) Reynolds number of the particle, Rep.
Rep

5'

6)

7)

= (~)
460.0

VI dp

(46)

6) Terminal velocity, Vt , using equation

(17).

(39)

Rep is
value of Rep
of V. The
substituted
converge.
7)

0.763

"0.0000109
.

= fq

lJ.

Gas deviation factor, Z.

The gas deviation factor is calculated
using the Hall and Yarborough (12)
correlation.
3) Air or gas density, p at PI and T 1.
4) Viscosity of gas, J.l g
g
Viscosity of gas isgdetermined using
Einstein's equation(7).
II

(44 )

"/3600.0

(45)

2)

T.

It -\.

Calculate the following parameters for the

gas and solid flows in the well bore
annulus.
1) Viscosity of gas, J.l , using equation
(40).
g
2) Temperature of formation, Tf2

A) Calculate the following parameters for the gas

flow inside the drill pipe.
1) Actual gas flow ra}e, Q.
520.0"

(40)
8)
9)

Reynolds number of the gas flow, Reg.

Friction factor of the gas flow, ff
The friction factor is calculated using
the Colebrook equation (9) iteratively
solving for ff using the secant method.
The pressure drop due to gas friction
and gravity, 11 Pf' 11 Pg'

10)
11)

12)
13)

a function of
was determined
value of Vt in
into step F-5

V and the initial

u~ing a first guess
step F-6 should be
until Rep and Vt

If the terminal velocity is greater

than the gas velocity go to step A and
increment gas flow.
Nusselt number, N , using eqn. (38).
Particle temperatHre, using eqn. (36).
Total number of particles in the
computational cell, N using eqn. (21).
The drag force due toPparticle-gas
interaction, F , using eqn. (22).
Source term duerlt to energy, 11 E , (eqn. 32)
Source term due to momentum, ~M .
P

(47)

(41)
(42)

14)
275

Repeat steps F5 through F13 for all

variations of particle sizes.

6 ANALYSIS OF AIR DRILLING CIRCULATING SYSTEMS WITH APPLICATION TO AIR VOLUME REQUIREMENT ESTIMATION SPE 15950
15)

Friction factor, ff

Force component due to gas friction, Ff

(eqn. 25).
17) Total volume of two phases in
computational cell.
18) Void volume, VOID.
19) Density of the mixture, Pm'
16)

20)

= VOID* P
Fg

21)
22)

(1.0 - VOID)* Pp

F~rce due toggravity, Fg

p.. *t.Y*A.

(48)
(49)

Heat transfer coefficient, HTC '

Hrc' 0.0000755 * Reg P/c;.

(50)
Heat flow from formation to wellbore, Q
(51)

23)

New conservative variables Y2 , and Z2'

y 2 Y, -AMp - F( - F, - F..
(52)
(53)
1, Z, t.Ep a

24)

Predict new gas velocity, Vg2 (eqn.

12).
New pressure value, P2 .

25)

P2 ' (Y2 - ~. Vg2/9,;> I A.

G)

Repeat step F until the top of the well is

reached.

H)

If the annular pressure in step F-25 at top

of the well is not above atmospheric
pressure increment the flow rate and repeat
steps A-H.

I)

If, after increasing flow rate an additional

100 SCF/M, the atmospheric pressure cannot
be achieved, output all results and the
computational model will stop.

(54)

RESULTS AND DISCUSSIONS

Three methods for determi ni ng pressure drop
due to the soli ds phase were studied. The study
was conducted because a literature search
revealed
that
the
information
needed
to
determi ne the pressure component of the soli ds
phase was limited.
The study was begun by
setting certain boundary conditions equal for
each of the three methods analyzed. They were
1) Surface temperature = 80F ,2) Nozzle size =
28/32 in. and 3.) Temperature gradient of the
formation = lOoF/lOOO ft. The cell size varied
for each method due to an optimization between
computer time and accuracy.
The results
produced by the computational model from the
three methods will now be discussed.
One theoretical model (7) and two empirical
correlations (1,5) were evaluated for their
accuracy in determining the pressure drop due to
the solids phase. The curves that are plotted
in Figure 2 represent the critical flow of gas
and solids for the given drilling situation.
The curve describing the critical flow for gas
solids suspension in this paper is defined as
the region above which cuttings will be
delivered to the surface and the region below
which there is insufficient ;!ir nrpc;c;lIrp i'lnd

276

therefore no cuttings are del ivered. Critical

flow curves wi 11 be used throughout the
discussions.
The modified Sharma and Chowdry (7) method
(theoretical model) for determining pressure
drop due to the solids phase was first employed
in the computational model. The method hpj been
enhanced in this paper as it no longer assumes
homogenous flow for calculation of the particle
number. The modification was tested and found
to compare closely with data used by Sharma and
Chowdry (7). The method is theoretical in
nature and is based on the total force applied
to all the particles in the flow field. The
cell size used in the computational model for
this method was 5 feet. This cell used was the
smallest of the three methods tested.
The
smaller size was required to obtain sufficient
accuracy.
The computati ona 1 model requi red
approximately two hours to compute one criti ca 1
flow point using the Prime computer, and is a
serious limitation with this method for small
The results of the Sharma and
computers.
Chowdry method are plotted in Figure 2 and are
compared with an industry experience curve. The
industry experience curve was compiled from
Amoco's air drilling experiences of over 3
mi 11 ion feet of hole with an overall average
penetration rate of 1,000 ft/day/rig in hard
rock areas. The experience curve is considered
"lower than what is actually needed to drill an
efficient trouble free hole" but "indicates a
good starting point for determining air
requirements" (13).
The modified Sharma and Chowdry method (7)
predicts a higher flow rate at depths below
13,000 feet than does Amoco's ex peri ence. At
depths above 13,000 feet a crossover occurs and
the modified Chowdry and Sharma method predicts
a lower flow rate. The curves at zero depth do
predi ct a fi nite flow rate because a gas
velocity must be maintained even though there are
no solids loading.
The second method for determining pressure
drop due to the solids phase that was employed in
the computational model was an empirical
correlation developed by Makado and Ikoku (1).
This method was chosen because they developed a
correlation which was derived from a lab size air
drilling annulus. The cell size used in the
computational model for this method was 50 feet.
The cell size was the largest for the three
methods tested. The method, probably due to its
empirical nature, yielded every improvement in
accuracy for smaller cell sizes. This method,
with a 50 foot cell size, outputs a critical flow
point in approximately 10 minutes.
The results using Makado and Ikoku's
correlation (1) are also plotted in Figure t.
Makado and Ikoku's correlation produces a curve
whi ch is consi stently lower than industry
experience. This difference is as high as 700
SCF/min and remains at this level over the range
of interest.
The reasons for this lower
prediction are felt to be caused by the way in
which the correlation was developed. Makado and
Ikoku's correlation was developed in the
laboratory and some of the conditions of the
test are not representative of those in actual
drilling operations. The solids flow rate that
they used corresponded to a drilling rate of ten
feet per hour, extremely low for an air drilling

SPE 15950

D. S. Wolcott & M. P. Sharma

NOMENCLATURE

application. Also they injected large amounts of

air in relation to their solids flow rate, and
this lowered the loading ratio even further.
The third method used in the computational
model for determining pressure drop due to the
solids phase was a correlation presented by Capes
and Nakamura (5). The cell size used in the
computational model for this method was 25 feet,
and output a critical flow point in approximately
20 minutes of computer run time. The results
yielded from this correlation are plotted in
the Figure 2 too. The f10wrates predicted by this
method are higher than Amoco's experience below
13,000 feet and lower above 13,000 feet.
The
crossover occurs because the pressure loss due to
solid and gas friction do not reduce the pressure
in the annulus to atmospheric pressure until
deeper depths. Therefore the curve predi cts a
lower f10wrate at deeper depths than does Amoco's
industry experience.
In
comparing
the
three methods
for
determining pressure drop due to the solids phase,
Makado and Ikoku's curve is found lower than
Amoco's experi ence and the lowest of the three
methods tested in the computational model. The
correlation presented by Capes and Nakamura and
the modified Chowdry and Sharma method over1 ie
each other. The reason for thi sis that both
methods predict a small and nearly equal pressure
drop due to the sol ids phase as compared to the
total annular pressure drop.
As can a1so be seen a 11 methods except the
modified Sharma and Chowdry (7) and the Capes and
Nakamura (5) methods predict lower than Amoco's
experience.
According to Amoco's extensive
experience only the two previously mentioned
methods could be used, without an experience
factor, in designing an air drilling circulation
system. The other methods would predict much
lower than what is needed to drill an efficient
trouble free hole.
The effects of particle size variations
were significant on all three methods evaluated.
The mean particle size may remain 0.1 inches but
because there are larger and smaller particles
of significant proportions the required flow
rates and standpipe pressures are changed. As
can be seen graphically on Figures 3, and 4, a
larger f10wrate is required because of the larger
particles. The larger f10wrate will increase the
pressure drop due to gas fri cti on and lower the
relative pressure drop due to solids.
Conclusions
1) The computational model can estimate
the minimum air or gas volumetric requirements
and the maximum depth that can be obtained for a
specific set of drilling conditions.
2) The experimental correlation developed
by Capes and Nakamura (5) and the theoretical
model of Sharma and Chowdry (7) are the two
methods studied that indicated good agreement
with Amoco's field experience.
3)
Particle
size
variation
has
a
significant effect on required flow rates and
standpipe pressures.
4\
Alternate
methods
of
determining
hydraulic diameter do not significantly change
the resul tant gas friction factor for most air
or gas drilling applications.

A area, sq rt
A. area of the annUlUS, sq ft
AH = cross sectional area of the hole, ft2
Iv! total area of the nozzles, sq ft
Ap - prOjected area of the particle
ap = acceleration of the particle
C discharge coefficient
Co = particle drag coefficient
Cpg = specific heat of gas, fHbf /lbm-F
CPI' specific heat of particle, ft-lbf /lbm-F
d = outside diameter, ft
D outside diameter of the annulus, ft
do inside diameter of the pipe, ft
dh hydraulic diameter, ft
Dp outside diameter of the pipe, ft
dp diameter of the particle, ft
e specific internal energy
~E energy term, ft-Ibf/sec
Fe force due to buoyancy, lbf
fo drag force coefficient
Fdt =total drag force due to particles, Ibf
Ff force due to gas friction, lbf ff friction factor of gas
fg friction factor of gas
Fg force due to gravity, lbf
G specific gravity of gas
g gravitational acceleration, ft/sq sec
gc gravitational constant, Ibm x 32.2 ftl (Ibf x sq sec)
h enthalpy of gas, ft - IbfIlbm
HTc heat transfer coefficient of gas
hrc heat transfer coefficient of a particle
K specific heat ratio
M molecular weight of the gas
m molecular weight
Mg. mass flow rate of gas, Ibm/sec
Mp mass flow rate of solids, Ibm/sec
Mp mass of solids, Ibm
~ change in momentum of solids
Hs mass flowrate of the fluid
Np - particle number
Nu - Nusselt number
P pressure, Ibf /sq ft
Pr Prandt I number
~P. = change in pressure of the solids
Q heat flow from the formation, ft-Ibf /sec
R - universal gas constant
Reg Reyno I ds number of the gas
Rep Reynolds number of the particle
Tg - temperature of the gas, 'R
~tg - time for gas to cross cell, sec
Tp temperature of the particle, 'R.
~tp time for particle to cross cell, sec
T standard temperature
V velocity, ftlsec
Vg velocity of gas, ftlsec
Vp velocity of particle, ftlsec
V velocity of solids, ftlsec
Vt = slip velocity
VOl D space occupied by gas
VOLS = volume of the solids
Wg = mass flow rate of the gas, Ibm/sec
W. = mass flow rate of the sol ids, Ibs/sec
Y momentum source term
y change in elevation, ft
Z energy source term
z gas compressability factor

277

8 ANALYSIS OF AIR DRILLING CIRCULATING SYSTEMS WITH APPLICATION TO AIR VOLUME REQUIREMENT ESTIMATION SPE 15950
GREEK

10. Olson, Reuben M., Essentials of

Fluid Mechanics, Harper and Row
(1980) .

~ = fgL
gc

11. Grovier, G.W., Aziz K., The flow of Complex

Mixtures in Pipes, Robert E. Kireger
Pub 1i shi ng Co. (I982).

K = Gas Thermal Conductivity

f = Density, lbm/cu It.

"( =Thermal

Characteristic of Time

12. Yarborough, L., and Hall, K.E., "How to

Solve Equations of State for Z-factor," The
Oil and Gas Journal, February 18, 1974, pp.
86-88.

11 = viscosity, lbm/ft-sec
m

= combined density of the gas and solid phases

= simplification of heat flow term

13. Hooke, R.A., Cooper, L.W., and Payne, E.W.,

"Amoco's Experience Gives Right Air Drilling
Techniques," The Oil and Gas Journal, June
1977, pp. 160-174.

SUBSCRIPTS

2
a
g
p
f
s

initial cell condition

final cell condition
annulus
gas
particle
formation
solids, if not otherwise defined

REFERENCES
1.

Angel, R.R., Volume Requirements for Air and

Gas Drilling, Gulf Publishing Co. (1958).

2.

Gray, K.E., "The Cutting Carrying Capacity

of Air at Pressure Above Atmospheric,"
Petroleum Transactions, AIME, April, 1958.

3.

Schoeppel, R.J., Spare, A.R., "Volume

Requirements in Air Drilling," AIME, 1967.

4.

Capes, C.E., Nakamura, K., "Vertical

Pneumatic Conveying: An Experimental Study
with Particles in the Intermediate and
Turbulent Flow Regimes," Canadian Journal
of Chemical Engineers (1973).

5.

Sharma, M.P. and Crowe, C.T., "A Novel

Physico-Computational Model for Quasi
One-Dimensional Gas-Particle Flows,"
Transactions of ASME, August, 1977.

6.

Makado, Carlos J., Ikoku, Chi U.,

"Experimental Determination of Solids
Fraction and Minimum Volumetric Requirements
in Air and Gas Drilling," Journal of
Petroleum Technology, November 1982, pp.
2645-2655.

7.

Sharma, M.P., Chowdry, D.V., "A

Computational Model for Drilled Cutting
Transport in Air (or Gas) Drilling
Operations," S.E. Conference on Theoretical
and Applied Mechanics, May 1984.

8.

Wolcott, D.S., "A Computational Model for

the Analysis of Air or Gas Drilling
Circulating System", M.S. Thesis, University
of Wyoming, 1985.

9.

Nind, T.E.W., Principles of Oil Well

Productiun, McGraw-Hill Book Company (1964).

ErQineerir~
Publisher~

278

COMPUTATIONAL CELL

L- I--'--t-+--'---;

Fig. 1-Computational cell.

FLOW RATE VS DEPTH

.
o

.;

Amoco's

Expe:oience
Modified Sharma and ChowdI'"J"
and
Canes and Nakamura

/
co

Makado and
!koku
Sa-pre

TyrB 0['" FORMATlOl'f = Si\NDSTO~E

SPECIflC GRt,VITY OF GAS = 1.0
PAllT1CLB SIZr:; = .10 in.
HOLE DAMBTlm = 7-:;/8 in
P1PE DlAMETEll = 4-1/2 in
nap = GU FT/HR

~~--~~~~--~--~----~--~--~~--~--~e.o
8.0
10.0
12.0
H.O
l~.O
18.0
DR."TH (,."1:) , TllOUSA.\'fDS

Fig. 2-Comparison of different methods.

279

FLOW RATE VS DEPTH

o

.n
....
c

...c:i

METHOD = Modified Sharma and Chowdry

TYPE OF FORMATION = SlJmSTONE
SPECIFIC GRAVITY OF GAS = 1.0
PARTICLE SIZE = .10 in.
PARTICLE SIZE = .07 - .13 in.
HOLE DIAMETER = 7-5/8 in
PIPE DL~METER = 4-1/2 in
Rap = 60 IT/HR

~~----~---r----~--~----~~~.----~----~--~
6.0
B.O
10.0
12.0
14.0
16.0
1B.0
0.0
2.0
~.O

DEPTH (FT) , THOUSANDS

Fig. 3-Effect of particle size (Sharma and Chowdhry method).

FLOW RATE 'VS DEPTH

/

..
c

ci

/
/
/

C/l

t:J,,;

C:: ..

;:J~

_0

.... '"

/
/
/

/
/

METHOD = MAK..WO &: IKOKU

n""PE OF FORMATION = SA..\,DSTO~E
SPECIFIC GRAV1TY OF GAS = 1.0
PARTICLE SiZE = .10 in.
PARTICLE SIZE = .07 - .13 in..
HOLE DIA.\fETER = 7-5/8 in
PIPE DIAMETER = 4-1/2 in
ROP = 60 IT/HR

/
/

/
/

o
c:i

~--~--~~~--~--~--~--~--~--~
0.0
2.0
~.O
6.0
8.0
10.0
12.0
14.0
16.0
18.0
DEPTH (FT), THOUSANDS
Fig. 4-Effect of particle size (Makado and Ikoku method).

280