Understanding Kick Tolerance
and Its Significance in
Drilling Planning and Execution
K.P. Redmann Jr., SPE, Chevron U.S.A. Inc.
Summary. Kick tolerance is a drilling parameter that has prompted both confusion and misunderstanding in the drilling industry,
yet its importance to drilling engineers may be increasing exponentially. The increasing number of worldwide drilling catastrophes
may spur government agencies to tighten controls on casing-setting-depth criteria, requiring pipe to be set once minimal kick tolerance
values are reached. A thorough understanding of kick tolerance is necessary in both drilling operations and casing program design.
Confusion involving kick tolerance may be attributed to the concept of zero gain, which is commonly referred to in many accepted
definitions of kick tolerance. This paper presents an innovative approach to determining true kick tolerance that not only incorporates
the conditions of an influx within the well bore but also considers the possible reductions in kick tolerance caused by the circulation
of that influx from the wellbore. New techniques are available for hand-held calculators, which are now more accurate in determining
influx pressure and volume anywhere within the wellbore. A typical well example with illustrations describes kick tolerance and emphasizes the influence of other drilling parameters. Integration of kick-tolerance considerations into the well planning process also is demonstrated.
Introduction
The concept of kick tolerance has been controversial in the drilling
industry. Many say it fosters a false sense of security. 1 Much confusion can be credited to the term "zero gain," which is used in
this commonly accepted definition: kick tolerance is the maximum
increase in mud weight allowed by the pressure integrity test of
the casing shoe with no influx (zero gain) in the wellbore. To the
drilling hand on the rig, this means, "How much I can weight up
to kill the well without breaking down the shoe, assuming zero pit
gain?" All too often, the zero-gain condition is either misunderstood or omitted entirely.
Previously published papers have defined kick tolerance in terms
of a particular field or operation, developing equations that include
safety factors, trip margins, and pit gains common to that environment. 2,3 Although interesting and discernible to the drilling engineer, this may add to the confusion of the average field drilling
hand. In addition, governmental regulations may lead to further
misunderstanding when improperly interpreted. Minerals Management Service 250. 54 (a) (6) states, "A safe margin, as approved by
the District Supervisor, shall be maintained between the mud weight
in use and the equivalent mud weight at the casing shoe as determined in the pressure integrity test." 4
Although each well should be considered individually in the determination of such a safe margin, many contend that the future
will see a standard value for this parameter defined as 0.5 Ibm/gal.
This requirement could mislead many drillers into believing that
they can continue to drill until the mud weight equals exactly 0.5
Ibm/gal less than their shoe test.
For a better understanding of kick tolerance, the derivation of
the kick tolerance equation, based on the above definition, is presented. This equation encompasses the effects of an influx in the wellbore at initial shut-in conditions. And, of course, no examination
of kick tolerance would be complete without consideration of the
effects as the influx is circulated from the wellbore.
It is likely that government regulatory agencies may soon dictate
not only a minimum value for kick tolerance, but also the method
of determining that value. A thorough understanding of kick tolerance and how to calculate it while drilling are very important for
the drilling representative at the rigsite.
The drilling engineer in the office also must consider kick tolerance during the well design. Pore pressure and fracture gradient
information, if available, are excellent when used effectively to
select casing setting points. However, kick tolerance must also be
incorporated, especially in the case oflong, openhole sections. Other
factors, such as hole stability, may require an increase in mud
weight. Should this occur, the minimum allowable kick tolerance
Copyright 1991 Society of Petroleum Engineers
SPE Drilling Engineering, December 1991
may be experienced earlier than anticipated, and governmental regulations may require casing setting.
Studies have shown an increase in the number of blowouts worldwide,5 resulting in escalating costs and increasing liability. The
drilling program may soon come under close scrutiny by the various government agencies, which will undoubtedly set stricter guidelines for the drilling of all wells, possibly including kick tolerance.
Background
The derivation of kick tolerance (based on the accepted definition)
must be understood.
For a given mud weight, the casing-shoe pressure-integrity test
will define the maximum allowable shut-in casing pressure that will
fracture the formation at the shoe (p cmax)' This relationship is
Pcmax =(s- We,,)0.052Dsh · .......................... (1)
The casing-shoe pressure-integrity test, or shoe test, may be determined by one oftwo different methods, each lithologically dependent. In either case, a surface pressure is obtained during the testing
procedure and is added to the existing hydrostatic pressure at the
casing shoe. The shoe test is the sum of these pressures in mudweight equivalent (pounds per gallon) and identifies that pressure
to which the casing shoe was exposed.
To avoid fracturing exposed formations, which will not heal when
pressure is reduced (such as in hard rock drilling), a simple pressure test may be incorporated. After a minimum of 10 ft is drilled
below the casing shoe, the bit is pulled into the casing; the blowout
preventer is closed around the drillpipe; and the casing and exposed
formations at the casing shoe are slowly pressured to some predetermined value, which is based on the maximum mud weight required to drill the next section of hole. Additionally, this value is
sufficiently below the estimated fracture pressure at the casing shoe
to prevent fracture. This pressure (to which the casing shoe and
drilled formations have been exposed) may be converted to equivalent mud weight in pounds per gallon and represents the shoe-test
value.
In softer areas (the offshore environment) where formations will
heal when pressure is reduced, a different type of casing-shoe
pressure-integrity test is performed. Called the leakoff test, it determines the pressure, in mud-weight equivalent, at which the drilling fluid initiates small, vertical fractures in the exposed formations.
This test is similar to the above test, except no predetermined pressure is used. The casing shoe and exposed formations are pressured
by the pumping of equal increments (usually \4 to Vz bbl in volume)
of drilling fluid. Surface pressures are recorded for each increment
pumped until the incremental pressure begins to decrease. The last
recorded surface pressure before the observed decrease is added
245
to the existing hydrostatic pressure at the casing shoe and represents the formation fracture pressure. When converted to mudweight equivalent, this value is called the leakoff test or shoe test.
For any given depth, and assuming no wellbore influx, the maximum formation pressure allowable by the pressure integrity test is
Pfmax =Pemax +Phex' ............................... (2)
If the required or new mud weight, Wn , to balance this maximum
formation pressure is incorporated, then
Pfmax =0.052WnD h · ............................... (3)
Likewise, the existing or old mud weight Wex will define the existing hydrostatic pressure:
Phex=0.052Wex D h . ................................ (4)
Combining Eqs. 2 through 4 yields
0.052WnDh =Pemax +0.052Wex D h . . . . . . . . . . . . . . . . . . . . (5)
Eq. 5 may be simplified to
Wn - Wex =Pcmax/(0.052D h ) . . . . . . . . . . . . . . . . . . . . . . . . . (6)
Eq. 6, which assumes no influx in the wellbore (zero pit gain), defines kick tolerance because the quantity (Wn - W ex ) is the maximum increase in mud weight allowed by the pressure-integrity test.
Therefore,
Ko =Pcmaxf(0.052D h )· . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)
Including Influx
Eq. 7 can be developed further to include the effects of an influx
in the wellbore. The following conditions, common to the worstcase well-control scenario, are assumed: the influx enters the bottom of the wellbore as a slug; the influx remains as a slug during
circulation; and the influx is gas. (Commonly, 0.1 psi/ft is used
as the gradient, unless a more accurate figure is known.)
Any annular influx of a lesser gradient than the drilling fluid will
cause a reduction of the hydrostatic pressure in the annulus and
a corresponding increase in the casing pressure at the surface. Based
on the above conditions, this increase is
Peine = [(0.052Wex )-gdL i· .......................... (8)
For a given influx size, Pcmax will be reduced by an amount
equal to that in Eq. 8, and kick tolerance may be calculated to include the effects of an influx in the wellbore at initial shut-in conditions:
Kin = (Pcmax - {[(0.052Wex )-gi1L d)/0.052D h · . . . . . . . . . (9)
Worst-case scenarios are used in well-control design to ensure
that the surface equipment, casing, and exposed formations are competent to withstand and contain any pressures encountered. To design on a less stringent criterion would risk the integrity of the
wellbore and would require extensive risk analysis using very ac-
curate formation data on those formations to be drilled. Such accuracy is often unobtainable. A departure from the worst-case
scenario typically reduces the risk to wellbore integrity. One example is the "stringing out" of the influx, which increases the effective gradient of the influx, thus minimizing the reduction of
annular hydrostatic pressure. A second example includes the gradient of the influx itself. As with the previous case, if the formation fluid gradient is unknown and 0.1 psi/ft is used, the reduction
of annular hydrostatic pressure will be lessened if the true influx
gradient exceeds 0.1 psi/ft.
No discussion of increasing formation pressure has been attempted. Under certain conditions, such as swabbing, an influx may enter
the wellbore even though the mud weight is sufficient for the exposed formation pressures. Formation pressure has been omitted
to gain a basic understanding of kick tolerance.
Under most conditions and for most well geometries, Eq. 9 may
be used to determine kick tolerance. In some cases, such as an unusually large influx or a tight hole geometry, 6 expansion of the
influx during circulation will cause the true vertical length of the
influx at the casing shoe to exceed greatly the true vertical length
of the influx at initial shut-in conditions. Expansion of the influx
during circulation is necessary to reduce the pressure of the influx
and to maintain constant bottomhole pressure. However, this expansion is accompanied by a reduction in the hydrostatic head of
the annulus and a corresponding increase in surface and casingshoe pressures. Modern well-control procedures consider this expansion and calculate its effects on surface and casing-shoe pressures. Therefore, it is necessary to examine this condition as it
pertains to kick tolerance.
Influx at Casing Shoe
Pressure within the influx when it has been circulated to the casing
shoe is calculated by considering the "driller's method" of well
control, which uses the existing mud weight to remove the influx
from the wellbore. This method is preferred for this analysis because higher casing-shoe pressures will be experienced (in keeping with the worst-case scenario) and because occasionally neither
time nor weighting material (barite) is available for use of the "engineer's" or "wait and weight" method. Therefore, the maximum
shoe pressure will be realized when the top of the influx has been
circulated to the casing shoe and will equal the pressure of the influx.
It is desirable to calculate the pressure of the influx when it reaches
the casing shoe. Advances in hand-held programmable calculators
efficiently solve the formerly time-consuming, iterative, pressure/volume equations. 7 Because the pressure and volume of the
influx are known at initial shut-in conditions, the drilling engineer
or representative can use these programs (see the Appendix) to
predict the pressure and volume of the influx at the casing shoe.
The equivalent mud weight, W eq , at the shoe may then be determined and a new value for kick tolerance computed:
Kc=s- Weq' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (10)
624
TVD : 10,000'
10 ppg
13 ppge
8 112"
4 112" 16.60 ppf
1" x 2 13/16" (200')
9 5/8" (Assume 8 112" 10)
0.1 psi 1ft
Mud Wt:
Shoe Test:
Hole Size :
Drill Pipe :
Drill Collars :
Casing:
Influx Gradient:
4000'
For either case, Max slep
has been reached without
drilling into pressure.
4000'
8514'
8514'
10,000'
10,000'
Fig. 1-Well schematic.
246
10,000'
69.5 Bbl Gain
104.3 Bbl Gain
Fig, 2-Signlficance of influx (pit gain).
SPE Drilling Engineering, December 1991
13.0
1.5.--r---'-=-=-:---::----::::::-:::--:-:-:--:-::--:I
• Kick Tolerance Decreases With True Vertical Depth
• Kick Tolerance Decreases With Increasing Pit Gain
• Kick Tolerance Decreases With longer DC lengths
r-r---I • Kick Tolerance Decreases With True Vertical Depth
• Kick Tolerance Decreases With Increasing Pit Gain
• Kick Tolerance Decreases With longer DC lengths
11.5
12.5
11.0
_8.000'
_10.000'
_12.000'
c:::J 14,000'
12.0
10.5
0.5
11.5
50
10.0
50
Pil Gain
bbl~
69.5 bbls
Fig. 3-Kick tolerance at initial shut-in conditions.
The value for kick tolerance computed from Eq. 10 is now compared with that calculated by Eq. 9. The lesser of the two is considered the actual kick tolerance.
Example
Fig. 1 shows a well schematic and gives some pertinent information. Because the true influx gradient is unknown, the worst-case
scenario of a gas influx is used, and 0.1 psilft is approximated as
the influx gradient.
Before determining kick tolerance for this example problem, we
consider the significance of an influx in the wellbore, with no increase in formation pressure.
From Eq. 1, P emax is found to be 624 psi. If the bit is on or near
the bottom of the hole and a full column of mud exists within the
drillstring, the shut-in drillpipe pressure is zero. Knowledge of the
hole geometry allows us to calculate the influx length and size that
will correspond to a shut-in casing pressure of 624 psi. Using the
information given, we determine that for a O.l-psilft influx gradient, an influx length of 1,486 ft (69.5 bbl) would produce 624psi shut-in casing pressure. Therefore, the casing-shoe integrity is
compromised by a 69.5-bbl kick, without drilling into pressure.
A second consideration involves the bit having been pulled uphole,
as on a trip, and an influx being swabbed in. The influx length to
broach the casing shoe remains the same (1,486 ft). In this example, however, the influx must fill the 8V2-in. hole, not just the
8V2 x4V2-in. annulus, requiring 104.3 bbl to reach the same length.
Also, shut-in casing and drillpipe pressures will be 624 psi, unless
a drillpipe float is used and is holding pressure. Understanding the
significance of an influx in the wellbore (Fig. 2) is essential if kick
tolerance as a drilling tool is to be used to its full potential. Armed
with this insight, let us now consider kick tolerance for this example problem.
Again, using the information given and applying Eq. 9, we can
now determine kick tolerance for any given influx size at initial
1.5
Pit Gain bbls
100
Fig. 4-Kick tolerance at initial shut-in conditions (mud weight
increased to 11.5 Ibm/gal).
shut-in conditions. Plotting kick tolerance vs. pit gain (Fig. 3) is
simple for different drilling depths (these values are based on the
use of the existing or current mud weight-in this case, 10.0
Ibm/gal). Any of the hand-held programmable calculators available today can easily provide the same information once programmed with Eq. 9.
Should the mud weight be increased, new kick-tolerance values
must be calculated because of the reduction in P cmax' Fig. 4 shows
that kick tolerance does indeed decrease with an increase in mud
weight. Also notice that the maximum kick size has now dropped
to 26 bbl. The ability of the rig crew to shut in the well efficiently
is now an even greater concern.
Figs. 3 and 4 also portray, on the far left axes, the maximum
formation pressure that may be drilled, given the existing shoe test,
depth, mud weight, and anticipated pit gain. (Recall that Eq. 2,
when divided by 0.052 D h , relates the maximum formation pressure to kick tolerance and existing mud weight.) Variations of these
diagrams are helpful to the drilling engineer and the drilling representative when discussing the current drilling situation. Fig. 5 represents the relationship between kick tolerance and pit gain at 10,000
ft for different mud weights at initial shut-in conditions. It is interesting to note that, if 0.5 Ibm/gal is determined to be the minimum kick tolerance and a horizontal line is drawn across Fig. 5
at 0.5 Ibm/gal, the use of mud weights greater than 11.0 Ibm/gal
cannot be recommended, to the dismay of those who felt comfortable with a 13.0-lbm/gal shoe test.
Fig. 6 displays the same example problem with some additional
pump information and an influx circulated to the casing shoe. To
complete our investigation of kick tolerance for this problem, we
must consider the pressure of the influx when its top reaches the
shoe. Using the pressure/volume calculator program previously
mentioned (see the Appendix), we plot the data obtained from Eq.
10 with that information gained from Eq. 9 (Fig. 7). We find that
above about 37 -bbl initial gain, expansion of the influx will cause
r-r--g--r=-.~K:iC~k~T:OI=er=a=nc=e-:D:-:-ec:-::r=ea=se=s~W:it=h~T=ru=e-=Y:-:-ert=i-ca-:I:De=p:th:l
• Kick Tolerance Decreases With Increasing Pit Gain
• Kick Tolerance Decreases With longer DC lengths
4000'
o~~~-L~~~·~~~~~~L-~~~~
11.5
14.5
2$
39
50 53J
o
bbl.
bbl.
bbl. Pil Gain
b~~
bbl.
100
Fig. 5-Kick tolerance at initial shut-in conditions. (Drilling
at 10,000 ft.)
SPE Drilling Engineering, December 1991
100
TVD :
Mud Wt :
Shoe Test:
Hole Size :
Drill Pipe :
Drill Collars :
Casing:
Pumps :
Pump Rate :
Assumptions :
10,000'
10 ppg
13 ppge
8 112"
4 112" 16.60 ppf
7" x 2 13/16" (200')
9 5/8" (Assume 8 112" 10)
7" x 12" Triplex @ 95%
45 spm
No Migration, Influx
Remains as a Slug
10,000'
Fig. 6-Circulating out influx.
247
1.5r-'--g--r:.-K;;i::;Ck;-:T;:o~18:::ra:nc::8:-;D;:8::cr::8a::S::8S;-:W;;;i;;;lh~l;:nf;;:lu:I-;EI::p:an::S:;:io:nl
...,
During Circulation
0
~!
2
....
A'\
4
--
.c
ca..
ID
Q
~
(,)
Fig. 7-Kick tolerance with Influx at shoe. (Drilling at 10,000
ft; mud weight 10.0 Ibm/gal.)
:e
ID
>ID
2
...=
...
ca
(,)
c
II)
II)
E
ID
ID
~
~.
"0
Q..
~?'
t-
...c
ID
=
-.....
C)
C)
C)
~
ID
ID
6
~
~
Q..
8
10
t-
12
0
14
2
A'\
~
4
--
.c
ca..
:e =
(,)
ID
C)
C)
C)
=
...
II)
II)
6
ID
Q
~
e
8
ID
Q..
...c
ID
~8
~
~
(0
ca
W
"
"
~
Mud Weight Equivalent (ppg)
n
~
~.
~
?'
Fig. 9-Chooslng casing points.
Q..
>- ::::!
...=
ID
10
BLOWOUTS/ I()() WELLS
0.5
0.395
0.4
12
14
0.4
0.3
0.3
0.2
0.2
0.1
18
Fig. B-Choosing casing pOints.
the shoe pressure experienced when the influx is circulated to the
shoe to exceed considerably that experienced initially. It is additionally shown that the maximum pit gain of 69.S bbl discussed
earlier could not have been circulated out with the driller's method
of well control without breaking down the shoe.
Diagrams like Figs. 3 through Sand 7 are useful to illustrate the
effects of other drilling parameters on kick tolerance. As previously shown, drilling personnel can easily develop these, not only
to perform their job responsibilities better, but also to emphasize
to the rig crew the importance of minimizing the influx. The failure
of the rig crew to react to the warning signs of a kick is a significant factor in many blowouts. It is also the principal reason behind
the tremendous amounts of time and effort invested in the training
of personnel. 8 It benefits the drilling representative to train his rig
crew and thus improve the efficiency of the drilling operation.
0.1
0.06
1950
10
12
14
16
Mud Weight Equivalent (ppg)
248
US GULF OF MEXICO-OCS
0.5
t-
1960
1970
1980
SURVEY FOR 25 YEARS
Fig. 10-Blowouts: exploration, development, production (after Hammett and DUdley 5).
Well Planning
When designing a well, the drilling engineer must consider kick
tolerance, especially when long, openhole sections are anticipated.
Commonly, O.S-lbm/gal kick and trip margins are plotted on the
diagrams of pore pressure/fracture gradient and are used to select
casing setting depths. 9 From the previously discussed example
problem, pore pressure and fracture gradient data were obtained
to develop Fig. 8. On the basis of the 0.5-lbm/gal margins, intermediate casing would be set at a depth of 11,700 ft. However, at
11,700 ft, the mud weight will exceed 12.0 Ibm/gal if the porepressure information is accurate. The earlier example indicated that
this mud weight offered little kick tolerance at 10,000 ft. Furthermore, Fig. 5 shows only O.S-lbm/gal kick tolerance available to
11. 7S-lbm/gal mud at 10,000 ft with zero pit gain. From a safedrilling standpoint, this should be considered absolute minimal standards at 10,000 ft.
SPE Drilling Engineering, December 1991
Once again, an examination of Fig. 5 shows that 11.0 Ibm/gal
is the maximum allowable mud weight at 10,000 ft for a 1O-bbl
influx and a 0.5-lbm/gal kick tolerance in this example. With this
mud weight, a 1O-bbl influx, and K=0.5 Ibm/gal, Eq. 9 indicates
that the well can be drilled to only 10,400 ft. Because this depth
is substantially shallower than the casing point proposed by Fig.
8, a lighter mud weight may be considered.
Returning to Eq. 9, the same conditions are applied for a 10.9Ibm/gal drilling fluid. The maximum allowable drill depth with this
fluid weight is found to be 11,261 ft. Fig. 9 incorporates this mud
weight with the margins previously discussed and depicts the intermediate casing setting depth at 10,900 ft. Although this casing
point is 800 ft shallower, the well can still be drilled to the planned
total depth. The prudent drilling engineer will continue this analysis until convinced that the casing point chosen does conform to
minimal kick-tolerance specifications.
Kick tolerance, in this respect, is offered as an additional tool
for the well-design engineer to incorporate. It is not to be looked
upon as the only casing-design criterion but should be considered
when this analysis is undertaken. Also, from both safety and economic standpoints, wells should be designed to reach total depth.
The practice of setting casing "as deep as possible" is often unnecessary, usually more expensive, and certainly risky because kick
tolerances are reduced to the point that any influx taken, even that
swabbed in, will compromise the integrity of the former casing shoe.
Conclusions
Current statistics (Fig. 10) point to an increasing trend in
blowouts. 5 Discussions with well-control experts and blowout
specialists confirm this trend. The future will hold stricter government and company regulations regarding the drilling of wells to
provide the utmost in safety and security for the drilling personnel
and the environment.
The significance of kick tolerance in drilling planning and execution cannot be underestimated. Safe drilling practices will demand that minimal kick-tolerance standards be considered on a
per-well basis. Regulatory bodies soon may hold all drilling personnel responsible for a working knowledge of kick tolerance. It
is hoped that through these simple but effective methods, a thorough
understanding has been achieved.
Nomenclature
Dh = true vertical depth of hole, ft
DR = reservoir depth, ft
Ds = true vertical depth of casing shoe, ft
gi = gradient of influx, psi/ft
K = kick tolerance, Ibm/gal
Kc = kick tolerance during circulation, Ibm/gal
Kin = kick tolerance including effects of influx, Ibm/gal
Ko = kick tolerance with zero pit gain, Ibm/gal
Lex = length of existing mud
Lg = length of gas
Li = true vertical length of influx, ft
Pcinc = increased casing pressure caused by influx, psi
Pcrnax = maximum allowable shut-in casing pressure, psi
Pfmax = maximum formation pressure, psi
Phex = existing hydrostatic pressure, psi
PR = reservoir pressure, psi
Ps = surface pressure, psi
Psidp = shut-in drillpipe pressure, psi
Ptob = pressure at top of bubble or influx, psi
s = shoe test, Ibm/gal
Vg = volume of gas
Weq = equivalent mud weight, psi
Wex = existing or current mud weight, Ibm/gal
Wn = new or required mud weight, Ibm/gal
Pg = density of gas influx, Ibm/gal
Acknowledgment
I express my appreciation to Chevron U.S.A. Inc. for permission
to publish this paper.
SPE Drilling Engineering, December 1991
Author
K.P. Redmann is a senior drilling en·
gineer in Chevron U.S.A.'s Central Profit
Center in New Orleans. Since joining
Chevron in 1981, he has held positions
in drilling and production engineering
and has worked both on· and offshore
in the Gulf of Mexico and in west Africa.
Before 1981, Redmann worked with Mul·
lins and Prichard Oil Producers in New
Orleans. He holds an MS degree in pe·
troleum engineering from Louisiana
State U. and is the current national president of the Ameri·
can Assn. of Drilling Engineers.
References
1. Pilkington, P.E. and Niehaus H.A.: "Exploding the Myths About Kick
Tolerance," World Oil (June 1985) 59-62.
2. Wilkie, D.l. and Bernard, W.F.: "Abnormal Pressure Detection and
Control in Beaufort Sea Wells," Ocean Industry (March 1981) 33-36.
3. Wilkie, D.l. and Bernard, W.F.: "Detecting and Controlling Abnormal Pressure," World Oil (July 1981)129-144.
4. MMS 250. 54(a)(6) , Rules and Regulationsfor Drilling, Completion, and
Workover Operations in All OCS Waters, Minerals Management Service.
5. Hammett, D.S. and Dudley, W.O.: "Day Rates Affect Rig Safety and
Training," paper SPE 18680 presented at the 1989 SPE/IADC Drilling
Conference, New Orleans, Feb. 28-March 3.
6. Nance, G.W.: "Annular Geometry - Its Effect on Kick Tolerance,"
paper presented at the 1978 ASME Energy Technology Conference,
Houston, November.
7. Brewton, J., Rau, W.E., and Dearing, H.L.: "Development and Use
of a Drilling Applications Module for a Programmable Hand-Held Calculator," paper SPE 16657 presented at the 1987 SPE Annual Technical Conference and Exhibition, Dallas, Sept. 27-30.
8. Redmann, K.P.: "Flow Characteristics of Commercially Available Drilling Chokes Used in Well Control Operations," MS thesis, Louisiana
State U., Baton Rouge, LA (1982).
9. Bourgoyne, A.T. et al.: Applied Drilling Engineering, Textbook Series,
SPE, Richardson, TX (1986) 2, 330.
Appendix-Gas Pressure at Depth Calculation
The calculation is as follows.
PR = (0.052D R W ex ) +Psidp' ........................ (A-I)
Initialize surface pressure for iterative solution:
Ptob(i) =P r ..................................... (A-2)
and czt(r) =4.03 -0.38 In Ptob(i)' ..................... (A-3)
Solve iteratively for Ptob:
Pg(i+ I) =0.037 In Ptob(i) -0.219 .................... (A-4)
Ptob(i+I) =Pr-0.052[(DR -Dtob-Lex -L g )P g2 +Lex Wex ] -LgP g .
.................................. (A-5)
czt(i+ I) =4.03 -0.38 In Ptob(i+ I)'
. . . . . . . . . . . . . . . . . . (A-6)
Then,
Vg(i+ I) =CztrPR V;lCzt(i+ l)Ptob(i+ I)'
.................
(A-7)
Eqs. A-4 through A-7 are repeated until Ptob(i+ I) and Vg(i+l) converge within 10 psi.
Weq =Ptobl(0.052Dtob) ........................... (A-8)
and Ps =Ptob -(0.052Wex D tob )· ...................... (A-9)
SI Metric Conversion Factors
E-Ol
bbl x 1.589873
E-Ol
ft x 3.048*
E-03
gal x 3.785412
E+OO
in. x 2.54*
E-Ol
Ibm x 4.535924
psi x 6.894757
E+OO
• Conve,sion factor is exact.
m3
m
m3
cm
kg
kPa
SPEDE
Original SPE manuscript received for review Feb. 27, 1990. Paper accepted for publication Sept. 3, 1991. Revised manuscript received Aug. 7, 1991. Paper (SPE 19991) first
presented at the 1990 IADC/SPE Drilling Conference held in Houston, Feb. 27-March 2.
249