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=0.052WexDh . ................................ (4)

Combining Eqs. 2 through 4 yields

0.052WnDh =Pemax +0.052WexD h . ................... (5)

Eq. 5 may be simplified to

Wn - Wex =Pcmax/(0.052Dh ) ......................... (6)

Eq. 6, which assumes no influx in the wellbore (zero pit gain), de­fines kick tolerance because the quantity (Wn - Wex) is the maxi­mum increase in mud weight allowed by the pressure-integrity test. Therefore,

Ko =Pcmaxf(0.052Dh )· .............................. (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)/0.052Dh · ......... (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-

246

4000'

10,000'

TVD : 10,000' Mud Wt: 10 ppg

Shoe Test: 13 ppge Hole Size : 8 112" Drill Pipe : 4 112" 16.60 ppf

Drill Collars : 1" x 2 13/16" (200') Casing: 9 5/8" (Assume 8 112" 10)

Influx Gradient: 0.1 psi 1ft

Fig. 1-Well schematic.

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)

4000'

8514'

10,000' 69.5 Bbl Gain

For either case, Max slep has been reached without

drilling into pressure.

624

104.3 Bbl Gain

Fig, 2-Signlficance of influx (pit gain).

8514'

10,000'

SPE Drilling Engineering, December 1991

11.5 r-r---I • Kick Tolerance Decreases With True Vertical Depth • Kick Tolerance Decreases With Increasing Pit Gain • Kick Tolerance Decreases With longer DC lengths

11.0

10.5 0.5

10.0 50 69.5 bbls 100

Pil Gain bbl~

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 624-psi 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 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

o~~~-L~~~·~~~~~~L-~~~~ o 14.5 2$ 39 50 53J

bbl. bbl. bbl. Pil Gain b~~ 11.5 bbl. 100

Fig. 5-Kick tolerance at initial shut-in conditions. (Drilling at 10,000 ft.)

SPE Drilling Engineering, December 1991

13.0

12.5

12.0

11.5

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

50 Pit Gain bbls

_8.000' _10.000' _12.000' c:::J 14,000'

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 Dh , 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

4000'

10,000'

TVD : 10,000' Mud Wt : 10 ppg

Shoe Test: 13 ppge Hole Size : 8 112" Drill Pipe : 4 112" 16.60 ppf

Drill Collars : 7" x 2 13/16" (200') Casing: 9 5/8" (Assume 8 112" 10) Pumps : 7" x 12" Triplex @ 95%

Pump Rate : 45 spm Assumptions : No Migration, Influx

Remains as a Slug

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

~!

Fig. 7-Kick tolerance with Influx at shoe. (Drilling at 10,000 ft; mud weight 10.0 Ibm/gal.)

0

2 A'\

~ 4 ~

~ e (0

= ca II) II) ~

6 ID ~. ... ~ Q.. ?'

ID ... c 8 Q..

.c -ca.. ID

Q -~ = (,) C) :e C)

ID C)

>- ::::! ID = 10 ... t-

12

14

10 12 14 16 18 Mud Weight Equivalent (ppg)

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.

248

.c -ca.. ID

Q -~ = (,) C) :e C)

ID C)

>- ..... -ID

2 t-

0

2 A'\ .... ~

4 ~ ID ID ~ ... (,) ca = c II) E II) ~

6 ID ID ~. ... "0 ~ Q.. t-ID

?' ... c 8 Q..

10

12

14

~8 W " " ~ n Mud Weight Equivalent (ppg)

Fig. 9-Chooslng casing points.

BLOWOUTS/ I ()() WELLS US GULF OF MEXICO-OCS 0.5

0.395 0.4

0.3

0.2

0.1 0.06

1950 1960 1970 1980

SURVEY FOR 25 YEARS

0.5

0.4

0.3

0.2

0.1

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 10.9-Ibm/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

P cinc = 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 P s = 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 Abnor­

mal 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 RWex ) +Psidp' ........................ (A-I)

Initialize surface pressure for iterative solution:

Ptob(i) =Pr ..................................... (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 -Lg)Pg2 +Lex Wex] -LgPg.

.................................. (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 -(0.052WexD tob )· ...................... (A-9)

SI Metric Conversion Factors bbl x 1.589873 E-Ol m3

ft x 3.048* E-Ol m gal x 3.785412 E-03 m3

in. x 2.54* E+OO cm Ibm x 4.535924 E-Ol kg psi x 6.894757 E+OO kPa

• Conve,sion factor is exact. 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