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Application of mass balance of kick fluid in well control
Journal of Petroleum Science and Engmeenng, 6 ( 1991 ) 161-174
161
Elsevier Science Publishers B V., A m s t e r d a m
Application of mass balance of kick fluid in well control J.A. Ajienka a and O.O. Owolabi b
aDepartment of Petroleum Engineering, Umversltyof Port Harcourt, Port Harcourt, Nigeria bpetroleum and Natural Gas Engineering, The Pennsylvama State Umverslty, UmversltyPark, PA 16802, USA (Received July 28, 1990; accepted after revision February 6, 1991 )
ABSTRACT Ajtenka, J A and Owolabi, O O , 1991 Apphcatlon of mass balance of lock fluid in well control. J Pet_Sct. Eng_, 6: 161174. A material balance equation of lock fluid in the annulus ~s derived Th~s equation can be used to determine the pressure head of the kick, whether or not the lock is intermittent or a continuous slug, the volume (or length) of the lock, the rate of rise of the lock fluid, the maximum casing pressure that will be encountered during the well control operation and the annular pressure as the lock reaches cnhcal points of interest such as the casing seat. When integrated with transient surface shut-in drill stem test analysis techniques, pertinent formatmn characteristics can be evaluated. These can be useful for optimizing the planning, design and drilling of subsequent wells within the particular field The model requires a m i n i m u m of assumptions and it is dynamic as it ~s based on the well control process. With speedy and accurate acquisition of the lock data, well control can become more efficient. The major limitations of the model include possible leakages in the flow system and high gas solubility in the drilling fluid The procedure for the application is discussed and examples of a gas kick and a saltwater kick illustrate the applicability of the model
Introduction
A kick is a discharge of gas, oil or salt water or a combination of the three from a well being drilled, into the atmosphere. Generally, it is caused by the penetration of a high-pressured formation in which the formation pressure exceeds the equivalent circulating pressure so that the formation fluids flow into the wellbore. This is caused by any of the following: (a) inadequate drilling mud weight; (b) not maintaining a completely filled hole; (c) swabbing during tripping; and (d) lost circulation. Kicks are early signs of possible blowouts which are very disastrous. Kick indicators (or warning signs) include: (a) rise in mud pit level; (b) drilling break; (c) decrease in circulation pressure; (d) saltwater-cut mud or chloride increase; (e) gas-cut mud; (f) traces
ofoil and gas in mud returns; and (g) casing pressure buildup. The proper identification of kick fluid composition is necessary for planning the well control operation. The annular pressure profile normally reflects the composition of the kick fluid. In general, gas kicks cause higher annular pressures than liquid kicks. This is because a gas kick has a lower density than a liquid kick and gas expands as it is pumped to the surface. These factors result in a lower hydrostatic pressure in the annulus and thus requires the maintenance of higher surface back pressure using the adjustable choke to control the well. Assuming that kick fluid entered the annulus as a slug, a detailed procedure for calculating the density of the kick fluid, from the initial drill pipe and casing pressures as well as the corresponding pit volume gain was given by Azar (1973). The inference to be drawn
0 9 2 0 - 4 1 0 5 / 9 1 / $ 0 3 . 5 0 © 1991 Elsevier Science P u b h s h e r s B V All rights reserved.
162
J A AJIENKAAND O O OWOLABI
Nomenclature a 4 4,
h B
10 cross-sectional area (It 2) annular capacity (ft s/It ) Pr=Pap+O 052pro Di formation volume factor (res vol_/surface vol )
T
Tw. / Tf
I V Z
volume (ft 3 ) total volume of gas in annulus= VmB+ Vgb fit s ) gas compressibility factor Zwh Zr porosity (fraction) density (lbr./ft s ) P2 = e x p C(P2--PL) Pl P P~ viscosity (cP) gas gravity
Z
¢ , 6 (a ('~
0 052 p~. G, Ca Pbh isothermal compresslblhty factor (psi-~ ) annular capacity (fts/ft) compressibility of the well fluid (fl3/ft)
P
6,
708kh ;5615 39754kh jlln(r:/r~) \/ . - - T - / /- A / 2 1 n (re/r~)
P.
D F g G, t' h h~ H /, L ~1 P Ptj
depth (ft) choke constant fluid gradient ( p s l / f l ) pit volume gain (It 3) formation thickness (ft) V/A 2 =mud-free kick length (It) depth (It) permeability ( m D ) length ( ft ) molecular weight of gas pressure (psi) 0 5 (log tD+0-81 )
emax
P~D q
.)
1 151 (log t o + 0 3 5 1 + 0 87S) flOW rate ( f t 3 / m m )
q'~,
q~,/B'~
r~ R t
wellbore radms (It) gas constant time (rain) 2 634)< lO-4kt
It, T
¢~C(r~)2 temperature ( ° R )
from the calculation is that kick is predominantly gas if the kick fluid density is less than 4 ppg; it is liquid if the density is greater than 8 ppg and it is a mixture of gas and liquid ff the density is greater or equal to 4 ppg and less or equal to 8 ppg. An alternative approach is to infer the composition from the pressure gradient. Sources of error m the above calculations are: hole washout, gauge problem and a slightly greater annular mud density than the mud density in the drill pipe due to entrained cuttings. If the kick fluid mixes with the mud, the slug model cannot accurately represent the reality. An improved calculation using the circulation rate was also given by Azar. Quahtatively, kicks can also be identified by
PR
1/ t'
Subscripts bh bottom hole csg casing dp drill pipe D dimensionless parameter f flowing g gas gb gas bubble in mud h depth 1 imtml condition k kick l hquld m mud max maximum mf m u d free 0 standard condition wh wellhead l p u m p shut-m, both the tubing and casing valves closed, inflow 2 valves opened, circulation resumed, outflow
the observation of the p~t gain and casing pressure buildup (Schurman and Bell, 1966 ). If the kick is gas, the casing pressure will rise and a gain will be observed in the pits. If the kick is water, the casing pressure will fall and no gain will be observed. This method of identification requires that early calculations be made for both gas and liqmd. The calculations mentioned above are still inadequate as they do not take into consideration the possibility of intermittent flow and gas solubility in the drilling fluid. Thomas et at. (1984) showed that hydrocarbon gas solubility in oil-base mud alters the surface responses to a kick during drilling.
APPLICATION OF MASS BALANCE OF KICK FLUID IN WELL CONTROL
163
helps in determining the bottom-hole pressure greater than the pore pressure to stop further influx of kick fluid. The casing pressure is the actual indicator of the state of the kick fluid as it is circulated up the annulus. Figures 1 and 2 illustrate the pressure profile during the kick and control periods. Bourgoyne ( 1977 ) made a number of simplifying assumptions which could have serious consequences particularly for high-pressure large-volume deep-formation kicks. With these assumptions, he derived a quadratic expression for calculating the maximum expected static casing pressure. Burgess et al. (1990) presented a new faster approach to kick detection and diagnosis. Schurman and Bell (1966) also presented a graphical method of calculating maximum static casing pressure. This method, like other methods cited earlier, is an approximation. It assumes that initial pit volume gain represented the total gas influx. It did not account for gas influx at the time of shutting-in of the drill pipe and the casing (at the surface, not at the sandface) and during the period of waiting
Kicks are removed by circulating the well through an adjustable choke at the surface. After an initial flow of the well, the formation is prevented from further flow by ensuring that the bottom-hole pressure of the drilling fluid is maintained above the pore pressure. The only complications particularly for very deep wells, is the danger of fracturing uncased weaker upper strata that are exposed to the applied mud weight which may lead to loss circulation problems, underground blowout and even loss of well. West ( 1977 ) suggested the use of hydraulic fluid flow equations as has been applied in the Delaware and Anadarko basins. The situation is further compounded when kick is taken below a liner. Kendall (1977) demonstrated how loss circulation can be caused in the upper strata by neglecting the effects of annular friction losses (even if low) and changes in the borehole configuration. Kendall indicated cases where annular friction loss can be as high as 65% of the total flowcirculating pressure. The drill pipe pressure approach in use only
DP CSG
),\\ J~ e~
Fr£ctuEe Pre98ure at Casing S e a t
L
Hydrostat:[e
~ Pressure
Fig. 1 P r e s s u r e profile at t i m e o f kick.
~ Formation
PresNure
164
J A AJIENKA AND O O OWOLABI
DP CSC
\ Annulus Profile Circulating with Casing Pressure Constant)
d=
Annulus Profile \~ (Circulating with Reduced Pressure to Compensate for Annular Friction Loss)
Annulus Profile (at time of shut-ln)
X Fracture Pressure at Casing Seat
Pressure
Formation Pressure
Fig 2_Pressureprofilewhaleorculatlng.
to record the stabilized pressures. Bemdes, the casing pressures calculated are static values which will differ from flowing pressures as kick is circulated out. These methods did not also take into account the rate of gas bubble rise (and thus the arrival time of the kick head) which is a function of buoyancy and kick-circulating velocity. These are lnformations which are necessary for the successful handling of the kick at the surface. Rader et al. ( 1975 ) and Chukwu and Ajienka (1989) presented models which calculate the rate of gas bubble rise independent of the kick control procedure. Other useful models exist which analyze the effect of annular back pressure variations during kick control (LeBlanc and Lewis, 1968; Hoberock and Stanberg, 1981 ). The mass balance of the flowing fluid in a condult has successfully been apphed to Closed Chamber Drill Stem Tests by Alexander (1977) and pumping well analysis by Kabir and Hasan ( 1982 ). In each case the analysis is carefully designed according to the operational procedure in use. Gas kicks in particu-
lar, depending on the dispersion of gas bubbles in the mud, are a multi-phase flow phenomenon. Thus for very accurate analysis this must be taken into consideration (Beggs and Brill, 1978). The objectives of this work are to apply the mass balance of kick fluid to kick data analysis. With minimum assumptions, the method can be used to determine the pressure head of the kick, whether or not kick is intermittent or a continuous slug, the volume of the kick, the rate of rise of kick fluid and the annular pressure profile. This method is dynamic as it is based on the well control process. Time-dependent casing pressure changes and pit volume gains reflect the intrumon, upward movement and expansion (if gas) of the kick fluid. The only assumption is that no kick fluid enters the drill pipe. Well test techniques can easily be incorporated to help in obtaining information about the kicking formation in postkick analysis for future well planning (Earlougher, 1977; Kazemi et al., 1983 ). However, any leakage in the system invalidates the
16 5
APPLICATIONOF MASSBALANCEOF KICK FLUID IN WELLCONTROL
model. High gas solubility in drilling fluid is not directly accounted for.
ZT q'~, -q~. =-if-- ( P V' + VP' )
(2)
/-wh
Gas kicks (theoretical aspects) The basis of the material balance equation for a single-phase gas flow into the annulus is that the mass rate of accumulation is equal to the mass rate of influx minus the mass rate out of the annulus. Using the familiar real gas equation: 0
P
M ~(pv)=M~(_~rqg_(~_~__T)whq,2] ZTR (1) Here Z and T of the accumulation term are evaluated as functions of the average depth of the body of the kick fluid. (Note that Z and T above are the gas compressibility factor and flowing temperature, respectively). Expanding and rearranging yields a mass balance equation (MBE):
The definitions of Z and Tin Eq. 2 and subsequent equations are shown in the Nomenclature. Figure 3 gives approximate values of Z. Equation 2 is the general MBE of the gas phase in the annulus and it is applied according to the well control procedure in use. The mud circulation rate and the required annular back pressure are not included in the MBE but are indirectly reflected in P' and q82. The following constant bottom-hole procedure is recommended by Azar for pumping kick out of the annulus: ( 1 ) shut-in the well kick, (a) shutoffthe pump and (b) shut the well in; (2) determine the shut-in drill pipe pressure; (3) circulate--using the choke; (4) reduce pump rate by one-half; (5) increase mud density, by (a) wait and weight method, (b) concurrent method and (c) driller's method; (6) control casing pressure; and (7) maintain a margin of safety. Figure 4 illustrates the well control pro-
I8 17 '° ,,
j-
0"84
6
8
10 12 Total Depth (ft. x 1,000)
14
|
16
18
Fig. 3. Compresslbtlity ratio versus depth for different kill mud weights. Source: Engineering Essentials of Modern Drilling (Nance, 1977, p. 126)
166
J A AJIENKAANDOO OWOLABI
Pump
Separator Adjustable Choke
BOP Casing
Pit
Open Hole
z~:C:::::.~'i;':" Strata of Minlmum Fracture Resistance
~
Formatlon Fluld Permeable High Pressure Strata
-//,A ,,-,,-~ ) :g.....,.. ::.'..?
"........'.
•::".':"';'::.'.'.'.','..~
,.
:.'L
.;..'. :V" .'.
Fig. 4 Well control process (Azar, 1973)
I\ I
\
I
i
i
8
•-" x J¢
ot
LT' l
-12
o
I-
16
I
i 20
0
100
200
T e m p e r a t u r e (~F)
Fig 5 Temperaturegradient
300
400
cess and the temperature profile is shown in Fig. 5. The well shut-in period should carefully be monitored in order not to allow casing pressure to build up to exceed open formation fracture and casing burst pressure limitations. The kicking and control procedure is summarized as follows: ( l ) well kick is observed through surface kick indicators such as pit volume gain and casing pressure; (2) stop the pump, shut-in drill pipe; (3) also shut-in casing annulus to watch the casing pressure buildup; and (4) open tubing and casing and circulate kick out by any chosen control method. Steps 1 and 2 are a very transient surface shut-in drawdown test while Step 3 is a buildup test and Step 4 is a regulated flow test (like the isochronal gas flow test). During the drawdown period, Eq. 2 holds; but during the annulus buildup period: ZT
q~2 = 0 and q'g, -Pwh (PV'~ + VP'~ )
(3)
APPLICATIONOF MASSBALANCEOF KICKFLUIDIN WELLCONTROL
Since Vg= Vm and no mud is displaced, V'I = 0, and thus: !
t
ZT
q~' =Pwh VP'~
(4)
If V is known from mud logging facilities, ~ l can be estimated. Using the initial pit volume rise and rate of change of casing pressure, the instantaneous gas influx rate can be calculated from Eq. 4. The annulus venting period is the period that corresponds to Steps 1 and 2, when the tubing is closed and the casing is open and step 4, during circulation. It is normal practice that the casing is closed last and opened first to avoid exceeding the burst pressure rating of the casing. During this venting period:
ZT
q;' -q'2
(PV' + vP' )
(5)
Combining Eqs. 3 and 5 yields the general form of the MBE of the gas phase in the annulus:
ZT q~:=-P-~h [V(P'~-P'2)+P(V'~-V'2)]
(6)
Since the total volume of the annulus is constant, the change in gas volume is equal and opposite to the change in mud volume (Eq. 7 ); and the change in the gas pressure is equal to the change in the casing pressure (Eq. 8 ): dV_ dt
dVm dt
(7)
(8)
/"wh
Over a short period of time of well control, the volumetric flow rate of mud can be assumed constant, implying that V~l = Vm,, thus Eq. 8 reduces to:
ZT q~ =-P--~h [ V( P'~ - P ~ ) ]
corded, a few points are necessary to establish P~ to aid in the control of the kick. Since qs2 is the choke flow rate, the actual total volume V of kick can be calculated from Eq. 9 as: V=
qu Pwh
(10)
Z T ( P'I - P'2) The difference between Vand the instrumentindicated value will reflect gas solubility. From the surface choke, calculate the outlet gas flow rate as (Kabir and Hasan, 1982):
(520 PF) 1/2
qg2 = \ -~-gZ--~ j
( 11 )
(Here Z is the gas compressibility and Tis the choke temperature). Alternatively, q~ can be estimated and the choke set accordingly, combining Eqs. 4 and 9:
q~ P'I__-P'2 l_(P'2~ qg,
PI
(9)
While the graph of PI versus t is easily re-
(12)
\P] ]
The pit volume gain with time, V(t); the bottom-hole pressure to control kick, Pbh, can be expressed as (Bourgoyne, 1977 ):
Pbh
V ( t ) = V,~(-i~ZT
(13)
Pbh =Pdp +0.052 pmH
(14)
Bourgoyne also observed that the maximum gain in pit volume will correspond to the point when the kick pressure attains the maximum value at the wellhead:
Pbh Vmax=V~m ZT
Rewriting of Eq. 6 gives:
q~=Z-~TIv(P'I-PI)+P(V'm2-V'm,)]
167
(15)
Equations 13 and 15 can be approximated by assuming that ratios Z = T = 1.0. Using these expressions and approximations, Bourgoyne derived a quadratic equation for calculating the maximum casing pressure as (Fig. 6 is the basis of the model): 2 a Pma,,-b Pm~ -c=O
(16)
Solutions of Eq. 16 were presented graphically. As indicated earlier, values obtained by
168
J A AJIENKAAND O_O OWOLABI
Adjustable Choke
method, the instantaneous flowing bottomhole pressure is given as:
Pwf = Pcsg + ( H - hmf ) gm + hmfgk of Interest
lck
u l a r C a p a c i t y , Ca
nslty, Pm
The m u d gradient, gm, and the kick gradient, gk, can be calculated. If the kick gradient is not well defined, use 0.12 psi/ft for gas (and 0.465 psi/ft for water).
Liquid kicks For oil and saltwater kicks (which are slightly compressible) the equation of state is expressed as follows:
P ~ Pbh
Fig 6 G a s k*ck (Bourgoyne, 1977).
this and other earlier methods predict maxim u m expected static pressures at the surface. They did not consider the choke and circulating rates. In place of pit volume gain, improved kick detection methods of Burgess et al. (1990) can be used. The differential flow measurement (delta flow) by use of sensors was found to be more accurate. The method proposed in this work is realistic as it predicts flowing pressures dependent on the choke venting and pumping rates. One can also use Schurman and Bell's (1966) generahzed expansion chart to determine the pressure profile. The above relationships by Bourgoyne (1977) are based on the change of initial kick fluid with temperature and pressure as functions of depth, and not the total volume of the kick fluid; however, they can give good working estimates. The bottomhole pressure to control the kick, Pbh, calculated with the stabilized shut-in drill pipe pressure is usually greater than the flowing bottom-hole pressure or pore pressure. With this
(17)
r=-V\OP//
(18)
Equation 18 assumes isothermal compressibility. For discrete intervals temperature can be assumed to be constant. The general MBE for this type of kick in the annulus is: 0
[qp(P,T) ], - (qP)2 =Ot (pV)
(19)
Expanding, rearranging and using Eq. 18:
qll
-
-
ql2Pn --P~ p l ( V' + VCP' )
(20)
During buildup, q~2= 0, Eq. 20 becomes:
__Ph ( V', + VCP', )
(21)
ql~ - P t During the annulus venting period: ql, - ql~on _P__~_h - P l ( V'2 + VCP'2 )
(22)
Combining Eqs. 21 and 22 yields the general form of the MBE of the liquid kick in the annulus: Ph q~2=~ [CV(P'~-P[)+(V',-V[)]
(23)
From earlier deduction, assume V'I = V[, therefore:
APPLICATIONOF MASSBALANCEOF KICKFLUIDIN WELLCONTROL
169
kh(P, -P,,,f) CV ( P] - P'2) =P2 Ph CV(P'~-P'2) qi~=-~R
(24)
Combining Eqs. 21 and 24, assuming V'~ = V " = 0 andpR= 1.0, ql2 can be estimated from Eq. 25 as:
ql2_ 1 - P [ ql,
(25)
P'l
The methods of analysis for gas kicks can apply to liquid kicks with some modifications. For liquid kicks, the maximum pressure at the surface is zero (Schurman and Bell, 1966). From Eqs. 24 and 18, respectively: gmax __
Vmax-
ql2
C(PI - P i ) GI exp [ - C ( P b h -- Prnax ) ]
1 C(P'j -P'2)G, - e x p [ - C(ebh --Pmax) ]
An alternative approach, simpler for liquid kicks, is given below; assuming steady state flow of an incompressible fluid from a single well penetrating a circular reservoir into the wellbore, the instantaneous flow rate is (Gatlin, 1960): 7.08 kh(Pe-Pwf)
q~-
Combining this with annular pressure buildup: ql
dv
Adh~
dt
5.615dt AdP,
AdP l
- 5.615 (0.433 p~)dt- 2.431/~dt (27)
(28)
Cdt=pedP~ -Pwf
d P l = 0.433 pldhl
Calculation of kicking formation characteristics
P2 - e l - - = C / ee -ewf
A time-dependent reservoir expression is used to predict the rate of flow into the wellbore (Earlougher, 1977; Kazemi et al., 1983; Thomas et al., 1984). The rate of flow is assumed to be constant during the flow period and the formation is infinitely acting. The reservoir drawdown with time and pressure for a reservoir, initially at uniform pressure, is: (29)
(32)
(33)
Where the pressure gradient in the annulus and the constant C are given by Eqs. 34 and 35, respectively:
Equation 28 can be used to determine the right venting rate. Practically, it implies that the surface pressure gradually decreases with circulation until it is almost zero when the top of the kick reaches the wellhead. A numerical example is used to illustrate this clearly.
kh(p2 - P w2r ) qgl = qg = 1424 Po ( Th + 460)/ZZ
(31)
Illn(re/rw)
(26)
Combining Eqs. 26 and 27: ql2
(30)
qh =ql -141.2lzBpw n
C-
17.22 khpl
A#ln(r¢/rw )
(34) (35)
Integrating Eq. 33 gives Eq. 36 (P~-Pwf is the reservoir pressure drawdown while dP1 is pressure change of kick fluid in the annulus): (36)
Since for liquid kicks w e can assume that (P2 - e l ) / t = P ' ~ , thus:
C(Pe - P w f ) = P ' l
(37)
Pe-Pwf is proportional to APcs~or rate of pit volume gain. In terms of height of rise of kick fluid, substitute the right hand side of Eq. 34 into Eq. 33 to obtain:
h=C' [Pe -Pwf( t) ]t
(38)
An evaluation of Eqs. 31 to 38 will give useful information of the kicking formation.
170
J A AJIENKA AND O O OWOLABI
Generation of drawdown data
few modifications can be used to predict annular pressure profile of the kick (Beggs and Brill, 1978 )
Even though the well was shut-in at the surface to obtain the stabilized tubing and casing pressures, during this period, the well continues to unload into annulus. Thus only drawdown analysis can be made with respect to the formation. Since the entire annulus is not filled with kink fluids, conventional methods of correcting casing pressure for bottom-hole flowing pressure cannot be used. Rather Eq. 17 can be used as follows: From the Pcsg and V, versus time data during the drawdown period, hmf(t) and thus Pwf(t) versus t data are computed. Thereafter, conventional tranment pressure drawdown test analysis of Drill Stem Test (DST) is carried out to obtain (kh/a), (OCt) and P1 (Kazeml et al., 1983). If sufficient data are not available, a m i n i m u m of three data points can be used to calculate the above values by solving the above equations simultaneously. For multiphase flow, the appropriate correlations with a
A - B
Annulus
build-up,
B - C
Further
kick
Top of kick
C - D
Venting
The procedure analyzed below is mainly for the more c o m m o n drill pipe pressure or drillers' method (modifications for other methods of well control can easily be made ): ( 1 ) Record initial kick indicators, by (a) pit volume gain G and (b) casing pressure Pcsg; (2) Record and plot, (a) Pcsg versus time, (b) G versus time, for both the annulus buildup period and the circulating or venting period (Figs. 7 and 8) and (c) obtain P',, r ! . Vm~ and if possible P~ and Vm2, (3) Note when, (a) p u m p is stopped, (b) drill pipe and casing are shut and further kick fluid intrusion is stopped and record stabilized Pap and Pcsg and (c) casing is reopened, p u m p started, to resume circulation; (4) Identify kick fluid composition and the
formation
fluid
kick circulated C
Data acquisition and analysis
intrusion
ouL - annulus
reaches
out kick
drawdown
wellhead,
checked, venting Pmax'
finally
Pmax
Pc~g
At1
t~ax Time
F~g_ 7 Hypothetical casing pressure profile for gas kicks
period
tmax
171
APPLICATION OF MASS BALANCE OF KICK FLUID IN WELL CONTROL
tion. This helps in planning subsequent wells. In the absence of systematically acquired data that suits this method, data from Schurman and Bell (1966) which provides good information are used with some modifications to illustrate this m e t h o d as in Appendix A. Use of this method, together with other known methods, can aid in the efficient and effective control of kicks.
Petebilized
P~|
Discussion
All Time
Fig 8 Hypotheticalcasingpressureprofilefor liquid kacks.
nature of kick, whether intermittent or a continuous slug from a plot Of Pl versus t; the plot provides qualitative information, a smooth plot indicates continuous slug and a wavy plot indicates intermittent kick fluid influx due to the pressure wave effect generated; (5) Calculate (in the field), (a) for the bottom of the hole (i) instantaneous ql, and (ii) instantaneous Pwf, (b) at the casing seat (i) the expected pressure when kick reaches casing seat, Ph and (ii) the time it takes to reach there, th, (C) at the wellhead (i) the m a x i m u m expected casing pressure, Pmax, (ii) the maxim u m volume of the kick, Vmax, and (iii) the time it takes to reach the surface, tma~; and (6) Later estimate the formation characteristics from the analysis o f d r a w d o w n data; this depends on the volume of the data generated.
Application A careful and fast (automated as in Measurement While Drilling) acquisition of all necessary kick data can help in efficient well control and post-kick data analysis to obtain pertinent characteristics of the kicking forma-
For gas kicks, the instantaneous gas influx rate qg, is a function of the unloading pressure gradient P~, the volume of gas, T and Z. For liquids, the influx rate is directly proportional to V, C and P'~. By controlling the choke flow rate qu, the annular back pressure can be controlled in order not exceed the fracture pressure of the exposed formation and casing burst pressure, while circulating kick out at the desired rate. The pressures calculated are flowing pressures unlike the static pressures calculated by previous methods. Also, earlier methods based most of the calculation of pressures on initial pit volume gain G,, which does not really correspond with the stabilized shut-in pressures. The tmax calculated, when compared to other methods, will indicate the earliest arrival time since flowing pressures are used in this work. The MBE method indirectly accounts for the circulating rate which is reflected in P~ and qg2. This method will be in error if there is wellhead leakage or tubing leaks. Any leak in the system invalidates the mass balance of the system. Estimation of the annular gas volume will be in error if cuttings are not lifted properly. Another limitation is the potential for error, if gas solubility in drilling fluid is high. Also accuracy in identification of kick is subject to hole gauge condition. In place of pit volume gain, the more accurate method of differential flow measurement can be used (Burgess et al., 1990).
172
Conclusions ( 1 ) A simple dynamic method of analyzing kick data is presented. The method does not interfere with present well control procedure, but can easily be integrated and with experience will contribute to the increased efficiency of kick control. (2) The method can easily be handled by the rig personnel and it is amenable to high speed computation such as with Measurement While Drilling ( M W D ) . (3) It is a realistic model with a minimum of assumptions, which helps in obtaining adequate information of the kicking formation, expected maximum kick pressure at the surface and at the casing seat. (4) A safe and successful control of a kick as well as acquisition of pertinent data can contribute to drilling optimization in the particular field.
J A AJIENKA AND O O OWOLABI
Determine the new mud weight New mud weight = 1300 15.0ppg + - 16 9ppg 0 052× 13,000 New mud gradient = 0_878 p s l / f l New bottom-hole pressure = 0 878 psl/ft × 13,000 fl = 11,420 psi (f) Calculate length of kick Volume gamed = 50 bbl Volume outside large collars (from basic data) = 10 bbl Kick volume above collars = 40 bbl Length of kick oppomte DP = 40 8 f t / b b l X 4 0 b b l = 1632 fl Total length = 700 ft collars+ 1632 DP=2332 ft (g) Identify kick Casing pressure, P~sg 2800 psi DP pressure,/°do 1300 psi D~fferentlal pressure 1500 psi Old mud gradient 0 779 psl/fl Differential pressure Differential pressure gradient = Length of kick 1500 0 644 psl/fl 2332 Gradient of kick fluid = (0 7 7 9 - 0 644) p s l / f l = 0 135 psl/ft--Thus a gas ktck. ( h ) Calculations From data obtained -
Appendix A--examples
Example l--gas kick Dunng two minutes of sounding of the pit level indicating dewce and actual closing of the preventers, gain=50 bbl and the following information obtained: depth=13,000 ft, G.=50 bbl, Pdp=1300 psl and Pcs~= 2800 psi (a) Other basic data Hole size 6~ in at 13,000 ft Ortglnal mud. 15 ppg, 0 779 psl/fl Drill pipe (DP): 341-in, 13 30 lb/ft, 12,300 ft Drill collars (DC) 4~ m OD>(2~ m ID, 700 ft (b) Annular capacmes DP × casing: 3 ½in × 6-~ m, 40 8 ft/bbl, 0_0245 bbl/ft Collar×hole: 4~ ln×6~ in; 69.0 ft/bbl, 0.0145 bbl/ft (c) Internal capacities DP: 3½ in OD; 0 0074 bbl/ft FC: 4~ in OD; 0 0049 bbl/ft (d) System capacity Annulus, DP×caslng: 12,300 ft ×0.0245 b b l / f t = 301 bbl Annulus, DCxhole: 700 f t × 0 0145 bbl/ft = 10 bbl Total annulus= 311 bbl Internal DP 12,300 ft >(0.0074 bbl/ft = 91 bbl Internal collar. 700 fl×0.0049 b b l / f l = 3 bbl Total internal = 94 bbl System total= 405 bbl (e) New mud and kick fluid calculations
P] - 2 7 0 = l,; _
1400 psl/mln
50>(5.615 2 - 140 375 ft 3/rain
(1) Calculate instantaneous gas influx rate From Fig. 3, Th= ( 2 5 0 + 4 6 0 ) ° R and (150+460) °R, take Zh=0 95 and Zwh=0-98
,
Twh=
ZT
qg~ =P~-~h (50+5 615)1400 ft3/mln= 124.412 ft3/min Using the new Pbh
B',--( -
-
2800 ~ / ( 11420 \0.98 × 610,//\0.95 × 7 l 0/
= 0 28 ft3/ft 3 and qg, =444.33 ft3/min (11) Calculated instantaneous flowing BHP Pwf=Pcsg + (H-hmf)gm +hmfgg = 2 8 0 0 + (13,000-2332) (0 779) + (2332) (0.135) = 11,425 192 psi P~f is shghtly greater than Pbh but with drawdown after 2
APPLICATIONOF MASSBALANCEOF KICKFLUIDIN WELLCONTROL minutes, Pbh will be slightly greater than P~f. (iii) Estimate P~, setting the choke flow rate If the choke flow rate, q~, is set at 100 ft3/mm, then from Eq 12, P~ can be estimated:
100
124 412] 1400 psi/mm = 275 psWmin (iv) Calculated maximum pressures. Based on these, calculate the maximum expected casing pressure and gas volume by solving Eqs. 10 and 13 simultaneously:
173 DP pressure 1300 psi Differential pressure 800 psi Old mud gradient 0.779 psl/ft Differential pressure gradient = 800 psl.-differential pressure = 0.343 psl/ft 2332 f t - l e n g t h of kick Gradient of kick fluid 0 436 psl/ft (h) Calculations From the given data. P'~ = ~ =
1050 psffmm
Vmax:t~)(Prl-Pr2)
(A-l)
V'~ = 5 0 X 5 . 6 1 5 _ 140.375 ft3/mm 2
VmaxraG, p---~a x (ZT)max
(A-2)
Assume compressibility of liquid, C = 5 × l 0 - 5 psi- l (1) Calculate instantaneous kick influx rate (Eq 21 ):
Dividing Eq A- l by Eq. A-2 gives
p
qh = (50X 5.615) (1050)5 X 10 -s ft3/min
/(P't -P'2)G,Pbh(ZT)2
(A-3)
= 14.74 ft3/min (n) Calculate instantaneous flowing BHP, P~r (Eq- 17 )'
= r ( 1400- 275) (50× 5.615)(11,420) (0.886)2] '/2 100
[
J
=5321.12 psi.
P~f= P-! + ( H - hmf)gm+ hm&l = 2100 + ( 13,000- 2332) (0.779) + (2332) (0.436)
Substituting back into Eq. A-1 above, calculate V ~ At any other depth, similar calculations as functions of Z ( h ) and T(h) can be made (v) Calculate time it takes to reach Pm,~.
(iii) Estimate P~, setting flow rate: If we set choke flow rate at 10 ft3/mm from Eq. 25.
t = Pmax-- Ps~b,hz~d__521 12 -- 2800_ 9.2 min P~ 275
"2~(1 --qh] ql2~p,I ~(l-
tm~=t~+ t2= (2 + 9.2)rain= 11.2 mm But i f q u = 120 ft3/min, P~=45 2 psl/min, Pm~=5331 psi, t2 = 56 min and tm,~= 58 mm The calculated times will be lower than the case where static conditions are assumed. Thus the earliest possible time of arrival is calculated. From these two calculations it is possible to adjust the surface flow rate in such a way that the well is controlled optimally. This part of the calculation is hypothetical, in practice, a more realistic pattern results. From the relationship, q',~ is used instead of qB,, thus flow at the surface is as close as possible to q~
Example 2--Water kick The same well conditions and kick volume are used here as in Example 1, except that the casing pressure for water kick was 2,100 psi as compared to 2,800 psi for the gas kick. This is due to the difference m hydrostatic gradients Steps (a) through (f) are the same with the gas kick/ (g) Identify kick Casing pressure, P=j 2100 psi
= 11,427 124 psi
141~074)
1050psi/rain
= 337.653 psffmm 0 v ) Calculate maximum pressure and volume at the surface Thus taking a pressure gradient of 11,420/13,000 = 0.8785 psi/ft, determine the pressure at any depth From Eq. 27, with P~x = 0. Vma~=
G, exp-- CPbh
substituting, Vm~,= 88.502 bbl. From Eq. 28, substituting values"
exp[--C(Pbh--P~'~')]=[C(P'L qu-P2)G,j' ]-'
emax= 1 r 10 -]--1 Pbh + ~ l n k ( 5 × 1 0 - ' ) (712.-3-47) (50× 5.615)]
Pm~,~Pbhimplying that
practically Pro,x=0 for flow to
174 take place Thus taking pressure gradient of 11,420/ 13,000= 0.8785 psi/ft, determine pressure at any depth. (v) Calculate time it takes to reach surface Pcss __2100 - 6 . 2 2 rain P~ -337.653 tma~=t~ +t2= (2+6.22 m m ) = 8 22 rain But assuming q12= 14 ft a/ram, 12= 40 mm and tma~= 42 mm With these two examples ofqt2, can compromise between time and expected pressures to decide an efficient venting rate
References Alexander, L G., 1977 Theory and practice of the closedchamber dnllstem test method J. Pet. Tech., 29 ( 12 ) 1539-1544. Azar, J J., 1973. Drllhng m Petroleum Engineering. Lecture Notes, Umverslty of Tulsa, Tulsa, Okla Beggs, H.D and Brill, J P., 1978 Two Phase Flow in Pipes. Lecture Notes, University of Tulsa, Tulsa, Okla. Bourgoyne, T., 1977. Graphical approach to kick severity calculations. In. Engjneenng Essentials of Modern Drilling. Energy Publications, Texas, pp 107-111_ Burgess, T , Starkey, A.A. and White, D., 1990. Improvement of kick detection. Odfield Rec, 2 ( 1 ). 43-51 Chukwu, G A and Ajlenka, J A., 1989. Prediction of fired flow parameters m a gas-cut mud, 2. Mathematical approach to the determination of the rate of gas bubble rise m a gas-cut mud J. Pet. Sci. Eng., 2(4) 305-309. Desbrandes, R and Bourgoyne, A T., Jr., 1987 MWD momtonng of gas kicks ensures safer drilhng Pet. Eng. Int, 59(7)- 43-52. Earlougher, R C., 1977. Advances m Well Test Analysis Soc Pet. Eng. ofAIME, Monogr 5, 264 pp
J A AJIENKA AND O O_ OWOLABI
Gathn, C, 1960. Petroleum Englneenng--Drilhng and Well Completions Prentice-Hall, Inc., N.J., Chap. 2, pp. 19-33 Hoberock, L L. and Stanberg, S R., 1981 Pressure dynamics in wells during gas kicks Part l--Fluid line dynamics; Part 2---Component models and results J. Pet Tech., 3 3 ( 8 ) 1357-1378 Kablr, C S and Hasan, A.R, 1982. Apphcauon of mass balance m pumping well analysis. J. Pet Tech., 34( 5 ) 1002-1010 Kazeml, H , Haws, G.W., Kunzman, W J , Milton, H W , Jr. and Halbert, W G., 1983 Complexmes of the analysis of surface shut-in drill stem tests in an off-shore volaUle oll reservoir. J. Pet Tech, 35( 1 ): 173-178 Kendall, H.A, 1977 How to control deep critical wells_ I n Engineering Essentials of Modern Dnlhng. Energy Pubhcauons, Texas, pp 112-118. LeBlanc, J L. and Lewis, R L, 1968. A mathematical model of a gas kick. J. Pet Tech., 20(8) 888-898 Nance, G , 1977. How to calculate maximum surface pressure for floating drilling I n Engmeenng Essentials of Modern Dnlhng Energy Pubhcations, Texas, pp. 125-128_ Rader, D W_, Bourgoyne, A_T_,Jr and Ward, R H , 1975 Factors affecting bubble rise velocity of gas kicks J Pet. Tech, 27(5): 571-584 Schurman, G.A_ and Bell, D.L., 1966. An improved procedure for handhng a threatened blowout J Pet Tech_, 18(4): 437-444. Thomas, D.C., Lea, J.F, Jr. and Turek, E.A., 1984. Gas solublhty in oil-based dnlhng fluids: Effects on kick detection. J Pet Tech., 36(7). 959-968. West, E.R, 1977 Hydraulic control of deep well blowouts. In. Engmeenng Essentials of Modern Drdhng. Energy Pubhcatlons, Texas, pp 119-123
161
Elsevier Science Publishers B V., A m s t e r d a m
Application of mass balance of kick fluid in well control J.A. Ajienka a and O.O. Owolabi b
aDepartment of Petroleum Engineering, Umversltyof Port Harcourt, Port Harcourt, Nigeria bpetroleum and Natural Gas Engineering, The Pennsylvama State Umverslty, UmversltyPark, PA 16802, USA (Received July 28, 1990; accepted after revision February 6, 1991 )
ABSTRACT Ajtenka, J A and Owolabi, O O , 1991 Apphcatlon of mass balance of lock fluid in well control. J Pet_Sct. Eng_, 6: 161174. A material balance equation of lock fluid in the annulus ~s derived Th~s equation can be used to determine the pressure head of the kick, whether or not the lock is intermittent or a continuous slug, the volume (or length) of the lock, the rate of rise of the lock fluid, the maximum casing pressure that will be encountered during the well control operation and the annular pressure as the lock reaches cnhcal points of interest such as the casing seat. When integrated with transient surface shut-in drill stem test analysis techniques, pertinent formatmn characteristics can be evaluated. These can be useful for optimizing the planning, design and drilling of subsequent wells within the particular field The model requires a m i n i m u m of assumptions and it is dynamic as it ~s based on the well control process. With speedy and accurate acquisition of the lock data, well control can become more efficient. The major limitations of the model include possible leakages in the flow system and high gas solubility in the drilling fluid The procedure for the application is discussed and examples of a gas kick and a saltwater kick illustrate the applicability of the model
Introduction
A kick is a discharge of gas, oil or salt water or a combination of the three from a well being drilled, into the atmosphere. Generally, it is caused by the penetration of a high-pressured formation in which the formation pressure exceeds the equivalent circulating pressure so that the formation fluids flow into the wellbore. This is caused by any of the following: (a) inadequate drilling mud weight; (b) not maintaining a completely filled hole; (c) swabbing during tripping; and (d) lost circulation. Kicks are early signs of possible blowouts which are very disastrous. Kick indicators (or warning signs) include: (a) rise in mud pit level; (b) drilling break; (c) decrease in circulation pressure; (d) saltwater-cut mud or chloride increase; (e) gas-cut mud; (f) traces
ofoil and gas in mud returns; and (g) casing pressure buildup. The proper identification of kick fluid composition is necessary for planning the well control operation. The annular pressure profile normally reflects the composition of the kick fluid. In general, gas kicks cause higher annular pressures than liquid kicks. This is because a gas kick has a lower density than a liquid kick and gas expands as it is pumped to the surface. These factors result in a lower hydrostatic pressure in the annulus and thus requires the maintenance of higher surface back pressure using the adjustable choke to control the well. Assuming that kick fluid entered the annulus as a slug, a detailed procedure for calculating the density of the kick fluid, from the initial drill pipe and casing pressures as well as the corresponding pit volume gain was given by Azar (1973). The inference to be drawn
0 9 2 0 - 4 1 0 5 / 9 1 / $ 0 3 . 5 0 © 1991 Elsevier Science P u b h s h e r s B V All rights reserved.
162
J A AJIENKAAND O O OWOLABI
Nomenclature a 4 4,
h B
10 cross-sectional area (It 2) annular capacity (ft s/It ) Pr=Pap+O 052pro Di formation volume factor (res vol_/surface vol )
T
Tw. / Tf
I V Z
volume (ft 3 ) total volume of gas in annulus= VmB+ Vgb fit s ) gas compressibility factor Zwh Zr porosity (fraction) density (lbr./ft s ) P2 = e x p C(P2--PL) Pl P P~ viscosity (cP) gas gravity
Z
¢ , 6 (a ('~
0 052 p~. G, Ca Pbh isothermal compresslblhty factor (psi-~ ) annular capacity (fts/ft) compressibility of the well fluid (fl3/ft)
P
6,
708kh ;5615 39754kh jlln(r:/r~) \/ . - - T - / /- A / 2 1 n (re/r~)
P.
D F g G, t' h h~ H /, L ~1 P Ptj
depth (ft) choke constant fluid gradient ( p s l / f l ) pit volume gain (It 3) formation thickness (ft) V/A 2 =mud-free kick length (It) depth (It) permeability ( m D ) length ( ft ) molecular weight of gas pressure (psi) 0 5 (log tD+0-81 )
emax
P~D q
.)
1 151 (log t o + 0 3 5 1 + 0 87S) flOW rate ( f t 3 / m m )
q'~,
q~,/B'~
r~ R t
wellbore radms (It) gas constant time (rain) 2 634)< lO-4kt
It, T
¢~C(r~)2 temperature ( ° R )
from the calculation is that kick is predominantly gas if the kick fluid density is less than 4 ppg; it is liquid if the density is greater than 8 ppg and it is a mixture of gas and liquid ff the density is greater or equal to 4 ppg and less or equal to 8 ppg. An alternative approach is to infer the composition from the pressure gradient. Sources of error m the above calculations are: hole washout, gauge problem and a slightly greater annular mud density than the mud density in the drill pipe due to entrained cuttings. If the kick fluid mixes with the mud, the slug model cannot accurately represent the reality. An improved calculation using the circulation rate was also given by Azar. Quahtatively, kicks can also be identified by
PR
1/ t'
Subscripts bh bottom hole csg casing dp drill pipe D dimensionless parameter f flowing g gas gb gas bubble in mud h depth 1 imtml condition k kick l hquld m mud max maximum mf m u d free 0 standard condition wh wellhead l p u m p shut-m, both the tubing and casing valves closed, inflow 2 valves opened, circulation resumed, outflow
the observation of the p~t gain and casing pressure buildup (Schurman and Bell, 1966 ). If the kick is gas, the casing pressure will rise and a gain will be observed in the pits. If the kick is water, the casing pressure will fall and no gain will be observed. This method of identification requires that early calculations be made for both gas and liqmd. The calculations mentioned above are still inadequate as they do not take into consideration the possibility of intermittent flow and gas solubility in the drilling fluid. Thomas et at. (1984) showed that hydrocarbon gas solubility in oil-base mud alters the surface responses to a kick during drilling.
APPLICATION OF MASS BALANCE OF KICK FLUID IN WELL CONTROL
163
helps in determining the bottom-hole pressure greater than the pore pressure to stop further influx of kick fluid. The casing pressure is the actual indicator of the state of the kick fluid as it is circulated up the annulus. Figures 1 and 2 illustrate the pressure profile during the kick and control periods. Bourgoyne ( 1977 ) made a number of simplifying assumptions which could have serious consequences particularly for high-pressure large-volume deep-formation kicks. With these assumptions, he derived a quadratic expression for calculating the maximum expected static casing pressure. Burgess et al. (1990) presented a new faster approach to kick detection and diagnosis. Schurman and Bell (1966) also presented a graphical method of calculating maximum static casing pressure. This method, like other methods cited earlier, is an approximation. It assumes that initial pit volume gain represented the total gas influx. It did not account for gas influx at the time of shutting-in of the drill pipe and the casing (at the surface, not at the sandface) and during the period of waiting
Kicks are removed by circulating the well through an adjustable choke at the surface. After an initial flow of the well, the formation is prevented from further flow by ensuring that the bottom-hole pressure of the drilling fluid is maintained above the pore pressure. The only complications particularly for very deep wells, is the danger of fracturing uncased weaker upper strata that are exposed to the applied mud weight which may lead to loss circulation problems, underground blowout and even loss of well. West ( 1977 ) suggested the use of hydraulic fluid flow equations as has been applied in the Delaware and Anadarko basins. The situation is further compounded when kick is taken below a liner. Kendall (1977) demonstrated how loss circulation can be caused in the upper strata by neglecting the effects of annular friction losses (even if low) and changes in the borehole configuration. Kendall indicated cases where annular friction loss can be as high as 65% of the total flowcirculating pressure. The drill pipe pressure approach in use only
DP CSG
),\\ J~ e~
Fr£ctuEe Pre98ure at Casing S e a t
L
Hydrostat:[e
~ Pressure
Fig. 1 P r e s s u r e profile at t i m e o f kick.
~ Formation
PresNure
164
J A AJIENKA AND O O OWOLABI
DP CSC
\ Annulus Profile Circulating with Casing Pressure Constant)
d=
Annulus Profile \~ (Circulating with Reduced Pressure to Compensate for Annular Friction Loss)
Annulus Profile (at time of shut-ln)
X Fracture Pressure at Casing Seat
Pressure
Formation Pressure
Fig 2_Pressureprofilewhaleorculatlng.
to record the stabilized pressures. Bemdes, the casing pressures calculated are static values which will differ from flowing pressures as kick is circulated out. These methods did not also take into account the rate of gas bubble rise (and thus the arrival time of the kick head) which is a function of buoyancy and kick-circulating velocity. These are lnformations which are necessary for the successful handling of the kick at the surface. Rader et al. ( 1975 ) and Chukwu and Ajienka (1989) presented models which calculate the rate of gas bubble rise independent of the kick control procedure. Other useful models exist which analyze the effect of annular back pressure variations during kick control (LeBlanc and Lewis, 1968; Hoberock and Stanberg, 1981 ). The mass balance of the flowing fluid in a condult has successfully been apphed to Closed Chamber Drill Stem Tests by Alexander (1977) and pumping well analysis by Kabir and Hasan ( 1982 ). In each case the analysis is carefully designed according to the operational procedure in use. Gas kicks in particu-
lar, depending on the dispersion of gas bubbles in the mud, are a multi-phase flow phenomenon. Thus for very accurate analysis this must be taken into consideration (Beggs and Brill, 1978). The objectives of this work are to apply the mass balance of kick fluid to kick data analysis. With minimum assumptions, the method can be used to determine the pressure head of the kick, whether or not kick is intermittent or a continuous slug, the volume of the kick, the rate of rise of kick fluid and the annular pressure profile. This method is dynamic as it is based on the well control process. Time-dependent casing pressure changes and pit volume gains reflect the intrumon, upward movement and expansion (if gas) of the kick fluid. The only assumption is that no kick fluid enters the drill pipe. Well test techniques can easily be incorporated to help in obtaining information about the kicking formation in postkick analysis for future well planning (Earlougher, 1977; Kazemi et al., 1983 ). However, any leakage in the system invalidates the
16 5
APPLICATIONOF MASSBALANCEOF KICK FLUID IN WELLCONTROL
model. High gas solubility in drilling fluid is not directly accounted for.
ZT q'~, -q~. =-if-- ( P V' + VP' )
(2)
/-wh
Gas kicks (theoretical aspects) The basis of the material balance equation for a single-phase gas flow into the annulus is that the mass rate of accumulation is equal to the mass rate of influx minus the mass rate out of the annulus. Using the familiar real gas equation: 0
P
M ~(pv)=M~(_~rqg_(~_~__T)whq,2] ZTR (1) Here Z and T of the accumulation term are evaluated as functions of the average depth of the body of the kick fluid. (Note that Z and T above are the gas compressibility factor and flowing temperature, respectively). Expanding and rearranging yields a mass balance equation (MBE):
The definitions of Z and Tin Eq. 2 and subsequent equations are shown in the Nomenclature. Figure 3 gives approximate values of Z. Equation 2 is the general MBE of the gas phase in the annulus and it is applied according to the well control procedure in use. The mud circulation rate and the required annular back pressure are not included in the MBE but are indirectly reflected in P' and q82. The following constant bottom-hole procedure is recommended by Azar for pumping kick out of the annulus: ( 1 ) shut-in the well kick, (a) shutoffthe pump and (b) shut the well in; (2) determine the shut-in drill pipe pressure; (3) circulate--using the choke; (4) reduce pump rate by one-half; (5) increase mud density, by (a) wait and weight method, (b) concurrent method and (c) driller's method; (6) control casing pressure; and (7) maintain a margin of safety. Figure 4 illustrates the well control pro-
I8 17 '° ,,
j-
0"84
6
8
10 12 Total Depth (ft. x 1,000)
14
|
16
18
Fig. 3. Compresslbtlity ratio versus depth for different kill mud weights. Source: Engineering Essentials of Modern Drilling (Nance, 1977, p. 126)
166
J A AJIENKAANDOO OWOLABI
Pump
Separator Adjustable Choke
BOP Casing
Pit
Open Hole
z~:C:::::.~'i;':" Strata of Minlmum Fracture Resistance
~
Formatlon Fluld Permeable High Pressure Strata
-//,A ,,-,,-~ ) :g.....,.. ::.'..?
"........'.
•::".':"';'::.'.'.'.','..~
,.
:.'L
.;..'. :V" .'.
Fig. 4 Well control process (Azar, 1973)
I\ I
\
I
i
i
8
•-" x J¢
ot
LT' l
-12
o
I-
16
I
i 20
0
100
200
T e m p e r a t u r e (~F)
Fig 5 Temperaturegradient
300
400
cess and the temperature profile is shown in Fig. 5. The well shut-in period should carefully be monitored in order not to allow casing pressure to build up to exceed open formation fracture and casing burst pressure limitations. The kicking and control procedure is summarized as follows: ( l ) well kick is observed through surface kick indicators such as pit volume gain and casing pressure; (2) stop the pump, shut-in drill pipe; (3) also shut-in casing annulus to watch the casing pressure buildup; and (4) open tubing and casing and circulate kick out by any chosen control method. Steps 1 and 2 are a very transient surface shut-in drawdown test while Step 3 is a buildup test and Step 4 is a regulated flow test (like the isochronal gas flow test). During the drawdown period, Eq. 2 holds; but during the annulus buildup period: ZT
q~2 = 0 and q'g, -Pwh (PV'~ + VP'~ )
(3)
APPLICATIONOF MASSBALANCEOF KICKFLUIDIN WELLCONTROL
Since Vg= Vm and no mud is displaced, V'I = 0, and thus: !
t
ZT
q~' =Pwh VP'~
(4)
If V is known from mud logging facilities, ~ l can be estimated. Using the initial pit volume rise and rate of change of casing pressure, the instantaneous gas influx rate can be calculated from Eq. 4. The annulus venting period is the period that corresponds to Steps 1 and 2, when the tubing is closed and the casing is open and step 4, during circulation. It is normal practice that the casing is closed last and opened first to avoid exceeding the burst pressure rating of the casing. During this venting period:
ZT
q;' -q'2
(PV' + vP' )
(5)
Combining Eqs. 3 and 5 yields the general form of the MBE of the gas phase in the annulus:
ZT q~:=-P-~h [V(P'~-P'2)+P(V'~-V'2)]
(6)
Since the total volume of the annulus is constant, the change in gas volume is equal and opposite to the change in mud volume (Eq. 7 ); and the change in the gas pressure is equal to the change in the casing pressure (Eq. 8 ): dV_ dt
dVm dt
(7)
(8)
/"wh
Over a short period of time of well control, the volumetric flow rate of mud can be assumed constant, implying that V~l = Vm,, thus Eq. 8 reduces to:
ZT q~ =-P--~h [ V( P'~ - P ~ ) ]
corded, a few points are necessary to establish P~ to aid in the control of the kick. Since qs2 is the choke flow rate, the actual total volume V of kick can be calculated from Eq. 9 as: V=
qu Pwh
(10)
Z T ( P'I - P'2) The difference between Vand the instrumentindicated value will reflect gas solubility. From the surface choke, calculate the outlet gas flow rate as (Kabir and Hasan, 1982):
(520 PF) 1/2
qg2 = \ -~-gZ--~ j
( 11 )
(Here Z is the gas compressibility and Tis the choke temperature). Alternatively, q~ can be estimated and the choke set accordingly, combining Eqs. 4 and 9:
q~ P'I__-P'2 l_(P'2~ qg,
PI
(9)
While the graph of PI versus t is easily re-
(12)
\P] ]
The pit volume gain with time, V(t); the bottom-hole pressure to control kick, Pbh, can be expressed as (Bourgoyne, 1977 ):
Pbh
V ( t ) = V,~(-i~ZT
(13)
Pbh =Pdp +0.052 pmH
(14)
Bourgoyne also observed that the maximum gain in pit volume will correspond to the point when the kick pressure attains the maximum value at the wellhead:
Pbh Vmax=V~m ZT
Rewriting of Eq. 6 gives:
q~=Z-~TIv(P'I-PI)+P(V'm2-V'm,)]
167
(15)
Equations 13 and 15 can be approximated by assuming that ratios Z = T = 1.0. Using these expressions and approximations, Bourgoyne derived a quadratic equation for calculating the maximum casing pressure as (Fig. 6 is the basis of the model): 2 a Pma,,-b Pm~ -c=O
(16)
Solutions of Eq. 16 were presented graphically. As indicated earlier, values obtained by
168
J A AJIENKAAND O_O OWOLABI
Adjustable Choke
method, the instantaneous flowing bottomhole pressure is given as:
Pwf = Pcsg + ( H - hmf ) gm + hmfgk of Interest
lck
u l a r C a p a c i t y , Ca
nslty, Pm
The m u d gradient, gm, and the kick gradient, gk, can be calculated. If the kick gradient is not well defined, use 0.12 psi/ft for gas (and 0.465 psi/ft for water).
Liquid kicks For oil and saltwater kicks (which are slightly compressible) the equation of state is expressed as follows:
P ~ Pbh
Fig 6 G a s k*ck (Bourgoyne, 1977).
this and other earlier methods predict maxim u m expected static pressures at the surface. They did not consider the choke and circulating rates. In place of pit volume gain, improved kick detection methods of Burgess et al. (1990) can be used. The differential flow measurement (delta flow) by use of sensors was found to be more accurate. The method proposed in this work is realistic as it predicts flowing pressures dependent on the choke venting and pumping rates. One can also use Schurman and Bell's (1966) generahzed expansion chart to determine the pressure profile. The above relationships by Bourgoyne (1977) are based on the change of initial kick fluid with temperature and pressure as functions of depth, and not the total volume of the kick fluid; however, they can give good working estimates. The bottomhole pressure to control the kick, Pbh, calculated with the stabilized shut-in drill pipe pressure is usually greater than the flowing bottom-hole pressure or pore pressure. With this
(17)
r=-V\OP//
(18)
Equation 18 assumes isothermal compressibility. For discrete intervals temperature can be assumed to be constant. The general MBE for this type of kick in the annulus is: 0
[qp(P,T) ], - (qP)2 =Ot (pV)
(19)
Expanding, rearranging and using Eq. 18:
qll
-
-
ql2Pn --P~ p l ( V' + VCP' )
(20)
During buildup, q~2= 0, Eq. 20 becomes:
__Ph ( V', + VCP', )
(21)
ql~ - P t During the annulus venting period: ql, - ql~on _P__~_h - P l ( V'2 + VCP'2 )
(22)
Combining Eqs. 21 and 22 yields the general form of the MBE of the liquid kick in the annulus: Ph q~2=~ [CV(P'~-P[)+(V',-V[)]
(23)
From earlier deduction, assume V'I = V[, therefore:
APPLICATIONOF MASSBALANCEOF KICKFLUIDIN WELLCONTROL
169
kh(P, -P,,,f) CV ( P] - P'2) =P2 Ph CV(P'~-P'2) qi~=-~R
(24)
Combining Eqs. 21 and 24, assuming V'~ = V " = 0 andpR= 1.0, ql2 can be estimated from Eq. 25 as:
ql2_ 1 - P [ ql,
(25)
P'l
The methods of analysis for gas kicks can apply to liquid kicks with some modifications. For liquid kicks, the maximum pressure at the surface is zero (Schurman and Bell, 1966). From Eqs. 24 and 18, respectively: gmax __
Vmax-
ql2
C(PI - P i ) GI exp [ - C ( P b h -- Prnax ) ]
1 C(P'j -P'2)G, - e x p [ - C(ebh --Pmax) ]
An alternative approach, simpler for liquid kicks, is given below; assuming steady state flow of an incompressible fluid from a single well penetrating a circular reservoir into the wellbore, the instantaneous flow rate is (Gatlin, 1960): 7.08 kh(Pe-Pwf)
q~-
Combining this with annular pressure buildup: ql
dv
Adh~
dt
5.615dt AdP,
AdP l
- 5.615 (0.433 p~)dt- 2.431/~dt (27)
(28)
Cdt=pedP~ -Pwf
d P l = 0.433 pldhl
Calculation of kicking formation characteristics
P2 - e l - - = C / ee -ewf
A time-dependent reservoir expression is used to predict the rate of flow into the wellbore (Earlougher, 1977; Kazemi et al., 1983; Thomas et al., 1984). The rate of flow is assumed to be constant during the flow period and the formation is infinitely acting. The reservoir drawdown with time and pressure for a reservoir, initially at uniform pressure, is: (29)
(32)
(33)
Where the pressure gradient in the annulus and the constant C are given by Eqs. 34 and 35, respectively:
Equation 28 can be used to determine the right venting rate. Practically, it implies that the surface pressure gradually decreases with circulation until it is almost zero when the top of the kick reaches the wellhead. A numerical example is used to illustrate this clearly.
kh(p2 - P w2r ) qgl = qg = 1424 Po ( Th + 460)/ZZ
(31)
Illn(re/rw)
(26)
Combining Eqs. 26 and 27: ql2
(30)
qh =ql -141.2lzBpw n
C-
17.22 khpl
A#ln(r¢/rw )
(34) (35)
Integrating Eq. 33 gives Eq. 36 (P~-Pwf is the reservoir pressure drawdown while dP1 is pressure change of kick fluid in the annulus): (36)
Since for liquid kicks w e can assume that (P2 - e l ) / t = P ' ~ , thus:
C(Pe - P w f ) = P ' l
(37)
Pe-Pwf is proportional to APcs~or rate of pit volume gain. In terms of height of rise of kick fluid, substitute the right hand side of Eq. 34 into Eq. 33 to obtain:
h=C' [Pe -Pwf( t) ]t
(38)
An evaluation of Eqs. 31 to 38 will give useful information of the kicking formation.
170
J A AJIENKA AND O O OWOLABI
Generation of drawdown data
few modifications can be used to predict annular pressure profile of the kick (Beggs and Brill, 1978 )
Even though the well was shut-in at the surface to obtain the stabilized tubing and casing pressures, during this period, the well continues to unload into annulus. Thus only drawdown analysis can be made with respect to the formation. Since the entire annulus is not filled with kink fluids, conventional methods of correcting casing pressure for bottom-hole flowing pressure cannot be used. Rather Eq. 17 can be used as follows: From the Pcsg and V, versus time data during the drawdown period, hmf(t) and thus Pwf(t) versus t data are computed. Thereafter, conventional tranment pressure drawdown test analysis of Drill Stem Test (DST) is carried out to obtain (kh/a), (OCt) and P1 (Kazeml et al., 1983). If sufficient data are not available, a m i n i m u m of three data points can be used to calculate the above values by solving the above equations simultaneously. For multiphase flow, the appropriate correlations with a
A - B
Annulus
build-up,
B - C
Further
kick
Top of kick
C - D
Venting
The procedure analyzed below is mainly for the more c o m m o n drill pipe pressure or drillers' method (modifications for other methods of well control can easily be made ): ( 1 ) Record initial kick indicators, by (a) pit volume gain G and (b) casing pressure Pcsg; (2) Record and plot, (a) Pcsg versus time, (b) G versus time, for both the annulus buildup period and the circulating or venting period (Figs. 7 and 8) and (c) obtain P',, r ! . Vm~ and if possible P~ and Vm2, (3) Note when, (a) p u m p is stopped, (b) drill pipe and casing are shut and further kick fluid intrusion is stopped and record stabilized Pap and Pcsg and (c) casing is reopened, p u m p started, to resume circulation; (4) Identify kick fluid composition and the
formation
fluid
kick circulated C
Data acquisition and analysis
intrusion
ouL - annulus
reaches
out kick
drawdown
wellhead,
checked, venting Pmax'
finally
Pmax
Pc~g
At1
t~ax Time
F~g_ 7 Hypothetical casing pressure profile for gas kicks
period
tmax
171
APPLICATION OF MASS BALANCE OF KICK FLUID IN WELL CONTROL
tion. This helps in planning subsequent wells. In the absence of systematically acquired data that suits this method, data from Schurman and Bell (1966) which provides good information are used with some modifications to illustrate this m e t h o d as in Appendix A. Use of this method, together with other known methods, can aid in the efficient and effective control of kicks.
Petebilized
P~|
Discussion
All Time
Fig 8 Hypotheticalcasingpressureprofilefor liquid kacks.
nature of kick, whether intermittent or a continuous slug from a plot Of Pl versus t; the plot provides qualitative information, a smooth plot indicates continuous slug and a wavy plot indicates intermittent kick fluid influx due to the pressure wave effect generated; (5) Calculate (in the field), (a) for the bottom of the hole (i) instantaneous ql, and (ii) instantaneous Pwf, (b) at the casing seat (i) the expected pressure when kick reaches casing seat, Ph and (ii) the time it takes to reach there, th, (C) at the wellhead (i) the m a x i m u m expected casing pressure, Pmax, (ii) the maxim u m volume of the kick, Vmax, and (iii) the time it takes to reach the surface, tma~; and (6) Later estimate the formation characteristics from the analysis o f d r a w d o w n data; this depends on the volume of the data generated.
Application A careful and fast (automated as in Measurement While Drilling) acquisition of all necessary kick data can help in efficient well control and post-kick data analysis to obtain pertinent characteristics of the kicking forma-
For gas kicks, the instantaneous gas influx rate qg, is a function of the unloading pressure gradient P~, the volume of gas, T and Z. For liquids, the influx rate is directly proportional to V, C and P'~. By controlling the choke flow rate qu, the annular back pressure can be controlled in order not exceed the fracture pressure of the exposed formation and casing burst pressure, while circulating kick out at the desired rate. The pressures calculated are flowing pressures unlike the static pressures calculated by previous methods. Also, earlier methods based most of the calculation of pressures on initial pit volume gain G,, which does not really correspond with the stabilized shut-in pressures. The tmax calculated, when compared to other methods, will indicate the earliest arrival time since flowing pressures are used in this work. The MBE method indirectly accounts for the circulating rate which is reflected in P~ and qg2. This method will be in error if there is wellhead leakage or tubing leaks. Any leak in the system invalidates the mass balance of the system. Estimation of the annular gas volume will be in error if cuttings are not lifted properly. Another limitation is the potential for error, if gas solubility in drilling fluid is high. Also accuracy in identification of kick is subject to hole gauge condition. In place of pit volume gain, the more accurate method of differential flow measurement can be used (Burgess et al., 1990).
172
Conclusions ( 1 ) A simple dynamic method of analyzing kick data is presented. The method does not interfere with present well control procedure, but can easily be integrated and with experience will contribute to the increased efficiency of kick control. (2) The method can easily be handled by the rig personnel and it is amenable to high speed computation such as with Measurement While Drilling ( M W D ) . (3) It is a realistic model with a minimum of assumptions, which helps in obtaining adequate information of the kicking formation, expected maximum kick pressure at the surface and at the casing seat. (4) A safe and successful control of a kick as well as acquisition of pertinent data can contribute to drilling optimization in the particular field.
J A AJIENKA AND O O OWOLABI
Determine the new mud weight New mud weight = 1300 15.0ppg + - 16 9ppg 0 052× 13,000 New mud gradient = 0_878 p s l / f l New bottom-hole pressure = 0 878 psl/ft × 13,000 fl = 11,420 psi (f) Calculate length of kick Volume gamed = 50 bbl Volume outside large collars (from basic data) = 10 bbl Kick volume above collars = 40 bbl Length of kick oppomte DP = 40 8 f t / b b l X 4 0 b b l = 1632 fl Total length = 700 ft collars+ 1632 DP=2332 ft (g) Identify kick Casing pressure, P~sg 2800 psi DP pressure,/°do 1300 psi D~fferentlal pressure 1500 psi Old mud gradient 0 779 psl/fl Differential pressure Differential pressure gradient = Length of kick 1500 0 644 psl/fl 2332 Gradient of kick fluid = (0 7 7 9 - 0 644) p s l / f l = 0 135 psl/ft--Thus a gas ktck. ( h ) Calculations From data obtained -
Appendix A--examples
Example l--gas kick Dunng two minutes of sounding of the pit level indicating dewce and actual closing of the preventers, gain=50 bbl and the following information obtained: depth=13,000 ft, G.=50 bbl, Pdp=1300 psl and Pcs~= 2800 psi (a) Other basic data Hole size 6~ in at 13,000 ft Ortglnal mud. 15 ppg, 0 779 psl/fl Drill pipe (DP): 341-in, 13 30 lb/ft, 12,300 ft Drill collars (DC) 4~ m OD>(2~ m ID, 700 ft (b) Annular capacmes DP × casing: 3 ½in × 6-~ m, 40 8 ft/bbl, 0_0245 bbl/ft Collar×hole: 4~ ln×6~ in; 69.0 ft/bbl, 0.0145 bbl/ft (c) Internal capacities DP: 3½ in OD; 0 0074 bbl/ft FC: 4~ in OD; 0 0049 bbl/ft (d) System capacity Annulus, DP×caslng: 12,300 ft ×0.0245 b b l / f t = 301 bbl Annulus, DCxhole: 700 f t × 0 0145 bbl/ft = 10 bbl Total annulus= 311 bbl Internal DP 12,300 ft >(0.0074 bbl/ft = 91 bbl Internal collar. 700 fl×0.0049 b b l / f l = 3 bbl Total internal = 94 bbl System total= 405 bbl (e) New mud and kick fluid calculations
P] - 2 7 0 = l,; _
1400 psl/mln
50>(5.615 2 - 140 375 ft 3/rain
(1) Calculate instantaneous gas influx rate From Fig. 3, Th= ( 2 5 0 + 4 6 0 ) ° R and (150+460) °R, take Zh=0 95 and Zwh=0-98
,
Twh=
ZT
qg~ =P~-~h (50+5 615)1400 ft3/mln= 124.412 ft3/min Using the new Pbh
B',--( -
-
2800 ~ / ( 11420 \0.98 × 610,//\0.95 × 7 l 0/
= 0 28 ft3/ft 3 and qg, =444.33 ft3/min (11) Calculated instantaneous flowing BHP Pwf=Pcsg + (H-hmf)gm +hmfgg = 2 8 0 0 + (13,000-2332) (0 779) + (2332) (0.135) = 11,425 192 psi P~f is shghtly greater than Pbh but with drawdown after 2
APPLICATIONOF MASSBALANCEOF KICKFLUIDIN WELLCONTROL minutes, Pbh will be slightly greater than P~f. (iii) Estimate P~, setting the choke flow rate If the choke flow rate, q~, is set at 100 ft3/mm, then from Eq 12, P~ can be estimated:
100
124 412] 1400 psi/mm = 275 psWmin (iv) Calculated maximum pressures. Based on these, calculate the maximum expected casing pressure and gas volume by solving Eqs. 10 and 13 simultaneously:
173 DP pressure 1300 psi Differential pressure 800 psi Old mud gradient 0.779 psl/ft Differential pressure gradient = 800 psl.-differential pressure = 0.343 psl/ft 2332 f t - l e n g t h of kick Gradient of kick fluid 0 436 psl/ft (h) Calculations From the given data. P'~ = ~ =
1050 psffmm
Vmax:t~)(Prl-Pr2)
(A-l)
V'~ = 5 0 X 5 . 6 1 5 _ 140.375 ft3/mm 2
VmaxraG, p---~a x (ZT)max
(A-2)
Assume compressibility of liquid, C = 5 × l 0 - 5 psi- l (1) Calculate instantaneous kick influx rate (Eq 21 ):
Dividing Eq A- l by Eq. A-2 gives
p
qh = (50X 5.615) (1050)5 X 10 -s ft3/min
/(P't -P'2)G,Pbh(ZT)2
(A-3)
= 14.74 ft3/min (n) Calculate instantaneous flowing BHP, P~r (Eq- 17 )'
= r ( 1400- 275) (50× 5.615)(11,420) (0.886)2] '/2 100
[
J
=5321.12 psi.
P~f= P-! + ( H - hmf)gm+ hm&l = 2100 + ( 13,000- 2332) (0.779) + (2332) (0.436)
Substituting back into Eq. A-1 above, calculate V ~ At any other depth, similar calculations as functions of Z ( h ) and T(h) can be made (v) Calculate time it takes to reach Pm,~.
(iii) Estimate P~, setting flow rate: If we set choke flow rate at 10 ft3/mm from Eq. 25.
t = Pmax-- Ps~b,hz~d__521 12 -- 2800_ 9.2 min P~ 275
"2~(1 --qh] ql2~p,I ~(l-
tm~=t~+ t2= (2 + 9.2)rain= 11.2 mm But i f q u = 120 ft3/min, P~=45 2 psl/min, Pm~=5331 psi, t2 = 56 min and tm,~= 58 mm The calculated times will be lower than the case where static conditions are assumed. Thus the earliest possible time of arrival is calculated. From these two calculations it is possible to adjust the surface flow rate in such a way that the well is controlled optimally. This part of the calculation is hypothetical, in practice, a more realistic pattern results. From the relationship, q',~ is used instead of qB,, thus flow at the surface is as close as possible to q~
Example 2--Water kick The same well conditions and kick volume are used here as in Example 1, except that the casing pressure for water kick was 2,100 psi as compared to 2,800 psi for the gas kick. This is due to the difference m hydrostatic gradients Steps (a) through (f) are the same with the gas kick/ (g) Identify kick Casing pressure, P=j 2100 psi
= 11,427 124 psi
141~074)
1050psi/rain
= 337.653 psffmm 0 v ) Calculate maximum pressure and volume at the surface Thus taking a pressure gradient of 11,420/13,000 = 0.8785 psi/ft, determine the pressure at any depth From Eq. 27, with P~x = 0. Vma~=
G, exp-- CPbh
substituting, Vm~,= 88.502 bbl. From Eq. 28, substituting values"
exp[--C(Pbh--P~'~')]=[C(P'L qu-P2)G,j' ]-'
emax= 1 r 10 -]--1 Pbh + ~ l n k ( 5 × 1 0 - ' ) (712.-3-47) (50× 5.615)]
Pm~,~Pbhimplying that
practically Pro,x=0 for flow to
174 take place Thus taking pressure gradient of 11,420/ 13,000= 0.8785 psi/ft, determine pressure at any depth. (v) Calculate time it takes to reach surface Pcss __2100 - 6 . 2 2 rain P~ -337.653 tma~=t~ +t2= (2+6.22 m m ) = 8 22 rain But assuming q12= 14 ft a/ram, 12= 40 mm and tma~= 42 mm With these two examples ofqt2, can compromise between time and expected pressures to decide an efficient venting rate
References Alexander, L G., 1977 Theory and practice of the closedchamber dnllstem test method J. Pet. Tech., 29 ( 12 ) 1539-1544. Azar, J J., 1973. Drllhng m Petroleum Engineering. Lecture Notes, Umverslty of Tulsa, Tulsa, Okla Beggs, H.D and Brill, J P., 1978 Two Phase Flow in Pipes. Lecture Notes, University of Tulsa, Tulsa, Okla. Bourgoyne, T., 1977. Graphical approach to kick severity calculations. In. Engjneenng Essentials of Modern Drilling. Energy Publications, Texas, pp 107-111_ Burgess, T , Starkey, A.A. and White, D., 1990. Improvement of kick detection. Odfield Rec, 2 ( 1 ). 43-51 Chukwu, G A and Ajlenka, J A., 1989. Prediction of fired flow parameters m a gas-cut mud, 2. Mathematical approach to the determination of the rate of gas bubble rise m a gas-cut mud J. Pet. Sci. Eng., 2(4) 305-309. Desbrandes, R and Bourgoyne, A T., Jr., 1987 MWD momtonng of gas kicks ensures safer drilhng Pet. Eng. Int, 59(7)- 43-52. Earlougher, R C., 1977. Advances m Well Test Analysis Soc Pet. Eng. ofAIME, Monogr 5, 264 pp
J A AJIENKA AND O O_ OWOLABI
Gathn, C, 1960. Petroleum Englneenng--Drilhng and Well Completions Prentice-Hall, Inc., N.J., Chap. 2, pp. 19-33 Hoberock, L L. and Stanberg, S R., 1981 Pressure dynamics in wells during gas kicks Part l--Fluid line dynamics; Part 2---Component models and results J. Pet Tech., 3 3 ( 8 ) 1357-1378 Kablr, C S and Hasan, A.R, 1982. Apphcauon of mass balance m pumping well analysis. J. Pet Tech., 34( 5 ) 1002-1010 Kazeml, H , Haws, G.W., Kunzman, W J , Milton, H W , Jr. and Halbert, W G., 1983 Complexmes of the analysis of surface shut-in drill stem tests in an off-shore volaUle oll reservoir. J. Pet Tech, 35( 1 ): 173-178 Kendall, H.A, 1977 How to control deep critical wells_ I n Engineering Essentials of Modern Dnlhng. Energy Pubhcauons, Texas, pp 112-118. LeBlanc, J L. and Lewis, R L, 1968. A mathematical model of a gas kick. J. Pet Tech., 20(8) 888-898 Nance, G , 1977. How to calculate maximum surface pressure for floating drilling I n Engmeenng Essentials of Modern Dnlhng Energy Pubhcations, Texas, pp. 125-128_ Rader, D W_, Bourgoyne, A_T_,Jr and Ward, R H , 1975 Factors affecting bubble rise velocity of gas kicks J Pet. Tech, 27(5): 571-584 Schurman, G.A_ and Bell, D.L., 1966. An improved procedure for handhng a threatened blowout J Pet Tech_, 18(4): 437-444. Thomas, D.C., Lea, J.F, Jr. and Turek, E.A., 1984. Gas solublhty in oil-based dnlhng fluids: Effects on kick detection. J Pet Tech., 36(7). 959-968. West, E.R, 1977 Hydraulic control of deep well blowouts. In. Engmeenng Essentials of Modern Drdhng. Energy Pubhcatlons, Texas, pp 119-123