Journal of Petroleum Science and Engineering 67 (2009) 1322

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Journal of Petroleum Science and Engineering

j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p e t r o l

Research paper

Deepwater gas kick simulation

Carolina S. Avelar a, Paulo R. Ribeiro a,, Kamy Sepehrnoori b
a
b

Department of Petroleum Engineering, Faculdade de Engenharia Mecanica, Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6122, Campinas, SP, 13083-970, Brazil
Petroleum and Geosystems Engineering, The University of Texas at Austin, 1 University Station C0300 Austin, TX 78712-0228, U.S.A

a r t i c l e

i n f o

Article history:
Received 19 May 2008
Accepted 5 March 2009
Keywords:
drilling
well control
deepwater
kick
kick simulation

a b s t r a c t
Important gas and light oil reserves have recently been found in the Tupi eld of Santos Basin, Brazil. The
Tupi is formed by subsalt hydrocarbon reservoirs 6000 to 7000 m deep, with water depths up to 3000 m,
subjected to high pressure and high temperature bottomhole conditions. The investigation of well control
aspects during exploratory and development drilling in that eld requires kick simulators that can handle the
pressure and temperature range encountered in deep and ultra deepwater scenarios.
Safety issues associated with well control situations demand precise predictions of wellbore pressures and
liquid/gas volumes as well as ow rates at the surface. The possibility of blowout occurrence needs to be
mitigated in order to avoid human casualties, nancial losses (production stop and equipment losses) and
environmental damage.
Several kick simulators have been developed during the last four decades in order to address well control
problems during the drilling operation. The simulators have an important mission that involve: i) helping the
drilling engineer to make decisions during well control procedures and kick situations, ii) personnel training
and certication and iii) better understanding and interpretation of eld observations. The evolution of the
codes has been driven by the increasing challenges in exploration and development of the remaining
hydrocarbon reserves. Increasing complexity of well geometry (diameters and trajectory), well location (land
and offshore) and bottomhole conditions (increasing pressure and temperature severity with depth) has
required more precise two-phase ow models and more representative rheological as well as compositional
models.
This work presents the mathematical modeling of a proposed gas kick simulator, the comparison between
simulated and measured results for a test well located in Brazil, and a sensitivity analysis regarding the effect
of water depth in well control parameters.
2009 Elsevier B.V. All rights reserved.

1. Introduction
The recent discovery of Tupi eld of Santos Basin in Brazil
has signicantly increased the possible country's hydrocarbon
reserves. The anticipation for the increased country's reserve has
lead to the expectation for rapid development of the Tupi eld. The
exploitation difculties associated with the deep and ultradeep
water depths, severe reservoir pressure, temperature conditions
and geomechanical issues pose important scientic and technological challenges.
In a drilling perspective, well design and construction require
addressing safety issues, particularly associated with well control
operations. Personnel training and certication as well as the proper
well control operation require reliable computational tools, such as
kick simulators. The advancement of kick simulators in the previous

Corresponding author.
E-mail address: ribeiro@dep.fem.unicamp.br (P.R. Ribeiro).
0920-4105/$ see front matter 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.petrol.2009.03.001

decades has allowed more accurate pressure, volume and uid ow

rate prediction during well control procedures. This has been very
helpful in designing different operational phases of the well, avoiding
potential wellbore stability problems by introducing kick tolerance concepts in the casing settling program and designing surface
separators to handle gas and liquid volume rates. Also, in helping the
drilling engineer to make correct decisions during a well control eld
operation.
The evolution of the well control simulators in the past four
decades, beginning with the simple well control model by Leblanc and
Lewis (1968), comprises the incorporation of physical issues related
to:

well trajectory (vertical, deviated and horizontal wells);

well location (land and offshore wells);
annular space geometry (open, cased and lined borehole sections);
well control method (driller's, wait and weight, and volumetric
method);
uid rheological behavior (one, two or three parameter rheological
models);

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C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

Conservation of momentum:

Nomenclature
Co
M
P
R
T
t
v
z
Z



A
A
2
2
v + g g v g +
v + g g v g + p
At l l l
Az l l l


= l l + g g g cos F:

distribution parameter
molecular weight
absolute pressure
universal constant
absolute temperature
time
velocity
axial position
compressibility factor

The relationship between the velocity of the two phases is given by



 
vg = C0 g vg + 1 g vl + vS

Greek letters

density

volume fraction

g =

l + g = 1:

two-phase ow pattern;
slip velocity between phases;
gas solubility in the drilling uid;
reservoir behavior accounting in the well (formation coupling).

Performing a literature search regarding the evolution of the well

control simulators is not the objective of this work and references
about the subject could be found elsewhere (Nunes et al., 2002).
The present work focuses on deepwater well control modeling
comprising the treatment of the following physical aspects: two-phase
ow slippage and pressure loss computation, classical two-parameter
rheology model and reservoir coupling. A nite difference formulation is
applied to solve the transient two-phase ow of a real gas and the waterbased drilling uid. The aim of this work is to compare simulated results
with real data from a test well. The test well conguration represents a
deepwater scenario with a 1240-meter vertical well with a 735-meter
choke line. The discussion of the effect of water depth on well control
simulated parameters is also addressed.
2. Mathematical formulation
The governing equations are the mass balance for the two phases,
momentum balance and three complementary relations. The temperature inside the well is equal to the formation temperature, but no
heat transfer was accounted for.
Conservation of gas mass:

The frictional pressure loss gradient (F term in Eq. (3)) is computed

for both the single-phase region (uncontaminated drilling uid) and
the two-phase region (gas contaminated zone). The single-phase
pressure losses are computed by analytical solutions (laminar regime)
and friction factor correlations (turbulent regime) for the Newtonian,
Bingham Plastic and Power Law model, according to Bourgoyne et al.
(1986). The two-phase ow region frictional pressure loss is computed
by Beggs and Brill (1973) correlation, where F can be determined
as a function of vl, vg, g, P, and T. The liquid is incompressible, which
makes l constant.
Eqs. (1) through (3) can be written in the following form, according
to Lage (2000):
A
A
w +
f = qj
At j
Az j

j = 1; 2 and 3

where the variables, wj, fj and qj are functions of the physical variables
(g, l, g, vl, vg and p), according to Table 1.
The nonlinear system of partial differential equations (strictly
hyperbolic nature for the physical problem, according to Fjelde, 1995)
can be solved using a numerical method. Discretization of the partial
differential Eqs. (1) through (3), using a nite difference method
(Nickens, 1987; Santos, 1991), results in the following equations:
n + 1
+ 1=2

w1 j i
t

n + 1
+ 1=2

w2 j i
t

w1 j i

w2 j i

+ 1= 2

+ 1= 2

f1 j ni ++ 11 f1 j ni
z

+ 1

f2 j ni ++ 11 f2 j ni
z

+ 1

=0

=0

1
n + 1= 2
n + 1=2
w3 j ni ++ 11= 2 w3 j ni + 1 = 2
f34 j i + 1
f34 j i
+
t
z

Conservation of liquid mass:

A
A
+
v = 0:
At l l
Az l l l

PM
ZRT

where, Z is the compressibility factor, which is computed according to

Yarborough and Hall (1974).
The phase volume fractions relationship is given by

Superscripts
n
related to time



A
A
g g +
g g vg = 0:
At
Az

where, C0 and vS are determined according to the ow pattern (Lage

and Time, 2000).
The real gas law is given by

Subscripts
g
gas
i
related to the node
j
related to the conservation equations
l
liquid
s
slip

pni ++ 11 pni
z

+ 1

n + 1=2
1= 2

= q3 j i +

10

C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

where, u j i +1 =2 = u j i +12 + u j i , u j n +1 = 2 =
n + 1

uji

n + 1
+ 1

+ uji

ujn

+ 1

+ ujn

n + 1= 2
+ 1=2

and uj i

+ uji + uji

+ 1

The simulation of the well control problem involves three stages:

i) drilling uid circulation prior to the gas entrance into the well,
ii) formation gas entrance into the well (Darcy's law radial ow),
and iii) application of driller's well control method until all the gas
is expelled from the well. The rst stage comprises a single-phase
ow with a xed pumping rate, corresponding to a xed liquid
velocity. During the second stage, reservoir pressure is greater than
the bottomhole pressure, which allows gas entrance in the wellbore. When the kick alarm sounds (certain volume of formation
inux is detected at the mud tanks), the wellbore is shut in (pump
is turned off, the choke and blowout preventer are closed) and
gas continues to enter the well until the reservoir and bottomhole pressure are equalized. The third and nal stage begins with
the gas distributed in the bottom part of the hole with a prescribed
volume fraction. Drilling uid circulation is resumed and maintained until the contaminated uid zone (uid plus formation gas)
is completely circulated out of the whole, when single-phase ow is
reestablished.
The single- and two-phase ow problems are modeled separately
since the former one is treated analytically by a steady-state approach.
The boundary and initial conditions follow the events described for
each stage. During the rst stage, there is a prescribed drilling pump
rate (vl is constant) with the wellbore open (atmospheric pressure at
the surface). In the second stage there are two events: i) gas inow
from the reservoir until the kick is detected at the surface (gas ow
rate driven by the pressure difference between the reservoir and the
well, prescribed drilling pump rate and the well is open at the surface)
and, ii) after the kick is detected, the pump is turned off (vl = 0 at the
bottomhole) and choke and BOP are closed (vl = 0 at the surface).
During the third stage, which begins after pressures stabilization,
there is a prescribed bottomhole pressure (equal to the reservoir
pressure, which prevents additional gas inux). The contaminated
zone (gas and liquid mixture) is circulated out of the well with a
prescribed pump rate (reduced circulation rate), until single-phase
ow is reestablished.
3. Case study
The case used to evaluate the consistency and accuracy of the
simulated results concerns a well control experiment that was performed in a test well located in the city of Taquipe (Bahia),
Brazil (Marques, 2004). The test well design consists of a 0.0889 m
diameter drillpipe concentric to a 0.1778 m diameter casing. The
casing stands inside of another 0.3397 m diameter casing that is
cemented from the bottom to the surface, whose annular space is
applied to lodge the kill and choke lines as well as the cables which
connect the six pressure and temperature gauges to the surface and
data acquisition station.
The experiment was comprised of the application of the driller's
method, which consists of circulating the gas inux out of the well
using the original mud to control an air kick in a water-based drilling uid considering an offshore well conguration (subsea BOP).

Table 1
Correspondence of terms.
wj

fj

qj

w1 = gg
w2 = ll
w3 = lll + ggg

f1 = ggg
f2 = lll
f3 = lll2 + ggg2 + p
f3 = l l 2l + g gg2

q1 = 0
q2 = 0
q3 = g(ll + gg)cos + F

15

Table 2
Input simulation parameters.
Parameter

Test well

Base case

Well depth, m
Water depth, m
Casing shoe depth, m
Mud ow rate during drilling, m3/s
Mud ow rate during kick circulation, m3/s
Wellbore diameter, m
Drillstring external diameter, m
Choke line internal diameter, m
Riser internal diameter, m
Inux detection volume, m3
Shut-in drillpipe pressure SIDPP, MPa
Mud density, kg/m3
Mud rheological parameters

1240
735

0
0.0027
0.1570
0.0889 m
0.0508 m
0.1570 m
0.6359 m3
2.482
1092
k = 7.0681 eqcP
n = 0.2763
0.028
27
0.029

2000

1500
0.0284
0.0126
0.2032
0.1270
0.0762
0.5334
1.5899
2.758
1200
= 35 cP

Gas molecular weight, kg/mol

Surface temperature, C
Geothermal gradient, C/m

0.016
27
0.025

Well design parameters (depths and diameters), drilling uid and

gas properties (density and rheology) and operational conditions
(ow rates and pressure) are displayed in Table 2 for the test well
simulations.
The simulation for this case was comprised of two conditions: i)
constant bottomhole pressure and ii) bottomhole pressure gauge
reading used as the boundary condition. This procedure allowed the
analysis of the pressure response of the mathematical model to be
compared to the real data. The test procedure was comprised of: i) air
is injected downhole through an auxiliary line maintaining the choke
open at the surface, ii) when the pit gain inside the well reaches the
prescribed alarm value, the well is closed and iii) drilling uid is
injected through the drillpipe with a xed rate to circulate the gas
kick out of the well, maintaining a possibly constant bottomhole
pressure by choke valve operation.
4. Results and discussion
Fig. 1 shows the gas entering the well as a function of time, which
was simulated by a hypothetical gas reservoir inux. The main
objective was to simulate the same gas mass that was injected into the
real wellbore.
Fig. 2 presents the bottomhole pressure response during the gas
injection and also throughout the entire well control process, where
the goal was to maintain a constant bottomhole pressure. As the choke
valve is manually operated, pressure oscillations at the surface can be
observed. As the gas enters the well that is open at the surface,
pressure drops at the bottom due to the decrease in the hydrostatic
head. When the well is closed, pressure increases inside the well until
the bottomhole pressure equals the formation pressure.
Fig. 3 shows the drilling uid injection rate as a function of time,
which begins just after the well is closed and driller's method
procedure resumed. The liquid velocity is a boundary condition to the
system of equations and was maintained constant throughout the
simulation.
Fig. 4 presents the liquid ow rate out of the well, which was
partially captured by the model. The liquid ow rate out of the well is
underestimated when the gas kick occurs, although the single-phase
ow was handled properly.
Fig. 5 displays the pit gain during the well control process, where
both simulated and real data reect the moment the well is shut in.
The liquid injection initiation could also be captured by the model,
although the intuitive pit gain increase that was expected was
not observed in the experiment. Gas withdrawal at the choke also
generates peculiar pit gain oscillations in the real data, which were

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C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

Fig. 1. Computed and measured entering gas ow rate in the test well. The simulations were conducted under two different boundary conditions for the bottomhole pressure (BHP):
constant bottomhole pressure and bottomhole pressure equal to the measured value in the test well.

not observed in the simulation results, and could indicate possible

tank level variations due to the free surface waving.
The pressure response of the bottomhole pressure data boundary
condition can be observed in Fig. 6 (pressure gauge at 985-meter
depth), Fig. 7 (pressure gauge at 735-meter depth) and Fig. 8 (surface).
Pressure differences between simulated results and data for the
985-meter and 735-meter depths are very small for the entire experiment time span. The predicted peak pressure for the choke,
shown in Fig. 8, which represents the moment the gas front reaches
the surface, is in fairly good agreement with the data. The gas
expelling process through the choke presents a different prole,
associated with a slower gas discharge compared to the simulated
case. As can be seen in the plots, the constant bottomhole pressure
simulation results could not capture pressure and volume oscillations, although they maintain consistent mean values.
The study of the effect of water depth in the well control
parameters was made considering the well schematics presented in

Fig. 9. The input simulation parameters for the base case are also
presented in Table 2. Water depths of 0 (land well), 500 and 1000 m
have been considered in the analysis.
The simulation procedure to represent the physical problem is
outlined in the following: i) gas enters the well until the prescribed
pit gain is detected at the surface (during this initial time the well is
opened at the surface), ii) mud pumps stopped, BOP is closed, choke
line is opened and choke valve is closed (this well shutting procedure takes some minutes and must be considered in the simulation),
and, iii) mud circulation resumed with a lower rate, keeping the
bottomhole pressure constant by choke valve operation at the
surface and, iiii) mud circulation continues until all the gas is
expelled from the wellbore. At this stage the well is lled with the
original drilling uid and the choke pressure equals the shut-in
drillpipe pressure (SIDPP).
In order to address the effect of water depth on the well control
parameters, the total vertical depth (TVD) was kept constant and the

Fig. 2. Measured and imposed bottomhole pressure for the two case simulations. The bottomhole pressure was maintained above the reference pore pressure in the simulations.

C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

17

Fig. 3. Measured and imposed entering liquid ow rate for the simulations.

water depth was increased from zero (land well), to 500 m (shallow
water well) to 1000 m (deepwater well). Due to the subsea blowout
preventer (BOP), the upper annular section of the well, which
corresponds to the riser section, is isolated as the BOP is closed
when the ow is diverted to the choke line during driller's well control
procedure. The reduction of ow area when the uid leaves the
annular section (0.2032 m OD 0.1270 m ID) and enters the choke line
section (0.0762 m ID) is approximately 80%, which causes a signicant
increase in the pressure losses during the kick circulation. In order to
maintain a constant bottomhole pressure greater than or equal to the
formation pressure, which prevents more gas from entering the well,
the choke should gradually be opened and choke pressure reduced.
Although the loss in hydrostatic head when the contaminated zone
enters the choke line causes an opposite effect in the bottomhole
pressure that should be compensated by the choke's operator.

Simulations are initiated at the time a methane gas inux (kick)

from a permeable formation enters the well, which requires the well
to be closed and a shut-in drillpipe pressure (SIDPP) registered at the
surface (Table 2).
Fig. 10 shows the gas ow rate entering the well which increases
with water depth due to the fact that friction pressure losses in the
single-phase region above the contaminated zone (gasmud zone)
decreases. This decrease is associated with the drastic increase of
annular ow area (approximate10-fold) when the wellbore annular
section is substituted by the riser annular section. Consequently, an
average increase in gas volume fraction is expected in the initially
contaminated zone, considering that the well shut-in time is equal to
1 min in all simulations.
The faster gas entrance into the well due to the increasing water
depth can be observed in Fig. 11. That happens before the bottomhole

Fig. 4. Computed and measured liquid ow rate out of the well, considering the two kinds of boundary conditions for the bottomhole pressure (BHP).

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C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

Fig. 5. Computed and measured pit gain, considering the two kinds of boundary conditions for the bottomhole pressure (BHP).

Fig. 6. Computed and measured pressure at 985-meter depth, considering the two kinds of boundary conditions for the bottomhole pressure (BHP).

Fig. 7. Computed and measured wellhead pressure (735-meter depth), considering the two kinds of boundary conditions for the bottomhole pressure (BHP).

C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

19

Fig. 8. Computed and measured choke pressure, considering the two kinds of boundary conditions for the bottomhole pressure (BHP).

Fig. 9. Schematic view of the land and offshore well applied in the analysis of the effect
of water depth in the well control parameters.

pressure reaches its constant value, which corresponds to the sum

of the shut-in drillpipe pressure (SIDPP) and the mud hydrostatic
head.

Fig. 12 presents the liquid ow rate out of the well as a function

of time. Two events can be observed. First, gas entrance into the
well and second, gas circulation out of the well. The second event is
characterized by the liquid rate increase until its maximum value (gas
expanding during kick circulation and reaching the surface or entering
the choke line) and its decrease to the original control circulation
value as the gas is expelled from the well. It can also be observed that
it takes longer for the gas to be circulated out of the land well due to
the larger contaminated volume.
Fig. 13 displays the gas ow rate out of the well as a function of
time. It can be seen that the increasing water depth promotes faster
gas removal with higher gas rates, which is associated with the twophase ow pattern that is reached with increasing average volume gas
fraction with water depth.
Fig. 14 shows the pit gain (volume of gas inside the well, evaluated
by the liquid volume inside the return mud tank) as a function of time,
where the initial gas volume entrance, gas expansion during circulation, and gas expelling from the well can be identied.
Although the well is not cased, a ctitious casing shoe was set at
the depth of 1500 m. The monitoring of the pressure at the casing shoe
during the well control procedure is very important in order to avoid
underground blowouts. Fig. 15 presents the pressure at that depth and
the well control events can be easily identied. At the time the top of

Fig. 10. Comparison among the computed entering gas ow rates for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

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C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

Fig. 11. Comparison among the bottomhole pressures for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

Fig. 12. Computed liquid ow rate out of the well for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

Fig. 13. Computed gas ow rate out of the well for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

Fig. 14. Computed pit gain for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

Fig. 15. Computed casing shoe pressure for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

Fig. 16. Computed choke pressure for a land well, shallow water well (500-meter water depth) and deepwater well (1000-meter water depth).

21

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C.S. Avelar et al. / Journal of Petroleum Science and Engineering 67 (2009) 1322

the gas contaminated zone reaches the casing shoe, the maximum
pressure at that point is attained. If this maximum pressure exceeds
the formation fracture pressure, the gas can ow into the weaker
formation resulting in an underground blowout.
Fig.16 presents the choke (surface) pressure as a function of time and
what can be observed is that the peak pressure increases with water
depth. This is associated with the higher contaminated columns inside
the well, due to the longer choke lines with depth. Beyond the loss of
hydrostatic head due to the gas, the viscosity of the contaminated zone is
also smaller than that of the original drilling uid and demands an
increase in choke pressure to maintain a constant bottomhole pressure.

Acknowledgements
Financial support from the Human Resources Program of the
National Petroleum Agency (PRH 15-ANP), Financiadora de Estudos e
Projetos (FINEP-CTPETRO) and Petrleo Brasileiro S.A. (PETROBRAS) is
greatly appreciated. Computational facilities were provided by the
Department of Petroleum Engineering of the Universidade Estadual de
Campinas (UNICAMP), Brazil. The authors thank Prof. Cristina C.
Cunha, Dr. Otto L.A. Santos and Dr. Heitor R. Lima for their important
contribution to this work.
References

5. Conclusions
The basic evolution of the well control simulators in the past four
decades has been presented in a condensed form considering the
incorporation of physical issues related to well trajectory, annular
space geometry, well control method, uid rheological behavior, slip
velocity between phases, thermodynamic phase behavior, reservoir
coupling, and two-phase ow pattern. A nite difference model to
predict the pressure, liquid and gas velocities, gas density and uid
volume fractions inside deepwater wells during well control operations has been developed.
The model presented satisfactory results for gas and liquid outow
rates, pit gain and pressures inside the wellbore in comparison to the
data from a test well. The model results were physically consistent for
both constant bottomhole pressure and bottomhole pressure gauge
reading as boundary conditions. The effect of the increasing water
depth in the gas and liquid ow rates, pit gain, annular pressure at the
casing shoe and choke pressure has been discussed. For a blowout
prevention perspective, the increase in water depth generates higher
pressures inside the wellbore, which should be accounted for during
well design and construction phases.

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