Journal of University of Shanghai for Science and Technology ISSN: 1007-6735

Taylor Bubble Model Validation During Pressurized MudCap Drilling

(PMCD) Operations: A Comprehensive Review

Hany M. Azab1*, Said K. Elsayed2, Taher.Elfakharany3

1
NEFT Energies Training Institute, Kingdom of Saudi Arabia
2
Faculty of Petroleum and Mining Engineering, Petroleum Engineering Department, Suez University,
Egypt
3
Faculty of Engineering, Mining and Petroleum Engineering Department, Al-Azhar University, Egypt
1
Hany.AzMa@pme.suezuni.edu.eg, 2 s.salem@suezuni.edu.eg, 3 Taher.elfakharany@azhar.edu.eg

Abstract: In some oil fields across the world, lost circulation can be so severe during drilling that
conventional treatments that might help the loss zone heal are ineffective. The Pressurized MudCap
Drilling (PMCD) technique has been introduced to drill such problematic wells, but the computation of
Light Annular Volume (LAM) and its pumping rate based on the gas migration rate determination is the
most critical part of PMCD operation design. The Taylor bubble model can be used to provide solutions
to equations describing the migration behaviour of gas kick through drilling fluids. However, the Taylor
bubble modelling approach yields undesirable outcomes when used to determine gas migration rate for
more complicated rheological models. To keep away from this, A literature review of PMCD principles
and field data was assessed. This comprehensive literature review demonstrated that if Taylor's
mathematical models employed for PMCD operations, it may result in unduly conservative calculations
of the fluid volume used and the surface pumping pressures which makes handling logistics more
difficult, resulting in PMCD operation’s complications.

Keywords: Taylor bubble, Gas migration, PMCD, LAM, Karst, Lost circulation

1. Introduction

Since the invention of rotary drilling, fractured formations have been a problem during drilling
operations. There are traditional methods of solving this issue such as cure the loss by using lost
circulation material. In the event of a lost circulation crisis, lost circulation material (LCM) must be
always available on the rig and the rig is constantly updated with a comprehensive strategy for when and
how to pump the LCM down the well. If big volumes of mud are unexpectedly lost, additional volumes of
LCM are always present on the rig or on surrounding boats. Due to the possibility of greater drilling fluid

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losses, these precautions are increased while drilling into karstified strata. On the rig, there will be
increased amounts of LCM and drilling fluid in addition to various types and particle sizes of LCM for
both materials, this makes handling logistics more difficult, especially for drilling rigs that may be
dispersed and far from a base [1]. Because of the abundant production linked to fracture porosity, many
operators target reservoirs that have significant natural fracturing. Therefore, it is not ideal to permanently
seal off the hydrocarbon-bearing fissures.
PMCD is a variation of Managed Pressure Drilling (MPD) that used when there is a high rate of lost
circulation, is sometimes referred to as the non-return drilling method. Depending on whether the lost
zone is above or below a gas zone, the technique often entails pumping a viscous slug of water base gel
mud into the annulus, and this column of mud is referred to as a "MudCap" [2].

2. Principle of MudCap Drilling

It is hard to drill through rocks with numerous big fractures using standard well control procedures
unless the cracks are sealed. Lost circulation technology has frequently failed to work in situations with
particularly big cracks or caverns (Figure 1), also plugging the cracks is counterproductive when drilling
a fractured deposit that is a pay interval [3].

Figure 1: Root Traces and Cracks in The Epikarst [4]

If total losses occurred, at point formation fluids may begin to enter the wellbore and well control may
become difficult. The difficulty increases when such formations include gas since the gas may easily enter
the wellbore and migrate upward to the surface. The industry has invented mudcap drilling MCD

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technology to effectively drill while managing the migration of the reservoir fluids, including
injecting gas, back into the formation for these types of reservoirs and drilling challenges [3].
Due to its availability, saltwater is typically utilized in this case as the drilling fluid (Also known as a
sacrificial fluid), getting the drilled cuttings into the fractures zone known as the interaction zone, this is
also utilized to cool and lubricate the bit [5]. The ability of the interaction zone to allow large volumes of
sacrificial fluid and cuttings into the crack is frequently characterized by high effective permeability. The
value of fluid density used in some mud cap drilling techniques is typically (0.2–0.4 sg) higher than the
pore pressure.
There are various MCD approaches, some of which feature an open annulus and others which use a
rotating control device (RCD) [6] as follows:

2.1. Floating (Dynamic) MudCap Drilling

During floating MCD, the annulus is exposed to the atmosphere and the liquid column is unrestricted.
In contrast to floating MCD, dynamic MCD continuously injects mudcap fluid into the annulus rather of
doing so just occasionally [6]. This prevents the potential for some formation gas to migrate to the surface
and balances the pore pressure against the fluid level in the annulus by using a heavy amount of mud.
Drilling, tripping, and injection can all be done simultaneously, cuttings down on non-production time.
The general procedure for floating/dynamic MCD is depicted in Figure 2. Along with the drilled
cuttings, sacrificial drilling fluid is injected into the formation by being pumped from the mud pit down
the drill string. Viscous mud cap fluid from another mud pit is continuously pumped into the annulus to
balance the pore pressure and prevent the gas from migrating to the surface. The ideal situation is to
continually inject mud cap fluid to prevent the gas from rising by utilizing heavier mud weight and a low
riser level so that the fluid injection into the annulus may be regulated [7].

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Figure 2: Dynamic MudCap Drilling.

2.2. Pressurized MudCap Drilling

According to the International Association of Drilling Contactors (IADC) Underbalanced Operations &
Managed Pressure Drilling Committee which held on December 2011[8]: “PMCD is a variation of MPD
that involves drilling without returning to the surface and maintaining an annular fluid column above a
formation that may accommodate fluid and cuttings with the help of surface pressure”. The loss
circulation zone will accept a sacrificial fluid that contains cuttings. Useful in situations where there is
considerable loss of circulation and standard wellbore construction cannot be used.
When the pore pressure is sufficient to support a column of fluid in the annulus, PMCD is used. It
makes use of LAM, which is injected through the annulus from the surface into the loss zone (Figure 3).
The surface back pressure (SBP), which is normally constructed to be +/- 200 psi, is the difference in
pressure between the reservoir pressure and the purposefully underbalanced hydrostatic pressure of the
LAM. Figure 3 below depicts the current state of PMCD [9].

Figure 3: Pressurized MudCap Drilling Illustration

The cycles of periodic flushing and shut-in periods are the most basic aspect of this technique (Figure
4). The annulus is closed at the surface during the shut-in time, and the monitored surface annular
pressure is reflecting the difference between the LAM column and reservoir pressure. The exchanging of
the lighter gas with LAM results in a continual gas influx at the bottom of the wellbore where pressure is
balanced with reservoir pressure [10].

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Figure 4: Pressurized Mudcap Drilling Process

During the shut-in period, this gas migrates through the static LAM column in the wellbore annulus and
when a predetermined casing pressure or height is attained, the gas is swept back into the formation
during the succeeding flushing period by pumping LAM fluid into the annulus at a rate greater than the
rate of gas migration. During the shut-in phase, when low density gas enters the wellbore, The hydrostatic
head of the fluid in the wellbore is decreased. As a result, the annular surface pressure rises to balance the
falling hydrostatic head and to maintain constant Bottomhole Pressure (BHP). As the gas is pushed back
into the formation during the flushing phase, annular pressure begins to progressively decrease. The
pumps are shut off, the annulus is sealed, and gas is once more let to migrate into the wellbore after the
gas has been completely displaced back into the formation. Constant BHP, which is close to reservoir
pressure conditions, is used for this cyclical process [11].
PMCD might no longer be required, and operations might switch back to conventional drilling if the
formation heals or partially heals itself because of the cuttings packing off in the fractures.
2.2.1. Factors Affecting on of PMCD Selection
When circulation is lost, the causes and extent of the losses should be assessed to determine the next
best course of action. Since PMCD is conducted with no returns, various choice factors must be
considered before choosing to activate the PMCD mode on the rig [12].
I. Are losses occurring because of improper mud weight or naturally occurring carbonate vugs?
The losses in the second option are essentially the same under static and dynamic events. The
mud needs to be weighted up if the losses under dynamic events are significantly more than
under static one.
II. Can LCM be used to cure losses of circulation? In carbonate reservoirs, it is typically
impossible.

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III. To determine whether the loss zone is appropriate for PMCD, an injectivity test should be
carried out. As many literatures stated that mud cap operations should only be employed in
the presence of open fissures that are at least three times the cutting diameter [13].
IV. Do the loss and other permeable zones have vertical permeability? If a geologic failure
confines this zone and no vertical permeability is found, after a time of continuous injection
of LAM and potential flushing and shut-in cycles, the loss zone may become over-pressured,
and an underground blowout may happen. As a means of pressure release, the vertical
permeability might be useful.

3. PMCD Technique and Related Field Calculations

To keep constant BHP at the fractured zone, PMCD uses a hydrostatically unbalanced fluid and applied
surface pressure. Kicks are typically not a problem because all returns are pumped back into the
formation, unless the capacity to pump down the annulus is compromised. A kick can also be thought of
as requiring more annular pump pressure to inject reservoir fluids back into the formation from a design
perspective. If the apparatus (an annular pump and rotating control head) does not have enough pressure
rating for the higher pressure, this could become a significant problem [9]. In this case, the annular fluid
density must be increased to lower the surface casing pressure if the reservoir pressure is too high (should
essentially be the same in a fractured formation) [2]. One can figure out the new necessary fluid density
by Eq. (1):
(Pann−PTarget)
MWnew = MWold +
0.052 X Dfracture

(1)

Where:

MWnew : Required mud weight to achieve target pressure (ppg)

MWold : Original fluid density (ppg)
Pann : Annular pressure with original mud weight (psi)
PTarget : Target annular pressure with new mud weight (psi)
Dfracture : Depth of fracture that annulus fluid is pumped into (ft)
When attempts to bridge the annulus to allow a trip are unsuccessful, the problem with PMCD
operations becomes more prevalent. To build a bridge that enables a trip, it frequently takes a few tries.

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To ensure that the gas percolation will be exceeded, and the inflow will begin to flow back down
annulus, the LAM injection rate (Qinj) must be greater than the gas velocity augmented by a safety factor
(SF). Eq. (2) and Eq. (3), respectively, provide the LAM injection rate and volume [2].
−
60 SF Vt π �ID2 hole−OD²dp�10 6
Qinj =
4

(2)

Vinj = Qinj t
(3)

Where:

Qinj : LAM injection rate (m3/min)

SF : Safety Factor
Vt : Gas migration rate
IDhole : Hole diameter (inch)
ODdp : Drill pipe outside diameter (inch)

4. Problem Statement of Gas Migration During PMCD Operations

The steps to design the best PMCD include [12]:

I. Designing the equipment to allow conventional drilling until significant losses are
experienced and then quickly switching to PMCD.
II. Choosing the right fluid.
III. Calculating the annular fluid velocity to prevent gas migration and drive formation fluids
back into the formation.
IV. Calculating the surface pressure using LAM to confirm the RCD's suitability.
V. Calculate influx’s volume.
Under typical field downhole conditions, it is seen that the large gas bubbles split into a swarm of
smaller bubbles. The resulting gas swarm migrates at about 0.7 feet per second in water and at about 0.4
feet per second in water base mud (WBM) with oil/surfactant. As the reservoir gas dissolves in synthetic
base mud (SBM), the rate of gas migration decreases to 12–15% of that in water, or to 0.1 ft/sec. These
findings do not consider how gas holdup affects gas velocity, which might further slowdown gas
migration during PMCD.
During PMCD operations, reservoir gas is anticipated to migrate uphole, and the uncertainty in gas
migration rates under downhole circumstances makes it difficult to plan logistics and fluid requirements

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as the estimated gas migration rate during the shut-in period is used to calculate the LAM volume and
horsepower needed to flush the gas back into the formation [14]. Lower gas migration rates and
dependable operation are anticipated because of improved logistics, storage, planning, and fluid
selection [15]. Current approaches for estimating migration velocities, such as the Taylor-bubble
correlation, are extremely cautious and rely on simplified assumptions.

4.1. Taylor Gas Bubble Velocity Model

Estimating the gas velocity in upward annuli is critical to understand how a gas kick develops under
PMCD working condition. To make things easier, the gas was assumed to migrate as solitary bubbles
while the CapMud will be shown as a motionless column of liquid. The Taylor bubble slip velocity in
vertical circular pipes [16] can be calculated using Eq. (4):
Vs = 0.345�g ODdp(ρl − ρg)/ρg
(4)

Where:

Vs : Taylor Bubble vertical slip velocity

g : The gravity acceleration
ODdp : Drill pipe outside diameter (inch)
ρl : Liquid density (ppg)
ρg : Gas density (ppg)

Later, Taylor bubble slip velocity was modified, takes into considerations the annulus shape [17], as
illustrated in Eq. (5):
IDdp
Vs = (0.345 + 0.1 )�g ODdp(ρl − ρg)/ρg
OD dp
(5)

With a variety of annular geometries, it is possible to examine the variation in gas velocity using Eq.
(5), which is thought to be the most appropriate for calculating gas rise velocity.
Most laboratory size investigations on air-water and other related fluid systems have established that the
correlation for the velocity of this type of bubble is consistent [18,19].
Taylor bubble velocity experimental data from the literature was used extensively to create a thorough
correlation for its velocity. The correlation considers the influences of diameter, gravity, surface tension,
fluid densities, and viscosity [20]. The formula for the correlated Taylor bubble velocity can be described
in Eq. (6):

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Δρ
V = Fr�g 𝐈𝐃𝐜𝐚𝐬𝐢𝐧𝐠( )
ρg

(6)

Where:

𝐕 : Correlated Taylor bubble velocity

𝐅𝐫 : Froude number
𝚫ρ : Difference in liquid and gas densities (ppg)

Froude number (Fr) may be calculated using the universal correlation between the Reynolds (Re)
number and the Eotvos (Eo) number [20] as show in Eq. (7), Eq. (8) and Eq. (9):
.
9.494E−3R1 026
If, Re B < 10, Fr = 6197 .
. �0 5793
�1+
E03 06

(7)

A
If, 10 < Re B < 200, Fr = R
�1+( )C�G
B

(8)

034
If, Re B <200, Fr = 3805 .
. �0 58
�1+
E03 05

(9)

Complex functions of fluid characteristics and wellbore dimensions are A, B, C, and D. For inclined
annuli, the Taylor bubble correlation was created adjusting (Fr) by this correction factor (Frcorrected)
considering hole inclination angle θ [17] as show in Eq. (10):
ODdp .
Frcorrected = Fr(1 + 0.29 )�cosθ(1 + sinθ)1 2
IDcasing

(10)

Where:

𝐅𝐫𝐜𝐨𝐫𝐫𝐞𝐜𝐭𝐞𝐝 : Corrected Froude number

𝐅𝐫 : Froude number
𝐎𝐃𝐝𝐩 : Pipe outside diameter (inch)
𝐈𝐃𝐜𝐚𝐬𝐢𝐧𝐠 : Casing inside diameter (inch)
θ : Hole inclination (Degree)

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4.2. Field Data Application in Gas Migration Velocity Calculations

Liquid velocity and pump speed are the main tools for regulating gas migration in the wellbore. The
continual injection LAM would be the greatest method to completely remove the possibility of gas
migration, however this is rarely an option. Instead, the gas is displaced from the annulus with a high
pump rate when well conditions permit, after which the injection is decreased or stopped, and the annulus
pressure is monitored. There are two methods to calculate the gas migration velocity using common field
data. Overall, the maximum and lower bounds of the gas migration rates can be determined by the annular
surface pressure based and flushing volume-based velocities, respectively [15].
4.2.1. Annular Surface Pressure-Based Method
The gas migration velocities in the field PMCD may be calculated using the rise in surface pressure
during the shut-in period as the gas inflow into the wellbore, lowers the fluid column's hydrostatic
pressure. The loss circulation zone keeps the well open at the bottom, keeping the bottomhole pressure
close to the reservoir pressure. To maintain this state, surface annular pressure must continuously rise
while the hydrostatic pressure of the fluid in the annulus continuously drops due to continuous gas inflow.
As a result, the volume of gas that moved into the annulus can be approximated by the change in surface
annular pressure.
More accurate image of the gas's position might be obtained by multiplying the estimated gas migration
rate by three times the surface pressure estimate. According to a typical field PMCD data, surface-
pressure growth during gas migration reveals an extremely rapid increase in pressure during the first few
minutes of the shut-in phase, followed by a moderate and steady rate of increase in pressure [14]. Every
shut-in phase begins with a fast influx rate since it is impossible to achieve balanced conditions along the
entire height of the reservoir at that time. A high initial influx drawdown rate from the upper, unbalanced
portion of the reservoir height results in a big volume of gas in the well since the reservoir is balanced at
its lowest point in height.
This approach naturally underestimates the migration velocity because it assumes that the migrating gas
fills the entire wellbore cross-sectional area. But the truth is that some of the gas will disperse in the LAM
as it migrates, so it won't completely fill the wellbore cross sectional area.
4.2.2. Flushing Volume-Based Method
The second method is used based on how much LAM is needed to sweep the migrating gas back into
the formation. The gas migration velocity is computed using the amount of LAM utilized for flushing and
the time since the last shut-in period. Assuming there is no slip velocity between the gas and liquid during
flushing, this technique overestimates the gas migration velocity [15].

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5. Taylor Bubble Velocity Versus Field Data During PMCD

In the study of the gas migration rates during drilling PMCD operations, there is much debate in the
published literature as it was determined experimentally in test wells with typical muds and modest flow
loops, and it was found to be 1.5 ft/sec [21,22]. because of these observations, the industry has adopted
the "rule-of-thumb" that the gas velocity in a wellbore is between 90 and 100 ft/min. These experimental
findings of rapid bubble migration are inconsistent with the available field data. Based on measurements
taken in the field on gas wells that have been shut in, some researchers have discovered that the gas
migrates at a rate of roughly 15 ft/hr [23,24]. In the PMCD shut-in period, it was recorded gas velocities
32TU U32T 32TU U32T

of 2.5–10 ft/min (150–600 ft/hr), depending on the LAM composition and wellbore geometry [1].
Therefore, The Taylor bubble model was validated using data on gas migration from test wells as the
industry standard is to measure the gas migration velocity during PMCD using the Taylor bubble velocity
correlation [25]. This is consistent with laboratory findings demonstrating that in a shut-in well with
normal field muds, the gas migrates at a rate from 90 to 100 feet per minute [24,25,26,27]. However, a
sizable body of field data indicated that gas migrates at 2-15 ft/min during the shut-in phase, which
contrasts with the standard industrial practice [28]. This indicates that, in comparison to typical field gas
migration rates, the industry standard anticipates velocities that are orders of magnitude greater.
To assess the Taylor bubble model against field data, a very high gas influx rate for a short period of
time was employed, resulting in the creation of a gas slug (Taylor bubble) at the bottom of the well [14].
For these simulations, initial gas holdups as high as 50–70% are attained. Figure 5 displays the simulation
results for migration of a big slug with a volume of 5 bbl.

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Figure 5: Dynamic gas migration’s results [14].

According to the results at t = 0 minutes from Figure 5, the initial gas migration velocity is about 1.5
ft/sec, and it fits with the Taylor bubble velocity under the specified conditions. The big bubble keeps
fracturing from its bottom as it moves upward and begins to form a "bubbly zone" with a gas holdup of
about 20%. Gas velocity in this area of smaller bubbles is approximately 0.7 feet per second, while the
gas cap flows at a quicker 1.5 to 1.6 feet per second (results at t = 4 minutes from Figure 6). In about 7
minutes, the 5 bbl Taylor bubble entirely bursts into a swarm of bubbles. This bubble swarm continues to
move at a steady-state speed of approximately 0.72 feet per second (results at t = 30 minutes).
Using field-data analysis, computational fluid dynamics (CFD) simulations, and multiphase flow
literature, A small-scale three-dimensional multiphase-flow CFD model was utilized by to better
understand the principles of gas migration in WBM. It was discovered that, under normal field downhole
circumstances, a huge bubble in a vertical wellbore annulus split into smaller slow-moving bubbles [15].

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During field PMCD applications, it was found that the anticipated gas migration velocity of the swarm of
smaller bubbles matched the observed gas migration velocity sensibly well. Due to the impact of the high
downhole pressure on the stable bubble size, it was shown that field gas migration rates are much lower
than Taylor bubble estimations. Taylor bubbles do not exist at high pressures (>2000 psi) under normal
PMCD working condition, hence it was advised against utilizing the Taylor bubble velocity correlation
for determining field gas migration rates [14].
The massive amount of multiphase flow literature demonstrates that the gas migration velocity would
be based on whether it behaves as a fast-moving big bubble/slug or a slow-moving swarm of smaller
bubbles, as well as whether the flow dynamics change while it migrates [29]. It was stated that, the fast-
moving elongated cap-bubble known as a Taylor bubble often takes up most of the conduit's cross-
sectional area [16].
Figure 6 show the disparity in gas migration rates found in PMCD field data using Taylor bubble type
correlations (a widely used industry rule of thumb), and when compared to field data, the industry
standard and existing correlations anticipate velocities that are orders of magnitude greater [15].

Figure 6: Comparison of gas migration rate of Taylor bubble model with field data application
during PMCD field data applications [15].

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Table 1 presents 5 case studies from Malaysian and Indonesian PMCD operations reflecting a contrast
in gas migration rate estimations based on Taylor Bubble model and field data calculation as follows:

Table 1: Literature's field data on PMCD

Case-1 [28] Case-2 [1] Case-3 [1] Case-4 [30] Case-5 [31]
Offshore
Suban field,
Sarawak, Malaysia - Malaysia - South Sumatra,
Location Indonesia -
Malaysia Petronas Petronas Indonesia
Conoco
Petronas
Hole Size
8.5 8.5 8.5 8.5 8.5
(inch)
DP/BHA Size
5.5 5.5 5.5 5.5 5.5
(inch)
Karstified Karstified
Formation Karstified Karstified Fracture
Fracture Fracture
Type Carbonate Carbonate Carbonate
Carbonate Carbonate
Reservoir
Gas Oil Gas Gas Gas
Fluid
Reservoir
9.3-9.5 NA NA 11.5 9.5
Pressure (ppg)
LAM Density
9.3 NA NA 11 8.34
(ppg)
Mud Type WBM NA NA WBM Fresh Water
Taylor Bubble
Estimates 1.9 1.9 1.9 2.37 1.93
(ft/sec)
Shut-in
Formula
0.38 <0.9 <0.9 0.20 0.59
Estimates
(ft/sec)
0.03-0.05 0.012-0.092
0.04-0.17 <0.1362 1.46-1.947
Actual (Est. from (Est. from
(Range from (Est. from LAM (Bullheading
(ft/sec) surface surface
several wells) rates) continues flow)
pressure) pressure)
% of Taylor <3 <5 2-9 6 ≈100

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5.1. Hole Angle Inclination Validation

Using 6-inch x 4-inch wellbore design with a 30o inclination to vertical, the effects of wellbore
inclination was evaluated on gas migration. Since eccentric annuli are common in inclined wellbores with
drill pipe, it was utilized an eccentricity range of 0.5–0.7. By applying drill pipe rotation (100 rpm) and
low-density mud (5 ppg), with a mud designed plastic viscosity (PV) and yield point (YP) (PV/YP of
21/65), It was discovered that the gas migration velocity equals the Taylor bubble velocity for the first
brief period (0.5 sec) then the gas's surface pressure-based velocity drops dramatically as it ascends, by
40% in 10 seconds [15]. It was stated that the gas velocity based on the bubble-top location is still high
and comparable to Taylor bubble velocity, though. This indicates that the gas is breaking from the bottom
and is traveling upward with a quick-moving bubble cap. The production of smaller, slowly moving
bubbles because of gas bubble rupture lowers the surface pressure-based velocity. Based on the location
of the bubble-top, the quickly moving bubble-cap aids in maintaining the velocity.
Table 2 shows that, the predicted Taylor bubble velocity is found contrasted with these CFD-based
velocities. These findings demonstrate that whereas surface pressure-based velocities decreased by more
than 50% with a declining trend over time, bubble-top based velocities remained nearly constant in about
10 seconds. The results are nearly the same when the drill pipe rotates at 100 rpm, indicating that there is
little to no effect of rotation on gas migration velocity. Since there is no correlation for Taylor bubble
migration in an eccentric annulus, the Taylor bubble velocity utilized for comparison is calculated for a
symmetric annulus (it is expected that the Taylor bubble velocity would be lower for an eccentric annulus
compared to the correlations for symmetric annulus). These simulations for inclined wellbore geometries
were also run for open-hole configurations, without an inner pipe. For the open hole simulations, they
also noticed similar order of magnitude velocities.

Table 2: gas migration rates in an inclined annulus with and without drill string rotation [15]

Surface pressure- Bubble-top based Taylor bubble

based velocity velocity velocity
(ft/sec) (ft/sec) (ft/sec)

Initial 0.5 sec 1.28 1.32 1.73 (Eccentricity

No rotation effects are not
End time 0.63 1.32 included)

Initial 0.5 sec 1.23 1.40

Rotation
(100 rpm)
End time 0.62 1.40

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Overall, it was discovered that gas migration in inclined wellbores bubble rupture occurs more slowly
than in vertical wellbores. Additionally, it was noted that the drill pipe’s rotation or the wellbore's
transition from an annulus to an open hole shape have no effect on the gas migration velocity [15]. These
two findings are consistent with field data observations that the rotation and the presence of drill pipe in
the wellbore have no discernible effects. In contrast to numerous Taylor bubble velocity correlations, the
diameter-independent gas migration rate is also consistent with theoretical correlations for tiny bubble
velocities.

5.2. Mud Viscosity Validation

CFD simulations were run for better understanding of the impact of viscosity on gas migration. These
simulations were conducted in a concentric vertical annulus with a geometry of 6-inch x 4-inch as low
and high viscosity muds, 1cP and 3000cP of fluids, respectively, were used. To study the combined
effects of pressure and viscosity, these simulations were run at both high and low pressure. the high
pressure chosen is 4000 psi with surface tension of 2-5 dyne/cm and gas density of 2 ppg. Meanwhile,
low pressure was chosen to be 300 psi with surface tension of 23 dyne/cm and gas density of 0.1
ppg [15].
The results of these simulations stated that in one side of view, increased mud viscosity aids in slowing
the Taylor bubble velocity. This could lead one to believe that greater viscosity drilling fluids would be
ideal because they slow down the rate of gas migration. However, it was demonstrated that drilling mud's
viscosity delays bubble breakdown and permits gas to flow as swiftly moving, resulting in larger bubbles.
In the other side of view, a low viscosity liquid was found stabilizes the homogenous flow regime,
enhances gas holdup, and thus produces more tiny bubbles. Higher viscosity liquids, on the other hand,
result in a heterogeneous flow regime with less gas holdup, which causes the presence of big bubbles.
After approximately 10 seconds of these simulations, it was found that gas migrates at a Taylor bubble
velocity at 300 psi, but at a greater pressure of 4000 psi, the gas migration velocity is considerably lower.
These findings demonstrate that the high pressure affects gas velocity by causing tiny bubbles in the low
viscosity fluid to move more slowly. Surface pressure and bubble-top based velocities also show the drop.
On the other hand, the high-viscosity data demonstrated gas migration at or near the Taylor bubble
velocity in both high- and low-pressure circumstances due to the decreased buoyancy [15].

6. Results and Discussions

By utilizing PMCD technology while drilling fractured carbonate formations, the target depth can be
reached without the pump of LCM, cement, or cure loss rate. Instead, PMCD used the complete loss

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circulation to its advantage and modified the annulus system so that the surface back pressure be positive
and slightly maintained below the formation pressure during drilling such as a problematic loss
circulation zone. From the flow dynamics side of view, the gas-liquid slug flow is a term that describes
the pattern of flow when gas bubbles enter a wellbore. A typical gas slug unit in a vertical tube has a
bullet-shaped with a cylindrical body called Taylor bubble, followed by a liquid slug. In comparison to
Taylor bubble velocities, field data consistently reveals orders of magnitude slower gas migration
velocities.
To fully comprehend the underlying causes of this discrepancy between Taylor Bubble Model and
actual field data, more research was performed. The studies of the field data showed unequivocally that
gas is not migrating in the form of huge Taylor bubbles and under downhole conditions, huge Taylor
bubbles are unstable and would break down into smaller bubbles with the typical stable bubble size.
Some scientists have used test wells and long-section laboratory equipment with a variety of fluids,
including water and non-Newtonian fluids to study gas migration in static fluids and co-current flow. It
was found that gas migrates as a swarm of smaller bubbles rather than as massive Taylor bubbles/slugs
that take up a significant portion of the hole. The real field gas migration velocities are substantially lower
than Taylor bubble model. If Taylor bubble model is utilized during PMCD, it results in designs with high
amounts of LAM fluid for a PMCD project that may even restrict the use of PMCD technology in
particular field situations.

7. Conclusion

PMCD has become a demand drilling technique due to the higher probability of lost circulation during
drilling in karstified carbonates. The primary objective of PMCD operations is to displace reservoir fluids
back to the reservoir. The first thing to ascertain is the gas migration rate, the corresponded optimum
LAM volume, and pumping rate is to control the formation flow during drilling. The following
conclusion can be drawn:
1. The Taylor bubble velocity is found substantially lower at greater pressure than at low
pressure.
2. Increased fluid viscosity helps maintain Taylor bubbles at higher pressures that are
reflective of downhole conditions and thus leads in higher migration rates compared to a
low-viscosity fluid.
3. For a specific mud formulation and wellbore shape, the pressure and available length-
scale determine when a bubble will break. Compared to a Taylor bubble, smaller bubbles
travel more gradually.

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4. Bubbles can be broken up more easily when there is less surface tension present.
5. To slow gas migration rates while applying PMCD in the field, it is advised to aim for a
low to moderate viscosity range.

Abbreviations

BHP : Bottomhole Pressure

CFD : Computational fluid dynamics
IADC : International Association of Drilling Contactors
LAM : Light Annular Volume
LCM : Lost circulation material
MPD : Managed Pressure Drilling
MCD : MudCap Drilling
PMCD : Pressurized MudCap Drilling
RCD : Rotating control device
SBM : Synthetic base mud
SBP : Surface back pressure
WBM : Water base mud

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