MULTIPHASE DRILLING KICK ANNULAR FLOW BEHAVIOUR IN VERTICAL AND INCLINED WELL PROFILES

INTRODUCTION

Well drilling has been changing to drilling deeper into more complicated reservoir at high pressure and high-temperature conditions. It has encouraged a rapid development of drilling technology in terms of equipment [1],[2], drilling fluid [3]-[5], well control [6],[7], and well design [8]. One of the fundamental concepts in well design is drilling kick determination.

Rabia [9] stated that drilling kick can be defined as a flow of formation fluids into the wellbore during drilling operations which must be circulated out of the well at a controlled rate to reduce its pressure and to keep its expanded volume at the surface to a manageable amount. In oil and gas well design, simulating the drilling kick is fundamental. Among its many functions are to determine the suitable number

and setting depth of casing strings, to see if it is safe to continue drilling or a casing string needs to be run, and also to identify if it is safe to circulate the kick out of the well of if bullheading is needed [10],[11].

Simply put, the larger the kick tolerance predicted at a certain depth, the deeper the last casing has to be set [12]. Santos and Catak [13] mentioned that although drilling kick tolerance is an important and essential concept in the drilling industry, the drilling contractors, operators, and training institutions is still conventionally using the assumption of a single bubble model in the annulus and slowly migrating upwards in constant geothermal temperature, and ideal gas behaviour besides ignoring the effect of gas compressibility (Z), gas solubility, dispersion, and migration. For the simplicity of the calculations, the single-phase model is assumed to be constant Received: 19 August 2021, Accepted: 6 September 2021, Published: 30 September 2021, Publisher: UTP Press, Creative Commons: CC BY-NC-ND 4.0

MULTIPHASE DRILLING KICK ANNULAR FLOW BEHAVIOUR IN VERTICAL AND INCLINED WELL PROFILES

Muhammad Fadrul Bin Jamaludeen, Muhammad Aslam Bin Md Yusof^* Department of Petroleum Engineering, Universiti Teknologi PETRONAS, Malaysia

*Email: aslam.myusof@utp.edu.my ABSTRACT

One of the exponentially important drilling parameter has many misconceptions, and prompt confusion is the drilling kick. The current conventional approach assume a single-phase bubble model and neglect the multiphase flow in the drilling kick calculations, which lead to diversified solutions and misconceptions in well design. Hence, this study presents a mathematical model to analyse the behaviour of gas-liquid flow in different well profiles, which are vertical and deviated wells up to 60 degree inclination. The model analysed the annular pressure and temperature profiles as the influx rise to the surface. The methodology constructed to achieve the objective involve an iterative mathematical model to calculate pressure drop across the wellbore and temperature gradient for single-phase and multiphase flow models, indicating the type of flow regimes at each depth. The results show the impact of the selected parameters on the pressure and temperature generated, which eventually influence the drilling kick calculations. The annulus pressure increases 44.37% from multiphase vertical well annulus pressure to single-phase annulus pressure, and the pressure increment is higher in highly deviated well profile. It is important to precisely and accurately estimate the gas void fraction since it influences all two-phase flow parameters such as pressure drop, mixture density, and gas velocity in the annulus. The pressure and temperature profile then developed into a model which incorporates the drilling kick concept. Apart from that, the Z deviation factor which indicates the gas solubility was also studied and included in the simulation.

Keywords: Annular flow, flow regime, multiphase drilling kick, vertical well, inclined well

throughout the wellbore and the compressibility factor, Z is assumed to be 1.

The conventional assumptions of how a gas kick develops in the wellbore mostly refer to a ‘dry gas bubble’ over a wellbore length equivalent to the total influx volume and – while fulfilling all requirements for volumetric/hydraulic well control calculations – are clearly unrealistic. Oversimplifications where temperature, influx density, gas compressibility and solubility factors are overlooked leads to overdesign and conservative casing design [9],[14],[15]. Johnson et al. [16] and Aarsnes et al. [17] seconded this claim as they said that the single-phase and homogenous wellbore model is unable to consider these important variables. As more deep wells are being drilled with higher pressure and higher temperature, there is a need for a better model to include more drilling, fluid, and wellbore parameters to predict and simulate a

“real kick” scenario in multiphase conditions.

While the single-phase drilling kick approach satisfies straightforward volumetric well control aspects, it ignores the distinct characteristic of multiphase flow [18],[19]. It is clear that the problem is magnified in a multiphase flow because of the unpredictable flow behaviour compared to a single-phase flow. While lesser importance for the volumetric and hydraulic calculations in well control operations, understanding the multiphase flow of well kick is critical to optimize the well design particularly in high-temperature and high-pressure well. Moreover, with the conventional single-phase bubble model, the prediction of gas influx become too conservative, which lead to a hot international research [20]-[24]. The flow consists of more than one phase of the fluid; liquid and gas.

Multiphase flow often presents a far more complex and unpredictable flow behaviour compared to single- phase flow [25]-[27]. Thus, a better and enhanced understanding of two-phase flow in an annulus when influx enters the wellbore will provide more consistent and reliable well control method. Therefore, the purpose of this paper is to assess the gas-liquid flow behaviour that has been carried out in terms of pressure and temperature relationship with vertical and deviated well profiles. Calculations to determine influx drilling kick and multiphase flow regime were also presented and discussed.

MULTIPHASE DRILLING KICK FLOW REGIME DEVELOPMENT

Single-phase Pressure Loss

Single-phase drilling kick in annular flow calculations is shown in Figure 1. The simplified approach is still being used as a standard template by oil and gas operators and established drilling and oil and gas agencies, IADC, IWCF, and American Petroleum Institute [13],[28]. This procedure is important because the single-phase pressure calculation will be used as the industrial benchmark with the multiphase drilling kick calculations developed in this paper. This single-phase approach used Driller’s Method to find the pressure at the casing shoe and the pressure when the kick reaches the surface.

Single Phase Model

Constant A

A = Ppore – (TD – CSD)ρmud – HshoeGBHP

Figure 1 Single-phase pressure loss calculation Constant B

B = (P_pore – H_shoeG_BHP) ρ_mudV ––––––––––––––––––––

CaP_shoe cos θ

Pressure with top gas at casing shoe P_cs =

(

^A–2

)

⁺

( (A–2)2 + B)0.5

Pressure with top gas at surface Psurface = BHP – (3.28GBHPDBHP)

Input Data GBHP = 0.1

Rabia [9] studied the pressure at casing shoe and surface during kick using the following equations:

P_cs =

(

^A–2

)

⁺

( (A–2 )2 + B)0.5 (1)

P_surface = BHP – (3.281G_BHPD_BHP) (2) An expression of annular pressure at any time may be derived using the assumption of:

1. No temperature change as the gas kick is circulated out.

2. No change in compressibility factor as the gas kick is circulated out.

3. Single gas bubble.

4. The hydrostatic head of the gas column is only affected by hole & string geometry, not due to gas expansion since the gas mass remains constant.

Circulating Temperature Distribution

Yu et al. [29] claimed that the flow patterns in annuli are different considering the effect on heat, momentum, and mass transfer. Thus, understanding of circulation fluid temperature distribution plays a key factor in determining the kick behavior [30]. The procedure to simulate the temperature profile of the single-phase and multiphase are shown in Figure 2. The annulus

Figure 2 Circulating drilling fluid temperature model Temperature

Constant A A = mc_p

–––––

2πr_ph_p

Constant B B = rU

r–––_ph_p

Constant C₁

C1 =

(

2A^B–

) [1 + (1 + B4–)1/2] CConstant C2 = (2AB–) [1 + 2 (1 + B4–)1/2]

Constant C₃

C3 = 1 + –––––––––––––B 2

[

^{1 +}

(

^{1 + B4–}

)

^1/2

]

Constant C₄

C4 = 1 + –––––––––––––B 2

[

^{1 +}

(

^{1 + B4–}

)

^1/2

]

Constant K₂

K2 = GA– [T_pi – T_s + GA]e^C1H(1 – C₃) ––––––––––––––––––––––––––

e^C2H(1 – C₄)– e^C1H(1 – C₃)

Constant K₁

K1 = Tpi – K2 – Ts + GA

Tubing temperature

Tt = K1e^C1x + K2e^C2x + Gx + Ts – GA

Annulus temperature

Ta = K1C3e^C1x + K2C4e^C2x + Gx + Ts

Heat energy at influx entry Tentry = (cflqmudpmudTmud) + (cgqgpgTg)

Temperature mixture T_mixture = Eentry

––––––––––––––––––

(qmudρmud) + (qgρg)eavg

Addition emperature from influx T_addition = T_mixture – T_mud

Specific heat of mixture Cavg = (c_flq_mudρ_mud) + (c_gq_gρ_g)

––––––––––––––––––

(qmudρmud) + (qgρg)

temperature of a single-phase, which is the Holmes and Swift correlation as given by:

Tα = K₁C₃e^C1x + K₂C₄e^C1x + Gx + T_s (3) The annulus temperature of multiphase flow is determined by:

T_addition = T_mixture – T_mud (4)

This function largely depends on the average specific heat of the mixture and the difference in mass flow through the annulus up to the surface.

The assumptions used to derive the equations are as below:

1. Constant mud-tank temperature.

2. Constant hole and tubing diameter.

3. Steady-state circulating mud temperature during drilling.

Influx Fluid Flow Rate

There are two different types of Z deviation factors used to determine the gas flow rate in this study;

Beggs and Brill Correlation and Dranchuk and Abou- Kessam Equation of State [32],[33]. Two different sets

Figure 3 Influx drilling kick calculations Influx Flow Rate

Pseudo critical pressure

Ppc = (678.5(γg – 0.5)) – (206.7N) – (440CO2) + (605.7H)

Preudo reduced pressure Tpr = ––P

P_pc

Beggs and Brill Deviation Factor z = A + (1 – A)e^–B + CP_pr^D

Gas density ρg = (28.9γgP)

––––––––

10.732TZ

Gas influx

qg= kh(Pr2 – Pa2)

––––––––––––––––––––

(142μ_g)ZT ln +

(

^––r^rew

+ s

)

Apparent molecular weight Ma = 28.97γg

Input Data N = 0.03 CO₃ = 0.06

H = 0.04 Pseudo critical pressure

Tpc = 326 + (315.7(γg – 0.5)) – (240N) – (83.3CO2) + (133.3H)

Preudo reduced temperature Tpr = ––T

T_pc

Gas viscosity

μg = Ag(10^–4)EXP

(

^Bb

(

^{62.4(P–––g)}

)

^Cc

)

Constants = A_a, B_b, and C_c

Figure 4 Drilling kick flow regime determination while circulating to the surface of algorithms were simulated to study the effect of

the Z deviation factor to the multiphase pressure and temperature. However, the Beggs and Brill is the one that has been used to analyse the type of flow regime in multiphase flow. Economides et al. [34] stated a more general method to estimate the gas viscosity, as shown by:

μ_g = A_a(10^–4)EXP

(

^Bb

(

_62.4^–––ρg

)

^Cc

)

⁽⁵⁾

This method is widely used for estimating the viscosity of natural gas from the pseudoreduced critical temperature and pressure. The viscosity calculation has the advantage of applying to multilateral wells in the same plane and is not limited to wells aligned with principal permeability. Figure 3 shows the mathematical model that has been developed to calculate the influx gas flow rate.

Flow Regime Liquid flow into wellbore

ql =

(

^(q–––––––––––^{mud / 7.48051)}

60

)

Gas flow into wellbore q_gas =

(

^{(1000q–––––––}86400^g)

)

Superficial liquid velocity vsl =

(

–––––––––––^(0.408qmud)

d²_n – d²_OT

)

Superfial gas velocity vsg =

(

A^{q–––gas}ann

)(

^P–––520^atm

)

^TZ––P

Constant C₄ σ = (ST/4535)

g = 32.17 ST = 180

Mixture velocity vm = vsl + vsg

Bubble rise velocity v∞ = 153

[

^{g(ρ––––––––l – ρρl g)σ}

]

^1/4

In-situ gas volume fraction fg =

(

C^{––––––––}_ov_m^vsg + v_∞

)

In-situ gas volume fraction (Slug Flow) fg =

(

^{––––––––}C_ov^v_m^sg + v^–_∞

)

Mixture density ρm = fgρg + (1 – fg)pl

In-situ gas volume fraction

(

^dp––dz

)

^{H = ρm}

(

^–––144¹

)

In-situ gas volume fraction (Slug Flow)

(

^dp––dz

)

^{F =}

(

^–––144¹

)

^{––––––fv}2g^m2c^ρmd

Flow Regime Criteria

Bubbly v > v_T OR v_sg < v_t & f_g < 0.25

Slug v_T > v & v_sg > v_t

Churn v_sg > 1.08v_sl

Annular f_g > 0.85 & v_sg > v_ann

Liquid density ρl = 7.48052ρmud

Taylor bubble rise velocity v_∞T =

[

^0.345

√

^{gd(ρ––––––––ρl – ρl g)}

]

^(Fθ)(Fa)

Annulus Factor F_a =

(

^{1 + 0.29d––––do i}

)

Bubble rise velocity (Slug) v_∞ = v_∞(1 – e^–vt/vsg) + v_∞Te^–vt/vsg Well Deviation Factor

F_θ = √cos θ (1 + sin θ)^1.2

Annulus velocity vann = 3.1

[

^{gσ(ρ––––ρl – ρg2 g)}

]

^1/4

Transition superficial velocity vt = 0.429vsl + 0.357v∞

Table 1 Input data for single phase and multiphase flow INPUT DATA

Geometry

Well Depth (ft) 7000

Depth of casing seat (ft) 5000

Inner diameter of casing (in.) 9.625

Open hole diameter (in.) 12.25

Length of drill-collars (ft) 105

OD drill-collar (in.) 8

ID drill-collar (in.) 2.5

OD drill-pipe (in.) 5.5

ID drill-pipe (in.) 4.5

Pipe roughness 0.00015

Length Increment (ft) 100

Mud flow

Mud flow rate (gal-min) 200

Mud density (ib/gal) 14

Bit nozzle

Bit nozzle (32nds in) 12

Number of Bit 3

Mud viscometer reading

R3 3

R100 20

R300 39

R600 65

Temperature data

Inlet mud temperature (°F) 70

Mud thermal conductivity (Btu/(ft-°F-har)) 1

Mud specific heat (Btu/(Ibm-°F)) 0.4

Formation thermal conductivity (Btu/(ft-°F-har)) 1.3

Formation specific het (Btu/(Ibm-°F)) 0.4

Formation density (Ibm/ft3) 180

Surface earth temperature (°F) 57

Geothermal gradient (°F/ft) 0.0127

Circulation time (°F/ft) 44

Gas Influx Data

Depth of entry (ft) 6000

Reservoir pressure (psi) 6500

Formation permeability (md) 3

Reservoir height (ft) 20

Re (ft) 800

Skin 0.5

Gas gravity 0.7

Flow Regime

The effect of compressibility and solubility factor in drilling fl uid also aff ects the phase identifi cation and fi nal multiphase kick calculations [35]-[37]. Gas migration and predicted kick pressure is diff erent in deviated and horizontal wells compared to vertical well. The gas is trapped at certain parts of the deviated section before continue migrating in the vertical section because of their buoyancy factor. Hence, overall understanding of the impact of each and unifi ed multiphase kick parameters are very critical to ensure reliable drilling kick calculation in well design. Hasan et al. [38] presented a simplifi ed two-phase fl ow model to well orientation by using the drift-fl ux approach.

The generalized form of gas void fraction, which takes the superfi cial velocity of gas and liquid phases into account can be written as:

f_g =

(

^{––––––––}C_ov^v_m^sg + v_∞

)

⁽⁶⁾

where f_g = in situ gas void fraction, C_o = fl ow parameter, v_∞ = small bubble rise velocity and v_m = velocity of gas/

liquid mixture.

The model presents fi ve fl ow regimes for the two- phase fl ow as: bubbly, slug, churn, dispersed bubbly, and annular which integrates the pressure drop as the

fl ow behavior changes. The pressure drop calculation largely depends on the accuracy of the in-situ gas void fraction measurement in order to calculate the pressure gradient through the annulus. However, in order to segregate the fl ow regimes, there are some equations such as single bubble terminal rise velocity, Taylor bubble velocity, superfi cial velocity, average bubble velocity, mixture velocity, and annular velocity that need to be determined and sort it according to the criteria shown in Figure 4.

Input Data

The study has divided the input data into six components; geometry, mud fl ow, bit nozzle, mud viscometer reading, temperature data, and gas infl ux data. This data can be altered according to the well data provided for each study. The VBA is already designed.

If the input consists of any numerical errors, it will not run until the error is corrected. The input in Table 1 is used for the procedures explained in Figures 1 to 4.

RESULT & DISCUSSION

Multiphase Annulus and Tubing Temperature Profi le

Figure 5 shows the simulated temperature profile of single-phase and multiphase, where the eff ect of

Figure 5 Annulus temperature profi le before and after drilling kick

gas influx decreases the temperature of the annulus compared to the single-phase annulus temperature.

Observing the trends shows that the temperature increases at the upper part as the function of depth and vice versa for the lower part. A similar trend was also reported by Xu et al. [8]. As the fluid flows downwards through the pipe, it gains heat by convection from the annulus fluid until it reaches the bottomhole. The bottomhole is where the fluids in the drill pipe and annulus are equal since both fluids are not separated by any boundary while directly in contact with the formation. This is also where the temperatures of both fluids are equal as they are not separated by any wall or boundary and are in direct contact with the formation.

Then, when the fluid flows up to the surface, it loses heat energy because of the convection with the drill pipe, which is relatively cooler than the annulus.

However, the changes in the temperature are very slight because of the low density of the gas. The two- phase temperature model accounts for the mass flow and specific heat of the mixture changes. The mass flow changes are calculated by using the mixture density of both fluid phases across the annulus area at mixture velocity. Meanwhile, the change in specific heat for the two-phase flow is determined by averaging the liquid and gas densities and flow rates.

The figure above shows that the temperature after the gas kick is lower compared to single-phase annulus temperature because the mixture temperature is directly proportional to the increase in mass flow of the mixture and inversely proportional to the specific heat of the mixture. Hence, it is proven that with the introduction of gas influx, the average specific heat and mass flow rate increases too.

Multiphase Annulus Pressure Profile for Vertical Well

Figure 6 shows the comparison in the annulus pressure before and after the gas kick occurs as the gas kick rises to the surface. As it can be seen, as the gas influx migrates to the surface, the annulus pressure proportionally decreases. This is because of the decrease in pressure drop inside the annulus as low-density gas diffuses into the circulating mud, which integrates the fluid density in the annulus to drop. The two-phase density continues to decrease as the gas migrates upwards due to the expansion factor as result of lower pressure on the mixture when the

surface approaches. The decrease in two-phase density reduces the hydrostatic pressure, which causes the overall pressure to decrease compared to the single- phase flow inside the annulus. Thus, the hydrostatic pressure drop in the two-phase flow is lower compared to single phase circulating mud because of the lower fluid density. It shows that the multiphase annulus pressure model was four times lower as compared to the single-phase model.

Apart from that, based on Figure 6, the flow patterns for the vertical well can be classified as bubbly, slug flow, and churn flow. This shows that, as the volumetric in-situ of the gas fraction increases, the flow regime changes and becomes larger. Based on the Figure 6, it shows that when the influx enters the wellbore, the flow regime is bubbly where the pipe is completely filled with the liquid, and the influx gas phase is small.

The influx is randomly distributed in this phase with random diameters. At this phase, the influx has little effect on the pressure gradient.

The influx phase is more pronounced when it reaches the slug flow regime. The transition from bubbly to slug occurs because of the zigzag paths followed by the bubbles when it rises through the liquid, resulting in collisions between bubbles. The increase in a collision frequency is influenced by the increased in-situ gas fraction, which leads to bubble accumulation and the formation of bullet-shaped Taylor bubbles that are slug flow characteristic. In a vertical well, the transition from bubbly to slug flow appears to occur in a void fraction of about 0.25.

Even though the liquid phase is still continuous during slug flow, the influx coalesce and form stable bubbles approximately the same shape and size. During this phase, the influx velocity is greater than the liquid velocity. Due to the inconsistent liquid velocity, it varies the wall friction losses and influences the flowing densities. The multiphase model shows that when the influx almost reaches the surface, the regime changes to churn flow. This is where the continuous liquid phase changes to continuous gas-phase. Due to the liquid slug virtually disappear between the bubbles, the effect of the gas-phase is predominant in this regime.

These results are consistent with those of Gruber et al. [19], who studied the transition of flow pattern in well annuli.

Furthermore, the Dranchuk and Abou-Kassem EOS (black line) in Figure 6 shows 23.99% reduction of annulus pressure. This is because, after the simulation, it shows that the Z deviation factor of Dranchuk and Abou-Kassem is higher than the Beggs and Brill Correlation. The increase in Z deviation factor will decrease the gas density and gas viscosity, which will infl uence the mixture velocity. Hence, it is proven that with the increase in Z deviation factor, the mixture density will decrease further, and overall pressure will decrease.

Multiphase Annulus Pressure Profi le for Deviated Well

Figure 7, Figure 8, and Figure 9 show the annulus pressure profi le of 30°, 45°, and 60° deviated wells, respectively. The three figures indicate a similar pattern when compared to the single-phase pressure profi le. The migration of the gas infl ux to the surface decreases the annulus pressure correspondingly due to the decline of the annulus pressure drop. The infl ux disseminates into the circulating mud and causes

the fl uid density in the annulus to fall. Then, as the gas moves up to the surface, the mixture density consistently decreases due to the expansion factor, and signifi cantly reduces the hydrostatic pressure. The decline of hydrostatic pressure continuously decreases the overall annulus pressure compared to the single- phase fl ow. Figure 7 shows that the multiphase annulus pressure model is about three times smaller compared to the single-phase model and 75.88% decrease in Figure 9, which indicates that as the inclination angle increases, the diff erence between single-phase model and multiphase model decline.

The analysis of the fl ow regime in the deviated wells shows that even though the bubbly fl ow can be easily seen, the void fraction range in which the bubbly fl ow can be detected by the void measurement is too small due to the gas phase that tend to fl ow along the upper wall of the pipe. The inclination directs the bubbles to migrate rapidly to the top of the pipe, colliding and agglomerating into slug flow bubbles. The figures show that this occurs at void fractions less than 10%, Figure 6 Diff erent drilling kick fl ow types in annular of a vertical well

Figure 7 The annulus pressure profi le before and after gas kick for 30° deviated well

Figure 8 The annulus pressure profi le before and after gas kick for 45° deviated well

resulting in a narrowly existing bubbly fl ow as the inclination angle increases. Analysing the fi gures below, it indicates that as the inclination angle increases, the static hydrostatic pressure will decrease because the tilt significantly increases the number of collisions between bubbles and promotes a rapid transition to slug fl ow, which eventually increases the volumetric in-situ of the gas fraction.

Figures 7 and 8 show that when the infl ux enters the wellbore, the fl ow regime is bubbly where the pipe is completely fi lled with the liquid, and the infl ux gas phase is small. However, the transition in deviated well is relatively higher compared to the vertical well hence promotes the transition to the slug fl ow in a small amount of time. Apart from that, as all the three fi gures show, the fl ow regime has undergone a rapid transition from single-phase straight to slug flow, even though the bubbly exists for a while in 30° and 45° deviated well. However, in Figure 7, the infl ux has undergone changes from slug fl ow to churn fl ow when it almost reaches the surface in a 30° deviated well.

This is where the continuous liquid phase changes to

continuous gas phase. Due to the liquid slug virtually disappear between the bubbles, the eff ect of gas phase is signifi cant in churn fl ow.

The reason why the infl ux manages to transform to the churn fl ow in a 30° deviated well because of the magnitude of the bubble-rise velocity, v_∞. The bubble- rise velocity largely depends on the drag forces and the balance of buoyancy, which could be dissimilar for inclined and vertical systems. Deviation from vertical causes a decrease in both drag and buoyancy forces.

The data indicate that in a pipe deviated up to 33°

from vertical, and the terminal bubble-rise velocity is not substantially aff ected by the inclination angle. This concludes that, for the same input data, the magnitude of bubble-rise velocity is almost similar for vertical and deviated well up to 33° deviation, which causes the existence of churn fl ow in Figure 7 while the regime does not exists in 45° and 60° deviated wells.

Therefore, based on Figures 7 to 9, it can be determined that with the decrease in static pressure drop, the overall pressure increases as the inclination angle Figure 9 The annulus pressure profi le before and after gas kick for 60° deviated well

increases. Apart from that, similar to Figure 6, the deviated wells were also simulated by using Dranchuk and Abou-Kassem Z EOS method. The Dranchuk and Abou Kassem method decreases the annulus pressure by 12.52%, 6.19%, and 2.15% for Figure 7, Figure 8, and Figure 9, respectively. The fi gures show that with the increase in deviation factor, the mixture density will decrease, hence will promote the static pressure drops decrease and will infl uence the decrease in overall pressure. However, as the inclination angle increases, the percentage of annulus pressure reduction from Beggs and Brill to Dranchuk and Abou-Kassem decreases.

Comparison of Multi-Phase Annulus Pressure Profi le for Diff erent Well Profi les

Figure 10 concludes the annulus pressure profi le of the simulated well profi les. It is shown that the highe r the inclination, the faster the transition of gas infl ux into the slug fl ow and increases the mixture density. The increase in mixture density promotes the increase in overall pressure. Four diff erent types of well profi le and a single-phase annulus pressure have been plotted in Figure 10, where the vertical pipe shows the lowest

annulus pressure between the well profi les when the infl ux enter the wellbore, and the annulus pressure is the highest for single-phase model followed by the 60° deviated well. The annulus pressure decreases 29.39% from 60° deviated well to 45° deviated well when it reaches the surface while the annulus pressure decreases 29.69% and 30.99% from 45° deviated well to 30° deviated well and 30° deviated well to a vertical well, respectively.

However, the annulus pressure increases 44.37%

from multiphase vertical well annulus pressure to single-phase annulus pressure, which indicates that the multiphase calculation plays a major role in well control and well design. The mutual mechanism between the vertical well and the three deviated wells are, as the infl ux moves up to the surface, the annulus pressure decrease uniformly because of the decrease in pressure drop inside the annulus as low- density gas diff uses into the circulating drilling fl uid, which infl uences the fl uid density in the annulus to decline. As the gas migrates upwards to the surface, the two-phase density continues to decrease due to the expansion factor as result of lower pressure on

Figure 10 The annulus pressure profi le after gas kick for diff erent well profi les

30° deviated well

Vertical Well

45° deviated well

60° deviated well

Single Phase Model

the mixture when the surface approaches. Therefore, the decline in two-phase density keeps on reducing the hydrostatic pressure, which causes the overall pressure to decrease.

CONCLUSION

In conclusion, this project developed a simulation model to study the pressure and temperature profiles as the influx rise to the surface. The study includes the analysis of different types of gas flow regime according to its well profile. It was found that the annulus pressure reduction at the surface is higher in deviated well compared to vertical well. This simulation model specifies the flow into different flow regimes according to its well profile to estimate the gas void fraction using a mechanistic approach compared to the conventional empirical models. The annulus pressure increases 44.37% from multiphase vertical well annulus pressure to single-phase annulus pressure, which indicates that the multiphase calculation plays a major role in well control and well design. It is important to precisely and accurately estimate the gas void fraction since it influences all the two-phase flow parameters, such as pressure drop, mixture density, and gas velocity in the annulus. The pressure and temperature profile then developed into a model which incorporates the drilling kick concept. Apart from that, the Z deviation factor which indicates the gas solubility was also studied and included in the simulation.

ABBREVIATION & NOMENCLATURES

A_ann annular area Co flow parameter, dimensionless A temperature calculation constant

B temperature calculation constant c_fl specific heat of fluid

c_g specific heat of gas c_p specific heat of fluid

C_a capacity between pipe and hole

C_o flow parameter

c_avg specific heat of mixture CSD casing setting depth d tubing ID

d_h hole diameter

d_OT outer tubing diameter D_BHP bottomhole depth

E_entry heat energy at the point of gas entry f_m Moody friction factor

f_g in-situ gas volume fraction f_l liquid holdup

F_a annulus factor F_θ well-deviation factor

G temperature geothermal gradient G_BHP bottomhole gradient of gas g gravitational acceleration g_c conversion factor, 32.17 h reservoir height

h_p overall heat-transfer coefficient for drillpipe H_shoe height of gas bubble at casing shoe

k formation permeability m mass flow rate of fluid M_a apparent molecular weight p_pc pseudo-critical pressure of gas p_pr pseudo-reduced property of pressure p pressure of gas

p_a annulus pressure p_r reservoir pressure P_pore pore pressure

P_shoe fracture pressure at shoe P_cs pressure at the casing shoe

P_surface pressure when kick reaches surface q_mud mud flow rate

q_g gas flow into the wellbore q_l liquid flow into the wellbore r_p drillpipe radius

r_w wellbore radius r_e reservoir radius s skin factor

T_pi inlet temperature of mud in drill pipe T_s temperature of earth’s surface T_a mud temperature in annulus T_t drillpipe fluid temperature

T_mixture temperature of the mixture from the heat energy at gas entry

T_addition addition of temperature from gas influx T_pc pseudo-critical temperature of gas T_pr pseudo-reduced property of temperature T temperature of gas

TD next hole total depth

U overall heat-transfer coefficient for annulus V volume of influx

x depth

x mass fraction

Z gas-law deviation factor ρ_g gas density

ρ_mud mud density γ_g gas gravity

μ_g gas viscosity

(dp/dz)_F frictional pressure gradient, psi/ft (dp/dz)_H hydrostatic pressure gradient, psi/ft v_sl superficial velocity of liquid

v_sg superficial velocity of gas v_m velocity of gas/liquid mixture v_∞ small bubble rise velocity v_∞T Taylor bubble rise velocity σ surface tension

θ well inclination with horizontal REFERENCES

[1] D. Xu, J. Yang, Y. Zhao, Y. Huang, M. Luo, Y.Chen, L. Li, Y. Yang, J. Wang, & M. Zhang, “Key Technologies and Practice of Ultra-HTHP Drilling in South China Sea,”

in SPE Gas & Oil Technology Showcase and Conference, 2019.

[2] R. Tucker, A. Palazzolo, & M. Gharib, “An Innovative Design for Drillstring Testbed for High Pressure High Temperature Drilling,” in ASME International Mechanical Engineering Congress and Exposition, pp 13, 2020, p. V008T08A034.

[3] O. E. Agwu, J. U. Akpabio, M. E. Ekpenyong, U. G.

Inyang, D. E. Asuquo , I.J. Eyoh, & O. S. Adeoye, "A comprehensive review of laboratory, field and modelling study on drilling mud rheology in high temperature high pressure (HTHP) conditions,” Journal of Natural Gas Science and Engineering, 94, pp. 104046, 2021.

[4] N. Wahid, M. A. Yusof, & N. H. Hanafi, “Optimum nanosilica concentration in synthetic based mud (SBM) for high temperature high pressure well,” in SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition, 2015.

[5] M. A. M. Yusof & N. H. Hanafi, “Vital roles of nano silica in synthetic based mud for high temperature drilling operation,” in AIP conference proceedings, p. 020029, 2015.

[6] T. Phi, R. Elgaddafi, M. Al Ramadan, R. Ahmed, & C.

Teodoriu, “Well integrity issues: Extreme high-pressure high-temperature wells and geothermal wells a review,”

SPE Thermal Well Integrity and Design Symposium, 2019.

[7] N. Xinming, Z. Jinshuang, & Z. Haobo, “Technological Challenges and Countermeasures in Well Control of Ultra-Deep, Ultra-High Temperature and Ultra-High

Pressure Oil and Gas Wells,” 石油钻探技术, 45, 04, pp. 1-7, 2017.

[8] Z. Xu, X. Song, G. Li, Z. Zhu, & B. Zhu, “Gas kick simulation in oil-based drilling fluids with the gas solubility effect during high-temperature and high-pressure well drilling,” Applied Thermal Engineering, 149, pp. 1080- 1097, 2019.

[9] H. Rabia, “Well Engineering & Construction”: Entrac Consulting Limited, 2002.

[10] O. Santos, I. Adasani, J.J. Azar, & F. Escorihuela,

“Determination of casing setting depth using kick tolerance concept,” Petroleum Computer Conference, 1995.

[11] A. E. Effiowan, O. Umahi, E. Richard, A. Tunde, J. Lamens,

& A. Oyibo, “Integrated Multidisciplinary Pore Pressure Prediction Leads to Accurate Casing Design: A Case Study,” SPE Nigeria Annual International Conference and Exhibition, 2014.

[12] M. Wessel & B. A. Tarr, “Underground flow well control:

the key to drilling low-kick-tolerance wells safely and economically,” SPE drilling engineering, 6, 04, pp. 250-256, 1991.

[13] H. M. Santos, E. Catak, & S. Valluri “Kick tolerance misconceptions and consequences to well design,”

SPE/IADC Drilling Conference and Exhibition, 2011.

[14] P. Sonnemann & H. M. Santos, “Transitional Kick Tolerance,”

SPE Annual Technical Conference and Exhibition, 2012.

[15] B. Sun, “Multi-phase Flow in Oil and Gas Well Drilling,”

John Wiley & Sons, pp. 250, 2016.

[16] A. Johnson, C. Leuchtenberg, S. Petrie, & D. Cunningham,

“Advancing Deepwater Kick Detection,” IADC/SPE Drilling Conference and Exhibition, 2014.

[17] U. J. F. Aarsnes, F. Di Meglio, R. Graham, & O. M. Aamo,

“A Methodology for Classifying Operating Regimes in Underbalanced-Drilling Operations,” SPE Journal, 2015.

[18] H. F. Spoerker & T. Tuschl, “Behaviour and Shape of Gas Kicks in Well Bores,” IADC/SPE Drilling Conference and Exhibition, 2010.

[19] C. Gruber, H. F. Spoerker, & W. Brandstaetter, “Dynamic Modeling of Gas Distribution in the Wellbore During Kick Situations: The Solutions,” in IADC/SPE Drilling Conference and Exhibition, 2014.

[20] Z. Wang, B. Sun, Y. Gao, Y. Ma, & R. Song, “Study on annular multiphase flow characteristic of gas kick during hydrate reservoir drilling [J],” Journal of Basic Science and Engineering, 1, pp. 016, 2010.

[21] W. Liu, Y. Liu, G. Huang, J. Fu, Y. Pan, & A. Singh, “A Dynamic Simulation of Annular Multiphase Flow during Deep-water Horizontal Well Drilling and the Analysis of Influential Factors,” Journal of Petroleum Science and Technology, 6, pp. 98-108, 2016.

[22] J. Feng, J. Fu, P. Chen, Z. Du, & L. Qin, “Experimental study and molecular simulation of gas dissolution and diffusion behavior in drilling fluid,” Journal of Natural Gas Science and Engineering, 36, Part A, pp. 424-433, 2016.

[23] K. Fjelde, J. Frøyen, & A. Ghauri, “A Numerical Study of Gas Kick Migration Velocities and Uncertainty,” in SPE Bergen One Day Seminar, 2016.

[24] G. Zhou, C. Leach, V. S. Denduluri, G. K. Wong, A.

Amritkar, R. Krishnamoorti, et al., “Pressure-Difference Method for Gas-Kick Detection in Risers,” SPE Journal, pp. 1-19, 2021.

[25] U. J. F. Aarsnes, T. Flåtten, & O. M. Aamo, “Review of two-phase flow models for control and estimation,”

Annual Reviews in Control, 42, pp. 50-62, 2016.

[26] U. J. F. Aarsnes, A. Ambrus, F. Di Meglio, A. K. Vajargah, O. M. Aamo, & E. van Oort, “A simplified two-phase flow model using a quasi-equilibrium momentum balance,”

International Journal of Multiphase Flow, 83, pp. 77-85, 2016.

[27] K. Manikonda, A. R. Hasan, N. H. Rahmani, O. Kaldirim, C. E. Obi, J. J. Schubert, et al., “A Gas Kick Model that Uses the Thermodynamic Approach to Account for Gas Solubility in Synthetic-based Mud,” SPE/IADC Middle East Drilling Technology Conference and Exhibition, 2021.

[28] J. Feng, J. Fu, P. Chen, J. Luo, & B. Kou, “Comparisons of the Driller’s Method and the Wait and Weight Method in Deepwater Well Killing Operation,” Arabian Journal for Science and Engineering, pp. 1-8, 2016.

[29] T. Yu, H.-Q. Zhang, M. Li, & C. Sarica, “A mechanistic model for gas/liquid flow in upward vertical annuli,”

SPE Production & Operations, 25, 03, pp. 285-295, 2010.

[30] D. Van Slyke & E. Huang, “Predicting gas kick behavior in oil-based drilling fluids using a pc-based dynamic wellbore model,” SPE/IADC Drilling Conference and Exhibition, 1990.

[31] C. S. Holmes & S. C. Swift, “Calculation of circulating mud temperatures,” Journal of Petroleum Technology, 22, 06, pp. 670-674, 1970.

[32] D. H. Beggs & J. P. Brill, “A study of two-phase flow in inclined pipes,” Journal of Petroleum technology, 25, 05, pp. 607-617, 1973.

[33] J. Abou-Kassem, L. Mattar, & P. Dranchuk, “Computer calculations of compressibility of natural gas,” J Can Pet Technol, 29, 05, pp. 105-108, 1990.

[34] F. Oka, A. Murakami, R. Uzuoka, & S. Kimoto, “Computer methods and recent advances in geomechanics,” “ CRC Press Taylor & Francis Group, R, 2014.

[35] D. C. Thomas, J. F. Lea Jr, & E. A. Turek, “Gas solubility in oil-based drilling fluids: Effects on kick detection,”

Journal of petroleum technology, 36, 06, pp. 959-968, 1984.

[36] N. Berthezene, J.-C. De Hemptinne, A. Audibert, &

J.-F. Argillier, “Methane solubility in synthetic oil- based drilling muds,” Journal of Petroleum Science and Engineering, 23, 2, pp. 71-81, 1999.

[37] N. Kim, P. Ribeiro, & P. Pessôa-Filho, “PVT behavior of methane and ester-based drilling emulsions,” Journal of Petroleum Science and Engineering, 135, pp. 360-366, 2015.

[38] A. R Hasan, C. S. Kabir, & M. Sayarpour, “Simplified two- phase flow modeling in wellbores,” Journal of Petroleum Science and Engineering, 72, 1-2, pp. 42-49, 2010.