1. Abbreviations:

G : acceleration of gravity, m/s2

Θ : angle of divergence or convergence, degrees

Ε : annular eccentricity, dimensionless

ΔPa : annulus pressure loss, psi

ṽ : average velocity in pipe or annulus, m/s

μo : base oil plastic viscosity at reference conditions, cp

μTP : base oil plastic viscosity at (T,P) pressure P,cp

Ca : cutting concentration, %

Db : diameter of drill bit, m

ρm1 : density of mud phase at reference condition (P1, T1)

ρ01 : density of oil phase at (P1, T1), ppg

ρ02 : density of oil phase at (P2, T2), ppg

ρs : density of solid content, kg/m3

ρw1 : density of water phase at (P1, T1)

ρw2 : density of water phase at (P2, T2)

Di : drill pipe diameter

PVo : drilling fluid plastic viscosity at standard conditions, cp

PVTP : drilling fluid plastic viscosity at (T, P), cp

X : depth of well, ft

Ψ : diameter ratio Di/Do, dimension less

Fe : eccentricity coefficient, dimensionless

N : generalized flow behaviour index, dimensionless

G : geothermal gradient oF/ft

kc : gradual contraction coefficient, dimensionless

ke : gradual enlargement coefficient, dimensionless

Tpi : inlet temperature of mud in drillpipe, oF

K : local resistance factor

M : mass flow rate, Ib/hr

Cp : mud heat capacity, BTU/(Ib.oF)

Ta : mud temperature in annulus, oF

Tp : mud temperature in drillpipe, oF

ρm : mud weight, ppg

U : overall heat transfer coefficient across wellbore face, BTU/ (sqft.oF hr)

hp : overall heat transfer coefficient across drillpipe BTU/(ft2.oF hr)

μp : plastic viscosity, cp

ΔPE : pressure drop of annulus eccentricity and pipe rotation, Pa

ΔPs : pressure drop of cutting concentration, Pa

P : pressure, psi

R : radius, ft

Rop : rate of penetration, m/s

rp : radius of drillpipe, ft

rp : radius of drillpipe, ft

σ : ratio of diameters of small to large pipes, dimensionless.

Fr    : rotation coefficient, dimensionless

Fw      : salt water volume fraction

T0 : standard temperature, 60 oF

VS : slip velocity of cuttings, m

γ : shear rate, 1/sec

τ : shear stress, lbf/100 ft2

H : true vertical depth of well, Ft

T : temperature, oF

Ts : temperature of formation’s surface, oF

ΔPJ : tool joint pressure loss, Pa

K’ : velocity profile correction factor, dimensionless

Do : wellbore diameter, m

τy : yield point at elevated temperature, lbf/100 ft2

τyo : yield point at reference temperature, lbf/100 ft2

2. Introduction

HPHT well is defined as the well have bottom hole temperature exceeds 300 oF and bottom hole pressure greater than 0.8 psi/ft. Nowadays, companies try to find petroleum in unconventional areas such as HPHT deep water, to decrease the gap between the demand and supply. Drilling of HPHT deep water wells involves high risk and cost; therefore, effective methods are required to solve these issues. Oil and gas industry offer advanced drilling technologies to reach HPHT deep water reservoir targets safely [1].

The margin between pore pressure and fracture pressure in HPHT deep water well is narrow, therefore accurate determination and optimization of well hydraulics is highly required. Managed Pressure Drilling (MPD) has been developed for overcoming the HPHT deep water well challenges. In MPD techniques, there is a method defined as Riser less drilling. The Riser less method uses two different annular fluid pressure gradients for well drilling. In the technique of Riser less drilling, the riser is completely filled with sea water and returned mud along with the cuttings is pumped by additional subsea mud pump to surface through small return line 6”, (Figure 1) [2].

There are pressure and temperature variations across wellbore during drilling by Riser less drilling technique; above seabed there is low temperature condition which will lead to increase in mud rheology, however below seabed there is opposite effect. Well hydraulics planning depends on how drilling fluid rheology is influenced by pressure and temperature effects inside wellbore; therefore, ignoring these effects in the well hydraulics calculations will give erroneous result [3]. Accurate well hydraulics planning for HPHT wells is needed to avoid drilling problems such as kick and loss of circulation. This paper presents a new approach for accurate determination and optimization well hydraulics of MPD (Riser less drilling) under HPHT conditions. This work shows the comparison between well hydraulics calculated by constant fluid properties (i.e independent on pressure and temperature conditions) and well hydraulics calculated by taking into account the effect of pressure and temperature on fluid properties. This research also shows the effect of tool joint, cutting, annular eccentricity and drill string rotation pressure losses on well hydraulics of MPD.

1. Theoretical Background

Temperature modelling, mud density and pressure modelling, plastic viscosity and yield point modelling and rheological hydraulic modelling are indeed important for accurate determination and optimization for well hydraulics of MPD under HPHT conditions.

2. Drilling Fluid Temperature Modelling

Temperature modelling inside the wellbore is necessary for determining well hydraulics. Wellbore temperature has great impact on mud properties such as density, hydrostatic pressure, yield point and viscosity, therefore it will influence on the determination of pressure losses and Equivalent Circulating Density (ECD) [ 4]. The Holmes and Swift model 5 assumes steady-state linear heat transfer between annulus fluid and the formation. The model is described in three steps [5].

Step 1: Calculation of A and B parameters, Equation1 and Equation 2 [5].

Step 2: Calculation of C1, C2, C3, and C4 parameters, from Equation 3 to E Equation 6 [5].

These equations represent the analytical solution of the wellbore temperature profiles inside the drill pipe and annulus

Step 3: Calculation of temperature in drill pipe and annulus. For the temperature of the mud in the drill pipe and annulus (Equations 7, 8, 9, 10) [5].

3. Density Behaviour Modelling

Drilling fluid density is affected by temperature and pressure [6]. The Hobe rock [7] Model assumes that drilling fluid density variations as a result of pressure and temperature changes occur due to liquid constituent’s volumetric behaviour such as water and/or oil.

Density of oil based drilling fluid can be described mathematically as follows: [7]

4. Plastic Viscosity and Yield Point Modelling

Politte [8] studied rheological data for oil based mud and concluded that the plastic viscosity follows the base oil behaviour. Therefore, the plastic viscosity can be normalized with the base oil viscosity [9]. The Politte [8] equation is described as follows.

Procedure of Politte correlation [8] can be used with any base oil. He established the following formula as a function of temperature and pressure for viscosity of base oil (Equation13) from analysis of diesel oil No. 2 [8].

A0 = -23.18 A1 = -0.00148 A2 = -0.950 A3 = -1.9776×10-8 A4 =3.3416×10-5 A5 = 14.67

Politte8 gives the following equation for yield point determination.

B0 = -0.186 B1 = 145.054 B2 = -3410.322

5. Rheological Hydraulic Modelling

First two-parameter model is Power law model. The model is the most popular one in drilling engineering and it is used inside the simulator, Equation15 [10].

Figure 1: Riser less drilling schematic [2].

Figure 2: Graphical user interface of input data.

Figure 3: Mud temperature inside wellbore.

Figure 4: Mud density inside wellbore.

Figure 5: Mud plastic viscosity profile inside wellbore.

Figure 6: Mud yield point profile inside wellbore.

Figure 7: ECD profile under HPHT.

Table 1:  Riser less drilling case study.

Table 2:  Effect of constant fluid properties on bottom hole ECD and total pressure losses.

Table 3: Effect of pipe rotation, tool joint and cutting concentration on total pressure losses and bottom hole ECD.

Table 4: Effect of constant fluid properties on hydraulic bit optimization (Bit hydraulic horsepower criteria).

1.       Dhameliya, JD, Jain S, Gupta V (2013) Liquid Lift Dual Gradient Drilling in Deep Water: Early Kick Detection and Control. Paper SPE 165372 presented at the SPE Western Regional & AAPG Pacific Section Meeting, California 19-25.

2.       Choe J, Schubert JJ, Juvkam-Wold HC (2007) Analyses and Procedures for Kick Detection in Subsea Mud lift Drilling. Paper SPE-87114 presented at the IADC/SPE Drilling Conference, Dallas, USA 22: 2-4.

3.       Marbun BH, Kurnia HA (2012) The Effect of High Pressure and Temperature Variation to the Hydraulic of Dual Gradient Drilling Operation. Paper IADC/SPE 156373 presented at the IADC/SPE Asia Pacific Drilling Technology Conference and Exhibition, Tianjin, china 9-11.

4.       Hasan AR, Kabir CS (1996) Determining Circulating Fluid Temperature in Drilling, Workover, and Well-control Operation. Paper SPE-24581 presented at the SPE Annual Technical Conference & Exhibition, Washington DC, USA 11: 4-7.

5.       Holmes CS, Swift SC (1970) “Calculation of Circuiting Mud Temperatures’’. Journal of Petroleum Technology 670-674.

6.       Zamora M, Roy S, Slater K, Troncoso J (2012) Study on the Volumetric Behavior of Base Oils, Brines, and Drilling Fluids Under Extreme Temperatures and Pressures. Paper SPE-160029-MS presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA 28: 8-10.

7.       Hoberock LL, Thomas DC, and Nickens HV (1982) Bottom-Hole Mud Pressure Variations Due to Compressibility and Temperature Effects. Paper SPE-11050 presented at Drilling Technology Conference of the International Association of Drilling Contractors, Pittsburgh, Pennsylvania USA, 9-11 March 1982.

8.       Politte MD (1985) Invert Oil Mud Rheology as a Function of Temperature. Paper SPE-13458 presented at the SPE Annual Technical Conference and Exhibition, New Orleans LA, USA 6-8.

9.       Methven NE, Baumann R (1972) Performance of Oil Muds at High Temperatures. Paper SPE-3743 presented at SPE-European Spring Meeting, Amsterdam, Netherlands, 16-18.

10.    10.  Bourgoyne AT, Millhcim KK, Chenevert ME, Young FS (1991) Applied Drilling Engineering. second edition, SPE Textbook Series - Drilling Series, Society of Petroleum Engineers.

11.    Yeon-Tae J, Subhash S (2004) “Analysis of Tool Joint Effects for Accurate Friction Pressure Loss Calculations,”. Paper SPE 87182 presented at the SPE Drilling Conference, Dallas 2-4.

12.    Singhai N, Shah SN, Jain S (2005) Friction pressure correlation for Newtonian and non-Newtonian fluids in concentric annuli. R. Paper SPE 94280 presented SPE Annual Technical Conference and Exhibition, New Orleans LA, USA, 10-13.

13.    Haciislamoglu M (1990) Non-Newtonian flow in eccentric annuli. Journal of Energy Resources Technology 112: 163-169.

14.    Bhattacharya A (1995) Flow of solid-liquid suspensions in vertical columns. Journal of Industrial and Engineering Chemistry 268-274.

15.    Ziegler R, Ashley P, Malt R. Stave R, Toftevag KR (2013) Successful Application of Deep Water Dual Gradient Drilling. Paper IADC/SPE164561 presented at IADC/SPE Managed Pressure Drilling and Underbalanced Operations Conference and Exhibition, San Antonio, Texas, USA 17-18.

16.    Ziegler R, Sabri MSA, Idris MRB, Malt R, Stave R (2013) First Successful Commercial Application of Dual Gradient Drilling in Ultra Deepwater GOM. Paper SPE-166272 presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA 30.