Mohanad Aly Saad^{*}, AbdelAlim Hashem ElSayed
Department of Petroleum, Cairo University, Egypt
^{*}Corresponding author: Mohanad Aly Saad, Department of petroleum, Cairo University, Egypt. Tel: +201271321573; Email: petroeng.mohanadaly@gmail.com
Received Date: 01 January, 2018;
Accepted Date: 11 January, 2018; Published Date: 17 January, 2018
1. Abstract
As exploring for oil and gas traps becomes more extreme in term of depths, the companies start to search for modern technologies and equipment for drilling under HPHT conditions. One of the challenges of HPHT deep water well is narrow margin between the fracture pressure gradient and pore pressure gradient, therefore prediction and control of well hydraulics is indeed vital. The solution for the HPHT deep water challenges is a technology of Managed Pressure Drilling (MPD). Riser less drilling is one of the types of MPD. It uses two different annular pressure gradients for maintaining required bottom hole pressure to drill a well
This study presents a new approach for accurate determination and optimization of well hydraulics for MPD (Riser less drilling) under HPHT conditions. This approach depends on accurate prediction and determination of borehole temperature, mud density and pressure, mud rheology and hydraulics profiles inside wellbore under HPHT conditions. This work shows the comparison between well hydraulics that calculated by constant fluid properties (i.e independent on pressure and temperature conditions) and well hydraulics that calculated by taking into account the effect of pressure and temperature on fluid properties. This paper also shows the effect of drill pipe tooljoint, drilled cutting, annular eccentricity and drill string rotation pressure losses on well hydraulics for MPD. The objectives were achieved by designing computer simulator called ‘’HPHT MAT’’. A case study by using ‘’HPHT MAT’’ simulator to show the correct procedure for optimization the well hydraulics of MPD is introduced.
The results show that accurate prediction and determination of temperature and mud rheology modelling is highly required for accurate planning and designing of MPD hydraulics. The pressure difference between the drill pipe and annulus in Riser less drilling must be taken into consideration during the calculation of the density, plastic viscosity, yield point and ECD profiles inside wellbore. Neglecting the effect of pressure and temperature on mud properties in the well hydraulics calculation will lead to erroneous results which may lead to a kick or a loss of circulation. Pressure losses due to drill pipe tooljoint, drilled cutting, annular eccentricity and drill string rotation have significant effect on well hydraulics of MPD. New technique for calculating the well hydraulics of MPD by using finite difference calculation is developed.
2.
Keywords: Dual Gradient Drilling; High
Pressure and High Temperature Condition; Managed Pressure Drilling; Riser Less
Drilling
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
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.
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.
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 steadystate 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].
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]
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 = 1.9776×108 A4 =3.3416×105 A5 = 14.67
Politte8 gives the following equation for yield point determination.
B0 = 0.186 B1 = 145.054 B2 = 3410.322
Rheological Hydraulic Modelling
First twoparameter 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.
Depth of bottom of well , ft 
30000 
Outside diameter of drill pipe, inch 
5 
Inside diameter of drill pipe , inch 
4.276 
Inside diameter of tool joint ,inch 
3.562 
Outside diameter of tool joint ,inch 
5.188 
Angle for internal upset (drill pipe),degree 
39.26 
Angle for external upset (annulus),degree 
8.6 
Average joint length ,ft 
30 
Outside diameter of HWDP , inch 
5 
Inside diameter of HWDP, inch 
3 
Length of HWDP,ft 
600 
Outside diameter of DC, inch 
8 
Inside diameter of DC, inch 
3.25 
Length of DC, ft 
300 
Inside diameter of last casing ,inch 
10.05 
Last casing shoe,ft 
25000 
Diameter of well, inch 
9.5 
Circulation rate, bbl/hr 
800 
Geothermal gradient , ^{o}F/ft 
0.0127 
Sea water gradient , ^{o}F/ft 
0.004 
Surface sea temperature, ^{o}F 
85 
Water depth, ft 
10000 
Mud heat capacity, BTU/(Ib^{o}F) 
0.4 
Mud density ,Ib/gal 
13 
Plastic Viscosity, cp 
20 
Yield Point , Ibf/100ft^{2} 
14 
Overall heat transfer coefficient across drill pipe , BTU/(sqft^{o}Fhour) 
45 
Overall heat transfer coefficient across well bore face , BTU/(sqft^{o}F 
1.5 
hour) 

Oil fraction 
0.591 
Water fraction 
0.18 
Surface pressure, psi 
14.7 
Nozzle sizes , 1/32 inch 
14 14 14 
Coefficient of discharge 
0.95 
Liner size , inch 
6.5 
Max HHP, HHP 
1600 
Stroke length, inch 
12 
Max SPM 
120 
Volumetric efficiency 
0.9 
Mechanical efficiency 
0.9 
Type of pump 
Single acting triplex pump 
Type of surface equipment 
Type 2 
Annular eccentricity(dimensionless) 
0 
Density of rock , ppg 
22 
Average cutting size, inch 
0.28 
ROP , ft/hr 
40 
Table 1: Riser less drilling case study.
Well hydraulics 
Case 1 : Fluid properties depend on temperature and pressure 
Case 2: Constant fluid properties 
Difference between two cases 
Total pressure loss(psi) 
3985 
3295 
690 
Bottom hole ECD (ppg) 
13.6 
13.2 
0.4 
Table 2: Effect of constant fluid properties on bottom hole ECD and total pressure losses.
Well hydraulics 
Case 1: Without influence factors of 
Case 2: With influence factor of 
Difference between two cases 
pressure loss 
pressure loss 

Total pressure loss (psi) 
3295 
4580 
1285 
Bottom hole ECD 
13.2 
13.7 
0.5 
(ppg) 
Table 3: Effect of pipe rotation, tool joint and cutting concentration on total pressure losses and bottom hole ECD.
Bit optimization 
First method : Bit optimization calculated by temperaturepressure dependence of the fluid properties 
Second method : Bit optimization calculated by constant fluid properties 
Optimum flow rate (gpm) 
315 
346 
Optimum nozzle area (in ) 2 
0.21 
0.23 
Hydraulic horsepower (hhp) 
534 
572 
Table 4: Effect of constant fluid properties on hydraulic bit optimization (Bit hydraulic horsepower criteria).
5.
Holmes CS, Swift SC (1970) “Calculation of Circuiting
Mud Temperatures’’. Journal of Petroleum Technology 670674.
7.
Hoberock LL, Thomas DC, and Nickens HV (1982) BottomHole
Mud Pressure Variations Due to Compressibility and Temperature Effects. Paper
SPE11050 presented at Drilling Technology Conference of the International
Association of Drilling Contractors, Pittsburgh, Pennsylvania USA, 911 March
1982.
14.
Bhattacharya A (1995) Flow of solidliquid suspensions
in vertical columns. Journal of Industrial and Engineering Chemistry 268274.
Citation: Saad MA, ElSaye AAH (2018) How to Optimize Well Hydraulics of MPD Under HPHT Environment. Arch Pet Environ Biotechnol: APEB125. DOI: 10.29011/ 25747614. 100025