Drilling Hydraulics Paper - Shashwat (PE14M013)

8/9/2019 Drilling Hydraulics Paper - Shashwat (PE14M013)

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1 Copyright © 2014 b

DRILLING HYDRAULICS - CALCULATIONS AND OPTIMIZATION

Shashwat Sharma

Indian Institute of Technology, MadrasChennai, India

ABSTRACT

The hydraulics system plays an active role during the drilling

operations; so its proper design and maintenance can accelerate

the drilling effort and lower the overall well cost. This paper

discusses the relevance of the hydraulics system in the

optimization of the drilling operations, in the enhancement of

penetration rate and reduction in system pressure losses to

allow more ‘useful’ pressure loss to occur across the bit. The

major requirements of the drilling hydraulics system arediscussed, along with the major considerations in each

application. A review of commonly used rheological models

has been done, with introduction of two recent and more novel

rheological models – Herschel-Bulkley and Casson models.

Impact of choice of the rheological model on the hydraulics

calculations is studied. Finally, a summary of the procedure that

is followed during the calculation and optimization of

hydraulics parameters is discussed via equations.

INTRODUCTION

The hydraulics system is the mud system in the wellbore when

it is in either a static or a dynamic state. The static system

occurs when the mud stands idle in the well. The dynamic state

occurs when the mud is in motion, resulting from pumping or pipe movement.

The hydraulics system serves many purposes in the well. Since

it is centered on the mud system, the purposes of mud and

hydraulics are often common to each other. Some of these

objectives are listed below:

Control subsurface pressures

Provide buoyancy to drill string and casing

Cuttings removal from below the bit

Increase penetration rate (ROP)

Control surge pressures created during lowering pipeinto the well

Minimize swab pressures generated during pulling out pipe from the well

The hydraulics system consists of a non-Newtonian suspension

(drilling mud) circulated from surface to the bottom hole

through the drill column, flowing through the bit nozzle

restrictions and returning to surface in the annular region

between the borehole and drill column (Figure 1).

Drilling hydraulics reflected by fluid flow and pressure

response is a key parameter in the well construction process. It

is a factor that is continuously present during drilling and

tripping operations. Special attention needs to be paid to the

optimization of drilling hydraulics in highly inclined and

extended reach wells where stuck and lost pipe situations

maybe encountered more easily and frequently.

FIGURE 1: SCHEMATIC OF THE CIRCULATION SYSTEM;

P1 - P5 INDICATE PRESSURES AT NODES

PRESSURE LOSSES

The circulating system can be divided into four sections for

nodal analysis – surface connections (including standpiperotary hose and swivel), tubulars (including drill pipe, heavy

weight drill pipe and drill collars), annular areas around the

tubular regions, and the drill bit. Hydraulics calculations for

drilling aim to calculate the pressure (energy) losses in every

part of the circulating system and then find the total system

losses. This will then determine the pumping requirements from

the rig pumps and in turn the horsepower requirements.


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2 Copyright © 2014 by ASME

1. Surface connection losses:

These pressure losses are determined by converting the

range of lengths and OD’s of surface equipments such as

standpipe, rotary hose, swivel and Kelly to an equivalent

length and then using the following general equation to

evaluate the pressure loss:

(1)where,

P1 = pressure loss (psi)

E = constant

2. Pipe and Annular losses:

These pressure losses take place due to frictional drag

between the pipe material and fluid. The magnitude of

these pressure losses depends upon:

Tubular dimensions (length, OD, ID)

Mud rheological properties (density, plastic viscosityand yield point)

Type of flow (laminar or turbulent)

Out of the above three factors, the choice of model used to

characterize the drilling mud, viz. Power law, Herschel-

Bulkley, Bingham plastic etc. has a major effect upon the

pressure loss determined from the conventional equations.

3. Drill bit losses:

Drill bits are provided with nozzles to provide a jetting

action required for cleaning and cooling. More often, the

nozzles used are a fraction of an inch. Hence, the pressure

requirements to pass, say 1000 gpm, through such small

nozzles are large.The pressure loss across the bit is greatly influenced by the

sizes of nozzles used, and volume flow rate. For a given

flow rate, smaller nozzles lead to greater pressure drop

and, in turn, a greater nozzle velocity. The pressure drop

across the bit is obtained by subtracting P c (= P 1 + P 2 + P 3

+ P 4 + P 5) from the pump pressure.

Drilling hydraulics optimization usually refers to

optimization of the bit hydraulics to achieve maximum bit

penetration rate through the formation. This can be

obtained by increasing mechanical parameters (weight-on-

bit and rotating speed) and hydraulic parameters.

Procedures followed for maximizing bit horsepower, jet

impact, and bit nozzle velocity are those presented byKendall and Goins1 and later modified by Bobo2. These are

discussed later using relevant equations.

MAIN REQUIREMENTS OF DRILLING HYDRAULICS

Drilling parameters such the annulus dimensions, the drilling

mud characteristics and the mud flow rate have to be chosen in

order to ensure:

1. Sufficient cuttings entrainment along the annulus

Unif orm annular velocity profi les : If turbulent, velocities are constant but two

difficulties appear: shear stress close to the

wall of the borehole is too high (dangerous

for the wellbore stability in soft formations)

and pressure circulation losses are high.

If laminar, velocities profile depends onrheological model.

Annular velocity vs. cuttings sedimentationvelocity :

Annular velocity greater than sedimentation

velocity of cuttings is required to prevent balling

up or stuck pipe incidents. The cuttings

sedimentation velocity depends on cuttings

density, cuttings shape, cuttings dimensions, mud

density, viscosity and rheological characteristics.

2. Wellbore stability

Min imum shear stress along borehole wall :Shear stresses close to the wall of the borehole

can erode it and cause caving. It strongly depends

on the velocity gradient, function of the mud

annular velocities curve. Laminar flow regime

induces lower velocity gradients and thus lower

shear stresses. So, it's recommended, in sof

sedimentary formations, to keep a laminar flow

regime inside the annulus.

Annulus pressure vs. formation breakdown

pressure :The annulus pressure is composed by the static

pressure (function of mud density and of depth)

and dynamic pressure (function of pressure

circulation losses (depending on mud

characteristics, annulus dimensions, depth, and

mud flow rate). Any increase in this total pressure

above the breakdown pressure of the formation

will result in leak-off problems.

3. Optimum bit performance

The mud flow rate must be sufficient to cool the bit to

temperatures that allow extended functional life at bottomhole drilling conditions. In addition to it, it's

important the mud flow rate is sufficient to carry up al

cuttings drilled. The cuttings discharge depends on the

rate of penetration, the drilled cross-section area (R).


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4. Minimum circulation power consumption

It's important to minimize pressure circulation losses, in

order to minimize power consumption. It depends on the

mud density, friction factor coefficient, annular velocity

and tubular dimensions, including eccentricity.

A large Yield stress (in laminar regime) strongly increases

the losses if annulus clearance is small. This ratio

"YP/Aannulus" is an important parameter about circulation

losses and can explain main differences observed between

conventional and slim hole drillings. It's possible to definethe optimized annulus dimensions to avoid too important pressure losses for a maximum mud flow rate given (by an

economic ROP).

The rapidity with which chips or cuttings are removed has a

considerable effect on ROP. It is the mud velocity that chiefly

governs this factor. Figure 2 shows ideally the velocity profiles

in the annulus. In laminar flow, there is a much larger velocity

variation across the annulus than in turbulent flow. In turbulent

flow, overturning effect of flattish chips will not occur due to amuch more gradual variation of velocity across annulus width.

It has, thus, been concluded (Williams and Bruce 3) that low

viscosity, low gel strength muds are most efficient cutting

lifters since the velocity at which turbulent flow occurs for

these muds is lower. Turbulent slip velocities used by Williams

and Bruce are determined from the following equation:

(2)where,

vc = cutting clip velocity in turbulent flow (ft/min)

tc/dc = thickness to diameter ratio of cutting

FIGURE 2: COMPARISON OF LAMINAR AND TURBULENT

VELOCITY DISTRIBUTIONS IN ANNULUS (AFTER

WILLAMS AND BRUCE)

DRILLING MUD RHEOLOGICAL MODELS

Most drilling fluids are non-Newtonian suspensions exhibiting

a characteristic rheogram response. Regular rheologica

measurements in drilling rigs are made by a coaxial cylinder

viscometer at two different speeds (300 and 600 rpm) which

only represent the high shear rate region. Since drilling fluids

are subjected to very different shear rates, from very low values

in the mud pits to very high values through bit nozzles, the

rheological parameters estimate based only on two

measurements will lead to significant imprecision such as yield

point overestimation.

Rheological models are useful tools to describe mathematically

the relationship between shear stress and shear rate of a given

fluid. Traditionally, the oil industry uses the Bingham and

Ostwald de Waele models. However, more realistic models

have been proposed to represent more adequately the behavior

from rheogram. We also consider two other rheological models

Casson and Herschel-Bulkley.

FIGURE 3: FLUID RHEOGRAM FOR DIFFERENT MODELS

1. Bingham Plastic model:

This model describes laminar flow using the flowing

equation:

(3)2. Ostwald de Waele model:

This is essentially a Power law model which provides

greater accuracy in determination of shear stresses at

low shear rates. The following relation is followed:

(4)

where,

K = Consistency index

N = Power law index

The “K” value is a measure of the thickness of the

mud. It is defined as the shear stress at a shear rate of

one reciprocal second. An increase in the value of 'K

indicates an increase in the overall hole cleaning

effectiveness of the fluid.


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The value of constant ‘n’ indicates the degree of non-

Newtonian behavior over a given shear rate range. If

'n' = 1, the behavior of the fluid is considered to be

Newtonian. As 'n' decreases in value, the behavior of

the fluid is more non-Newtonian and the viscosity will

decrease with an increase in shear rate.

3. Casson model:This model considers the variation of shear stresses

with the square roots of shear rate and Yield stresses in a fluid under laminar regime. The relation is as

follows:

(5)4. Herschel – Bulkley model:

It is a Yield – Power law model which uses a Yield

stress value in addition to the Power law relation to

describe the rheological behavior more accurately than

any other model: (6)The model is very complex and requires a minimum of

three shear stress/shear rate measurements for a fluid.

It, however, can be reduced to the Bingham Plastic

model when n ≈ 1 or to the Power law model when τ0= 0.

However, as already discussed, the first two models tend to

represent inaccurately the drilling fluids behavior, especially at

medium and low shear rate ranges. Casson model can surpass

this shortcoming, but it’s a two parameter model that issomewhat simplistic in nature for oilfield applications. The

Herschel-Bulkley model presents more adequate rheological

parameters as compared to traditional calculations involving

Newtonian shear rates. However, the most adequate model for a

particular application is always determined by the minimum

standard error deviation value for the experimental results.

HYDRAULICS CALCULATIONS

Drilling hydraulics aims to maximize the rate of penetration of

the bit through the formation. To optimize hydraulics the

pressure relationships throughout the well must be defined. A

nodal analysis of pressure at different points in the circulating

system gives us the following relation:

(7)where,

P p = Pump pressure

PF = Sum of all pressure drops except bit loss

∆P b = Bit pressure loss

For a given length of drill string (drill pipe and drill collars) and

given mud properties, pressure losses P1, P2, P3, P4 and P

(Figure 1) will remain constant. However, the pressure loss

across the bit is greatly influenced by the nozzle size, which

directly needs to reflect the cleaning requirements and chip

transport requirements from the drilling mud. Features such as

extended nozzles and varying the number of nozzles have been

shown to affect drill rate.

Attempts have been made to optimize certain bit hydraulics

variables to cause perfect cleaning. The variables mos

commonly optimized are impact force, hydraulic horsepower

or jet velocity. Each optimized variable yields different values

of bit pressure drop and, in turn, different nozzle sizes. Thus,

it’s a difficult engineering decision over which criterion should

be used and optimized. Moreover, in most drilling operations

the flow rate for each hole section has already been fixed to

provide optimum annular velocity and hole cleaning. This

leaves only one variable to optimize: the pressure drop across

the bit, P b.

Both criteria are directly dependent on the bit friction loss, and

consequently maximum bit friction loss is desired. The bifriction loss is calculated by the following equation:

(8)where ∆P parasite is the energy dissipated by fluid circulation

through the drilling column and the annular region. Since the

surface pressure is limited by pumping equipments, the

maximum bit pressure loss can occur when ∆P parasite is

minimized.

The two criteria most commonly used are maximum bit

hydraulic power and maximum jet impact force. These are

discussed below:

1. Bit Hydraulic Power:

The general relation for hydraulic power can be

written for the drill bit as:

(9)Using calculus, the equation relating surface (pump)

pressure and bit pressure loss can be optimized to

show that:

(10)

where ‘m’ is the flow exponent, with values between

1.75 to 2. Keeping m=2 on a conservative approach, i

can be seen that:

(11)


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In other words, for optimum hydraulics, the pressure

drop across the bit should be 65% of the total available

surface pressure.

2. Jet Impact Force:The general relation for jet impact force for the drill

bit can be written as:

(12)Using calculus, the descriptive equation for impact

force by the jet can be maximized and resolved as:

(13)With the value of ‘m’ as 2, the relation reduces to:

(14)

This implies that 50% of the pump pressure must be

expended at the bit for optimum impact conditions.

The optimum flow rate for both criteria must be searched inside

a range defined by the minimum flow rate required to transport

the solids cut by the bit to the surface and the maximum

allowed by the pumping equipment. The optimum flow rate

corresponds to either the maximum hydraulic power or impact

force. Once calculated the optimum flow rate, the bit nozzle

diameters are calculated by:

(15) The nozzle velocity (in ft/s) is given by:

(16)The total flow area from the nozzles (in sq. inches) is given by:

(17)The main advantage of the jet bit is its higher efficiency in

removing rock cuttings from the hole. In order to utilize the full

potential of the jet bit, a proper nozzle size and pump pressure

must be used. Figure 3 illustrates the large increase in bit

hydraulic power that can be achieved by the selection of a

proper hydraulics program of bit nozzle size and pump

operating conditions. Large increases in penetration rate and

thus decreases in the cost per foot of hole drilled have been

achieved through optimizing bit hydraulics.

It has been generally agreed in the literature that better

hydraulics increases the penetration rate by cleaning the hole

bottom to prevent regrinding of cuttings. In addition, increased

weight and rotary speed may be applied to the bit before bit

balling occurs. However, since the rate of bit wear increases as

bit weight and rotary speed increase, there exists an optimum

weight and rotary speed even in a perfectly clean hole. Once

the optimum cleaning needs have been obtained, there is no

additional advantage to a further increase in hydraulics.

FIGURE 4: BIT HYDRAULIC POWER OBTAINED BY

MAXIMUM EQUIPMENT AS COMPARED TO

CONVENTIONAL JET PROGRAM

(AFTER KENDALL AND GOINS)

SUMMARY OF PROCEDURE FOR HYDRAULICS

CALCULATIONS

The procedure for calculating the various pressure losses and

hydraulics parameters for a circulating system is summarized

below:

1. Calculate surface pressure losses using equation (1).2. Determine the rheological model that suits the

condition under study most adequately – Bingham

Plastic/Power law/Herschel-Bulkley.

3. Calculate the pressure drops inside the drill pipe anddrill collars:

Calculate critical flow velocity (vcritical) Calculate average flow velocity (vavg)

Determine whether flow is laminar orturbulent:

If vavg < vcritical - flow is laminar If vavg > vcritical - flow is turbulent

Use appropriate equation to calculate pressure drop.


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4. Divide the annulus around drill collars and drill pipeinto open and cased sections and calculate annular

flow for both cases.

5. Add the values for pressure losses obtained fromabove steps. This is termed system pressure loss.

6. Determine the pressure drop available for bit usingequation (8).

7. Determine the nozzle velocity, nozzle size and totalflow area using equations (15) through (17).

CONCLUSION

There is considerable potential for performing much of the

drilling operations more efficiently. This would imply lower

cost and better use of available energy. Drilling hydraulics is

the key area of focus when it is required to optimize the

penetration rate into the formation, eliminating lost t ime to the

greatest possible degree by maximizing cutting removal and

improving energy dissipated at bit for rock removal.

Hydraulics calculations are rooted in accurate determination of

rheological models. However, as the mud is subject to a wide

range of shear rates during circulation, it is imperative to

perform specific non-linear regression numerical methods so

that shear stress vs. shear stress behavior is more representative.

In addition to this, it must be stressed that simplified

formulations must not be used which restrict hydraulics

calculations to inaccurate values. More realistic rheological

models and friction loss prediction correlations must be used

for this purpose.

NOMENCLATURE

ROP = rate of penetration (ft/s)O.D. = outer diameter (in.)

I.D. = inner diameter (in.)

ρm = mud density (ppg)

ρc = cuttings density (ppg)

Q = mud flow rate (gpm)

PV, µ p = plastic viscosity (cP)

P = pressure (psi)

τ = shear stress (lb/100ft2)

τ0 = Yield point (lb/100ft2)

γ = shear rate (s-1)

Cd = nozzle discharge coefficientQ = mud flow rate (gpm)

d j = nozzle diameter (in.)n j = number of nozzles

vn = nozzle velocity (ft/s)

vcritical = critical flow velocity (ft/s)

vavg = average flow velocity (ft/s)

REFERENCES

1. Kendall, H. A. and Goins, W. C., Jr.: “Design andOperation of Jet Bit Program for Maximum Hydraulic

Horsepower, Impact Force, Jet Velocity”, Trans., AIME

(1960) 219, 238.

2. Bobo, R. A.: “Application of Hydraulics to Rotary DrillingRigs”, presented at 1963 Spring Meeting of API Division

of Production Southern District, New Orleans, Louisiana.

3. Williams, C.E., Jr., and Bruce, G.H.: “Carrying Capacityof Drilling Muds”, Trans. AIME, Vol. 192, (1951), p. 111.

4. Kendall, H. A. and Goins, W. C., Jr.: “How Drilling Rateis affected by Hydraulic Horsepower”, Oil and Gas

Journal, (1972).

5. Bourgoyne, A.T., and Kimbler, O.K.: “A CriticaExamination of Rotary Drilling Hydraulics”, Society of

Petroleum Engineers of AIME, Dallas (1969)

6. Bourgoyne. Jr., A.T., Chenevert, M. E., Milheim, K.K. andYoung Jr., F. S., “ Applied Drilling Engineering ”, S.P.E

Print., Richardson, Texas, USA. (1986).7. De Sa, C.H.M., Martins, A.L., and Amaral, M.S.: “A

Computer Programme for Drilling Hydraulics

Optimization Considering Realistic Rheological Models”

Society of Petroleum Engineers paper 27554, presented at

European Petroleum Computer Conference, Aberdeen

(1994)

8. Rabia, H “Rig hydraulics” Textbook, Entrac (1989)


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Drilling Hydraulics Paper - Shashwat (PE14M013)