Hydraulic Optimization

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Hydraulic Optimization

Introduction

The main objectives of circulation during drilling are

bull To clean cuttings from the bottom of the hole and prevent re-grinding

bull To clean cuttings from the bit and prevent bit balling

bull To carry the cuttings up the annulus and out of the hole

bull To cool the bit

Maximum bottom hole cleaning is important to obtain the highest penetration rate It

is achieved by either

bull Maximum hydraulic power at the bit or

bull Maximum hydraulic impact force

In the first case it has been assumed that cutting removal from the bottom is related to

the fluid energy dissipated at the bit (bit hydraulic power) In the second case it has

been assumed that the cutting removal is optimized when the fluid impact on the

bottom is maximized (impact force on bottom) The parameters that influence the

cleaning effect in both cases are the flow rate and the nozzle area

Effective removal of cuttings from the borehole by the drilling fluid is possible onlywhen an annular velocity that creates an upward movement exceeding the

gravitational settling of the cuttings is maintained The parameters that influence the

efficiency of cutting transport are the carrying capacity of the drilling fluid the

annular clearance (referred to as the hydraulic diameter) and the flow rate The power

delivered by the rig pump is required to overcome the total hydraulic friction

throughout the circulating system Only part of this power can be used for bottom

hole cleaning because of the power losses in the system These system or parasitic

pressure losses are influenced by the drilling fluid properties the length and hydraulic

diameter of the conduit (eg string annulus and surface lines) and the flow rate

The hydraulic parameters which will affect drilling operations will be examined indetail including methods for calculating and measuring them Ideas will be extended

to consider ways of reducing pressure losses how to calculate the surface power

needed the hydraulic power developed at the bit the limits of annular velocities and

pump pressure and optimum bit hydraulics

The focus of concern in this part is the fluid behaviour of the drilling fluid as it flows

through the surface lines standpipe and hose down the drill string through the

nozzles and up the annulus When the drilling fluid is circulating it is necessary to

consider the mechanics of the drilling fluid in motion This is necessary to calculate

the pressure at any depth in pipe or annulus or the pressure on bottom The hydraulic

parameters to be considered in this Part are summarized in the accompanying figure

Eng Fayez Amin Makkar 1



Fig1 Important parameters in drilling hydraulics

No matter what the nature or stage of the project there are three effects resulting

directly from local pressure control that must be considered These are shown in

Figure 2 In this context local pressure means the pressure at the place under

consideration be it at the bottom of the hole or at any intermediate depth inside the

drill string or annulus Of these three effects it is the influence of pressure on

achieving an efficient penetration rate that is the prime interest in this Part

Figure2 Important considerations relating to pressure




Efficient penetration occurs when proper control is exercised over a number of

conditions Drilling rate increases in direct proportion to weight on bit only when the

cuttings are effectively removed from beneath the bit The drilling fluid stream

provides the energy needed to clean both the bottom of the hole and the bit and

hydraulic conditions have to be selected to achieve this with the greatest effect It

must be stressed that the objective is to optimise the penetration rate The limitingfactors are on the one hand the hydrostatic head and the necessity to clean the hole

(lower boundaries) and on the other the prevention of losses and possibly the pump

capacity (upper boundaries) There are a number of variables over which you have

direct control the more important ones in drilling hydraulics are as follows

bull flow rate

bull pump pressure

bull nozzle size

bull drilling fluid gradient

bull drilling fluid viscosity

The main concern in this Part is with the first three of these flow rate pump pressure

and nozzle size

The hydraulic parameters

In this Topic each of nine hydraulic parameters which must be considered are

separately introduced

bull Pump volumetric output and circulation pressure (Pt )

bull Flow rate

bull Bit nozzle jet velocity

bull Annular velocity

bull Pressure losses in the system

bull Pump hydraulic power output

bull Pressure drop across the bit nozzles

bull Hydraulic power developed at the bit

bull Jet impact force

Some can be measured directly at the surface Most have to be calculated All relate to

the operational activities The well is considered as a closed system in which energyand power are conserved Therefore the total hydraulic power developed by the pump

is either dissipated within the system or is used at the bit

PUMP VOLUMETRIC OUTPUT AND CIRCULATING PRESSURE

PUMP OUTPUT

The pump volumetric output or pump output depends on the type of pump and the

size of the liners installed




The volume output for double acting pumps is obtained with the following equation

The value of factor K in this equation is

0middot0257 when the flow rate Q is in dm3min (lmin)

0middot00679 when the flow rate Q is in galsmin

0middot000162 when the flow rate Q is in bblmin

0middot000909 when the flow rate Q is in ft3min

For single acting triplex pumps the equation to be used is

where the value of K is





In both the equations

L = stroke in inches

D = inside diameter of liner in inches

d = outside diameter of piston rod in inches

spm = strokes per minute

nvol = volumetric efficiency as percentage

The pump or circulating pressure (Pt ) is usually measured directly at the surface with

a standpipe gauge It can also be estimated using the following

bull

the dimensions of the hole and drill stringbull rheological drilling fluid properties




bull nozzle area

bull flow rate

The units for Pt are kPa or psi

CIRCULATING PRESSURE AND PRESSURE DROP IN THE HYDRAULICSYSTEM

Since the drilling fluid returns to the surface at atmospheric pressure (in normal

drilling operations) all the pressure developed by the pump is used between it and the

flowline

Thus Pt = Ps + P b

Where

Pt is the pump or circulating pressure (kPa or psi)

Ps is the total of all pressure losses except at the bit (kPa or psi)

P b is the pressure drop across bit nozzles (kPa or psi)

FLOW RATE (Q)

The flow rate is the volume of drilling fluid passing any point in unit time It is

usually expressed in m3s or m3min (m3sec will be used throughout this Part) In

oilfield units it is expressed in bblsmin or galsmin (gpm)

The flow rate can be measured directly with a flow meter in the surface lines usually

between pump and standpipe

BIT NOZZLE JET VELOCITY (Vn)

The jet velocity is the governing parameter in the impact-force method of maximized

bottom-hole cleaning The higher the jet velocity the better the cleaning effect The

accepted minimum value for optimized bottom hole cleaning is approximately 100

ms (350 fts)

The jet velocity is calculated from the jet nozzle area and the flow rate




ANNULAR VELOCITY (Van)

The annular velocity is the speed with which the drilling fluid rises in the annulus and

is expressed in mmin (ftmin)

The annular drilling fluid velocity is confined by an upper and a lower limit

MAXIMUM ANNULAR VELOCITY

The upper velocity limit is determined by the effects of erosion on soft formations (or

maximum possible pump output volume) Wash-outs can easily be created in such

situations

The maximum annular velocity in sensitive formations is often limited to 30 mmin

(100 ftmin) to prevent wash-outs

MINIMUM ANNULAR VELOCITY

The lower limit is always governed by the cuttings transport capacity of the drilling

fluid

Too much build-up of cuttings in the drilling fluid will result in an increase in the

density of the fluid in the annulus The consequent increase in hydrostatic head

against exposed weak formations could cause formation break-down and loss of

circulation It could also cause stuck pipe in a deviated well (building up of cuttings

bed)

The annular velocity should therefore in relation to the cuttings generated be

sufficient to maintain densities within formation strength limits

However the minimum annular velocity is also dependent on the slip velocity (rate of

settling of the cuttings) As a result of gravity the cuttings tend to drop through the

drilling fluid Therefore when the slip velocity exceeds the annular velocity the

particles will not be carried out of the well There will be insufficient returns of large

cuttings over the shale shaker and due to regrinding erosion and deterioration the

solid content and density of the drilling fluid will increase

APPLIED ANNULAR VELOCITY

The annular velocity depends on the flow rate and the flow area the latter of which is

not constant The drill-pipe open-hole area must be considered when determining the

maximum or minimum value for the velocity This means that the actual velocity in

the drill-collar open-hole annulus may be higher than the recommended value

However that often has to be accepted The DC-OH section is comparatively short so

that the wellbore wall in soft formations will be exposed only briefly to these higher

erosive effects In harder formations erosion often becomes negligible

The annular velocity at a given flow rate can be calculated by the following equations

derived from the general equation Q = VA




When drilling hard formations where penetration rates are low lower annular

velocities can be used In soft formations with high penetration rate often

encountered in top-hole drilling higher annular velocities will be required to remove

the cuttings from the well

Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is

critical because weak formations are exposed the drilling rate may have to be

adjusted to reduce the amount of cuttings generated

Generally speaking the minimum practical annular velocity is maintained above a

value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the

smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually

applies (the smaller hole size is usually at greater depth where the formations are

more consolidated)

Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions

Actual annular velocities are uncertain due to the irregularity of the hole size and

configuration During drilling the actual hole size is not known for this reason the bit

size is taken as the internal diameter of the hole or the last measured average caliper

hole size obtained from logs for calculation purposes

Between the maximum annular velocity and the minimum annular velocity is an

annular velocity which under the given circumstances is the best annular velocity to

be used This is called the optimum annular velocity

OPTIMUM ANNULAR VELOCITY

The optimum annular velocity is that velocity which is obtained through a flow rate

which gives an annular velocity sufficiently high to effectively remove cuttings from

the hole and having the lowest possible erosion effect on the borehole

Over time any flow results in erosion It is therefore advisable to obtain the minimum

flow rate required to effectively remove cuttings from the hole and to avoid

circulating any faster than is required to obtain this flow rate If this rate is a

calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate




You should be able to distinguish clearly between flow rate and annular velocity

PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE

LOSSES)

What is the system

The system is made up of all parts between the pump and the flowlines with the

exception of the bit nozzles These are excluded because pressure drop across the

nozzles is considered a useful loss of pressure It represents the change in kinetic

energy used to clean the bottom of the hole Pressure losses in the system represent

wasted energy used in overcoming friction These pressure losses are called parasitic

losses

The main sections of the circulating system which contribute to the system losses may

be summarized as follows

bull The surface lines (from pump to kelly saver sub)

bull The drill string (drill pipe and drill collars)

bull The annulus (open hole and cased hole)

In addition we will look at

bull causes of changes in circulating pressures

bull flow regimes

PRESSURE LOSSES IN SURFACE EQUIPMENT

Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly

The pressure loss occurring in this equipment depends on the length and the internal

diameters of each of the items mentioned A simple practical method to find the

surface equipment pressure losses is to hang the kelly or top drive open ended in the

rotary table and pump at different rates

Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules

They are now also used to identify different surface pressure loss situations to be used

in calculations




PRESSURE LOSSES IN THE DRILL STRING (Pf d)

The pressure loss in the drill string represents the major portion of the parasitic losses

The fluid velocities are usually high and therefore friction loss is significant as the

flow regime in most cases is turbulent The losses calculated across the drill pipe and

the drill collars are based on the Bingham Plastic Flow model

When drilling the flow pattern in the drill string is normally turbulent (With

reference to the factors above consider why this should be true) There is no exact

method of calculating pressure losses in the drill string because there is no exact

method of establishing the degree of turbulence However it is possible to estimate

pressure losses in the drill string with sufficient accuracy to select appropriate bit

nozzles for optimizing hydraulic conditions

Pressure losses in the drill string can be calculated by the following equations

You should have noticed the introduction of a new term the friction factor (f) It can

be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness

and has been determined empirically

If circulating a given drilling fluid at a given depth only V and f can vary and both of

these are proportional to flow rate The equations for pressure losses in the drill string

as given above can also be expressed in the equation




Where c is a constant incorporating the values of all the parameters which are fixed at

a given depth

N is found empirically and is not the same n as in the equations in the paragraphs on

the following pages dealing with pressure losses in the annulus The latter is called a

rheological n

c is given in SI units or API units respectively by

Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182

PRESSURE LOSSES IN THE ANNULUS (Pfa )

Since the annular pressure loss acts as an applied pressure on the formation this loss

should be kept as low as possible to minimise the risk of formation break down To

monitor the pressure against the formation during circulation the equivalent

circulation density (ECD) is often used which is defined as

Where

ECD = equivalent circulating density (kPam psift)

ρm = density of the drilling fluid (kPam psift)

Pan = total pressure drop in the annulus (kPa psi)

L = total length of the annulus (m ft)

The value of the annular pressure loss is relatively small compared to that developed

in the drill string and is often neglected in cases where the circulation rate is low eg

during well killing

It is more difficult to find pressure losses in the annulus because conditions are less

well defined than in the drillpipe

The following uncertainties exist




bull the actual flow condition is not clear the flow pattern is commonly near the

transitional region

bull the hole size and shape are irregular so it is not possible to get an accurate

value for the annular velocity or the hydraulic diameter

bull the downhole viscosity is very uncertain because it varies with temperature

and flow conditionsbull pipe rotation and eccentricity effects

For efficient drilling conditions it is found that the power lost in overcoming friction

in the system absorbs approximately 30-50 of the circulation energy The remainder

will be expended at the bit It is found that the majority of the system losses are in the

drill string For medium depth drilling the annular pressure losses probably total no

more than 3 to 7 of the pump output pressure at normal circulation rates

Although pressure losses in the annulus are small they are very important because of

their effect on the exposed formations

The effects of annular pressure losses are that

bull they increase the bottom hole pressure when circulating

bull they reduce the initial severity of a kick by providing a hidden safety margin

but they increase the risks of lost circulation during killing (only while

circulating)

bull they cause formation damage if the pressure losses are due to establishing

circulation When establishing circulation the pressure drop in the annulus

increases significantly due to the initial high viscosity (gel strength) of the

drilling fluid

Much research effort has been devoted to improving knowledge of the flow

characteristics of drilling fluids particularly in order to reduce pressure losses This is

a complicated and specialized subject because of the complexity of the fluids

The following expressions provide values for annular pressure losses

Where

Pfa is the annular pressure loss (kPa) Pfa is in psi

L is the pipe length (m) L is in ft

Va is the annular velocity (ms) Va is in ftmin

d is the hydraulic diameter (dh - dp) (mm) d is in inches

n is the Power Law index of flow behaviour

(dimensionless)n is dimensionless




n and K are derived from viscometer data

Note that K here is an approximation to that given for the Power Law model found in

the section on Drilling Fluids The number 511 results from using a specific type of

viscometer with particular values of spring constant and cylinder surface speed

With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all

values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency

to assume that all pressure losses in the system follow the same equation as shown

below

Where c and N are constants whose values are empirically determined in particular

cases (see under Pressure losses in the drill string)

Pressure losses can be calculated for all parts of the system using the equations givenin this Part

CAUSES OF CHANGES IN CIRCULATING PRESSURES

According to Pt = P b + Ps a change in the circulating pressure can be induced by a

change in either P b Ps or both

Increases in surface pressure

A sudden increase in circulation pressure although drilling fluid properties flow rate

and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging

A gradual increase in surface pressure could be the result of several causes (excepting

hole problems)

bull Increased flow rate

bull Extending the string while deepening the hole

bull Change in drilling fluid rheological properties




Decreases in surface pressure

A spontaneous sudden decrease in circulating pressure while conditions remain

unchanged can be caused by

bull decrease of P b resulting from the loss of a nozzle

bull a twist-off in the drill string

A gradual decrease in pressure could signal the following

bull A developing wash-out (leak) in the drill string or in pump valves

bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg

gas or formation water)

bull An increase of hydrostatic head in the string

Caution Any change of the surface pressure or change in pump strokes not

deliberately instigated should be investigated immediately

To a limited extent pressure losses can be measured directly for example by

pumping through the standpipe and open kelly and through drill collars It is also a

useful exercise to observe the total circulating pressure at various flow rates

Pressure losses in the system can be derived from actual circulating pressure values

by subtracting the pressure drop at the bit which can be calculated accurately

Pressure losses in the system can also be calculated However although the

dimensions are known for all parts of the system the calculation also depends on

knowing the type of fluid flow regime in the drill string and annulus The flow may be

turbulent or laminar or of some transitional type between the two The calculations are

also based on a rheological model If the drilling fluid in use behaves slightly variant

to the model the calculation results will be less than accurate

Pressure losses within the system are minimised by reducing the fluid friction in each

part

bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes

bull drill string reduce friction by using a larger internal diameter pipe coated with

plastic

bull drill collars increasing the internal diameter will again reduce friction but

only at the expense of decreasing their weight a balance has to be made

between these opposing effects

bull annulus losses are usually small and only become significant in deep small

diameter holes pressure losses depend on the hydraulic diameter found from

the difference between the hole size and the pipe od it is actually desirable to

reduce the pressure developed against the formations




Flow regimes

The differences between laminar and turbulent flow are illustrated in the table

overleaf The type of flow is determined by calculating Reynolds number (Re) for the

known well conditions from the following equations

The value obtained is compared with those shown in Table2 (figures are based on

Newtonian fluid properties)

Table2 Deciding the flow condition from the Reynolds number

Inspection of the equations shows that turbulent flow is more likely with the

conditions below




bull denser drilling fluid (ρ higher)

bull lower viscosity (micro lower)

bull higher flow rate (Q higher)

bull decreased pipe bore or hydraulic

diameter

(d lower)

PUMP HYDRAULIC POWER OUTPUT

In rig operations the amount of available hydraulic power is determined by the size

number and types of pump(s) on site However the demand in terms of output volume

(Q) and pump pressure (P) varies considerably with hole size and depth Once the

pump output or flow rate Q has been selected the available power input determines

the maximum circulating pressure (Pt) that can be achieved

This circulating pressure Pt (total pressure drop in system) is consumed partly by

friction in the fluid and the system (Ps = system pressure loss) and partly by the

pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt

is normally given by the pump pressure gauge

The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss

The bottom-hole cleaning action is provided by the hydraulic energy expended at the

bit Therefore the amount of hydraulic power expended at the bit is a measure for the

cleaning effectiveness (This assumes that the bit is properly matched to the formation

- if a bit designed for a hard formation is run in a soft formation no amount of power

will keep it clean )

The hydraulic power available at the surface from the pump is used to drive the

drilling fluid round the system power the bit and flush the cuttings to the surface If

you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface

Since Power = work done in unit time

and Work done = pressure x volume

then Power = pressure x volume pumped in unit time




Therefore the power available at surface is given by

The power output of the pump is generally assumed to be 85 of the mechanical or

electrical power input of the pump

PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)

The pressure drop across the bit nozzles P b depends on

bull The flow rate Q

bull The total cross-sectional area of the nozzle openings A

bull The drilling fluid density ρ

Once the desired (optimum) annular velocity has been determined the flow rate (Q )

and the hydraulic power expended at the bit for a given nozzle size are fixed

Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power

expended at the bit is also fixed Both jet velocity and hydraulic power at the bit

determine the cleaning action on bottom

Pressure losses through the bit nozzles are not frictional but represent a change in

kinetic energy as the drilling fluid changes its velocity from that above the bit to that

leaving the jets The pressure expended is therefore dependent only on the drilling

fluid density and the square of the jet velocity

The pressure drop across the bit nozzles is calculated using the following equations

Where

P b is the pressure loss across the bit nozzles (kPa)

ρ is the drilling fluid gradient (kPam)

Q is the flow rate (m3s)

A is the total nozzle area (mm2)




Cn is the nozzle coefficient (dimensionless)

The nozzle coefficient for jet nozzles is usually taken as 0middot95

Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless

HYDRAULIC POWER DEVELOPED AT THE BIT

As stated Pt = Ps + P b where the symbols have their previous meanings

It was later shown that the total power available is given by or

according to the system of units where the symbols again have their previous

meanings

Similarly the power lost in the system is given by or

But the power generated at the pump must either be lost in the system or used at the

bit so the hydraulic power developed at the bit is given in SI units and oilfield units

respectively by




Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by

JET IMPACT FORCE (I) BELOW THE BIT

Consideration may also be given to the actual force with which the drilling fluid

jetting from the bit strikes against the formation This is called the jet impact force (I)

The jet impact force can be calculated using the following equations

Where

I is the jet impact force (N)



Vn is the jet velocity (ms)

and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts

These equations can be modified by substituting for Vn




You should note the following points

bull the result obtained does not take into account the extremely complicated flow

conditions at the bottom of the hole

bull impact force is an important measure of the hole cleaning effort which is

applied on bottombull impact force theory is very important in the design and operation of extended-

nozzle and high-impact jet bits

SUMMARY

In this topic nine important hydraulic parameters have been described The important

equations from this section are listed below and these indicate how the parameters are

related Note in particular the importance of the flow rate and the nozzle area

Evaluation of the parasitic pressure losses

This Topic will provide some theoretical background information to explain how the

parasitic pressure losses can be related to the flow rate It will deal with

bull Aspects of fluid flow

bull Practical application

bull Determination of c and N




ASPECTS OF FLUID FLOW

The movement of fluid through a conduit is caused by an external force provided in

this case by a pump This force must overcome the internal fluid friction and the

friction between fluid and conduit which results in the pressure drop It and the

pressure drop is a function of

bull The flow rate

bull The fluid properties

o fluid density

o viscosity

bull The type of conduit and its dimensions

o length

o flow area ie hydraulic diameter

o roughness of the system wall

bull The flow regime

Basically these parameters are related as follows

(1)

and since and then (2)

The friction factor f in equations (1) and (2) is a function of the drilling fluid

properties flow regime and Reynolds number and is expressed as follows

(3)

where the friction factor coefficients are functions of the plastic viscosity (PV) and

yield point (YP) of the drilling fluid

The magnitude of the Re number determines the flow regime which under most

drilling conditions will be turbulent inside the drill string and laminar in the annulus

In its most general form the Reynolds number (Re) is determined by the equations

(4)

In equations (1) to (4)

P = pressure drop (kPa) (psi)

k 1234 = conversion factors

ρ = drilling fluid gradient (kPam) (psift)

V = average fluid velocity (ms) (fts)

Q = flow rate (m3

s) (ft3

s or gallmin)L = length of conduit (m) (ft)




d = hydraulic diameter of conduit

for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)

(inch)

f = flow friction factor

η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients

As stated previously once drilling has started with a particular drilling assembly and

bit the circulating pressure is composed of two parts

The bit pressure drop can be calculated accurately as explained

The system pressure drop could be calculated by substituting equations (4) and (3) in

equation (2) A rather complicated equation then evolves which can be simplified to

The following variables are included in this general expression for the parasitic

pressure losses

In cρ η L d

In N friction factor coefficient b

PRACTICAL APPLICATION

The effect of changes in depth circulating rate and drilling fluid gradient on the

circulating pressure will now be explained

While drilling a section of hole with one bit (a certain bit run) the circulating rate is

determined by the annular velocity which is usually kept constant The drilling fluid

properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable

that changes is the string length L

For pressure drop calculations the drill string is divided into two sections iedrill

pipe and drill collars which are considerably different in both internal and external

diameters During a bit run the length of the drill collars does not change

Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the

following approximation may be used to determine the change in Ps




If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the

following section

During well control operations however a reduced circulating rate is used and at the

same time the drilling fluid gradient is changed

The effect of a change in drilling fluid gradient ρ on P b is proportional and for

practical purposes the same proportional change is applied to Ps

Scrutinizing the theoretical equations in the previous section the change in P s is not

exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the

following proportional relation is used

DETERMINATION OF c AND N

Theoretically the value of the exponent N and the factor c can be calculated from

two standpipe pressure readings observed at two different pump rates

knowing that

Since the value of N can be solved by the ratio

Therefore it follows that or

(The value of N is often quoted as 182 in literature Where insufficient information is

available to make the calculation 182 can be assumed to make an estimate of the

pressures which can be expected




As soon as operations allow pressure readings should be taken and N calculated)

c can be determined from the equation

As small inaccuracies in pressure readings and pump stroke counts can result in

considerable errors in N and c it is recommended to monitor pressures at more

than just two pump rates These readings should cover the expected range of both

drilling and well killing pump rates

Operating limits

Decisions regarding hydraulic parameters may be necessary before the hole is drilled

In this Topic attention is focused upon the annular velocity pump pressure and flow

rate Knowledge of their allowable maximum and minimum values is important in the

process of establishing the optimum values of the variables under your control at the

surface

When considering the operating limits there are three important processes

bull DECIDING the limits for the annular velocity pressure and flow rate

bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is

the hole to be of unusual diameter Will there be high temperatures Will it be

a deviated hole What is the hydraulic capacity of the rig

bull REVIEWING the hydraulic parameters when there are hole problems

SELECTING THE ANNULAR VELOCITY

As a first step the most suitable annular velocity should be decided The purpose here

is not to show how a precise value is selected but to indicate the factors that affect the

minimum and maximum values of the annular velocity that can be selected

SELECTING THE PUMP PRESSURE AND FLOW RATE

It is normal practice to operate circulating pumps at a constant pressure The pressure

used is either the rated delivery pressure (inclusive of a safety factor) for the size of

liner installed or a rate selected to minimize pump maintenance if this still allows

good hole cleaning and adequate power at the bit




MAINTENANCE COSTS

These increase sharply above a critical operating pressure If used above this pressure

wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig

downtime Table 3 lists the maximum normal running pressures for most duplex and

triplex pumps (however the manufacturers instructions are the determining factor)

These values only apply to rig surface equipment that is suitably rated

Table 3 Maximum normal running pump pressures

LINER SIZE

This should be selected to minimize the need for changing liners through the project

They should also be such that they provide both an adequate flow rate for the surface

hole and the pressure needed at depth

MINIMUM VALUE OF ANNULAR VELOCITY

The minimum value of the annular velocity is governed by the ability of the drilling

fluid to clean the well If the well is not efficiently cleaned there will be cuttings build

up leading to increased hydrostatic and ECD pressures which might cause drilling

fluid losses to the formation In inclined holes a significant amount of the cuttings

might drop to the lower side of the hole and form a cuttings bed When the annular

velocity is not sufficient the cuttings bed will grow thereby increasing the risk of

differential and mechanical sticking of the drill string

Vertical wells

In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings

suspension will be homogeneously distributed over the entire cross section of the

annulus Given that cuttings settle relative to the upward flowing mud then as long as

the fluid velocity is greater than the cuttings settling velocity transport will occur

Figure 223 shows how the cutting velocity varies with annular velocity for different

drilling fluid thicknesses Four coloured areas are shown corresponding to different

amounts of cuttings being removed




Figure3 The relationship between annular velocity drilling fluid and cuttings velocity

Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling

fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30

ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only

slightly more than 25 In other words drilling fluid thickness (viscosity and gel

strength) is an important factor

A practical method of estimating the minimum annular velocity to ensure hole

cleaning is based on Fullertons approximation which assumes that the diameter of

the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling

velocity




The approximation is

Note drill string rotation does not benefit transport much in these well sections

because it does not effect the distribution of cuttings over the wellbore cross section

Penetration rate and hole size must also be considered In large diameter shallow

holes it may not be possible to achieve the necessary minimum velocity and special

precautions may be necessary to ensure that the hole is properly cleaned At such

depths penetration rates are likely to be high anyway so there may be less emphasis

on the need for optimum hydraulics

Fig 4




Inclined sections

In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the

low side of the wellbore and form an unstable deposit As the deposit grows it will

avalanche downhole with increasing velocity When the velocity becomes too high

the deposit breaks up and re-suspends in the flow (see also Figure4) The most

important factors to enhance transport are

bull Annular drilling fluid velocity increase (see also under vertical sections)

bull Drill string rotation ampendash faster is better Drill string rotation results in a

more homogeneous distribution of cuttings over the cross section of the

annulus and consequently enhances transport

bull Viscosity increase A viscosity increase will usually enhance transport in

intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections

Highly inclined sections

In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not

stay in suspension but will settle towards the lower side of the hole to form a

stationary cuttings bed As the height of the deposit grows the area of the annulus

open to flow decreases leading to an increase in the average drilling fluid velocity

above the bed At a certain bed height the velocity of the fluid above the bed (and the

associated stresses on the bed surface) will exceed a critical value above which

cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)

Operational problems can be minimized by setting the operational variables in such a

way that cuttings accumulation is minimized The following parameters have the most

impact on cuttings transport in highly inclined well sections

bull Annular drilling fluid velocity (flowrate) higher is better

bull Drill string rotational velocity faster is better (see also above) The impact of

rotation on cuttings accumulation can be very large In troublesome wells

avoid slidingorient mode drilling Consider the use of rotary steerable

systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level

of drilling fluid viscosity In horizontal well sections transport is obtained by

erosion of the bed surface Erosion can be optimized by a high shear stress at

the surface of the deposit (which requires a high viscosity) or by increasing

turbulence intensity (turbulence is intensified by a viscosity decrease)

Furthermore the resistance to erosion of a cuttings bed depends on the

consistency of the (stationary) drilling fluid in the pores between the cuttings

A high gel strength or yield point tends to glue the particles together High

yield points should therefore be avoided




These conflicting mechanisms usually mean that medium viscosity fluids should

preferably be avoided It is usually better to choose either a high or a low viscosity

drilling fluid Which one is preferable depends on the specific case and can only be

evaluated using cuttings transport software

Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice

will therefore always be a compromise

MAXIMUM VALUE OF ANNULAR VELOCITY

Erosion of the formation face will occur over time as the drilling fluid flows over it

However the rate of erosion is only slightly influenced by the actual annular velocity

Far more important is the flow type Turbulent flow is more erosive than laminar

flow hence the need to calculate the Reynolds Number Also important is the

formation type the softer the formation the faster it erodes

Once the range of acceptable values for the annular velocity is known it is then

possible to consider the selection of pump pressure and flow rate

Optimum bit hydraulics

This Topic discusses optimized drilling performance in general and two possible

approaches to obtaining optimum conditions at the bit These are to maximize the

hydraulic power at the bit or to maximize the jet impact force

OPTIMUM DRILLING PERFORMANCE

Opinions vary both as to what the optimum conditions are and how they can be

achieved There is agreement that the aim is to achieve the best penetration rate All

efforts should be made to minimize costs per foot The first factor affecting the costs

is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning

is inadequate drilling progress will be jeopardized

Optimum drilling performance therefore is closely related to optimum use of the

available hydraulic power within the constraints posed by the drilling fluids and the

hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings

effectively as they are produced by the bit In roller cone bits the bit teeth crush the

rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings

from the hole bottom Significant fluid forces are required since the cuttings are

pushed against the hole bottom due to the difference between the borehole pressure

BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the

chip hold-down effect It causes regrinding of the cuttings which greatly reduces the

rate of penetration




Figure5 Cutting action of a roller cone bit

Soft formation roller cone bits have therefore been designed not only to crush the

rock but also to remove the cuttings from the hole bottom by a dragging action of the

teeth (this would cause mechanical failure of the bit teeth or inserts in harder

formations) In these formations part of the hydraulic power should therefore be used

to remove the rock from between the teeth and to prevent clogging of the bit

Penetration rate can be reduced significantly if the layer of rock cuttings on the cones

of the bit is so thick that it can hamper the penetration of the teeth into the formation

This process is called bit balling and can be so severe in some soft and sticky

formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into

the centre of the bit

PDC bits have a very different cutting action than roller cone bits as shown in

Figure6 The PDC cutters drag through the rock continuously the cuttings are

therefore immediately removed from the hole bottom Hydraulic forces now have to

break the cuttings and remove them from the bit face

Figure 226 Cutting action of a PDC bit




If this is not done properly the cuttings will be pushed upwards towards the bit face

where they might stick to the bit surface This will also ball up (part of) the bit which

can again reduce the rate of penetration significantly In drag bits the available

hydraulic power should therefore be used to clean the cutters and the bit surface PDC

bit designs for soft and sticky formations should achieve high fluid velocities along all

cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling

The remainder of this paragraph will be limited to optimization of bottom hole

cleaning for roller cone bits

In general two theories on the subject of bottom hole cleaning are supported

bull Bit hydraulic power It is assumed that chip removal depends on the fluid

energy dissipated at the bit Therefore the hydraulic power at the bit should be

maximized

bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact

force should be maximized

The magnitudes of both impact force and hydraulic power expended at the bit vary

according to the following factors

bull Diameter and number of nozzles fitted at the bit

bull Circulating rate through the bit

bull The drilling fluid density or drilling fluid gradient

There are a number of limitations or constraints for any given circulating system

which directly affect optimization These constraints are

bull Upper and lower limits set on annular velocity

bull Maximum pumping speed and therefore circulating rate with the pumps

available on the rig

bull Maximum practical operating pressure often dictated by the pump liner size

fitted or the pressure rating of the surface equipment

The pump output and standpipe pressure can be determined accurately for any given

drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the

bit is included in the total sum

To simplify a direct approach to optimizing drilling hydraulics the pressure drop at

the bit is separated as the only useful pressure drop System or parasitic pressure

losses in and around the drill string are however unavoidable The only direct control

over the hydraulic energy expended at the bit is by keeping the system losses to a

minimum or in proper relation to the useful pressure drop across the bit

This can be achieved by

bull Proper selection of nozzle sizes




bull Operating at optimum flow rate but within rated pressure

In the latter case it should be remembered that operating rig pumps at high pressure

ratings will be uneconomical with regard to spare parts and fuel consumption

The two approaches will now be considered in more detail In the first approach the

assumption is that the best penetration rate is achieved if cuttings are removed

efficiently from below the bit It is then assumed that the most efficient cutting

removal is achieved by maximizing the hydraulic power available at the bit In the

second approach the assumption is that the formation is best removed by maximizing

the jet impact force These two approaches are summarized in the following Table

The most popular approach is that of maximizing the hydraulic power developed at

the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet

velocity and optimizing the fluid energy with respect to the bit diameter These

approaches are seldom used hence they are not considered here

Each of the two main approaches the maximum hydraulic power at the bit and the

maximum jet impact force will be examined in turn The procedure for optimizing

drilling hydraulics using the two approaches is summarized in the flowchart below




MAXIMUM HYDRAULIC POWER AT THE BIT

An expression was found for the hydraulic power at the bit in terms of the pump or

circulating pressure the pressure losses in the system and the flow rate

Thus in order to maximize the hydraulic power at the bit we have to ensure that this

expression has a maximum value

It was said that it is normal practice to operate circulating pumps at a constant

pressure So in the expression for the hydraulic power at the bit Pt will be effectively

constant for a particular well Thus the only variable on the right hand side of the

expression is Q the flow rate Therefore the maximum hydraulic power will be

developed at the bit when its derivative with respect to the flow rate is zero

ie Maximum hydraulic power at the bit is when




Differentiating

Thus maximum hydraulic power at the bit is when

that is when

But since the hydraulic power at the bit will be a maximum

when

To obtain a similar relationship between the power at the bit and the system losses P s

from the equation can be substituted in the above to give

MAXIMUM JET IMPACT FORCE

When maximizing the hydraulic power at the bit the method was as follows

bull Obtain an expression for the hydraulic power at the bit in terms of one

variable Q (This was possible because the pump operating pressure was taken

to be fixed)bull Differentiate with respect to Q and equate the derivative to zero

bull Obtain an expression for Ps in terms of Pt and N

bull Obtain an expression for P b in terms of Pt and N

By a worked example it was then possible to show that given values of Pt and

calculated Q and N led to a value of P b The method is essentially the same for

maximizing the jet impact force Thus the first step is to obtain an expression for the

jet impact force in terms of the flow rate Q

In the jet impact force is given by

If we consider that for a given situation the drilling fluid gradient is constant then

the expression for the jet impact force can be written as




where k is a constant







It is now possible to obtain an expression for P b in terms of Pt and N when the jet

impact force is maximized

Reduced drilling hydraulics

So far we have been concerned to achieve optimum hydraulic conditions in order to

drill at the best possible speed without reservations However sometimes there are

factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates

will not be achieved

The occasions when reduced drilling hydraulics are used include the following

bull when drilling poorly consolidated formations

bull when losses are anticipated

bull when large nozzles are being used or nozzles have been omitted to allow the

use of lost circulation material

bull when using hydraulic motors

bull when using special deviation tools eg MWD

The major concern is with poorly consolidated formations

In these formations erosion by the drilling fluid can occur and the hole may be

enlarged greatly above its nominal size Once a washout is started conditions can

deteriorate rapidly and large quantities of formation slough into the hole Eventually

the hole can collapse and bridging off results

Large washouts also contribute to mechanical problems with the drill string

(vibration) They interfere with logging and with running casing Large irregular holes

make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in

these situations often later proves very costly since lost production frequently occurs

as a result of remedial action It is better to drill an in-gauge hole using reduced

drilling hydraulics than a hole that was drilled in record time but which needs some

remedial repair work later in its life time

Hole enlargement in these cases can be avoided by

bull ensuring that annular flow conditions are kept in the laminar range

bull limiting the annular velocity to a specified value

bull limiting jet velocity to a locally determined empirical value




Appendix 1

SOLUTION IN FIELD UNITS







Appendix 2


For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm

for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi

Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic

power at the bit method can be used

3 times 13 nozzles gives the closest match with 0aacute3889 inch2

The actual pressure drop over the nozzles will be

Bit hydraulic horsepower

Total hydraulic horsepower

ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA

Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x

11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken

Pump rate Circulating pressure

spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230

Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of

210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5

daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)

Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5

volumetric efficiency

The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2

REQUIRED

Calculate for each circulation rate (Q)

Calculate N and c for a minimum of three combinations and obtain the average

SOLUTIONS

The solutions are given in SI units and in Field units




Appendix 4

Determination of other parameters

DATA

Use the data of Appendix 1

REQUIRED

bull For max hydraulic horsepower at the bit calculate and assuming the

maximum pump pressure to be used is 22500 kPa (3250 psi)

bull Determine the size of the nozzles for the next bit to obtain optimum

hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run

bull Calculate annular velocity around drill pipe 127 mm (5)

bull Calculate nozzle velocity

SOLUTION

FOR MAXIMUM HYDRAULIC POWER AT THE BIT

We have seen that the optimum flow rate is determined by the carrying capacity of the

drilling fluid and the degree of erosion the flow will give in the open hole We have

established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean

the hole Knowing this velocity drill pipe size and hole size the optimum flow rate

can then be obtained





Appendix 5

































Fig1 Important parameters in drilling hydraulics

No matter what the nature or stage of the project there are three effects resulting

directly from local pressure control that must be considered These are shown in

Figure 2 In this context local pressure means the pressure at the place under

consideration be it at the bottom of the hole or at any intermediate depth inside the

drill string or annulus Of these three effects it is the influence of pressure on

achieving an efficient penetration rate that is the prime interest in this Part

Figure2 Important considerations relating to pressure













bull flow rate

bull pump pressure

bull nozzle size




and nozzle size





bull Flow rate












PUMP OUTPUT


























bull





bull nozzle area

bull flow rate





flowline

Thus Pt = Ps + P b

Where




FLOW RATE (Q)










ms (350 fts)












situations





fluid





bed)

































more consolidated)






















LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5










































bull flow rate

bull pump pressure

bull nozzle size




and nozzle size





bull Flow rate












PUMP OUTPUT


























bull





bull nozzle area

bull flow rate





flowline

Thus Pt = Ps + P b

Where




FLOW RATE (Q)










ms (350 fts)












situations





fluid





bed)

































more consolidated)






















LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5





















































bull





bull nozzle area

bull flow rate





flowline

Thus Pt = Ps + P b

Where




FLOW RATE (Q)










ms (350 fts)












situations





fluid





bed)

































more consolidated)






















LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































bull nozzle area

bull flow rate





flowline

Thus Pt = Ps + P b

Where




FLOW RATE (Q)










ms (350 fts)












situations





fluid





bed)

































more consolidated)






















LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5








































situations





fluid





bed)

































more consolidated)






















LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5












































more consolidated)






















LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5



































LOSSES)

What is the system






losses








bull flow regimes









in calculations


























a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5























































a given depth



rheological n








Where







during well killing








transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5


































transitional region
















circulating)




drilling fluid





Where

















below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5








































below











hole problems)































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

























































part



plastic











Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































Flow regimes








conditions below








diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5





































diameter

(d lower)












































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5



















































Where










Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5



































Where

P b is in psi

ρ is in psift

Q is in gpm

A is in inch2

Cn is dimensionless





meanings




respectively by









Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5






































Where





and

Where

I is in lbf

ρ is in psift

Q is in gpm

Vn is in fts











SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5







































SUMMARY


















bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5






































bull The flow rate


o fluid density

o viscosity


o length





(1)




(3)






(4)






Q = flow rate (m3

s) (ft3







(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5



































(inch)









pressure losses

In cρ η L d


















following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5


































following section











knowing that















Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5







































Operating limits





surface



















MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































MAINTENANCE COSTS







LINER SIZE












Vertical wells




















velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5










































velocity












Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5









































Fig 4




Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































Inclined sections








































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5


































































rate of penetration


































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5































































maximized





























































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5


































































Differentiating


that is when


when




























































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5









































































Appendix 1








Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5




































Appendix 2










ANNULAR VELOCITY




Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































Appendix 3

Determining c and N

DATA




spm kPa psi

160 24000 3480

135 18200 2640

110 12480 1810

88 8480 1230







REQUIRED



SOLUTIONS





Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































Appendix 4


DATA


REQUIRED







SOLUTION











Appendix 5

































Appendix 5































Hydraulic Optimization

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Transcript of Hydraulic Optimization