reliability and temperature evaluation of boilers

8/11/2019 reliability and temperature evaluation of boilers

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CHAPTER 1

INTRODUCTION


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INTRODUCTION

The common causes of the metallurgical failure of the tubes in water tube boiler are due

to tube temperature higher than expected in the original design. A major challenge for the

maintenance activities which are to be performed now a days in industries is not only to learn the

available techniques, but to decide which are suitable for the particular industries. The new

developments include: Decision support tools, such as hazard studies, failure modes and effects

analysis and expert systems, new maintenance techniques, such as condition monitoring and

designing equipment with a much greater emphasis on reliability and maintainability analysis of

the systems in the industries.

The primary problem associated with reliability assessment is the selection and

specification of the most appropriate reliability model. This requires the collection and analysis

of failure and repair data in order to empirically fit the model to the observed failure or repair

process. The derivation of the reliability and maintainability models is an application of the

probability theory, whereas the collection and analysis of the failure and repair data are primarily

an application of descriptive and there are two general approaches to fitting reliability

distributions to failure data. The first and usually preferred method is to fit a theoretical

distribution such as normal, exponential, lognormal and weibull. The second is to derive directly

from directly from the data an empirical reliability function or Probability density function

function. The later method is also called as Distribution Free method and it is very easy toconduct for the analysis. The objective of this method is to derive directly from the failure and

repair times, the failure and repair times, the failure distribution, reliability function and

Probability density function functions.

Tube temperature increases slowly over many years or rapidly caused either by loss of

internal steam or water flow. Internal oxide scale or deposit formation usually results in long

term overheating that gradually increases the temperature [1]. Although steam temperature

occasionally measured in a boiler, local tube temperature and temperature distribution are rarely

measured and some times impossible due to temperature range which is very high, load

fluctuation and steam side oxide scale growth during operation [2]. However, the remaining life

span of the boiler tubes that installed in a fossil fuelled power station can be predicted if the

stress and average temperature of the tubes are known, together with the way the tubing is

thinned or scarred as a result of erosion and corrosion processes [3]. Arguably, the average tube


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temperature plays a more significant role than stress does in determining the creep life of a boiler

tube. In order to avoid the tube failure, detection of tube temperature distribution is necessary to

take proper action. Therefore, temperature distribution in the tubes in water tube boiler needs to

be analyzed numerically. Therefore, this paper presents the application of finite element method

(FEM) to analyze the tube temperature distribution in a water tube boiler.

1.1 INTRODUCTION TO VISAKHAPATNAM STEEL PLANT:

The Visakhapatnam Steel Plant (VSP) is a 3Mt Integrated Steel Plant under the corporate

entity, Rashtriya Ispat Nigam Limited (RINL). VSP is the first shore based integrated steel plant

in country. The plant produces steel through the BF BOF route. VSP has the distinction of being

the first integrated steel plant in the country to adopt 100% continuous casting. Currently the

plant is operating at 4.0MT of hot metal, 3.56 MT liquid steel and 3.17 MT of saleable steel

representing capacity utilization of over 115%.

Steel industry being energy intensive in nature from raw material stage to finishing stage.

About 470-480 KWH of electricity is used for every tonne of steel produced and steel industry

requires about 250-260MW of electricity for running various drives in the plant .RINL realized

that electrical energy demand in integrated steel works can be met through installation of captive

power plant and support from grid. RINL has captive power plant of 247.5MW, and an

additional 39MW installed capacity for waste energy recovery to meet energy recovery, to meetenergy requirements in VSP.

1.2 INTRODUCTION ABOUT THERMAL POWER PLANT

Integrated Steel Plants are major consumers of electricity, with specific

consumption of power at around 600-650 MW Hrs/Ton of liquid steel. Power requirement of

VSP is met through captive power plant generation as well as supply from APSEB grid. The

captive capacity of 270MW is sufficient to meet all the plant needs in normal operation time. Incase of partial outage of captive generation capacity due to breakdown, shutdown or other

reasons, the shortfall of power is availed from APSEB grid. Turbo generators of VSP normally

operate in parallel with state grid. Excess generation over and above plant load is exported to

APSEB. The following are the main objectives of Thermal Power Plant of Visakhapatnam Steel

Plant.


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To supply uninterrupted cold blast to Blast Furnace as per furnace requirements.

To supply uninterrupted Power to critical Category-1 loads of Steel Plant.

To supply 13 ata process steam for other process units of Steel Plant.

To supply DM water and soft water to meet both internal and external plant needs.

To supply chilled water to meet both internal and external plant needs.

To reduce dependency on State Power Grid by ensuring maximum internal in-house

Power Generation.

Thermal Power Plant has 5 Boilers each generating of 330 T/Hr steam at 101KSCA and 400C.

the boilers are of BHEL make, capable of firing combination of fuels namely Coal, Coke Oven

Gas, Blast Furnace Gas ands Oil. Crushed coal is conveyed from Raw Material Handling Plant to

TPP through conveyors. The coal is pulverized in Bowl Mills and fired in the furnace. Normally,

4 boilers are kept in full load operation to produce 247.5 MW of power, supply steam to 2 Turbo

Blowers and process needs boilers outlet flue gas as it passes through Electro Static Precipitators

to control air pollution. The Fly ash and bottom ash generated are pumped in slurry form to ash

pond through on ground pipelines. The clarified water is recalculated back to ash system

BOILERS:

Thermal Power plant has 5 Boilers each generating 330 T/hr. steam at 101 KSCA and

540oC. The boilers are of BHPL make, capable of firing combination of fuels namely Coal,

Coke Oven Gas, Blast Furnace Gas and Oil. Crushed coal is conveyed from Raw Material

Handling Plant to TPP through conveyors. The coal is pulverized in Bowl Mills and fired in the

furnace. Normally 4 Boilers are kept in full load operation to produce 247.5 MW of Power,

supply steam 2 turbo Blowers and process steam needs boiler outlet flue gas passes through

electro Static Precipitators to control air pollution. The Fly ash and Bottom Ash Generated are

pumped in slurry form to ash pond through on-ground pipe lines. The clarified water is

recirculate back to ash system.

TURBO GENERATORS:

Thermal power plant has 4 Turbo Generators, three of 60MW capacity each and fourth

67.5 MW. Special features of the turbo sets are: Electro hydraulic turbine Governing System


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controlling extractions at 13 ata and 4 ata for process steam needs in TG1, 2 and 3. Central

admission of steam to reduce axial thrust.

AIR COOLED GENERATORS:

Power is generated and distributed at 11KV for essential loads. Remaining power from

TG-1, 2 and 3 is transferred to plant grid.

TURBO BLOWERS:

VSP has two Blast Furnaces. To meet the blast air requirement 3 Turbo Blowers each

of 6067 NM3/Min @ 6.5 Kg/ Cm2 capacity, are installed at TPP. These Blowers are of axial type

and are the largest blowers installed in India. To meet the varying needs of Blast Furnace, the

blowers are provided with adjustable stator guide blades in the low pressure compression stages.

The Blowers are provided with suction filters, pre- coolers and intercoolers.

AUXILIARIES OF TPP:

These include coal conveyers; cooling towers and pump house No. 4 for cooling water

system; pump house for ash water, ash slurry, fire water and fuel oil and HSD; air compressor

station; emergency Diesel Generators; electric switch gear for power distribution; ventilation

and air conditioning equipment etc.

CHEMICAL WATER TREATMENT PLANT (CWTP):

Chemical Water Treatment Plant located in TPP Zone produces high purity

Demineralised Water and Soft Water. There are six streams of Demineralising units each

capable of producing 125 cubic meters per hour and two softening units of 125 M 3/Hr each.

DM water is supplied to Chilled Water Plant-I, II and SMS mould cooling. The return

condensate from Thermal Power Plant, chilled water plant no. I and chilled water plant no. II is

polished at CWTP in 2 streams, each of 100 M3/hr capacities. All the demineralised water

produced/polished at CWTP is deareated and dosed with Ammonia before pumping for this

purpose.


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CHILLED WATER PLANT:

Chilled Water Plant No.2 located in TPP zone is having nine chillers, each having a chilling

capacity of 337 cu.M of water per hour. The chillers operate on liquid absorption technique

having Lithium Bromide cycle. The chilled water is supplied to TPP, Blast Furnace and sinter

Plant for air conditioning Purpose of 70c. The return water temperature is 16oC. Steam and

cooling water requirements are met by TPP and pump House No.4 respectively.

COKE DRY COOLING PLANT (CDCP) BOILERS:

In VSP, hot Coke produced in the coke Oven Batteries is cooled by circulating Nitrogen in

Coke Dry Cooling Plant. The hot circulating gas is passed through waste Heat Boilers in which

steam is produced at 40 KSCA pressure and 4400

c temperature. There are four Waste HeatRecovery Boilers each of 25T/hr capacity in each Coke Dry Cooling Plant. There are three

CDCP for 3 Coke Oven Batteries. These Boilers are forced circulation Boilers. Deaerators and

Boiler feed pumps, serving all the three plants, are located at CDCP-1.

BACK PRESSURE TURBINE CHILLED WATER PLANT:

The 40 KSCP steam generated in CDCP Boilers is utilized for driving 2 Nos. of 7.5 MW

Back Pressure Turbines for generation of power. The 2.5 ata exhaust steam is utilized for

production of Chilled Water in CWP-1. The 7-ata-extraction steam is used for process

requirements of CO7CCP zone. The CWP-1 has 5 chillers installed, each capable of cooling

337m3 of water per hour from180c to 10

oC. The Chilled Water is supplied to Gas Coolers and

for air conditioning need s of CO&CCP zone. BPTS and CWP-1 are housed in a single building

located near Batters No.3 of CO&CCP zone.


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CHAPTER 2

LITERATURE SURVEY


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LITERATURE SURVEY:

In water tube boilers, water is converted into steam inside the tubes, while hot gases pass

over and around the outside of the tubes. Water tube boilers can operate at higher pressures than

fire tube boilers. The flow of steam and water within a water tube boiler is called circulation.

This circulation is critical in preventing tubes from overheating. When tubes are overheated,

metal softens, weakens and may eventually rupture. In a simple water tube circuit, bubbles of

steam form in the heated tubes or "risers". The resulting steam and water mixture is lighter than

cooler water on the unheated side of the boiler, and rises to a steam drum at the top of the boiler.

Here the bubbles rise to the surface and steam is released. The water then flows from the drum

down through the cooler rubes, or "downcomers", completing and repeating the cycle.

The Metallurgy Department of the Riley Stoker Corp. [1] that has many

experiences for the 25 years period ending in 1980 gives the list of the breakdown between

mechanical and corrosion failure and further classify the various kinds of failures, locations, and

materials. 81% of the boiler tube failure is due to mechanical, consist of high temperature failure

(short time) 65.8%, creep (high temperature/long time) 8.6%, and others 6.6%, while boiler

failures caused by corrosion is 19%. Analysis of the North American Electric Reliability Council

(NERC data) indicates that the coal fired boilers are among the highest economic risk

components in any power plant. By far, the greatest number of forced outages in all types ofboiler is caused by failures [6]. Elimination of boiler tube failure could save the electric power

industry about $5 billion a year [7]. Metallurgists from David N. French, Inc. [1] published data

of the top 10 causes of failures where creep (long-term overheating) is 23.4%, followed by

fatigue (13.9%) (thermal 8.6%, corrosion 5.3%), ash corrosion (12.0%), hydrogen damage

(10.6%), weld failures (9.0%), high temperature (short-term overheating) (8.8%), erosion (6.5%),

oxygen pitting (5.6%), caustic attack (3.5%) and stress corrosion cracking (2.6%). In general,

30% of all tube failures in boilers and reformers are caused by creep [8].

Dillon.AR et.al.,(2003), described that the prevention of the fast fracture damage of the

mechanical equipment important for the safety of nuclear power plant by conducting the

reliability analysis.


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Almeida.A.B and Ramos. H. M (2010) have conducted the diagnosis and reliability

analysis in a pumping system. Weak points in the design and in the operation can then be

detected and future accidents can also be avoided.

Chapman, et.al.,(2010), have conducted the Structural lifetime, reliability and risk analysis

for power plant components and systems.

Deepika Garg et.al.,(2009), have described the reliability of a Pharmaceutical plant using

MAT LAB. The purpose of paper is to compute reliability of a Pharmaceutical plant . A

Pharmaceutical plant consists of nine sub-systems working in series. One subsystem namely

Rotary Compression Machine is supported by stand-by units having perfect switch over devices

and remaining eight subsystems are subjected to major failure only.

Ray et.al., (2003) have conducted assessment of service exposed to boiler tube of the super

heater and preheater made of 2.25 Cr-1 Mo steels in a120MW boiler of thermal power plant.

Husain and habib et.al., (2008) have investigated the steel tubes failure in a super aterboiler

at one of Kuwait electrical and power plants which suffered localized overheating.

Baoyou et.al.,(2006) have analysed a boiler tube rupture through chemical analysis,

scanning electron microscope and energy dispersive spectroscopy.

Chattoraj et.al., (1997) have investigated the corrosive degradation and failures of vertical

furnace wall tubes of a cogeneration boiler.The results showed that under isothermal condition,

the creep damage depends only on the stress.

Caligiuri et.al., (2006) have conducted simulation to identify the effect of thermal

constraint in design of a heat recovery boiler. The finite element model using thermal and

structural analysis was applied, and commercially available finite element software namely

Ansys was used.


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CHAPTER 3

INTRODUCTION TO BOILERS


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3.1 BOILER :

A steam generator or boilers is usually, a closed vessel made of steel. Its

functions is to transfer the heat produced by combustion fuel (liquids, solid or gaseous) to water

and ultimately to generate steam. The steam produced may be supplied:

To steam engines or turbines (turbo generators)

At low pressures for industrial processes work

For producing hot water which can be used in vapour absorption processes.

In TPP,5 Boilers are installed with a capacity of 330 ton/hr each with 101 ata

and 12 auxiliary waste heat recovery boilers installed capacity 25 ton/hr each 40ata,to supply

steam to turbo generators for power generation and 13 ata,7 ata steam for different processes

throughout the plant.

GENERAL SPECIFICATIONS OF BOILER:

Make : BHEL, Tiruchy

Type of unit : Single drum, natural circulation, 3 stages super heated

Balanced draught, multi fuel firing, non reheat

Type of furnace : Fusion welded dry bottom

Type of super heater : Radiant and convection

Type of steam temperature

Control : Spray

AIR / FLUE GAS PATH:

Air used for combustion of lignite or any other fuel applied in power generation, should

be preferably hot. Air pre heaters are arranged in the flue gas ducts for preheating the air,

utilizing the heat in waste gases. FD fans suck atmosphere air and pass it through ducts of rotary

air heaters then temperature of air is raised up to 370 deg C.

FUELS AND FIRING:

A coal fired unit incorporates oil burners also to a firing capacity of 25% of boiler load

for the reason of:

1. To provide necessary ignition energy to light off coal burner

2. To stabilize the coal flame at low boiler / burner loads


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3. As a safe start up fuel and controlled heat input during light off

LIGHT FUEL OIL:

The fuel for the igniter is light fuel oil. Normally LFO is used for cold start ups

and it is sometimes referred as `warm-up fuel. Being a distillate, LFO burns clean ad completein a cold furnace without any un burnt oil conveyors. LFO has the advantage of being low

viscous at ambient temperatures requiring no heating, and it can be air atomized.

COKE OVEN GAS:

Coke oven gas is supplied to the boiler from coke oven batteries. This gas can be

used for warming up and for load carrying. This gas gives stable flame normally without any

need for support by igniters. There are totally 32 COG gas spuds arranged in four elevations in

the auxiliary air compartments.

BLAST FURNACE GAS:

This is supplied from Blast furnaces. The calorific value of the gas is low and

hence needs support at low loads when the burnt separately. Also as no reliable flame scanning

can be obtained with this gas flame, an auxiliary firing either oil or coal firing is resorted to

whenever there is need for BFG firing. Also the gas is characterized by its high level of toxicity

and hence utmost care should be taken for handling this gas.

COMBUSTION IN FURNACE:

Furnace is the place where combustion of the pulverized fuel and oil fuel takes place

with the aid of air supplied. We can say that two processes occur in the furnace simultaneously.

One process is that of a chemical reaction exothermic in nature which releases a lot of heat and

the other process is the transfer of this heat to the medium inside the water walls. So the

efficiency of the furnace depends on the utilization of heat energy for evaporation of water and inreduction of radiation and other losses. In our boilers the furnace is a dry bottom pulverized fuel

furnace having suspension system of firing. Furnace is screened by water walls on all the four

sides. Furnace bottom is hopper shaped and is immersed in water in the slag bath. The maximum

temperature encountered in the furnace is 1250 C to 1300 C. Since the ash function temperature

is 1450 C fly ash collects at the bottom of the furnace in solid state. 15% of ash below in the


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furnace into the slag. They are cooled by the water in the slag bath and removed by two slag

conveyors.

WATER WALL FURNACE:

Furnace volume : 2300cu m

Heat transfer area : 1230sq m

Area of refractory exposed : nil

Tube Outer Dia * thickness : 63.5 * 4.8 sq mm

Tube material : SA 192

Pitch : 76.2 mm

No. of tubes in front and

Rear walls each : 132

No. of tubes in left and right

Side walls each : 92

Design metal temperature : 373 deg C

Design pressure : 121 kg/sq cm

WATER WALL PLATEN:

Number off : 4

Tube OD * thickness : 50.8 * 4.1 sq mm

Heat transfer area : 120 sq.m

Number of tubes/platen : 26

Design metal temperature : 373 oC

design pressure : 121 kg/sq.cm

FEED WATER SYSTEM:

Requirement of the boiler feed water is met by a DM plant. Feed water is deaerated

and then pumped by a feed Pump into a common header from where the feed water is passed

through two HP heaters. Feed water from HP heaters passes through a common header from

where individual boilers are fed.


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Feed pump:

Number off : 5+2 (stand by)

Type of drive : motor driven through step up gear box

Capacity : 375 m3/ hr

Head : 1441 m/c

Temperature of water : 142oC

Density : 924.3 kg/m3

Speed : 4305 rpm

Power input : 1680 kw

THE PRESSURE PARTS OF BOILER:

The pressure parts of a boiler are the parts which are most prone to failure due to the

acting of pressure and temperature and other factors such as corrosion due to natural causes

which occur during operation.

The pressure parts of a boiler are the tubing, header, boiler drum, and the pipe work

which contain the steam that are the fundamental operating fluids of the thermodynamic cycle. In

operation, these components are protected by avoiding large temperature differentials through

the walls or gross heating by lack of coolant. The operating temperature plays an important role

in the failure than the operating pressure. In addition to the long term aspects we also face short-

term aspects such as boiler explosion, which take the unit off-load.

BOILER DRUMS:-

The boiler drum is usually the largest single piece of equipment in the boiler. It is also the

most difficult to replace. Drum is basically a thick walled cylinder, made up of rolled plates

welded together, susceptible from thermal shock due to operational error. The detailed inspection

of the supporting structure can be carried out by detailed non-destructive testing.

All inlet and outlet connections to the boiler are welded. In older designs, unfused land

was included from which cracks propagated. A vast majority of these connections have site wells

very close to the drum. If any of these fail, the escaping fluid may corrode the drum. Short term

repairs to a drum are possible, but would require expensive heat treatment, making them

expensive and time consuming.


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The bulk of drum inspection and repairs are concerned with the fitting inside the drum

such as water distribution pipe work, sampling and dosing pipe work, steam separators, driers

and baffles. They are bolted to the drum and there are some flanged connections. All these

connections must be checked for any indications of corrosion and erosion. Failures of a number

of fasteners indicate a fault or undue stress somewhere in the system. The most likely result of a

bolt falling off in the drum is a blockage and tube leaks.

Finally, the drum and its surrounding area must be checked to ensure that it is not being

locally corroded by intermittent spillage from safety valve drains or airlocks.

Fig 3.1 Boiler drum

Headers:

Header creep lives must be assessed by considering temperature, materials and dimensions.

1. Based on the noral station instrument header temperature records, with correction

for operating temperature spread along the header.

2. Based on the actual header temperature, as part of the specific recording exercise

with actual physical dimensions.

3. Physical and NDT inspection of headers.


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TUBE ATTACHMENTS:

Tube attachments are a general description of any device attached to the pressure tubing

of the boiler. Attachment failure and subsequent loss of alignment can lead to tube heating or

soot blower erosion, both leading to subsequent failure. Therefore attachment welding should be

checked.

MAIN PIPE WORK :

The main pipe work of a boiler unit can be classified as the pipes linking the drums and

headers within a boiler. Cole pipe work tends to present a few problems in actual operation of

plant. Hot pipe works is often subject to defect which grow in size in service due to the elevated

temperature of the boiler.

3.2 TYPES OF BOILERS:

This section describes the various types of Boilers:

Fire tube boiler

Water tube boiler

Fluidized Bed Combustion Boiler

Atmospheric Fluidized Bed Combustion Boiler

Pressurized Fluidized Bed Combustion Boiler

Fire Tube Boiler:

In fire tube boiler, hot gases pass through the tubes and boiler feed water in the shell side

is converted into steam. Fire tube boilers are generally used for relatively small steam capacities

and low to medium steam pressures. As a guideline, fire tube boilers are competitive for steam

rates up to 12,000 kg/hour and pressures up to 18 kg/cm2. Fire tube boilers are available for

operation with oil, gas or solid fuels. For economic reasons, most fire tube boilers are nowadaysof packaged construction (i.e. manufacturers shop erected) for all fuels.


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WATER TUBE BOILER:

In water tube boiler, boiler feed water flows through the tubes and enters the boiler

drum. The circulated water is heated by the combustion gases and converted into steam at the

vapor space in the drum. These boilers are selected when the steam demand as well as steam

pressure requirements are high as in the case of process cum power boiler / power boilers. Most

modern water boiler tube designs are within the capacity range 4,500 120,000 kg/hour of

steam, at very high pressures. Many water tube boilers nowadays are of packaged construction

if oil and /or gas are to be used as fuel. Solid fuel fired water tube designs are available but

packaged designs are less common.

The features of water tube boilers are:

Forced, induced and balanced draft provisions help to improve combustion efficiency.

Less tolerance for water quality calls for water treatment plant.

Higher thermal efficiency levels are possible

Fluidized Bed Combustion (FBC) Boiler:

Fluidized bed combustion (FBC) has emerged as a viable alternative and has

significant advantages over conventional firing system and offers multiple benefits compactboiler design, fuel flexibility, higher combustion efficiency and reduced emission of noxious

pollutants such as SOx and NOx. The fuels burnt in these boilers include coal, washery rejects,

rice husk, bagasse & other agricultural wastes. The fluidized bed boilers have a wide capacity

range- 0.5 T/hr to over 100 T/hr.

3.3 BOILER TUBE FAILURES CAUSES AND REMEDIES:

The causes of failures of boiler tubes, while most of the causes of failures are attributed tooperational mistakes and malfunctions of boiler, a few can be attributed to defective design,

material of workmanship. The details various causes of failures and the remedial measures to be

adopted to avoid such failures are.

The main causes of tube failure are:

1. Overheating


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2. Erosion

3. Corrosion

4. Material

5. Other defects

1.OVERHEATING:

Overheating can be localized, extensive, prolonged or of short duration. Metallographic

analysis indicates the approximate temperature to which the tube was subjected before failure

occurred. Observation of the grain growth and microstructure of failed tube material also

indicates if the overheating was of prolonged or short duration. Water-wall tube failure results in

a burst with a fish mouth opening. Occasionally cracks will also appear up to lengths of 2

meters on either side of the burst. Bursting occurs due to excessive reactive force caused by

change of state from water to steam. In the case of super heaters, tube failures take the form of a

narrow opening with multiple satellite cracks. The reasons for overheating of waterfall or

superheated tube are:

a) Starvation due to

(i) Improper circulation (ii) Insufficient flow

b) Flame impingement

c) Secondary burning of fuel

d) Excessive air

a) Starvation

i) Due to improper circulation:

Insufficient circulation in the water walls may lead to departure from onset of nucleate

boiling and may lead to overheating, which in turn will result in tube failures. Where the failures

are traced to improper circulation, the same can be improved in that region of water wall by

providing additional down comers/spider tubes to the existing down comers.

ii) Due to insufficient flow:

Starvation can occur in super heater tubes due to an insufficient flow resulting in

overheating. This is generally observed in the binder tubes of the platen super heater. These

binder coils have a number of bents, and are longer in length than the other coils in the platen.


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The flow through these binder coils is, therefore inadequate. The prolonged overheating in such

tubes results in creep failure.

Such failures can be avoided by replacing the long binder tube with shorter tubes which

in turn increases internal flow and prevents overheating Overheating can also be avoided by

changing the material. The materials of the bottom portion of the outermost coils of platen can

also be replaced by stainless steel to enhance their life since the bottom most portion faces direct

radiation from the furnace.

b) Flame impingement:

Water wall failures occur mostly near the burners. This is due to the flame impingement

from burners, which get distorted in service. To avoid such failures new burner nozzles such as

the honeycomb type which resist distortion are now used.

c) Secondary burning of fuel:

In certain cases oil from the oil gun may flash on to the tubes. Even in coal fired boilers,

the unburned fuel particles may catch at the top of the furnace or in the second pass cause in

secondary combustion, explosion, or over heating of the tubes.

This can be avoided by proper controlled of the atomization of oil, coal particle size and

the firing rate.

d) Excessive air:

Too much of excess air leads to higher furnace temperature resulting in higher radiation,

heat absorption and slagging problems. In oilfired boilers, too much of excess air is favorable to

the formation of SO3due to the increased availability of O2, thereby promoting a higher rate of

low temperature corrosion.

To avoid such failure the O2content in flue gases should be measured periodically during

operation and adjustments made to achieve design values as closely as possible. Further, to avoid

condensation, the flue gas temperature in different zones should be closely monitored and kept

within the design limits.

2. EROSION:

Erosion is the second major cause of tube failures. The tube wall thickness gets reduced

due to erosion and when the thickness is not sufficient to withstand the operating pressure and

temperature of the tube, the tube will fail.

Erosion of the super heater and economizer tubes may be due to the following reasons:


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i) Flue gas erosion

ii) Erosion due to steam or water

i) Flue gas erosion:

Since the rate of erosion is proportional to the cube of velocity, erosion may occur on the

super heater and economizer tubes due to the high abrasive ash content of Indian coals if the

velocity of the gases in the narrow gaps is high. Such insufficient gaps may occur between coils

and walls, and super heater coils and ash hoppers blow them. Boilers, therefore, have to be

designed with gas velocities limited to values below critical.

ii) Erosion due to steam or water:

Whenever there is a tube failure the water or steam from the faulty tube escapes in the

form of a high velocity jet and when it impinges on the adjacent tubes they get eroded. If the

boiler is not shut down immediately after detection of the failure and allowed to operate for a

protracted period the damage due to steam or water erosion will be considerable.

3. CORROSION:

Corrosion is another cause of the tube failure. Corrosion can be on the gas side of the tubes the

steam side. The gas side corrosion occurs in oil fired boilers. High temperature corrosion occurs

due to the presence in oil of sodium and vanadium, the oxides of which form flux with the

protective oxide of the material, thereby causing further attack on the material by the gas. This

can be prevented by using low vanadium content oil or by employing certain additives like MgO

powder in the oil. The MgO powder can be sprayed through a separate nozzle into the furnace or

magnesium wires can be burnt in the furnace.


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Fig 3.2 Damage of boiler tube due to corrosion

Low temperature or dew point corrosion occurs in oil fired boilers in the air heater

or economizer if the flue gas temperature approaches the dew point temperature. Sulphur in the

oil transforms to SO3 in the furnace and then to Sulphuric acid with the water vapour in the flue

gas at low temperatures and causes corrosion. Low temperature corrosion can be avoided by

controlling the inlet temperature of the feed water to the economizer.

If the feed water contains dissolved oxygen or Carbon Dioxide, these gases will

react with the tube material and cause corrosion inside the water wall or super heater tubes

Water-side corrosion

It is of the following three types:-

Stress Corrosion Cracking (SCC)

Symptoms: Failures from SCC are characterized by a thick wall, brittle-type crack

May be found at locations of higher external stresses, such as near attachments.

Causes: SCC most commonly is associated with austenitic (stainless steel) Super heater materials

and can lead to either transgranular or intergranular crack propagation in the tube wall. It occurs

where a combination of high-tensile stresses and a corrosive fluid are present. The dame results

from cracks that propagate from the ID. The source of corrosive fluid may be carryover into the

super heater from the steam drum or from contamination during boiler acid cleaning if the super

heater is not properly protected.


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Hydrogen Damage:

Symptoms: Inter granular micro-cracking. Loss of ductility or embrittlement of the tube material

leading to brittle catastrophic rupture.

Fig 3.3 hydrogen damage

Causes: Hydrogen damage is most commonly associated with excessive Deposition on ID tube

surfaces, coupled with a boiler water low pH excursion. Water chemistry is upset, such as what

can occur from condenser leaks, particularly with salt water cooling medium, and leads to acidic

(low pH) contaminants that can be concentrated in the deposit. Under-deposit corrosion releases

atomic hydrogen which migrates into the tube wall metal, reacts with carbon in the steel

(decarburization) and causes inter granular separation.

Fire Side Corrosion:

Fig 3.4 Fire side corrosion

Tubes develop a series of cracks that initiate on the outside diameter surface and

propagate into the tube walls. Since the damage develops over longer periods, tube surface tends


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to develop appearance known as iron hide, or craze cracking. Most commonly seen a s a series of

circumferential cracks. Usually found on furnace wall tubes of coal- fired once- through boiler

designs, but also has occurred to tubes in drum type boilers.

Damage initiation and propagation results from corrosion in combination with thermal

fatigue. Tube outer diameter experiences thermal fatigue stress cycle, which can occur from

normal shedding of slag, soot blowing or from cyclic operation of boiler.

It is mainly due to the following reasons:-

(i) Low temperature

(ii) Water wall

(iii) Coal ash

Water side Corrosion Fatigue:

Symptoms: ID initiated, wide trans granular cracks which typically occur

Adjacent to external attachments.

Causes: Tube damage occurs due to the combination of thermal fatigue and Corrosion. Corrosion

fatigue is influenced by boiler design, water chemistry, boiler water oxygen content and boiler

operation. A combination of these effects leads to the breakdown of the protective magnetite on

the ID surface of the boiler tube. The loss of this protective scale exposes tube to corrosion. The

locations of attachments and external weldments, such as buck stay attachments, seal plates and

scallop bars, are most susceptible. The problem is most likely to progress during boiler start-up

cycles.

4.MATERIAL DEFECTS:

High-temperature Oxidation:

Similar in appearance and often confused with fireside ash corrosion, high-

temperature oxidation can occur locally in areas that have the highest outside surfacetemperature relative to the oxidation limit of the tube material. Determining the actual root cause

between the mechanisms of ash corrosion or high-temperature oxidation is best done by tube

analysis and evaluation of Both ID and OD scale and deposits.


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Drum Cracking:

The durability of steam drums, relative to other boiler components, cannot be

attributed to stable, low-stress operations: They operate in a very dynamic mode, especially

during major transients. Aging, combined with cyclic duty, is beginning to take its tollthe

incidence of cracking is increasing for units 30 years and older.

Fig 3.5 Drum Cracking

Grinding and localized weld repair can address initial cracking problems, but

extensive drum cracking poses a threat to the structural integrity and continued safe and reliable

operation of the unit. Pressure stresses and the environmental influence of corrosion fatigue play

the dominant role in drum cracking for both types of boilers.


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CHAPTER 4

INTRODUCTION TO FAILURE MODE

EFFECTS AND CRITICALITY ANALYSIS


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INTRODUCTION TO FAILURE MODE EFFECTS AND CRITICALITY ANALYSIS

CONDUCT FMECA :

The next step is to conduct FMECA analysis on each boiler tubes of the thermal power

plat, which can be done as follows:

Failure Modes and Effects Analysis (FMEA) is a simple analysis method to reveal

possible failures and to predict the failure effects on the system as a whole..If we describe or

rank the criticality of the various failures in the FMEA, the analysis is often referred to as an

FMECA (Failure Modes, Effects and Criticality Analysis). The criticality is a function of the

failure effect and the frequency/probability as seen below. To ensure a systematic study of the

system, a specific FMEA form is used. The FMEA form may for example include the following

columns:

IDENTIFICATION:

Here the specific component is identified by a description and/or number. It is also

common to refer to a system drawing or a functional diagram. The function of the component,

i.e. its working tasks in the system, is briefly described. The state of the component when the

system is in normal operation, is described.

FAILURE ZONES:

All the possible ways the components can fail to perform its function are listed in

this column. Only the failure modes that can be observed from outside are included. The

internal failure modes are to be considered as failure causes.

Effect on other units in the system:In those cases where the specific failure mode affects

other components in the system, this is stated in this column. Emphasis should be given to

identification of failure propagation, which does not follow the functional chains of the

functional diagrams.

EFFECT ON SYSTEM:

In this column, we describe how the system is influenced by the specific failure

mode. The operational state of the system as a result of failure is to be expressed, for example,

whether the system is in the operational state, changed to another operational mode, or not in an

operational state.


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Corrective measures:

Here we describe what has been done or what can be done to correct the failure,

or possibly to reduce the consequences of the failure. We may also list measures that are aimed

at reducing the probability that the failure will occur.

FAILURE EFFECT RANKING:

The failure is ranked according to its effect with respect to reliability and

safety, the possibilities of mitigating the failure, the length of the repair time, the production loss,

etc. We might for example use the following grouping of failure effects:

Level C:A failure that does not reduce the functional ability of the system more than normally is

accepted.

Level B:A failure that reduces the functional ability of the system beyond the acceptable level,

but the consequences can be corrected and controlled.

Level A:A failure that reduces the functional ability of the system beyond the acceptable level

and which creates an unacceptable condition, either operational or with respect to safety.

Remarks: Here we state, for example, assumptions and suppositions. By combining the failure

frequency (probability) and the failure effect (consequence), the criticality of the specific failure

mode is determined.

4.1FMECA FOR BOILER-1 TUBES:

Boiler tubes are used to convert water into steam.It is havig we have conduct the

FMECA and results are shown table

Table 4.1 FMECA for Boiler-1 Tubes

S.NO Failure

zone

Level of

probability

occurrence

Failure

cause

Failure

effect

Remedies

1 Near LHSwater wall

screen tube

B Overheatingof boilers

Hazardousproblem

Hard facingdone and

tubechanged

2 RHS

economizer B Due to

Fuction of

economizer

Replacement

tubes


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upper bank

lower tubes

corrosion decreases

3 Failure of

water wall

at 39 mtrs

height

A Continuous

overheating

Decreases

efficiency

Replacement

with new

tubes

4 Economizer

lower bank

lower side

C

Due to

erosion

steam

temperature

decreases

Economizer

coil bends

are changed

After conducting the FMECA for boiler-1 tubes we found that the main causes to failure

of tubes are water wall tubes and economizer tubes and remedies are shown in table 4.1.

4.2

FMECA FOR BOILER-2 TUBES:

Boiler tubes are supply water to the boiler and converts steam.As like above we have

conduct the FMECA and results are shown table


S.NO Failure

zone

Level of

probability

occurrence

Failure

cause

Failure

effect

Remedies

1 Water wall

screen tube C

Overheating

of boilers

Steam

temperature

increases

Water wall

screen tubes

are replced

2 Furnace

area A Due to

overheating

Boiler may

stops

Hard facing

done

3 Economizer

lower bank C

Continuous

overheating

Economizer

may stops

Replacement

with new

tubes

4 Super

heater

upper zone

C

Due to

erosion

Super

heater may

stops

Replaced

with new

tubes


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After conducting the FMECA for boiler-2 tubes we found that the main causes to

failure of tubes are water wall tubes and economizer tubes and remedies are shown in table 4.2.


Boiler tubes supplies high temperature steam to superheater.As like above we have

conduct the FMECA and results are shown table


S.NO Failure

zone

Level of

probability

occurrence

Failure

cause

Failure

effect

Remedies

1 Wall soot

blower

C Pin holes

developed

Leakage of

flue gases

Welding is

done

2

Economizer A Due to

erosion

Parts

damaged

New tubes

are placed

3 Water wall

buck stays B

Due to

high

pressure

Temperature

decreases

Pad welding

done

4 Super

heater

lower bank

B

Due to

erosion

Temperature

of steam

reduces

Tubes were

replaced

After conducting the FMECA for boiler-3 tubes we found that the main causes to failure

of tubes and remedies are shown in table 4.3


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4.4 FMECA FOR BOILER-4 TUBES:

Boiler tubes are supply water to the boiler and converts steam.As like above we

have conduct the FMECA and results are shown table


S.NO Failure

zone

Level of

probability

occurrence

Failure

cause

Failure

effect

Remedies

1 Tube

leakages A

Due to

hydrogen

damage

Boiler

functions

decreases

Replacement

of tubes

2 Water wall

screen

tubes fails

B

Due to

erosion

Temperature

of steam

decreases

Window

welding to

failed tubes

3 LHS super

heater

upper coil

A Overheating

of steam

Tube

efficiency

decreases

Tubes and

coils was

chaged

After conducting the FMECA for boiler-4 tubes we found that the main causes to

failure of tubes and remedies are shown in table 4.4


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Boiler tubes are supply water to the boiler and converts steam.As like above we

have conduct the FMECA and results are shown table


S.NO Failure

zone

Level of

probability

occurrence

Failure

cause

Failure

effect

Remedies

1 Corner-4

water wall

Area

A

Due to

power

disturbance

Boiler

stops

Power

disturbance

rectified

2 Corner-4

steam

cooled

waterwall

header area

B Due to high

temperature

Steam

temperature

increases

Bend

replaced

3 Economizer

inlet header A

More

supply of

steam

Tubes

efficiency

decreases

All 3 tubes

replaced

4 Water wall

sootblower

failure

C

Due to

high

temperature

Reduces

steam

temperature

Window

welding

done

After conducting the FMECA for boiler-5 tubes we found that the main causes

to failure of tubes are water wall tubes and economizer tubes and remedies are shown in table

4.5


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4.6 RESULTS FROM FMECA:

After conducting FMECA analysis, the following failure modes have been found as

critical and needs immediate action:

1) In boiler-1 tubes have more failures has been found in water wall screen tubes due

corrosion remedies for this problem is regularly check the boiler thoroughly and maintain

constant temperature.

2) In boiler-2 tubes the main failures are boiler tubes due to high temperature for this have

to maintain the temperature.

3) In boiler-3 tubes mostly failures occurs at super heater tubes and economizer tubes due

corrosion and erosion of the parts the remedies for this problem replace the tubes.

4) In boiler-4 tubes failures obtained due overheating of boilers and so the steam

temperature increases then the leakages are raised. The remedy for this is the

maintenance of boiler tubes the required temperature.

5) In boiler-5 tubes water wall tubes are failed due to corrosion, erosion and scale formation

remedy for this check water walls regularly.


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CHAPTER 5

RELIABILITY EVALUATION OF

BOILER TUBES


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RELIABILITY ANALYSIS OF BOILER TUBES:

In the present chapter, reliability analysis has been performed for boiler tubes. In this

work two methods namely empirical or non parametric and Weibull or parametric methods are

employed. In this work, first empirical method is used for reliability assessment process.

INTRODUCTION:

The primary problem associated with reliability assessment is the selection and

specification of the most appropriate reliability model. This requires the collection and analysis

of failure and repair data in order to empirically fit the model to the observed failure or repair

process. The derivation of the reliability and maintainability models is an application of the

probability theory, whereas the collection and analysis of the failure and repair data are primarily

an application of descriptive and there are two general approaches to fitting reliability

distributions to failure data. The first and usually preferred method is to fit a theoretical

distribution such as normal, exponential, lognormal and weibull. The second is to derive directly

from directly from the data an empirical reliability function or Probability density function

function. The later method is also called as Distribution Free method and it is very easy to

conduct for the analysis. The objective of this method is to derive directly from the failure and

repair times, the failure and repair times, the failure distribution, reliability function and

Probability density function functions.

5.1 Reliability analysis using empirical method:

In the present study, initially the empirical method has been considered for the reliability

assessment of the boiler tubes as follows:

The generation or the observation of failure (or repair) times can be represented by

t1,t2,t3,tn where ti represents the time of failure of the ithunit. It is assumed that each failure

represents an independent sample from the same population. The population is the distribution of

all possible failure time and may be represented by f(t),R(t),F(t) or (t).The basic problem is to

determine the best failure distribution implied by the n failure times comprised in the sample. In

all cases the sample is assumed to be a simple random(or probability) sample. A simple random

sample is one in which the failure or repair rates are independent observations from a common

population. If f(t) is the probability density function of the underlying population then f(ti) is the


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probability density function of the ith sample value. Therefore, if the sample consists of

nindependent values, the joint probability distribution of the sample is the product of n identical

and independent probability distributions, or

ft1,t2,tn(t1,t2,.tn)=f(t1)f(t2)f(tn)

Empirical methods of analysis are also referred to as nonparametric methods or

distribution free methods. The objective is to derive directly from failure times, the failure

distribution, reliability function and Probability density function function. Generally the

parametric approach consisting of fitting a theoretical distribution is preferred. This method

however is used in case when no theoretical distribution adequately fits the data. The data here is

Grouped Complete Data.

Grouped Complete Data:

Failure times that have been placed into time intervals, their original values no longer

available, let n1,n2,nk be the no. of units having survived at the ordered times t1,t2,..tk

respectively. Then a logical estimate for R(t) is

R(ti)=ni/n i=1,2,k

When n is the no. of units at risk at the start of the test. Because of the larger sample size

of the grouped data, it is generally unnecessary to obtain more precise estimates by considering

plotting positions.

Following are the terms associated with empirical method and data collection:

(1)RELIABILITY: It is defined to be the probability that a component or system will

perform a desired function for a given period of time when used under stated operating

conditions. It is denoted by symbol R(t). and is expressed by the formula: R(ti)=ni/n

(2)FAILURE DENSITY: The cumulative failure distribution or the probability density

function of the failure of the component at that particular instant of time. It is denoted by

symbol f(t) and is expressed by the formula: f(t)=(ni-ni+1)/{(ti+1-ti)*n}

(3)

PROBABILITY DENSITY FUNCTION FUNCTION: It is also known as instantaneous

Probability density function function or failure rate function. It is denoted by (t) and

provides an alternative way of describing the failure distribution. It is expressed by the

formula:


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(t)=(ni-ni+1)/{(ti+1-ti)*ni}

Data Collection And Analysis:

In the present study, the data regarding failure rates of the boiler tubes in the processing

industry has been collected from the maintenance log books. The failure rates have been

analyzed both theoretically and graphically as follows:

By using the above formulas and steps of empirical method, the reliability modeling and

analysis using empirical method has been performed and results are shown as below.

MODEL CALCULATIONS:

Sample calculations for the BOILER-1 tubes have been conducted using formulas as follows:

Reliability R(ti) = ni/n

Failure density f(t) = (ni-ni+1)/(ti+1-ti).n

Probability density function (t) = f(t)/R(t) = (ni-ni+1)/(ti+1-ti).ni

Where ni (i= 1,2,..k) =no.of.units survived at time ti (i=1,2,.k)

n = no.of.units at risk at the start of the test.

Reliability R(3) = ni/n= 17/20 = 0.85

Failure density f(3) = (ni-ni+1)/(ti+1-ti).n = (17-12)/(18-12).20 = 0.041666667

Probability density function (3) = f(t)/R(t)= 0.04166667/0.85 = 0.049019608

5.2 RELIABILITY ANALYSIS OF BOILER-1 TUBE:The boiler tubes are used to allow water to flow and by supplying heat outside of tubes

the water converted into steam. The calculations of reliability, failure rate, probability density

functions are listed in below table and graphs for variation of reliability, failure rate and f(t) are

shown with respect to time as shown in table 5.1

Table 5.1 Reliability analysis for boiler-1 tube

Time

No. of

failures

No. of

survivals Reliability Failure rate Probability

density

function

0 0 11 1 0.0075 0.0075

12 1 10 0.9 0.0303 0.0336


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24 4 6 0.54 0.015 0.027

36 2 4 0.36 0.0075 0.0208

48 1 3 0.27 0.0075 0.0277

After calculation of reliability, failure rate and f(t) for boiler-1 tubes, results are plotted.

Reliabilty Graph:

Fig 5.1:Reliabilty Graph for boiler tubes

Fig 5.1 shows that the reliability of boiler-1 tube decreases with time.

Failure Rate Graph:

Fig 5.2: Failure rate graph of boiler-1 tube

Fig 5.2 shows that the failure rate is increasing with time upto some time after that it decreases.


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Probability Density Function Graph:

Fig 5.3: Probability density function graph for boiler-1 tube

Fig 5.3 shows the variation of Probability density function with respect to time. Probability

density function increases with time.

5.3 RELIABILITY ANALYSIS OF BOILER-2 TUBES:

Here we use water tube boilers it is a type of boiler in which water circulates in tubes heated

externally by the fire. Fuel is burned inside the furnace, creating hot gas which heats water in the

steam-generating tubes. In smaller boilers, additional generating tubes are separate in the

furnace, while larger utility boilers rely on the water-filled tubes that make up the walls of the

furnace to generates steam. The calculations of reliability, failure rate, probability density

functions are listed in below table and graphs for variation of reliability, failure rate and f(t) are

shown with respect to time as shown below.

Table 5.2: Reliability analysis for boiler-2 tube

Time No.of

failures

No.of

Survivals Reliability Failure rate Probability

density

function

0 0 15 1 0.0222 0.0222

12 4 11 0.73 0.0277 0.0379

24 5 6 0.4 0.00606 0.01515

36 1 5 0.33 0.00606 0.0183

48 1 4 0.26 0.0166 0.0638


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After calculation of reliability, failure rate and f(t) ,Probability density function for boiler-2 tubes

results are plotted in graph.

Reliabilty Graph:

Fig 5.4: Reliabilty Graph for boiler-2 tube

From fig 4.4 we found that reliability for boiler-2 tube decreases with time.

Failure Rate Graph:

Fig 5.5: Failure rate graph for boiler tube-2From Fig 5.5 we observe that failure rate increases for some time after that it decreases with

time.


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Fig 5.6: Failure density graph for Boiler-2 Tube

Above figure shows that Probability density function increases with time.


Table 5.3:Reliability analysis for Boiler-3 tube

Time No.of

Failures

No.of

survivals Reliability Failure rate Probability

density

function

0 0 6 1 0.0277 0.0277

12 2 4 0.666 0.0138 0.0207

24 1 3 0.5 0.0138 0.0276

36 1 2 0.333 0.0138 0.0414

48 1 1 0.166 0.0138 0.0828

After calculation of reliability, failure rate and f(t) ,Probability density function for boiler-3 tubes

results are plotted


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Reliabilty Graph :

Fig 5.7: Reliabilty Graph for boiler 3 tube

From fig 5.7 we found that reliability for boiler tube decreases with time.

Failure Rate Graph:

Fig 5.8: Failure rate graph for Boiler-3 tube

From fig 5.8 we found that failure rate for boiler tube decreases with time for some time period

after that it is constant.


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Fig 5.9: Probability density function graph for Boiler-3 tubeFrom fig 5.9 shows variations in rhe Probability density function with time and it is increases

with time.


Table 5.4 Reliability analysis for boiler-4 tube

Time No. of

failures

No. of

survivals

Reliability Failure rate Probability

density

function

0 0 11 1 0.0075 0.0075

12 1 10 0.909 0.0151 0.0166

24 2 8 0.727 0.0151 0.0207

36 2 6 0.545 0.0378 0.0693

48 5 1 0.0909 0.0075 0.0833

After calculation of reliability, failure rate and f(t) ,Probability density function for

boiler-4 tubes results are plotted in graphs.


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Reliabilty Graph:

Fig 5.10: Reliabilty Graph for boiler-4 tube

From fig 5.10 we found that Reliability for boiler tube decreases with time.

Failure Rate Graph:

Fig 5.11: Failure rate graph for boiler-4 tube

From the fig 5.11 it is found that the failure rates are increases for some time period and after

that it decreases.


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Fig 5.12: Probability density function graph for Boiler-4 tube

From the fig 5.12 it is found that the failure rate increases with time.


Table 5.5: Reliability analysis for Boiler-5 tube

Time No. of

failures

No.of

survivals


density

function

0 0 10 1 0.016 0.01612 2 8 0.8 0.025 0.031

24 3 5 0.5 0.025 0.05

36 3 2 0.2 0.0083 0.041

48 1 1 0.1 0.0083 0.083

After calculation of reliability, failure rate and f(t) ,Probability density function for

boiler-5 tubes results are plotted in graphs.


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Reliabilty Graph:

Fig 5.13: Reliabilty Graph for boiler -5 tubeFrom fig 5.13 we found that Reliability for boiler tubes decreases with time.

Failure Rate Graph:

Fig 5.14: Failure rate graph for boiler-5 tube

From the fig 5.14 it is found that the failure rate increases with time for some period and after

that it decreases.


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Probability Density FunctionGraph:

Fig 5.15: Probability density function graph for boiler-5 tube

Fig 5.15 shows the variation of Probability density function with respect to time and it is

increases with time.

5.7 SYSTEM RELIABILITY USING EMPERICAL METHOD:

System Availability is calculated by modeling the system as an interconnection of parts

in series and parallel. The following rules are used to decide if components should be placed in

series or parallel:

If failure of a part leads to the combination becoming inoperable, the two parts are

considered to be operating in series

If failure of a part leads to the other part taking over the operations of the failed part, the

two parts are considered to be operating in parallel.

(1) Reliability in Series

As stated above, two parts X and Y are considered to be operating in series if failure of either of

the parts results in failure of the combination. The combined system is operational only if both

Part X and Part Y are available. From this it follows that the combined reliability is a product of

the reliability of the two parts. The combined reliability is shown by the equation below:


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(2) Reliability in Parallel:

Two parts are considered to be operating in parallel if the combination is considered

failed when both parts fail. The combined system is operational if either is available. From this

it follows that the combined reliability is 1 - (both parts are unavailable). The combined

reliability is shown by the equation

Combined series parallel Operation :

In such systems where failure of a component leads to some users loosing service, system

reliability has to be defined by considering the percentage of users affected by the failure. The

reliability for this system can be computed by calculating A(p,q) as specified below:

A(p,q) = C(q,p) * A^(q-p) * (1-A)^p

Here pis the number of failed units and qis the total number of units.

The present system is system of combined series and parallel systems and the Reliability Block

Diagram for the present processing industry is as follows:

Fig 5.13 Reliability Block Diagram for WATER TUBE BOILERS IN TPP using empiricalmethod.


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BOILER-1 BOILER-2 BOILER-3 BOILER-4

BOILER-5

Fig 5.16: boilers in series

E1 = The event that component 1 does not fail


Then P(E1)=R1 and P(E2)=R2

Where R1= The reliability of component 1

Where R2= The reliability of component 2

Therefore Rs = P(E1E2) = P(E1) P(E2) =R1 R2 assuming that the two components are

independent.

Generalizing to n mutually independent components in series, then

Rs(T) = R1(t)*R2(t)**Rn(t) < min {R1(t),R2(t),,Rn(t)}

Generalizing to n mutually independent components in parallel, then

Rs=P(E1UE2) = 1- P(E1UE2)c

= 1-P((E1cUE2

c) = 1-P((E1

c)P(E2

c)) = 1-(1-R1)(1-R2)

For combined series and parallel systems both these formulas are used.The System Reliability is calculated as follows:

For boiler-1 tube:

R(1)=0.614

For boiler-2 tube:

R(2)= 0.5464

For boiler-3 tube:

R(3)= 0.533

For boiler-4 tube:

R(4)= 0.654

For boiler-5 tube:

R(5)= 0.5234


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The complete system is now in combined series and parallel combination system. So, the system

reliability is given as:

R(s)= [R(1)R(5)]* [R(2)R(5)]*[R(3)R(5)]*[R(4)R(5)]

=[1-(1-R(1))(1-R(5)]*[1-(1-R(2)(1-R(5)]*[1-(1-R(3))(1-R(5)]*[1-(1-R(4)(1-R(5)]

=0.816*0.783*0.777*0.835 = 0.4113

It is found from the above analysis by using empirical method the system reliability is 0.4113.


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CHAPTER 6

RELIABILITY EVALUATION BY

PARAMETRIC METHOD


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6.1 INTRODUCTION TO PARAMETRIC METHOD:

In this work the next step is to evaluate the system reliability using parametric method.

In parametric method there are four types of distributions which are explained as follows.1) Normal Distribution

2) Lognormal Distribution

3) Exponential Distribution

4) Weibull method

6.1.1 Introduction to Normal Distribution:

In probability theory, the normal (or Gaussian) distribution is a continuous

probability distribution that has a bell-shaped probability density function, known as the

Gaussian function or informally the bell curve.

Where parameter is the mean or expectation (location of the peak) and is the variance.

is known as the standard deviation. The distribution with = 0 and 2 = 1 is called the

standard normal distribution or the unit normal distribution. A normal distribution is often used

as a first approximation to describe real-valued random variables that cluster around a single

mean value. The normal distribution is considered the most prominent probability distribution in

statistics. There are several reasons for this:[1] First, the normal distribution is very tractable

analytically, that is, a large number of results involving this distribution can be derived in

explicit form. Second, the normal distribution arises as the outcome of the central limit theorem,

which states that under mild conditions the sum of a large number of random variables is

distributed approximately normally. Finally, the "bell" shape of the normal distribution makes it

a convenient choice for modelling a large variety of random variables.

The probability density function (pdf) of a random variable describes the relative frequencies of

different values for that random variable. The pdf of the normal distribution is given by the

formula explained in detail in the previous section:


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This is a proper function only when the variance 2 is not equal to zero. In that case this

is a continuous smooth function, defined on the entire real line, and which is called the

"Gaussian function".

Properties:

Function f(x) is uni modal and symmetric around the point x = , which is at the same

time the mode, the median and the mean of the distribution.

The inflection points of the curve occur one standard deviation away from the mean (i.e., at x =

and x = + ).

Function f(x) is log-concave.

The standard normal density (x) is an Eigen function of the Fourier transform.

The function is super smooth of order 2, implying that it is infinitely differentiable. The first

derivative of (x) is (x) = x(x); the second derivative is (x) = (x2 1)(x). More

generally, the nth

derivative is given by (n)(x) = (1)nH

n(x)(x), where Hn is the Hermite

polynomial of order n

6.1.2 Introduction to Lognormal Distribution:

In probability theory, a log-normal distribution is a continuous probability distribution of

a random variable whose logarithm is normally distributed. If X is a random variable with a

normal distribution, then Y = exp(X) has a log-normal distribution; likewise, if Y is log-normallydistributed, then X = log(Y) is normally distributed. (This is true regardless of the base of the

logarithmic function: if log(Y) is normally distributed, then so is logb(Y), for any two positive

numbers a, b 1.)Log-normal is also written log normal or lognormal. It is occasionally referred


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astheGaltondistributionor,Galton'sdistribution.

6.1.3 Introduction to Exponential Distribution:

In probability theory and statistics, the exponential distribution (a.k.a. negative

exponential distribution) is a family of continuous probability distributions. It describes the time

between events in a Poisson process, i.e. a process in which events occur continuously and

independently at a constant average rate.

Note that the exponential distribution is not the same as the class of exponential families ofdistributions, which is a large class of probability distributions that includes the exponential

distribution as one of its members, but also includes the normal distribution, binomial

distribution, gamma distribution, Poisson, and many others.


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6.1.4 Introduction to Weibull method:

In probability theory and statistics, the Weibull distribution is a continuous probability

distribution. It is named after WaloddiWeibull, who described it in detail in 1951, although itwas first identified by Frchet (1927) and first applied by Rosin &Rammler (1933) to describe

the size distribution of particles.

The probability density function of a Weibull random variable x is:

where k > 0 is the shape parameter and > 0 is the scale parameter of the distribution. Its

complementary cumulative distribution function is a stretched exponential function. The Weibull

distribution is related to a number of other probability distributions; in particular, it interpolates

between the exponential distribution (k = 1) and the Rayleigh distribution (k = 2).


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Fig 6.1 :Probability Distribution fitting curve for boiler-1 tube

The parameters obtained from the above figure are =0.5342, =2.0123by using

these parameters reliability, failure rate and f(t) have been calculated according to Weibull

distribution. And results have been shown in table.

Table 6.1: Reliability of boiler-1 tube

time number of

failures

reliability failure rate f(t)

0 0 1 0.265 0.265

12 1 0.873 0.100 0.115

24 4 0.43 0.035 0.083

36 2 0.32 0.022 0.069

48 1 0.15 0.009 0.060

By using the obtained results the graphs have been plotted for reliability, failure rate and

probability distribution with respect to time.


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Reliability Graph:

Fig 6.2: Reliabilty Graph for boiler tube using Parametric method

Here from fig we can observe that reliability decreases with increase of time.

Failure Rate Graph:

We take the values from table and drawn the graph between failure rate and time.

Fig 6.3 Failure rate graph for boiler tube using parametric method

From figure 6.3 we can say that failure rate decreases with time increases.


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Fig 6.4: Probability density function graph for boiler-1 tube using Parametricmethod

From the above figure graphical analysis it is observed that reliability is decreases as the

time increase.

6.3 PARAMETRIC ANALYSIS OF BOILER-2 TUBES:


The parameters obtained from the above figure are =0.4982, =2.6322 by using

these parameters reliability, failure rate and f(t) have been calculated according to Weibull

distribution. And results have been shown in table.


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Table 6.2 reliability analysis of boiler-2 tube using parametric method

time number of

failures


0 0 1 0.1891 0.1891

12 3 0.75 0.0666 0.0883

24 4 0.45 0.0280 0.0623

36 2 0.35 0.0177 0.0508

48 1 0.28 0.0123 0.0440


probability distribution with respect to time.

Reliability Graph:

Fig 6.6 Reliabilty Graph for boiler-2 tube using parametric method

Fig 6.6 shows the reliability decreases with increases in time.


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Failure Rate Graph:

Fig6.7 Failure rate graph for boiler-2 tube using parametric method

Here observe that failure rate decreases with time increases.


From table 6.2 drawn the graph between Probability density function and time in months.

Fig 6.8: Probability density function graph for boiler-2 tube using Parametric method

From the above graphical analysis it is observed that Probability density function is

decreases as the time increase.


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The parameters obtained from the above figure are =0.6598, =1.1129 by using these

parameters reliability, failure rate and f(t) have been calculated according to Weibull distribution.

And results have been shown in table.

Table 6.3 reliability analysis of boiler-3 tube using parametric method

Time number of

failures


0 0 1 0.5921 0.5921

12 2 0.69 0.1815 0.2631

24 3 0.55 0.1142 0.2077

36 2 0.37 0.0664 0.1809

48 1 0.24 0.0328 0.1640


Probability density function with respect to time.


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Reliabilty Graph:

Fig 6.10 Reliabilty Graph for boiler-3 tube using parametric methodHere the reliability is decreases with time.

Failure Rate Graph:

Fig 6.11 Failure graph for boiler-3 tube using Parametric method

Here failure rate decreases with time.


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Probability Density Function:

Fig 6.12 Probability density function graph for boiler-3 tube using parametric method

Here Probability density function decreases with increase in time.







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Table 6.4: Reliability analysis of boiler-4 tube

time number of

failures

Reliability failure rate f(t)

0 0 1 0.274 0.2741

12 2 0.925 0.108 0.1178

24 3 0.752 0.064 0.0854

36 2 0.602 0.042 0.0707

48 1 0.152 0.009 0.0619

Reliabilty Graph:


Fig 6.14 shows the reliability decreases with time

Failure Rate Graph :


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Fig 6.15 shows failure rate decreases with time


Fig 6.16 Probability density function Graph for boiler-4 tube using parametric method

Fig 6.16 shows the Probability density function decreases with time


Fig 6.17:Probability Distribution fitting curve for boiler-5 tube





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Table 6.4 Reliability of boiler-5 tube using parametric method

Time Number of

failures


density function

0 0 1 0.298 0.298

12 2 0.87 0.112 0.129

24 3 0.62 0.058 0.094

36 3 0.26 0.020 0.079

48 1 0.12 0.088 0.689

From the table we have drawn the graphs between time and reliability,failure rate, hazard rate

Reliabilty Graph:

Fig6.18 Reliabilty Graph for boiler-5 tube using parametric method

Here reliability decreases with time.

Failure Rate Graph:


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Fig 6.19 failure rate Graph for boiler-5 tube using parametric method

Here failure rate decreases with increase of time


Fig 6.20 Probability density function Graph for boiler-5 tube using parametric method

Here Probability density function decreases and then increases with increase of time

6.10 SYSTEM RELIABILITY USING PARAMETRIC METHOD:



Then P(E1)=R1 and P(E2)=R2

Where R1=the reliability of component 1

Where R2=the reliability of component 2

Therefore Rs = P(E1E2) = P(E1) P(E2) =R1 R2 assuming that the two components are

independent.

Generalizing to n mutually independent components in series, then

Rs(T) = R1(t)*R2(t)**Rn(t) < min {R1(t),R2(t),,Rn(t)}

Generalizing to n mutually independent components in parallel, then

Rs=P(E1UE2) = 1- P(E1UE2)c = 1-P((E1cUE2c

= 1-P((E1c)P(E2c)) = 1-(1-R1)(1-R2)

For combined series and parallel systems both these formulas are used.

The System Reliability is calculated as follows:

For boiler-1 tubes


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R(1)=

For boiler-2 tubes

R(2)=0.4059

For boiler-3 tubes

R(3)=

For boiler-4 tubes

R(4)=Total system reliability R(s) = [R(1)R(5)]* [R(2)R(5)]*[R(3)R(5)]*[R(4)R(5)]

=[1-(1-R(1))(1-R(5)]*[1-(1-R(2)(1-R(5)]*[1-(1-R(3))(1-R(5)]*[1-(1-R(4)(1-R(5)]

=

6.12 COMPARITIVE ANALYSIS BETWEEN EMPIRICAL AND PARAMETRIC

METHODS:

In this work a comparative analysis have been performed between empirical method and

parametric method to identify which method is best suitable and all the machines reliabilities

which are calculated as earlier are shown below.

Comparison of reliability:

Table 6.6 Comparison of Reliability by Empirical and Parametric methods

S.NO

NUMBER OF

BOILER TUBES

RELIABILITY BY

EMPIRICAL

METHOD

RELIABILITY BY

PARAMETRIC

METHOD

1 BOILER-1 TUBE 0.614 0.564

2 BOILER-2 TUBE 0.5464 0.567

3 BOILER-3 TUBE 0.5334 0.562

4 BOILER-4 TUBE 0.654 0.686

5 BOILER-5 TUBE 0.528 0.588


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Boiler tube-1:

Fig 6.21 Comparison of reliability for boiler-1 tube

Figure shows the reliability of boiler-1 tube. Here reliability by the empirical method is more

than the reliability by parametric method.

Boiler-2 tube:


Figure shows the reliability of boiler-2 tube. Here reliability by the parametric method is more

empirical than the reliability by method.


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Boiler-3 Tube:




Boiler-4 Tube:





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Boiler-5 Tube:




Comparison of failure rates:

Table 6.7 Comparison of Failure rates by Empirical and Parametric methods

S.NO NUMBER OF THE

BOILER TUBES

FAILURE RATE BY

EMPIRICAL

METHOD

FAILURE RATE BY

PARAMETRIC

METHOD

1 BOILER-1 TUBE 0.01646 0.0552

2 BOILER-2 TUBE 0.01663 0.0409

3 BOILER-3 TUBE 0.0829 0.1188

4 BOILER-4 TUBE 0.01662 0.05605

5 BOILER-5 TUBE 0.01653 0.06158

Table shows the failure rates of boiler tube by empirical and parametric methods and failure

rates values more by the parametric method.


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Comparison of Probability density functions:

Table 6.8 Comparison of Probability density functions Empirical and Parametric methods

S.NO NUMBER OF THE

BOILERS TUBES

f(t) BY

EMPIRICAL

METHOD

f(t)

BY PARAMETRIC

METHOD

1 BOILER-1 TUBE

2 BOILER-2 TUBE

3 BOILER-3 TUBE

4 BOILER-4 TUBE

5 BOILER-5 TUBE

Table shows the Probability density functions of boiler tube by using both empirical and

parametric methods and it shows the values are high in parametric method.

System reliability:Table 6.9 System reliability of boilers

RELIABILITY ANALYSIS SYSTEM RELIABILITY

Using Empirical method 0.4114

Using parametric method 0.4722

Table 6.9. shows that the system reliability of boiler tubes is more by the parametric method and

from this it can conclude that the parametric method is the best method when compared to

empirical method for system reliability evaluation process.


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CHAPTER 7

INTRODUCTION TO ANSYS


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ANSYS:

ANSYS is general-purpose finite element analysis (FEA) software package. Finite

Element Analysis is a numerical method of deconstructing a complex system into very small

pieces (of user-designated size) called elements. The software Implements equations that go

Documents

reliability and temperature evaluation of boilers