Process Engineering Equipment Handbook Episode 3 Part 6 ppsx

The primary separation elements vane-type mist extractor or cyclonesection are completely maintenance-free and self-cleaning, with no replacement ormoving parts to cause shutdown.. Havin

Cyclone inlet section. As the mist-laden gas enters the separator, the entrainedliquids and solid particles are subjected to centrifugal force The gas enters thecyclone tube at two points, designated A, and sets up a swirling motion Solid andliquid particles are thrown outwardly and drop from the tube at point B Theswirling gas reverses direction at the vortex C and rises through the exit portion

of the tube, designated D See Fig S-21

Separators S-17

FIG S-20 Horizontal with horizontal lower barrel and vertical configuration (Source: Peerless.)

Mist extractor inlet section (alternate for some applications). As the gas enters the vaneunit, it is divided into many vertical ribbons (A) Each ribbon of gas is subjected tomultiple changes of direction (B) as it follows its path through the vanes Thiscauses a semiturbulence and rolling of the gas against the walls of the vanes (C).The entrained droplets are forced to contact the vane walls where they impinge andadhere to the vane surface (D) This liquid then moves into the vane pockets (E)and out of the gas stream It is then drained by gravity into the liquid reservoir.The collected liquid can then be disposed of as desired See Fig S-22.

Final separation element. The final separation section consists of one or morecylindrical coalescing elements mounted vertically on support tubes The gas andfine mists pass from the inside to the outside of the elements In passing throughthe coalescing elements, the entrained mist particles diffuse and impinge on theclosely spaced surfaces of the element and are agglomerated into larger liquiddroplets The larger liquid droplets emerge on the outer surface of the coalescingelement and run down the sides of the element to the liquid collection chamber Thegas, free of liquid particle entrainment, rises and passes out of the separatorthrough the upper gas outlet nozzle

Design features. Replacement of the final separation elements can be made with aminimum of time and effort through the use of a full opening O-ring or float ringclosure The primary separation elements (vane-type mist extractor or cyclonesection) are completely maintenance-free and self-cleaning, with no replacement ormoving parts to cause shutdown

The absolute separator could be guaranteed to remove 100 percent of all liquidparticles above 3 microns; and, depending on design conditions, it will remove up

to 99.98 percent of all particles less than 3 microns This efficiency is maintainedthroughout the entire flow range to design capacity

S-18 Separators

FIG S-21 Cyclone operation filter/separator See text for key to components (Source: Peerless.)

FIG S-22 Mist extractor section (Source: Peerless.)

The normal pressure drop through the final separation elements is limited bydesign to 5 in of water column or less The pressure drop across the primary sectionwill depend on operating conditions and the type of separation elements used.See Figs S-23 and S-24.

Vane-type separator

Line separators are designed and fabricated to conform fully to all current ASMErequirements and are usually furnished in carbon steel for most industrialapplications; however, units can be fabricated in part or entirely from stainlesssteel, Monel, or other special alloy materials See Figs S-25 and S-26 See also TableS-2

Although standard units are designed for 275- and 720-psi working pressure(412.5- and 1080-lb test pressure), vessels can be furnished in virtually unlimited

Separators S-19

FIG S-23 Mist particle removal chart (Source: Peerless.)

TABLE S-2 Vane-Type Separators

Body Diameter (O.D.) 6 5 / 8 ≤ 8 5 / 8 ≤ 12 3 / 4 ≤ 14 ≤ 16 ≤ 18 ≤ 20 ≤

B Approximate overall height 36 ≤ 38 ≤ 47 ≤ 49 1 / 2 ≤ 52 1 / 2 ≤ 60 ≤ 63 ≤

C Body length, seam-to-seam 29 ≤ 30 ≤ 36 ≤ 38 ≤ 40 ≤ 46 ≤ 48 ≤

D Top head seam centerline inlet and outlet 4 1 / 2 ≤ 4 1 / 2 ≤ 8 1 / 2 ≤ 9 ≤ 9 ≤ 11 ≤ 11 ≤

G Lower head seam to

-0- Liquid capacity (gal.) 2 3 / 4 3 3 / 4 8 1 / 4 11 1 / 16 14 7 / 8 21 21 7 / 8

NOTES :

1 All dimensions are ± 1

/ 4 ≤.

2 Base support is optional.

3 Vessels stocked with design pressure of 275 psig 150# RF and 720 psig 300# RF.

4 Vessels equipped with these accessory fittings:

A 2, 3

/ 4 ≤ 6,000# gauge glass connections.

B 2≤ 3,000# equalizer connection.

C 2≤ 3,000# drain connection (1 1 / 2 ≤ on 6 5 / 8 ≤ and 8 5 / 8 ≤ O.D sizes).

D 2, 1≤ 3,000# high-level shut-down connections on 14≤ O.D and larger sizes.

E 2≤ 3,000# vent connection (1 1

/ 2 ≤ on 6 5

/ 8 ≤ and 8 5

/ 8 ≤ O.D sizes).

FIG S-24 Absolute separator (Source: Peerless.)

S-20

FIG S-25 Vane-type separator performance curves (Source: Peerless.)

FIG S-26 Vane-type separator (external) (Source: Peerless.)

S-21

S-22 Separators

ratings for greater pressures if required (pressures in the 20,000-lb range are notuncommon)

Vertical gas separators

These vessels employ many physical means to separate the liquids from gases

in addition to the mist extractor Foremost among these various separation forcesare: impingement, centrifugal force, gravitational force, and surface tension SeeFig S-27

Inlet baffle. Of prime importance to the separation is the inlet impingement baffle,which acts to eliminate heavy slugging problems set up by excess amounts of liquid

in the stream See Fig S-28 As the slugs of liquid come into contact with the baffle,they are deflected at an angle and are broken up by a hooked vane attached to theedge of the baffle This breaking up of the slugs causes them to drop out of thestream and to the bottom of the separator The baffle is made of extra thick material

to protect against excess erosive wear

Rise to mist extractor. Having removed a majority of the entrained liquid or slugs,the gas flow continues its travel to the mist extractor that is above the inlet baffle.During this travel, a centrifugal and gravitational action takes place that separatesmore of the entrained liquid The distance the vapor (gas and liquid) must rise toenter the mist extractor aids in the separation by supplying time necessary topermit coalescing or the forming of small droplets into larger drops that have agreater rate of fall than the upward velocity of the gas By this method, maximumseparation, using impingement, centrifugal motion, and gravity, has been obtainedwith a minimum pressure drop

This settling effect, utilized in the vertical gas separator, removes all but a verysmall portion of the liquid This remaining liquid continues to rise toward the gasoutlet in the form of a fine spray To solve this final separation problem, the mistextractor is used

Mist extractor. The mist extractor combines maximum scrubbing area with anabsolute minimum pressure drop It utilizes the forces of impingement, centrifugalmotion, and surface tension to obtain its high efficiency See Fig S-29

The path of the gas through the unit is constantly bending, causing theimpingement of the liquid droplets against the walls of the vane, separating some

of the entrained mist Centrifugal force aids by throwing the heavier liquid dropletsout of the main gas stream and impinging them on the scrubbing surface Theentrained liquid, after coming into contact with the metal surface and other liquiddroplets of the vane unit, is coalesced and adheres to the vane surface by utilizingthe forces of surface tension Gravity and impact of the gas stream then drives thedroplets into the pockets provided at each turn of the vane where they roll downout of the gas stream After going through the complete process of scrubbing andseparation, the gas finally reaches the outlet opening of the separator clean anddry

Liquid control. The large liquid reservoir is adequate to store incoming slugs ofliquid during the time required for opening the liquid valve The volume of thevessel is large enough to allow the gas to break out of the solution and to escapethe liquid in the bottom of the separator

Separators S-23

FIG S-27 Vertical gas separator (Source: Peerless.)

S-24 Separators

Line separators

The vane-type line separator offers efficient separation of entrained liquids from agas or vapor stream This separator design has been used successfully for over 25years in chemical plants, refineries, natural gas pipelines, and all types of industrialprocessing plants where efficient liquid-gas separation has been required See Figs.S-30 and S-31

These separators incorporate the vane-type mist extractor as the separatingelement This unit offers a number of operating characteristics not found in othertypes of separators:

 100 percent removal of all entrained droplets 8–10 microns and larger

 Extremely low pressure drop—less than 6 in of water column

 Small housing requirement for ease of installation and economy

 Flat efficiency curve with no decrease in efficiency from rated capacity down tozero flow

FIG S-29 Mist extractor (Source: Peerless.) FIG S-28 Interbuffer—vertical gas separator (Source: Peerless.)

Separators S-25

FIG S-30 Line separator installation (Source: Peerless.)

Principle of operation. The vane unit is the heart of the separator (see Fig S-32)

As the gas enters the vane unit, it is divided into many vertical ribbons (A) Eachribbon of gas is subjected to multiple changes of direction (B) as it follows its paththrough the vanes This causes a semiturbulence and rolling of the gas against thewalls of the vanes (C) The entrained droplets are forced to contact the vane wallswhere they impinge and adhere to the vane surface (D) This liquid then moves intothe vane pockets (E) and out of the gas stream where it is drained by gravity intothe liquid reservoir The collected liquid can then be disposed of as desired

It is significant to note that the liquid drainage in the vane-type mist extractordiffers from the drainage in other impingement-type mist extractors, in that vanedrainage occurs with the liquid out of the gas flow and at a right angle to thedirection of flow through the separator

The individual vane corrugations, depth and size of the liquid pockets, and thevane spacing are critical features of the vane-type mist extractor Many years oftesting and operating experience eventually arrive at optimum dimensions andspacing The slightest variation in any one of these three features will materiallydecrease the capacity and performance of this type of separator

Efficiency and capacities. The vane-type line separator (see Fig S-33) will removeall of the entrained liquid droplets that are 8–10 microns and larger The efficiency

of the unit decreases on droplet sizes less than 8 microns as shown on the chart

In order to separate these smaller droplets, the separator must be preceded by anagglomerating or coalescing device to increase the size of the droplets so that theycan be removed by the mist extractor Several types of agglomerating devices areavailable Some of these are capable of achieving efficiencies as high as 991

/2percentremoval of 1 micron size droplets

Low-pressure drop. Since the vane-type mist extractor is self-cleaning and contains

no small openings that can fill up and restrict the flow—such as are present in wiremesh pads or filter screens—the pressure drop across the separator is very low Thedrop is as small as 2–3 in of water in the larger sizes

Vari-line separators. Vari-line separators are specifically designed for thoseinstallations where space is at a premium and piping limitations prevent the use

S-26 Separators

LINE SEPARATOR FIG S-31 Line separator (Source: Peerless.)

of a straight pattern line separator, which has the gas inlet and outlet connections

on the same horizontal centerline These units consist of the vane-type mistextractor with internal baffling designed to permit virtually any combination oflocations for the gas inlet and gas outlet connections The principle of operation andperformance characteristics for the vari-line separators are the same as thosedescribed for the straight pattern line separator

Typical inlet and outlet connections are: side in–top out, side in–bottom out, topin–side out, top in–bottom out, bottom in–side out, and bottom in–top out

High-pressure separators. High-pressure separators are designed for pressures inexcess of 1500 lb There is no upper limit on design pressures Several separatorshave been fabricated with design pressures in excess of 20,000 lb These separatorscontain the vane-type mist extractor and the internal design and principle ofoperation is the same as discussed for the lower pressure units

The pressure vessel housing for these separators can be fabricated using eitherA105 Grade 2 forged steel or A216 WCB cast steel Virtually all of the separatorsnow used in plant designs are fabricated of forged material

These separators have application in any service where high-efficiency separation

of entrained liquids from a gas is required

Horizontal gas separators

Principle of operation. The gas is directed into the inlet separator section (A) (seeFigs S-34 and S-35) where most of the liquid is removed This separated liquiddrains into the first downcomer (B) The remaining liquid is then scrubbed by the

Separators S-27

FIG S-32 Section of vane unit on line separator (Source: Peerless.)

FIG S-33 Line separator performance curve (Source: Peerless.)

S-28 Separators

FIG S-34 Horizontal gas separator (Source: Peerless.)

FIG S-35 Horizontal single barrel design (Source: Peerless.)

mist extractor (C) This entrainment drains into the lower barrel (D) throughdowncomer (E) This second downcomer is submerged in liquid, and this liquid sealprevents the gas from following a path through the lower barrel and bypassing themist extractor.

Advantages of the lower barrel. The lower barrel makes it possible to get theseparated liquid away from the gas flowing in the upper barrel, thus eliminatingreentrainment It also makes possible the installation of larger separation elements

in the upper barrel, which results in a higher capacity The lower barrel alsoprovides a quieting chamber for gas to break out of solution to effect a cleanseparation

Ordinarily, liquid level in the lower barrel is controlled by torque tube level controls and diaphragm-type valves Connections for liquid level gauges, pressuregauges, and drains are provided

Capacities. Horizontal separators have high gas capacities because the mistextractor is installed longitudinally in the vessel This arrangement permits theuse of a large mist extractor inlet area

Mist extractor design. This mist extractor incorporates a series of closely spacedbaffles, which combine impingement, centrifugal force, surface tension, and gravity

to effect separation High capacity and low pressure drop are combined in thisdesign The high efficiency is maintained over the entire range of flow frompractically zero to maximum rated flow

Stacks

Stacks can be used to conduct gases to be flared The lit gas flame can be seen from

the top of the stack in that case This kind of stack may be called a flare stack.

Another kind of stack is a stack that exhausts the gaseous products ofcombustion, including water vapor and carbon dioxide to the atmosphere The mostsevere application stresswise for a freestanding stack might be its use in an offshoreenvironment due to wind loading and additional stress due to wave and watermovement on a platform Although this book is not intended to be a dedicated designtext, it is useful for a process engineer in operations and maintenance to understandwhat to look for in a stack design The following illustrates a stack design that helpscope with these stresses in an offshore environment Note, however, that the designfeatures presented apply to onshore designs as well

The following material* describes the methods developed to optimize themechanical design of a freestanding exhaust stack and its supporting structure.These particular methods have been used for the design of three gas turbineexhaust systems on a UK sector offshore platform currently under construction.The driving force behind the choice of a freestanding stack was to save weight andtherefore cost The move toward the development of marginal fields in deeperwaters will only increase the need for lighter, and therefore more cost-effectivedesign solutions

Stacks S-29

* Source: Altair Filters International Limited, UK Adapted with permission.

Although national standards that cover the basic design philosophy are available,these have serious limitations when applied to this type of structure The aim ofthis section is to demonstrate how the limitations may be overcome by undertakingfundamental design analysis, and also to indicate those critical areas that demandspecial consideration The detailed design analysis presented here considers thepossibility of failure due to local instability, the effect on the dynamic response ofthe flexible foundation provided by the platform, and the determination of thermalstresses at critical locations.

Although this design has been developed for offshore use, the techniques utilizedcan be applied equally to onshore applications

Nomenclature

V s design wind velocity, m/s

w design wind load per unit length of stack, N/m

L = L4 - L3 unsupported height of stack, m

L o = L3 - L2 spacing of upper pinned support, m

D mean diameter of exhaust stack, m

D1 spacing of main bearings, m

k v vertical elastic stiffness of foundation, kN/m

R A , R B and R C transverse support reactions, kN

V vertical reaction at main bearing, kN

t stack section material thickness, mm

s 0.1 percent proof strength of stack material, MN/m

a semiangle subtended by imperfection

n vortex shedding frequency, Hz

S vortex shedding coefficient

x distance along stack axis, m

w s = rpDt2 exhaust stack weight per unit length, kg/m

E elastic modulus of stack material, GN/m

second moment of area of stack section, m4

k elastic stiffness of supporting foundation, kN/m

g acceleration due to gravity, ms-2

r specific weight of stack material, kg m-3

m circular frequency for transverse vibration, rad/s

fundamental frequency in Hz

u o radial displacement at flange/shell intersection, mm

fo rotation at flange/shell intersection

The design of gas turbine exhaust systems on offshore platforms generally fallswithin well-proven parameters The gas-carrying duct is suspended inside anexternal structural steel framework and connected via a system of mounts andguides to allow for thermal growth

Extending the ductwork or stack above the steelwork such that the stack itselfcarries structural loads would appear to be a simple extension of proven designs.When the design of such a system was undertaken in practice, this was shown to

be a long way from the truth

Offshore oil and gas production platforms are well known for providing a particularly hostile environment for mechanical equipment operation The North

Sea is probably one of the harshest examples of an offshore environment Windstrengths are uncommonly high, with wind speeds of 45 m/s not unusual Inaddition to the high wind strength, the rapid changes and gusting make conditionsextremely unpredictable Humidity levels are also high leading to problems withchloride attack by the saliferous atmosphere.

From a mechanical viewpoint major problems are caused to a tall slender structure by the flexibility of the platform Consideration of its dynamic responsecompared with the wind-induced excitation is therefore of paramount importance.Thermal effects due to the hot exhaust gases are a further factor for consideration.The design must consequently take account of thermal stresses at critical locations.Choices of construction materials must be carefully considered In this instancestainless steel grade 316 L was chosen as the most suitable to meet all the projectrequirements

Choice of Design Philosophy

A typical design for an offshore gas turbine exhaust system is shown in Fig S-36.The exhaust ducting is surrounded on all sides by a substantial steel framework.Upright structural members would typically be 254 mm ¥ 254 mm ¥ 73 kg/m universal column and horizontal members 457 mm ¥ 191 mm ¥ 67 kg/m universalbeam This structure would then be diagonally braced with 168 mm ¥ 8 kg/m circular hollow section A 2-m-diameter exhaust duct would require approximately

9 tonnes of such steelwork for every 5 m of stack height

The steelwork would support the dead weight of the exhaust system andwithstand all dynamic loads due to wind The mounting system connecting the duct

to the steelwork enables the loads to be transferred while allowing for thermalexpansion of the system during operation Normally the fixed support would be nearthe base of the stack and be capable of supporting the dead weight Longitudinalthermal growth would then be vertically upward, with a system of guides allowingvertical movement while providing horizontal restraint

The total exhaust stack length for the design in question is 24.4 m The weight

of platform steelwork required to fully support such a system would consequently

be 45 tons Recent North Sea developments have tended to be on more marginalfields, and therefore consideration of capital costs versus revenue has becomecrucial With a typical installed platform cost of £3500 per ton of steelwork weightsaving now takes a high profile

The 45 tons of stack support structure is located at a high level on the platform.For this reason it is necessary to provide a further 45 tons of steel in the topsidestructure

A freestanding exhaust system has a significant proportion of the upper ductworkunsupported by steelwork, as shown in Fig S-36 The main support would be atthe base of the freestanding section, with a system of guides for ductwork belowthis support as necessary

The design study considered the option of both 10 m and 20 m of freestandingstack Figure S-37 shows the relationship between the free length of stack andplatform steelwork saving for a single stack of 2 m diameter The design andfabrication costs can then be compared directly with the savings in steelwork toshow the net savings Table S-3 shows the results The cost savings can be seen to

be substantial With three identical stacks being utilized on the platform inquestion, savings of £440,000 can be achieved with a platform weight reduction of

156 tons This equates to a saving of 35 percent when compared with the totalinstalled cost of the fully supported exhaust system

Stacks S-31

TABLE S-3 Net Cost Savings for Various Lengths of Freestanding Stack

Length Stack Manufacturing Platform Steelwork Saving Percentage

1 The percentage saving relates to the total installed cost of a fully supported system This is £425,000 made

up from a stack cost of £110,000 plus 90 tons of steel at £3,500 per ton.

2 The stack manufacturing cost includes fabrication and design by an acoustic equipment manufacturer.

3 All prices quoted are UK pound sterling, and based on 1990 rates.

Design Parameters

The following base design parameters are defined as an example:

Power turbine gas exit temperature 475°C

From the turbine exhaust flow and system pressure loss limitations the ductinternal diameter was sized at 2 m Under maximum flow and temperatureconditions the mean gas velocity in this duct is 60 m/s Previous work on free-standing exhaust systems had highlighted the lack of a comprehensive standardthat covered the structural aspects of such a system Further investigations for thisproject confirmed this situation The most applicable standard is BS4076 (1978).This specification offers guidelines for the design of freestanding chimneys, but hasdefinite limitations The most serious of these with respect to this design is that itmakes no allowance for nonrigid foundations The empirical formulae used are alsobased entirely on using carbon steel as the construction material It is not clearwhat modifications would be needed to make these formulae applicable to stainlesssteels or other metallic alloys

A further consideration highlighted by this standard is the warning on theinteraction between pairs, rows, or groups of chimneys In this case the threesystems are positioned in a row at close pitch The use of aerodynamic devices such

as helical strakes to alter the response to gust loading of a single stack are wellproven Deeper investigation into the effectiveness of such arrangements onmultiple arrays has again emphasized the serious limitations of available codes.Designers should, however, look closely at the possible impact of aerodynamiceffects from nearby structures before finalizing their design In this sectionconsideration of structural aspects only are considered The aerodynamic interaction

of the three stacks on the platform in question played a major part in the decision

to limit the freestanding height to 10 m above the steelwork

Because of the unique aspects of this design and the considerable uncertainties

in available design codes, a decision was made to develop directly applicableanalysis methods from fundamental principles

See Table S-3

Steady-State Wind Loading

The wind loading on an isolated exhaust stack will depend on its geographiclocation, height, and the nature of the surrounding terrain The design wind speedand aerodynamic force on the freestanding stack design have been determined inaccordance with the recommendations of BSI (a British standard) CP3, Chapter V,Part 2 (1972) Typical values for an offshore environment are a design wind speed

of 53 m/s, which for a 2-m-diameter exhaust stack corresponds to a drag force of

w = 3.6 kN/m For a stack mounted on pinned supports at three discrete levels

as shown in Fig S-38 the support reactions are not statically determinate

It is necessary to integrate the general expression for the bending moment and

Stacks S-33

introduce the boundary conditions in the resulting displacement function Thisyields four simultaneous equations that may be solved to give the individualreactions in the form:

and

where

Figure S-39 shows the bending moment diagram for a stack with a free length of

10 m

The maximum bending moment of 182 kN occurs at the main support where the

transverse reaction R C = 86 kN Introducing a typical value k v= 2 MNm-1 for thevertical stiffness of the supporting steelwork at the main bearing, it is interesting

to find that the corresponding vertical force (V = 1 kN) is low when compared with the self-weight of the exhaust stack when the design wind load is applied Consequently this element can be ignored during subsequent analysis

1 2

2

1 2

2 1 2

FIG S-38 Stack idealization for steady wind load (Source: Altair Filters International Limited.)

The loading conditions have been determined in accordance with therecommendations of BSI CP3, Chapter V, Part 2 (1972), which is appropriate to theproposed location in the North Sea For locations in the vicinity of North America

it might be more appropriate to use the equivalent American National Standard(ANSI A58.1 1982)

Effects of Gust Loading

In addition to steady drag forces the exhaust stack is required to sustain the effects

of gust loading Appendix B of BS (a British standard) 4076 (1978) highlightsprocedures for avoiding aerodynamic excitation In particular, the vortex sheddingfrequency for an isolated cylinder is given by the empirical formula

For a 2-m-diameter cylinder supported in a turbulent airstream having a mean

velocity V s = 53 m/s, the coefficient S will have a value of 0.25, and the frequency

of vortex shedding from the sides of the exhaust stack will be 6.2 Hz

For practical installations it is known that the flow pattern will be threedimensional with additional vortices being generated by the flow over the top of thestack The shedding frequency for such vortices may well be different from the value calculated above To avoid any difficulties associated with aerodynamic excitation

it is prudent to ensure that the fundamental frequency for transverse vibration ofthe exhaust stack is well above the primary vortex shedding frequency

Unfortunately the formula given in BS 4076 calculates the natural frequency fortransverse vibration of a cantilever mounted on a rigid foundation While this issuitable for most land-based chimney designs it will yield an unduly optimisticestimate for an exhaust stack supported on pinned joints The error will beincreased further when consideration is also given to the flexibility of the supportingstructure It is clear that a more detailed analysis of the vibration behavior isrequired

Examination of the bending moment diagram for inertia loading of an exhauststack supported at three levels suggests that the natural frequency for thefundamental mode of transverse vibration will be almost entirely determined bythe geometry of the upper sections Accordingly for the purpose of frequencycalculations only the two upper supports and corresponding stack sections have

n

SV D

been modeled as a uniform beam mounted on pinned supports as shown in Fig

S-40a This simplification has an immediate advantage in that the support reactions

are statically determinate with values given by:

Calculation of the fundamental frequency for transverse vibration of the beamsystem has been undertaken using Rayleigh’s method, in which the maximumkinetic energy of the vibrating system is equated to the maximum bending strainenergy It is necessary to select realistic displacement functions that satisfy theboundary conditions of the problem The supporting structure is flexible This willaffect the transverse displacement, and hence the natural frequency of the vibratingstack

Suitable displacement functions for a foundation with stiffness k are illustrated

in Fig S-40 For vibration with a circular frequency m, these may be written

In section AB

where

and in section BC

whereEquating the maximum values of the kinetic and bending strain energies, putting

w s = rpDt and , the fundamental frequency for transverse vibration isobtained as:

L

X Y

= 12

13

19

12

47

5 1215

13

2 4

125

131

9

12

47

5 1215

25

13

ˆ

¯

ÈÎÍ

of the freestanding stack with a height of 20 m is too low for this configuration to

be an acceptable design solution The natural frequency of a stack with a free length

of 10 m, mounted by pinned supports on a rigid foundation, is calculated to be 15.1 Hz

It is interesting to note that the corresponding natural frequency for a 10-m-highcantilever mounted on a rigid foundation is 19.6 Hz The difference between thesevalues emphasizes the importance of ensuring that the recommendations of the relevant standard have been interpreted correctly

For the pin-jointed configuration with a free length of 10 m the reduction innatural frequency with support flexibility is shown in Fig S-42 It is convenient toexpress the flexibility of the support in terms of the tip deflection obtained with arigid foundation

For the proposed design it is important to note that even for a relatively stifffoundation, with a flexibility 1/k = 145 MN/m, which is typical of the supportstructure, the natural frequency falls to 10.9 Hz It follows that the stiffness of aconventional support structure will be sufficiently low to have an adverse effect onthe ideal dynamic response of the stack assembly

The significant commercial benefits available from the correct choice of the designfor offshore gas turbine exhaust systems and their supporting structures is evident

By using a freestanding exhaust the cost savings are shown to be substantial

No comprehensive standard is available to assist the designer for this application.Should a design analysis be undertaken without appreciating the limitations ofexisting standards, the consequences could be disastrous

These limitations have been highlighted, and a number of analysis procedurespresented to illustrate how the deficiencies may be overcome Use of the proposedprocedures will allow a detailed and comprehensive design analysis to be completedfor a freestanding stack The method is simple to apply and allows parameter andoptimization studies to be carried out within commercially viable time scales.Freestanding stacks of even greater length can be achieved by prudent selection

of configuration, material type, thickness, and support arrangement

Steam Generator and Steam Supply

A steam generator consists of a boiler (see Some Commonly Used Specifications,

Codes, Standards, and Texts, at the back of the book, for boiler specifications) itsfuel system, and all controls and accessories Steam supply is now a sophisticatedscience in itself, especially with supercritical steam now increasingly used to boostefficiency on steam-turbine cycles and other operations Service factors on steamvalves, lines, and other accessories are consequently more severe

S-38 Steam Generator and Steam Supply

T Tanks

Tanks are used for storage in process plants and refineries Tanks forpetrochemicals, oil, and other potentially explosive products are highly specialized

A more common kind of tank is used for bulk dry storage of products in agricultureand a variety of other process industries A variety of designs exist The principlebehind one of these types (trade name TecTank SealWeld) follows

General Storage Tanks*

TecTank SealWeld tanks (see Fig T-1) from Engineered Storage Products Companyare designed for simple precision assembly The critical flange-to-shell fabricationprocess incorporates positioning clamps and automated welding Dual weld seamsare used to increase the joint strength and to avoid warpage and distortion Duringjobsite panel fit-up, flange connections are secured with structural bolts, not rivets.(See Fig T-2.)

The interior welding of the assembled silo can proceed without the problems thatplague traditional field-welded silos Location costs are reduced, and the weldingcan be accomplished under controlled conditions The welded interior of the productzone is free of ledges and gaskets

Carefully controlled tank coating processes ensure the product within the tanks

is not contaminated Some examples of products stored are:

ABS PelletsAlfalfa (Dehydrated)Alumina Ore

Ammonium NitrateBarium CarbonateBarium SulfateBark AshBarleyBauxiteBentoniteBisphenol “A”

Blood (Dried)BonemealBoraxBoric AcidBrewers GritsBurnt LimeCalcium CarbonateCalcium ChlorideCalcium Silicate

T-1

* Source: A.O Smith Engineered Storage Products Company, USA Adapted with permission.

The 1 in (25 mm) flange

FIG T-1 Generic storage tank (TecTank SealWeld tank) (Source: Peabody TecTank.)

T-2