Module # 6 - NPTEL
NPTEL – Chemical Engineering – Chemical Engineering Design - IIModule # 6DESIGN OF TALL VESSELS: INTRODUCTION, AXIAL STRESSDUE TO DEAD LOADS, AXIAL STRESSES DUE TO PRESSURS,LONGITUDINAL BENDING STRESSES DUE TO DYNAMIC LOADS,DESIGN CONSIDERATIONS OF DISTILLATION (TALL) ANDABSORPTION COLUMN (TOWER)1. INTRODUCTION2. STRESSES IN THE SHELL (TALL VERTICAL VESSEL)3. AXIAL AND CIRCUMFERENTIAL PRESSURE STRESSES3.1 Tensile stresses resulting from internal pressure4. COMPRESSIVE STRESS CAUSED BY DEAD LOADS5. THE AXIAL STRESSES (TENSILE AND COMPRESSIVE) DUE TO WINDLOADS ON SELF SUPPORTING TALL VERTICLE VESSEL6. THE STRESS RESULTING FROM SEISMIC PRESSIVE)8. ESTIMATION OF HEIGHT OF THE TALL VESSEL (X)9. COLUMN INTERNALS9.1 Design and construction features of plate and trays9.1.1 Loading conditions of trays and plates9.1.2 Deflection and stressesJoint initiative of IITs and IISc – Funded by MHRDPage 1 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IILecture 1: INTRODUCTION, AXIAL STRESS DUETO DEAD LOADS4. INTRODUCTIONSelf supporting tall equipments are widely used in chemical process industries. Tallvessels may or may not be designed to be self supporting. Distillation column,fractionating columns, absorption tower, multistage reactor, stacks, chimneys etc. comesunder the category of tall vertical vessels. In earlier times high structure (i.e. tall vessels)were supported or stabilized by the use of guy wires. Design of self supporting verticalvessels is a relatively recent concept in equipment design and it has been widely acceptedin the chemical industries because it is uneconomical to allocate valuable space for thewires of guyed towers. In these units ratio of height to diameter is considerably large dueto that these units are often erected in the open space, rendering them to wind action.Many of the units are provided with insulation, number of attachments, piping system etc.For example distillation and absorption towers are associated with a set of auxiliaryequipments i.e. reboiler, condenser, feed preheater, cooler and also consists of a series ofinternal accessories such as plates or trays or variety of packings. Often the verticalvessels/columns are operated under severe conditions, and type of the material thesecolumns handles during operation may be toxic, inflammable or hazardous in other ways.Structural failure is a serious concern with this type of columns. As a result the, theprediction of membrane stresses due to internal or external pressure will not be sufficientto design such vessels. Therefore, special considerations are necessary to take intoaccount and predict the stresses induced due to dead weight, action of wind and seismicforces.5. STRESSES IN THE SHELL (TALL VERTICAL VESSEL)Primarily the stresses in the wall of a tall vessel are: a) circumferential stress, radial stressand axial stress due to internal pressure or vacuum in the vessel, b) compressive stresscaused by dead load such as self weight of the vessel including insulation, attachedequipments and weight of the contents.Dead load is the weight of a structure itself, including the weight of fixtures or equipmentpermanently attached to it; Live load is moving or movable external load on a structure.This includes the weight of furnishing of building, of the people, of equipment etc. butdoesn‟t include wind load. If the vessels are located in open, it is important to note thatwind load also act over the vessel. Under wind load, the column acts as cantilever beamas shown (Figure 6.1). Therefore while designing the vessel stresses induced due todifferent parameters have to be considered such as i) compressive and tensile stressJoint initiative of IITs and IISc – Funded by MHRDPage 2 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIinduced due to bending moment caused by wind load acting on the vessel and itsattachments; ii) stress induced due to eccentric and irregular load distributions frompiping, platforms etc. iii) stress induced due to torque about longitudinal axis resultingfrom offset piping and wind loads and iv) stress resulting from seismic forces. Apart fromthat, always there are some residual stresses resulting due to methods of fabrication usedlike cold forming, bending, cutting, welding etc.Figure 6.1: Bending moment diagram under wind load3. AXIALSTRESSESANDCIRCUMFERENTIALPRESSURE3.1 Tensile stresses resulting from internal pressureThe simple equation may be derived to determine the axial and circumferential stressesdue to internal pressure in the shell of a closed vessel. Figure (6.2a) shows a diagramrepresenting a thin walled cylindrical vessel in which a unit form stress, f, may beassumed to occur in the wall as a result of internal pressure.Where, l length, inchesd inside diameter, inchest thickness of shell, inches and p internal pressure, pounds/square inch gageJoint initiative of IITs and IISc – Funded by MHRDPage 3 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IILongitudinal stress: In case of longitudinal stress, if the analysis limits to pressurestresses only, the longitudinal force, P, resulting from an internal pressure, p, acting on athin cylinder of thickness t, length l, and diameter d is:PAnda force tending to rupture vessel longitudinally (p area of metal resisting longitudinal rupture t d2)/4 dThereforef stress P/a p d 2 / 4pd induced stress, pounds per square incht d4tort pd4f(6.1)Figure 6.2a: Longitudinal forces acting on thin cylinder (internal pressure)Joint initiative of IITs and IISc – Funded by MHRDPage 4 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IICircumferential stresses: Fig (6.2b) shows the circumferential force acting on the thincylinder under internal pressure. The following analysis may be developed, if oneconsiders the circumferential stresses are induced by the internal pressure only.P force tending to rupture vessel circumferentially p d la area of metal resisting force 2 t lf stress ort Ppdl pd a2tl2tpd2f(6.2)Figure 6.2b: Circumferential forces acting on thin cylinder (internal pressure)Equation 6.1 and 6.2 indicates that for a specific allowable stress, fixed diameter andgiven pressure, the thickness required to restrain the pressure for the condition of eq.(6.2) is double than that of the equation (6.1). Therefore, the thickness as determined byequation (6.2) is controlling and is the commonly used thin walled equation referred to inthe various codes for vessels. The above equation makes no allowances for corrosion anddoes not recognize the fact that welded seams or joints may cause weakness. Experiencehas shown that an allowance may be made for such weakness by introducing a jointefficiency factor “j” in the equations and this factor is always less than unity and isspecified for a given type of welded construction in the various codes. The thickness ofmetal, c, allowed for any anticipated corrosion is then added to the calculated requiredJoint initiative of IITs and IISc – Funded by MHRDPage 5 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIthickness, and the final thickness value rounded off to the nearest nominal plate size ofequal or greater thickness.Equation (6.1) and (6.2) rewritten based on the foregoing discussion asWhere,t pd c4f j(6.3)t pd c2f j(6.4)t thickness of shell, inchesp internal pressure, pounds per square inchd inside diameter, inchesf allowable working stress, pounds per square inchE joint efficiency, dimensionlessc corrosion allowance, inches4. COMPRESSIVE STRESS CAUSED BY DEAD LOADSThe major sources of the load acting over tall vertical vessel are the weight of the vesselshell and weight of the vessel fittings which includes the internal, external and auxiliaryattachments. Internal fittings: trays, packing, heating and cooling coils. External fittings:platforms, piping, insulation, ladders. Auxiliary attachments: instruments, condenser etc.Therefore, Stresses caused by dead loads may be considered in three groups forconvenience: (a) stress induced by shell and insulation (b) stress induced by liquid invessel (c) stress induced by the attached equipment.Stress induced by shell and insulation: Stress due to weight of shell and insulation atany distance, X from the top of a vessel having a constant shell thickness, Wshell 4 D2o Di2 s X(6.5)Where, W weight of shell above point X from topD0 & Di outside and inside diameter of shellX distance measured from the top of the vessel s density of shell material,Joint initiative of IITs and IISc – Funded by MHRDPage 6 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIAndstress due to weight of insulation at height „X‟Winsulation Dins ins X t ins(6.6)Where, Wins weight of insulationDins mean diameter of insulationX height measured from the top of the columntins thickness of insulationρins density of insulationCompressive stress is force per unit area,f d wt shell /4 (Do2 -Di2 ) X s X s /4(Do2 -Di2 )(6.7)Similarly, the stress due to dead weight of the insulation is:f d wt ins (D t)ins X Dm t s(6.8)Dm mean diameter of shell (Dm (Do Di)/2)Dins Dm diameter of insulated vesselts thickness of shell without corrosion allowanceTherefore,f d wt ins ins t ins X(6.9)tsStress induced due to liquid retained in column. It will be depend upon internal e.g. intray column, total number of plates, hold up over each tray, liquid held up in the downcomer etc. will give the total liquid contents of the column.f d liquid Wliquid Dm t s(6.10)Dm mean diameter of vessel, feetJoint initiative of IITs and IISc – Funded by MHRDPage 7 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIts thickness of shell without corrosion allowanceStress induced by the attachment, like trays, over head condenser, instruments,platform, ladders etc.f dattachments Wattachments Dm t s(6.11)The total dead load stress, ftotal, acting along the longitudinal axis of the shell is then thesum of the above dead weight stresses.ftotal fdead wt shell fdead wt ins fdead wt liq fdead wt attach.Joint initiative of IITs and IISc – Funded by MHRD(6.12)Page 8 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IILecture 2: AXIAL STRESSES DUE TO PRESSURS5. THE AXIAL STRESSES (TENSILE ANDCOMPRESSIVE) DUE TO WIND LOADS ON SELFSUPPORTING TALL VERTICLE VESSELThe stress due to wind load may be calculated by treating the vessel as uniformly loadedcantilever beam. The wind loading is a function of wind velocity, air density and shape oftower.The wind load on the vessel is given byPw ½ CD Vw2 A(6.13)Where,CD drag coefficientρ density of airVw wind velocityA projected area normal to the direction of windIf wind velocity is known approximate wind pressure can be computed from thefollowing simplified relationship.Pw 0.05 Vw2(6.14)Pw min wind pressure to be used form moment calculation, N/m2Vw max wind velocity experienced by the region under worst weather condition, km/hWind velocity varies with height. This can be observed from the figure shown below(Figure 6.3). The velocity of wind near the ground is less than that away from it.Therefore, to take into account this factor a variable wind force may be taken. It isrecommended to calculate the wind load in two parts, because the wind pressure does notremain constant through the height of the tall vessel. Say for example in case of vesseltaller than 20 m height, it is suggested that the wind load may be determined separatelyfor the bottom part of the vessel having height equal to 20 m, and then for rest of theupper part.Joint initiative of IITs and IISc – Funded by MHRDPage 9 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IILoad due to wind acting in the bottom portion of the vessel.Pbw K1 K2 p1 h1 DoWhere,Pbw – total force due to wind load acting on the bottom part of the vessel with heightequal to or less than 20 m.Do - outer diameter of the vessel including the insulation thicknessh1 – height of the bottom part of the vessel equal to or less than 20 mK1 – coefficient depending upon the shape factor (i.e. 1.4 for flat plate; 0.7 for cylindricalsurface)Figure 6.3: Tall column subjected to wind pressureLoad due to wind acting in the upper portion of the vessel.Puw K1 K2 p2 h2 DoWhere,Puw – total force due to wind load acting on the upper part above 20 m.Do - outer diameter of the vessel including the insulation thicknessh2 – height of the upper part of the vessel above 20 mK2 – coefficient depending upon the period of one cycle of vibration of the vessel(K2 1, if period of vibration is 0.5 seconds or less; K2 2, if period exceeds 0.5seconds)Stress due to bending moment: Stress induced due to bending moment in the axialdirection is determined from the following equations.(i)Mw Pbw h1/2 ;h1 20m(ii)Mw Pbw h1/2 Puw (h1 h2/2 ) ;h1 20mTherefore, the bending stress due to wind load in the axial directionfw 4 Mw t (Di t) DiJoint initiative of IITs and IISc – Funded by MHRD(6.15)Page 10 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIWhere,fw - longitudinal stress due to wind momentMw - bending moment due to wind loadDi – inner diameter of shellt – corroded shell thickness6. THE STRESS RESULTING FROM SEISMIC LOADSThe seismic load is assumed to be distributed in a triangular fashion, minimum at thebase of the column and maximum at the top of the column. It is a vibrational load, itproduces horizontal shear in self supported tall vertical vessel (Figure 6.4).Figure 6.4a: Seismic forces on tall columnJoint initiative of IITs and IISc – Funded by MHRDPage 11 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIFigure 6.4b: Seismic forces on tall columnThe load may, therefore be considered as acting at a distance 2/3 from the bottom of thevessel.Load, F Sc W(6.16)Where, W weight of the vesselSc seismic coefficientSeismic coefficient depends on the intensity and period of vibrations. For example if thevibration lasts for more than one second seismic coefficient value varies from minimum,moderate to maximum Sc 0.02, 0.04, and 0.08 respectively.Stress induced due to bending moment up to height X from the top of the column is givenby:Sc W X 2 (3 H - X)MsX (6.17)3H2Where X H, maximum bending moment is at the base of columnMsb 2/3 Sc W H(6.18)The resulting bending stress due to seismic bending moment is given by:4 MsXfsb (6.19)π D2 t0Joint initiative of IITs and IISc – Funded by MHRDPage 12 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IIThe maximum bending moment is located at the base of the vessel (X H). Thussubstituting H for X in Eq. (6.17)Sc W H 2 (3 H - H)(6.20)f 4 sb3H 2 π Do2 t2 Sc W H(6.21)sb3 π R2 tThe possibility of the wind load and seismic load acting simultaneously over the columnis rare. So both the loads are computed separately and whichever is more severe is usedto calculate the maximum resultant stress.Maximum tensile stress at the bottom of the skirtftensile (fwb or fsb) - fdbMaximum compressive stress on the skirtfcompressive (fwb or fsb) fdb,here, fdb - dead load stressTaking into account the complexity of the final equation for maximum stresses, it iscustomary to assume a suitable thickness „t‟ of the skirt and check for the maximumstresses, which should be less than the permissible stress value of the material.f 7. STRESS DUE TO ECCENTRICITY(TENSILE OR COMPRESSIVE)fe M e (e)( /4) Do2 (t s c)OFLOADS(6.22)Me summation of eccentric loade eccentricityKey words: wind load, bending moment, seismic load, eccentric loadsJoint initiative of IITs and IISc – Funded by MHRDPage 13 of 29
NPTEL – Chemical Engineering – Chemical Engineering Design - IILecture 3: LONGITUDINAL BENDING STRESSESDUE TO DYNAMIC LOADS, DESIGNCONSIDERATIONS8. ESTIMATION OF HEIGHT OF THE TALL VESSEL (X)Height of the tall vessel „X‟ can be estimated be combining all the stresses acting in theaxial direction may be added and equated to the allowable tensile stress, excluding thestresses due to eccentricity of load and seismic load.Stress due to wind load at distance 'X' Longitudinal stress due to internal pressure -Stress due to wind load at distance 'X' Longitudinal stress due to internal pressure - Wattachments Dm t s Wattachments Dm t sHere, ts is the thickness of the shellIn the above equation ft max is replaced by ft allHence, above equation can be represented in the following forma X2 b X c 0b 2 4ac(6.23)2aOnce the value of „X‟ is estimated, it is described to adjust the plate thickness, t, for thetop portion of the column, so that the height of portion X will be multiple of the platewidth used. The plate thickness which is originally selected is satisfactory up to aconsiderable height. Trays below the distance X of the column must have an increasedthickness. If the above condition does not satisfy then calculation of the axial stress withan increase in the thickness according to equation (6.5, 6.23) are repeated, and thisrepetitive steps in calculation helps to estimate subsequent height ranges to correspondswith increase thickness. The procedure is repeated till the entire height of the vessel iscovered.from whichX -b Joint initiative of IITs and IISc – Funded by MHRD(X )Page 14 of 29(X ) f t max- f t all J 0
NPTEL – Chemical Engineering – Chemical Engineering Design - II9. COLUMN INTERNALS9.1 Design and construction features of plate and traysPlate or trays can be constructed either as one piece trays or as sectional trays. Severalfactors control the design and construction features of plates or trays. These factorsincludes 1) down coming liquid impact, liquid weight, load on the tray due to deadweight; 2) expansion due to rise in temperature; 3) fabrication and installation ease; 4)support type; 5) material of construction and safety.One piece tray may be made of material such as cast iron, copper or steel including therisers and down comers, with a thickness of 2 to 6 mm depending on the diameter and thematerial. The sectional tray is made from section in the form of floor plates cut formsheets, which are laid on the supporting beams and peripheral ring. A clearance isprovided between adjacent sections and clamping devices are used for fixing.The cast iron tray is able to withstand compressive forces created due to thermalexpansion within reasonable limits and their diameters are also limited to small sizes.Whereas the one piece shaped tray made of ductile material is comparatively thin and hasa limited ability to absorb forces due to thermal expansion. Therefore, in order to preventthe distortion of the tray floor, provision of packing seal between the edge of the tray andcolumn wall help to relieve these problem. On the other hand one of the main advantagesof the sectional tray is its ability to cope with thermal expansion. The individual sectionsof the tray are placed on the supporting structures, an asbestos jointing material insertedbetween the section and the support member. Each section is finally held by frictionalclamping devices. Sectional trays are also necessary when these are to be taken insidethrough the limited size of column man holes in parts and assembled inside.9.1.1 Loading conditions of trays and platesPlates and trays used in the tall column have to be maintained flat in order to provide auniform seal of the liquid on their surfaces. During operation various loads acts on theplates and trays, and due to that plates and trays are likely to deflects greatly, unless theyare provided with sufficient supporting systems or and made adequately thick.Deflections caused by the different loads are: a) tray weight with contacting devices anddown comers; b) liquid weight; c) impact load of the down comin
design of tall vessels: introduction, axial stress due to dead loads, axial stresses due to pressurs, longitudinal bending stresses due to dynamic loads, design considerations of distillation (tall) and absorption column (tower) 1. introduction 2. stresses in the shell (tall vertical vessel) 3. axial and circumferential pressure stresses
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