Chemical Engineering Design Problems (Undergrad level)

CH3205: Equipment Design Problem Sheet A. Problems on criteria of failure of process equipment 1. A full floating head condenser has 400 admiralty metal tubes. The floating tube sheet and head assembly 4000 N when the head is filled water. If the tube support plate is located 0.45 m from the centre of the load of floating head assembly and assumed to behave as a simple cantilever beam: a) What bending stress is developed in the tubes as a result of this load? b) What is the floating head deflection from the horizontal at the centre of the load? c) Is the design satisfactory if the allowable stress is 4.1×106 N/m2? 2. A horizontal stiffener supporting a bubble cap tray in a fractionating column may be considered to act as a uniformly loaded, simply supported beam. The deflection equation for such a beam is-

1  wlx 3 wx 4 wl 3 x     EI  12 24 24  Where, y = deflection at a point x, m x = distance from the l = total length of stiffener, m E = modulus of elasticity, N/m2 I = moment of inertia, m4 w = uniformly distributed load, N/m The stiffener has a moment of inertia of 74.30×10-8 m4 and a section modulus of 16.72×10-6 m and is of steel (E = 2.06×1011 N/m2 ). The stiffener has a length l of 2.5 m and carries a uniformly distributed load of 420 N/m. Determine: a) The maximum deflection at the centre of span, x = 1.25 m. b) The maximum stress at the centre of the span. c) The stress at 0.5 m from the support. d) The shear load at x = 0.5 m. y

3. A copper fractionating column has vertical tray support rods between trays. The trays are 0.5 m apart and the rods are spaced so as to support a load of 445 N each, under column action. What is the diameter of the rods required to limit the column loading to one half of the critical column load if, a) The rods are free to pivot at both ends. b) The rods are fixed at both ends. Data: E = 1.03×1011 N/m2.

4. A vessel is to be fabricated of type 316 stainless steel. The vessel is intended to be used at 977.4 K for an expected service life of 5 years. The creep deformation permitted during the service life of the unit is not to exceed 5%. Determine the allowable stress if the allowable stress not to exceed either (a) two thirds of the stress to produce the creep rate or (b) 50% of the stress to rupture. Also estimate the total creep and rupture life if the allowable design stress as determined in this manner is used in the design of the vessel. Data: Creep and rupture of 316 SS is given in Fig-2.15 and 2.16 of Brownell & young. B. Problems on shell under internal pressure 1. A cylindrical process vessel for non-lethal substance is to be designed for the maximum operating pressure of 1000 kN/m2 and maximum operating temperature of 350ºC. The nominal diameter of the vessel is 1.5 m. The vessel is to be fabricated of IS:2002-1962 2B grade steel. The suggested corrosion allowance is 2 mm. Specify the standard plate thickness for fabricating the shell of the vessel. 2. A cylindrical pressure vessel of 1.5 m nominal diameter is to be designed for 5×106 N/m2 pressure and 400ºC. The material of construction is IS:2002-1962 grade 2B quality steel. Corrosion allowance is 3 mm. if the vessel is used at room temperature service, what will be the maximum working pressure that the vessel will with stand? 3. An autoclave of 1.5 m nominal diameter and 2 m tangent to tangent length is provided with a steam jacket over a straight section 1.5 m long. The space between the jacket and autoclave is 50 mm. The maximum working pressure inside the autoclave is 500 kN/m2 and working temperature 150ºC. The steam pressure inside the jacket is 350 kN/m2 . The material of construction of autoclave and jacket is IS:2002-1962 grade 2B steel. Specify the plate thickness for fabricating the autoclave shell and jacket shell. 4. The shell of a shell and tube heat exchanger of nominal diameter of 1.2 m is to be fabricated from steel plate conforming to IS:2002-1962 grade 2B. Shell side fluid is steam at 7 atm (g). Specify the standard plate thickness for fabricating the shell. Estimated corrosion over the service life of the exchanger is 1.5 mm. 5. Specify the standard plate thickness required to fabricate the shell of a pressure vessel as per IS:2825 code recommendations of the following specifications: Nominal diameter 2.5 m Design pressure 3.15×106 N/m2 Design temperature 300°C Material IS:2002-1962 2B grade steel Corrosion allowance 1.5 mm 6. A cylindrical pressure vessel of 1.5 m nominal diameter is to be designed for 5×106 N/m2 and 400°C. The material of construction is IS:2002-1962 2B grade steel. Corrosion

allowance is 3 mm. If the vessel is used at room temperature service (≈25°C), what will be the maximum working pressure that the vessel will withstand? C. Problems on closure under internal pressure 1. A pressure vessel of 1.2 m nominal diameter is provided with a welded flat plate cover on one end and a torispherical cover on the other end. The maximum working pressure and temperature are 500 kN/m2 and 250°C respectively. Materials for shell and closures are IS:2002-1962 grade 2B quality steel. Assume 2 mm corrosion allowance. Design the heads. Do you recommend the welded flat plate closure for the vessel? 2. Design different types of end closures for a pressure vessel having the following specifications: Nominal diameter 1.5 m Maximum working pressure 1000kN/m2 Design temperature 350°C Material IS:2002-2A grade steel Corrosion allowance 2 mm The pressure vessel is to be used for non-lethal substance. 3. Design a torispherical closure for a pressure vessel subjected an internal pressure of 500 kN/m2 at 550 K. The nominal diameter of the vessel is 2 m. The torisperical closure is having inside crown radius 0.8 times the outside diameter and inside corner radius 0.06 times the inside diameter. The material of construction of the vessel and the head is steel conforming to IS:2002-1962 grade 2a. 4. A torispherical head having inside crown radius equal to the outside diameter is to be fabricated. The head is provided with a 250 mm hole at its centre. Specify the standard plate thickness for fabricating the head if (i) the hole is uncompensated and (ii) the hole is fully compensated. The other specifications of the pressure vessel are: OD of shell 2m MWP 3.5×106 N/m2 Shell wall thickness 50 mm CA 3 mm Allowable stress at the design temperature 96×106 N/m2 5

A torisperical head of 1.5 nominal diameter is to be designed as per IS:2825 code specifications. The maximum operating pressure (internal) and temperature are 8.0×105 N/m2 (gage) and 300°C. Material if steel conforming to IS:2002-1961 2B grade. Corrosion allowance may be taken as 1.5 mm. Specify the standard plate thickness for fabricating the head.

D. Problems on compensation 1. A pressure vessel is subjected to an internal working pressure of 3×106 N/m2 at 550 K. The outer diameter and tangent to tangent length are 1.5 m and 3 m respectively. The vessel is provided with ellipsoidal heads with major to minor axis ratio of 2:1. The vessel

and the heads are fabricated from steel conforming to IS:2002-1962 grade 2B. The estimated corrosion allowance over the service life of the vessel is 3 mm. a) Calculate and recommend the plate thickness for fabricating the shell and heads. b) An inlet nozzle is attached to the shell of the pressure vessel has an internal diameter of 155 mm and outer diameter of 170 mm and is made from steel conforming to IS-19141961. The nozzle projects 20 mm inside the vessel and 75 mm outside the vessel. Suggest a suitable reinforcement for the nozzle, if required. 2. A 200 mm internal diameter nozzle is welded on the cylindrical shell of a pressure vessel of 1 m nominal diameter and 8 mm thick. The nozzle projects 50 mm inside and 100 mm outside from the inner and outer surface respectively. The maximum operating pressure and temperature are 1×106 N/m2 and573 K respectively. Both the nozzle and the shell are fabricated from steel conforming to IS:2002-1962 grade 2B. Calculate the nozzle thickness if no external compensating pad is allowed. 3. Examine the data given below to evaluate the requirement of compensation for the nozzle opening in a cylindrical shell. OD of shell 2m MWP 3.5×106 N/m2 Shell wall thickness 50 mm CA 3 mm Allowable stress at the design temperature 96×106 N/m2 OD of nozzle (seamless) 250 mm Nozzle wall thickness 16 mm Inside protrusion of nozzle not required Length of the nozzle above surface 100mm 4. A pressure vessel, subjected to a maximum working pressure of 3.5×106 N/m2 and maximum working temperature of 550 K, is provided with a torispherical head having a fully compensated centrally located hole. The nominal diameter of the vessel is 2 m and the hole diameter is 250 mm. The crown radius of the torispherical head is equql to the outside diameter of the vessel and the corner radius is 0.1 times of inner diameter. Both the vessel and the head are fabricated from steel conforming to IS:2002-grade I. specify the dimensions of a suitable ring pad compensator for the hole. Assume 2 mm corrosion allowance. 5. A pressure vessel of 1.2 m nominal diameter is subjected to a maximum operating pressure of 500 kN/m2 at 250°C. a) Design a suitable torispherical closure having a centrally located uncompensated hole 30 cm diameter. The material of construction is IS:2002-1962 2B grade steel. CA may be taken as 2 mm. b) Examine the requirement of compensation of the hole and design a suitable ring pad compensator, if required. E. Problems on shells under external pressure 1. A vacuum crystallizer of 3.5 m nominal diameter is provided with a 60° apex angle conical bottom and a torispherical head at the top. The distance from the junction of the cone with the shell to the point of tangency of the top closure is 5.5 m. opearating

temperature is 350 K. Material of construction is IS:1570-1961 04Cr 19Ni9 stainless steel. Specify the design of the shell, torispherical head and conical bottom. 2. An autoclave 2 m inside diameter has a tangent to tangent length of 4 m, and is provided with ellipsoidal closures (2.6:1) at both ends. The working temperature of the process fluid inside the autoclave is 150°C and under vacuum. The autoclave has a steam jacket 0.5 m below the point of tangency from the top and steam pressure in the jacket is 3.5×105 N/m2 (g). The space between the jacket and autoclave is 50 mm. The material of construction of autoclave is stainless steel conforming to IS:1570-1961 04Cr 19Ni9. Specify the thickness of standard plate to fabricate the autoclave shell and its closures. 3. A cylindrical vessel made of low carbon steel is provided with torisperical heads. The inside diameter is 3 m and tangent to tangent length is 10 m. The thickness of the heads and the shell are 10 mm. Working temperature is 120°C. a) Determine the maximum allowable vacuum that can be applied to the vessel. b) Determine the minimum number of equally spaced stiffeners required to permit the use of full vacuum in the vessel. c) Specify the dimensions of suitable channel stiffener for part (b). 4. The shell for a vacuum crude tower 10 m diameter is constructed with low carbon steel plate of 28 mm thick. Circumferential sheet stiffeners are used and located 2m apart. Determine the required moment of inertia for the stiffeners, and suggest a possible design for the stiffeners. A corrosion allowance of 3 mm is required. 5. A cylindrical vessel made of stainless steel is fabricated with torisperical heads. The nominal diameter is 3 m and tangent to tangent length is 10 m. the thickness of the heads and shell are 10 mm. Ro and ro of the torispherical heads 3 m and 0.3 m respectively. Working temperature is 120°C. a) Determine the maximum allowable vacuum that can be applied to the vessel. b) Can full vacuum be applied to the vessel by providing shell stiffeners? If so, find the minimum number of equally spaced stiffeners. 6. A cylindrical vessel of nominal diameter 1.5 m and tangent to tangent length of 5 m and provided with torispherical heads (Ri = 1.5 m and ri = 0.09 m) is to be designed for full vacuum operation and 150°C. The material of the vessel and heads are stainless steel. If the vessel is designed with one circumferential stiffener, where you will locate the stiffener and why? How much steel can be saved by providing the above stiffener over that of the vessel without stiffener? 7. A vessel 4m nominal diameter and 6 m tangent to tangent length is provided with ellipsoidal heads of 2.6:1 major to minor diameter (based on outside diameter) and 5 circumferential stiffening rings 1 m apart. The vessel is subjected to full vacuum at 200°C. The material of construction of the shell and heads are stainless steel. a) Specify the plate thickness required for fabricating the head and shell. b) Can a 18 cm channel of the following specifications be used as stiffening rings? 18 cm channel specifications: Weight 14.6 kg/m

I AS E

8.9×10-6 m4 1.87×10-3 m2 1.87×1011 N/m2

F. Problems on tall towers 1. Make a preliminary estimate of the plate thickness required for the distillation column specified below: Height, between tangent lines 50 m Nominal diameter 2m Skirt height 3m Sieve plates, equally spaced 100 Nos. Operating pressure 10 bar (abs) Operating temperature 200°C Insulation, mineral wool 75 mm thick Material of construction Stainless steel: Design Stress 135 N/mm2 at design temperature 200°C Welded joint efficiency factor, J 1 2. A plate distillation column has the following specifications: Nominal diameter 2m Number of trays 30 Operating pressure 200 mm of Hg (abs) Operating temperature 100°C Tray spacing 0.6 m Top disengaging space 1.0 m Bottom separator space 2.5 m Skirt height 3m Top and bottom closures Torispherical with ho = 0.5 m Tray loading (including liquid) 1.5×103 N/m2 Insulation thickness 7.5 cm Bulk density of insulation 800 kg/m3 Material of construction Stainless steel: Allowable working stress at the design temperature = 139 ×106 /m2 and E = 1.87×1011 N/m2 Accessories One caged ladder, weight of which is 365 N/m length Design group specifies 10 mm standard plate for fabricating the entire shell (i.e. uniform shell thickness) as well as torisperical heads. You are required to check only, based on “Maximum Principal Stress Theory”, whether the recommended shell thickness is adequate under actual operating conditions. You can use the following assumptions/ estimation for your calculations.

i) Effective wind area for the external attachments is estimated to be 20% of the uninsulated column; ii) Wind pressure upto 300 m height is 1000 N/m2 and shape factors is 0.7; iii) Negligible seismic effect; iv) Density of stainless steel is 7500 kg/m3 ; v) Weight of accessories other than caged ladder is negligible; vi) Weight of the head with insulation may be taken as 7500 n. 3. A packed absorption tower has the following specifications: Inner diameter 1.5 m Tangent to tangent length 15 m Top and bottom cover Ellipsoidal (2:1) Packings 50 mm ceramic rashig ring Bulk density of packing 595 kg/m3 Void fraction 0.74 Liquid Water Pressure (g) 1.0×105 Temperature 320 K Top empty space 1.0 m Bottom empty space 0.8 m Skirt length 2.5 m Shell material IS:2002-1962 grade 2A Insulation Nil CA 3 mm Based on maximum principal stress theory, calculate the thickness of the absorption tower. Data: Maximum wind pressure (upto 20 m) 750 N/m2 Earthquake effect Negligible Effect of attachments and accessories may be neglected. 4. A rotating disc extraction column to extract pyridine from pyridine-water solution with benzene has been designed and the information are recorded below. You are required only to check the shell thicknesses recommended and comment on it. Shell diameter 90 mm Shell length, tangent to tangent 16.5 Design pressure 0.35 MN/m2 Design temperature 30°C Material of construction Mild steel with allowable stress 96 MN/m2

CA 3 mm Welded joint efficiency factor 0.8 Top and bottom heads Torisherical Straight flange length 50 mm From working pressure consideration, the thickness including corrosion allowance for shell and heads are recommended to be 10mm. Skirt support height 1.8 m Insulation Nil Sp. gr. of steel 7.85 Mean liquid density 980 kg/m3 Accessories: a 2.5 hp motor to be secured on top of the column; one caged ladder to the motor; rotor; stator etc. Weight of motor 5.0 kN Weight of rotor, stator arrangement for rotating disc 500 N/m length Weight of ladder 350 N/m length Wind pressure for the entire tower height 1.0 kN/m2 Seismic load negligible G. Problems on vessel support 1. A cylindrical skirt and bearing plate is to be designed for a fractionating column to the following specifications: Skirt height 1.5 m Effective diameter of the vessel 2.1 m Length of the column, tangent to tangent 16 m Weight of the column with its contents 465×103 N Skirt and bearing plate material IS:2002-1962 grade 2B Maximum wind pressure upto 20 m 750 N/m2 Seismic effect negligible a) Specify the standard plate thickness to fabricate the skirt. b) Design a suitable bearing plate H. Problems on storage tanks 1. An open top storage tank for storing 18,000 m3 of a liquid of specific gravity 1.2 is to be designed. The tank will be fabricated from steel conforming to IS:2002 grade I. the land and foundations are available free of cost. The annual cost of fabricated shell per unit area is 1.3 times the annual cost of fabricated bottom per unit area. a) Determine the optimum proportions of the tank. b) Determine the number of shell courses and thickness of each course. c) Suggest a suitable wind girder.

d) Suggest a suitable top curb angle. 2. A distillery producing 25 m3 of alcohol per day is required to hold the production of 60 days. A fixed roof storage tank fabricated from steel conforming to IS:2002 grade I is recommended for the purpose. a) Determine the optimum diameter and height of the tank if annual cost of fabricated shell, roof, and installation and fabrication taken together are 1.8, 1.5 and 0.5 times the annual cost of the fabricated bottom respectively. b) Specify the plate thickness of bottom two and top two shell courses. c) Do you recommend a self supported conical roof or a column supported roof for the tank? Justify your recommendation. 3. A column supported roof of a mild steel storage tank of 24 m diameter is to be designed. The thickness of the roof plate is 5 mm and roof slope is 1:16. Design the rafters for the above roof support. 4. Design a suitable wind girder for an open tank of 40 m diameter and 24 m height. 5. A storage tank for concentrated nitric acid will be constructed from aluminum to resist corrosion. The tank is to have an inside diameter of 6 m and a height of 17 m. The maximum liquid level in the tank will be 16 m. estimate the plate thickness required at the base of the tank. Take the allowable design stress for aluminum as 90 N/mm2. [CR V6 4th Ed. P 13.9] 6. An open top storage tank for storing 10,000 m3 (design capacity) 0f liquid of specific gravity 1.1 is to be designed. The tank will be fabricated steel conforming to IS:20021962 2B grade. The land and foundation are available free of cost. The annual cost of fabricated shell per unit area is same as that of bottom. a) Determine the optimum proportions for the tank. b) Determine the number of shell courses and thickness of each course. c) Suggest a suitable wind girder. M. Miscellaneous problems 1. Make a preliminary estimate of the plate thickness required for the distillation column specified below: Height, between tangent lines 50 m Diameter 2m Skirt support, height 3m 100 sieve plates, equally spaced Insulation, mineral wool 75 mm thick

Material of construction, stainless steel, design stress 135 N/mm2 at design temperature 200°C. Operating pressure 10 bar (abs) Vessel to be fully radiographed (J = 1) a) Make a preliminary estimate of the plate thickness required for the distillation column. b) Design a skirt support for the column. [CR V6 4th Ed. E 13.3 & 13.4] 2. A jacked vessel is to be used as reactor. The vessel has an internal diameter of 2 m and is fitted with a jacket over a straight section 1.5 m long. Both the vessel and jacket walls are 25 mm thick. The spacing between the vessel and jacket is 75 mm. The vessel and jacket are made of carbon steel. The vessel will operate at atmospheric pressure and the jacket will be supplied with steam at 20 bar. Check if the thickness of the vessel and jacket is adequate for the duty. Take the allowable design stress as 100 N/mm2 and the value of Young’s modulus at the operating temperature is 180,000 N/mm2. [CR V6 4th Ed. P 13.7] 3. A vacuum crystallizer 3.5 m nominal diameter is to be fabricated with stainless steel and is to have a 60° cone (apex angle) at the bottom and a torispherical closure at the top. The distance from the junction of the cone with the shell to the point of tangency of the top closure is 5.5 m. Specify the design for (i) the torispherical head, (ii) the shell, and (iii) the cone.