Most of the evaporator drums operate under vacuum condition and designed for an external pressure of 0.1 N/m^{2}. Conical bottom portion designed for similar pressure rating and top head section preferred to be flanged or flared, dished or conical shape. Calandria, having tubular heating surface designed as per shell and tube heat exchanger model. Since steam under pressure in usually accepted as the heating medium, the design is based on the pressure so the calandria and vapor drum are connected by flanged joints or directly welded. The vapor drum made up of separate cylindrical pieces and joined by flanges. Large nozzles like manholes, slight glasses are reinforced with compensating rings. Supports placed below the brackets are welded to the vapor drum or to the calandria. External calandria is also designed as shell and tube heat exchanger.The design factors, heating surface area and steam requirement are derived by the overall and individual heat balance of multiple-effect chemical evaporation system.
The nomenclature for quadruple effect calculations for design of sugar industry evaporators :- C_{F }= Specific heat of feed (KJ/Kg^{o}C)
- T_{F }=Temperature of feed,^{o}C
- W_{F} = Feed, Kg/hr
- Ts = Saturation temperature of steam to first effect, ^{o}F
- Ws = Steam to first effect, Kg/hr
- W_{1-4 }= Total water removed by evaporation
- m = mass flowrate
- p = product
- v = vapor
- f = feed
- U = heat transfer coefficient
Design of five effect evaporators system:
Overall balance of the evaporator would be: m·f = m·p_{4} +m·vOverall vapor balance: m·v = m·v_{1} + m·v_{2} + m·v_{3} + m·v_{4}
Solute balance | Energy balance equations _{ } | |
First effect | m_{f} = m_{p1} + m_{v1} m_{f}x_{f } = m_{p}x_{p1} |
m_{s .}λ_{s }= m_{f }Cp_{f }(T_{1}-T_{f}) + m_{v1 }.λ_{v1} |
Second effect | m_{p1} = m_{p2} + m_{v2} m_{p1}x_{p1} = m_{p2}x_{p2 } |
m_{v1 }.λ_{v1}= m_{p1}Cp_{f} (T_{2}-T_{1}) + m_{v2 }.λ_{v2 } |
Third effect | m_{p2 }= m_{p3} + m_{v3} m_{p2}x_{p2} = m_{p3}x_{p3} |
m_{v2 }.λ_{v2} = m_{p2}Cp_{f} (T_{3}-T_{2}) + m_{v3 }.λ_{v3} |
Fourth effect | m_{p3} = m_{p4} + m_{v4} m_{p3}x_{p3} = m_{p4}x_{p4} |
m_{v3 }.λ_{v3}= m_{p3}Cp_{f} (T_{4}-T_{3}) + m_{v4 }.λ_{v4} |
Fifth effect | m_{p4} = m_{p5} + m_{v5} m_{p4}x_{p4} = m_{p5}x_{p5} |
m_{v4 }.λ_{v4}= m_{p4}Cp_{f} (T_{5}-T_{4}) + m_{v5 }.λ_{v5} |
Assuming the steam temperature 120^{o}C
The energy value of steam = 2201.6 KJ/kg from steam tables
Basis: For the mass flow rate of the entering juice ‘m’= 208.33tonnes/hr.
Pressure maintained | Temperature from steam tables | Latent heat of vaporization | |
First effect | 1.60687atm= 755 mm Hg | 99.819^{o}C | 2257.4 KJ/kg |
Second effect | 1.19989atm = 480.6 mm Hg | 87.616^{o}C | 2289.4 KJ/kg |
Third effect | 0.81229atm = 302.8mm Hg | 75.844^{o}C | 2319.2 KJ/kg |
Fourth effect | 0.44407atm = 99.6mm Hg | 60^{o}C | 2379.1 KJ/kg |
Fifth effect | 0.09527atm | 50^{o}C |
Assuming the value of x_{f} =0.15
By substituting the values in the balance equations and solving the simultaneous equations we get the following values:
Type | Vapor flow rates(tonnes/hr) | Product flow rate(tonnes/hr) | Massfractions in terms of x_{p} |
1^{st} effect | 66 | 142.33 | 0.1804 |
2^{nd} effect | 64 | 79.33 | 0.2313 |
3^{rd} effect | 17 | 62.33 | 0.32 |
4^{th} effect | 10 | 52.33 | 0.6 |
5^{th} effect | 1 | 51.33 | 0.6 |
Assuming the mass flow rate of steam, m_{s} = 66tonnes/hr
Steam balance:
- Steam consumption m_{s} is = 66tonnes/hr
- Capacity m_{v} = 41532.3499 Kg/hr
- Steam economy = 4.619
Where Q=m_{s} λ_{s}
- m_{s} λ_{s} = Q_{1} = U_{1}A_{1}ΔT_{1}
- m_{s} λ_{s} = Q_{2 }=U_{2}A_{2} ΔT_{2}
- m_{s} λ_{s} = Q_{3} =U_{3}A_{3} ΔT_{3}
- m_{s} λ_{s} = Q_{4} =U_{4}A_{4} ΔT_{4}
m_{s} λ_{s}=U_{}A_{ }ΔT | U, KJ/(m^{2}.hr.^{ o}C) | |
First effect | 66000×2187.18 = U_{1}×2700×(125-110) | 3564. 3 |
Second effect | 63000×2201.6 = U_{2}×2500×(110-102) | 7012 |
Third effect | 17000×227.168 = U_{3}×1200×(102-90) | 2530.6 |
Fourth effect | 9310×2281.6 = U_{4}×800×(90-80) | 2658.861 |
Fifth effect | 9320×2353 = U_{5}×300×(80-60) | 3663.41 |
Calculation for number of tubes:
Formula for number of tubes= n × π × D × L = AType | Vapor flow rates(kg/hr) | Product flow rate(kg/hr) | U(KJ/m^{2}.hr^{ o}C) | Area, A=m^{2} | n, no.of Tubes |
1^{st} effect | 66000 | 142.33 | 3564.3 | 2700 | 4775 |
2^{nd} effect | 63000 | 79.33 | 7012 | 2500 | 4421 |
3^{rd} effect | 17000 | 62.33 | 2530.7 | 1200 | 2122 |
4^{th} effect | 9320 | 52.33 | 2658.86 | 800 | 1415 |
5^{th} effect | 1000 | 51.33 | 3663.41 | 300 | 531 |
Model mechanical design of sugar industry evaporators: _{ }
- Temperature in evaporator = 99.819^{ o}C
- Diameter of tubes: 42 ID × 45 OD
- No. of tubes: 4775
- Length of the tube = 4m
Calandria:
- Pressure = 755 mm
- Heating surface area = 2700 m^{2}
- Material of construction: Stainless Steel
- Permissible stress for low carbon steel—98 N/mm^{2}
- Modulus of elasticity for low carbon steel = 19.0 X 10^{4} N/mm^{2}
- Modulus of elasticity for SS 304= 9.5 X 10^{4}N/mm^{2}
- No. of tubes N_{t} = 4775
- Pitch of the tube = Pt/D_{o} = 67.5mm
- Area occupied by tubes As = n X 0.866 X S_{T}^{2} / β = 18.4 m^{2}
- Required area for central down take = 40% X Cross sectional area of the tube = 0.4 X 2110 X π X0.045^{2} / 4 = 3.04m^{2}
- Actual area of down take is 3.1m^{2}
- Total area of tube sheet is = 24.03m^{2}
- Diameter of the tube sheet is = 5.96m
- Calandria sheet thickness: t_{s} = pD / 2fJ – p = 5.48mm
Tube sheet thickness:
F = √(K/[2+3K])
Where K = E_{s}t_{s}(D_{0}-t_{s}) / E_{t}N T_{i}(d_{0}-t_{t})
- E_{s} = modulus of elasticity of shell material
- t_{s }= Sheet thickness
- t_{t }= Tube thickness
- k = 0.15527
- F = 0.250936
- t = FG√(0.25p)/f = 5.48mm
Bottom flange of calandria:
- Thickness of the flange = 40mm
- Number of bolts = 112
- Outside diameter = 3894mm
- Pitch circle diameter = 3825mm
- Size of bolts = 20M
Evaporator drum:
- Rd = V/A 0.0172 X (ρ_{L } – ρ_{V }/ ρ_{V})^{1/2}
- Let Rd = 0.8
- Here V = volumetric flow rate of vapor in m^{3}/sec = 66
- A = 31.32m^{2}
- Diameter of drum is 8m