I. INTRODUCTION
Several factors are considered in properly designing an efficient and economical production plant. Equipment design and its importance are significant in the industrial manufacturing plants that is at par with the production o f cost-effective and high quality products. With the reference with the previous chapters, an ideal process flow diagram was produced that determine the plant capacity and detailed computation of the mass and energy balances of the equipment. Equipment will be subject to determine their capability while being subjected to different parameters such as temperature, pressure and the likes. This manuscript will be providing an optimum design for the Fermentor, Rotary Drum Filter, Carbon adsorber and Evaporator. The importance of appropriate materials of construction must also be recogn ized. Products desired cannot be manufactured without considering the selection of appropriate and optimum materials of construction. This will be used to consider the container safe, economical for manufacturing and maintaining of the product quality. The materials to be selected must resist corrosion and sufficient strength to prevent breakdown caused by external parameters and processing of the product. Operating conditions con ditions are also one on e of the major considerations consider ations for the design of equipment. The design must be capable of producing the desired condition and must withstand any stresses and extreme conditions of the operation. Designing involves in the preparation of individual equipment specification sheet that is derived from the fabrication of different kinds of units with the help of available brochures. Modernization and development of new processes requires the use of chemical engineering principles and theories that is blended with actual limits with concern on the environmental and safety standards. 279
II. SPECIFICATION SHEETS A. Specification Sheet for Fermenter SPECIFICATION SHEET IDENTIFICATION Name of Equipment Equipment Code Equipment Type Operation Number required BASIC DESIGN DATA Function Operating Temperature Operating Pressure Material Handled VESSEL DESIGN Vessel Capacity Height Diameter Material of Construction Shell Thickness Head Thickness Welding Type IMPELLER DESIGN Impeller Type Rotational Speed No. of Baffles Baffle Width Impeller Clearance at the Bottom POWER REQUIREMENT Motor Size COOLING SYSTEM DESIGN Jacket Area Jacket Diameter Distance of Outer Shell to Jacket Thickness of Jacket Material of Construction Cooling Medium Cooling Temperature
Fermenter R – 2 2 Stirred-Type Bioreactor Batch Operation 2 units To ferment glucose into lactic acid 24 - 37°C 1.20 atm C6H12O6 (glucose), H2O, Na2SO4, Yeast Extract, CaCO3 6 m3 5.50 m 3.00 m SS304 3.00 mm 3.00 mm Double Welded Butt Joints (fully radiographed) 4-Pitched Blade 150 rpm 4 0.25 m 1m
No. of Impeller Impeller Diameter Impeller Width Impeller Length Distance between Impeller
3 1m 0.2 m 0.25 m 1.25 m
5 hp 3.25 m2 11.00 m 4.50 m 2.00 mm SS304 Water 25°C
280
II. SPECIFICATION SHEETS A. Specification Sheet for Fermenter SPECIFICATION SHEET IDENTIFICATION Name of Equipment Equipment Code Equipment Type Operation Number required BASIC DESIGN DATA Function Operating Temperature Operating Pressure Material Handled VESSEL DESIGN Vessel Capacity Height Diameter Material of Construction Shell Thickness Head Thickness Welding Type IMPELLER DESIGN Impeller Type Rotational Speed No. of Baffles Baffle Width Impeller Clearance at the Bottom POWER REQUIREMENT Motor Size COOLING SYSTEM DESIGN Jacket Area Jacket Diameter Distance of Outer Shell to Jacket Thickness of Jacket Material of Construction Cooling Medium Cooling Temperature
Fermenter R – 2 2 Stirred-Type Bioreactor Batch Operation 2 units To ferment glucose into lactic acid 24 - 37°C 1.20 atm C6H12O6 (glucose), H2O, Na2SO4, Yeast Extract, CaCO3 6 m3 5.50 m 3.00 m SS304 3.00 mm 3.00 mm Double Welded Butt Joints (fully radiographed) 4-Pitched Blade 150 rpm 4 0.25 m 1m
No. of Impeller Impeller Diameter Impeller Width Impeller Length Distance between Impeller
3 1m 0.2 m 0.25 m 1.25 m
5 hp 3.25 m2 11.00 m 4.50 m 2.00 mm SS304 Water 25°C
280
Inoculation Pipe
Stirrer Shaft Seal
Vent
Working level
Impeller HT HL Baffle
Y Sampling point
Da
E
Drain Point
D
281
W La
282
ASSUMPTIONS 1. The fermentation will be conducted in a batch reactor. 2. 1 units of fermenter will be used per batch. 3.
An allowance of 5-6 hours for the cleaning and start-up of the fermenter will be allocated.
4. The material of construction of the fermenter will be S S304 for corrosion resistance. 5. ASME-UPV vessel design code will be used for the vessel design. 6. The impellers to be used will be Four-Pitched Blade turbines. 7. Motor efficiency of the agitator is 80 %. 8. The cooling system of the fermenter will be a jack eted type.
Design Equations: Residence Time of Fermentation From Bioprocess Engineering (2nd Edition) by Doran, P. M.:
t = μ1 ln1 μxq p p q =Yμm where: µ max – maximum specific growth rate x0 – initial cell density q p – specific rate of product formation pf/0 – final(f) / initial (0) product concentration 283
t b – batch culture time ms - maintenance coefficient
Vessel Design (Ref: Principles of Fermentation Technology by Stanbury, P.F. et al:Table 7.2. Details of Geometrical Ratios of Fermenters with Three Multi-bladed impellers)
•
Height of the Liquid (L):
V = H •
Internal Pressure (P):
P=P ρH gg •
Shell Thickness: For Cylindrical shell (Ref: Plant Design and Economics by Peters and Timmerhaus, Table 4 p.537)
t = SE 0.Pr 6P C
284
•
Head Thickness: For Ellipsoidal head (Ref: Plant Design and Economics by Peters and Timmerhaus, Table 4 p.537)
t = 2SEPD0. 2P C Impeller Design (Ref: Principles of Fermentation Technology by Stanbury, P.F. et al:Table 7.2)
•
Impeller Diameter:
= 13 •
Impeller distance from Vessel floor:
= 13 •
Length of Impeller Blade:
= 14 •
Width of Impeller Blades:
= 15 •
Baffle Width:
= 121 285
•
Distance between Impellers:
= 1.3 (Ref: Plant Design and Economics by Peters and Timmerhaus, page 241)
•
Power Requirement: For NRe>10,000 (Ref: Unit Operations of Chemical Engineering by McCabe and Smith, 5 th Edition)
P= N = Da – impeller diameter
•
Viscosity of Fermentation Broth: (Ref: Chemical Engineering Design Principles, Practice, and Economics of Plant and Process Design by G. Towler, et al. p. 440 Eq. 8-11.)
= ∑
286
Cooling System (Jacket) Design ( Ref: Ch.E. Handbook 8 th Edition, p. Eq. 5-31)
•
Surface Area of Jacket (Heating Area):
A = UΔTQ •
Log Mean Temperature Difference: (Ref: Ch.E. Handbook 8 th Edition, p. 5-7 Eq. 11-5a)
′ " ′ " (t t )t t ∆T = ln (t′′ t"" ) t t
Where 1- inlet condition, 2- outlet condition ’-hot fluid , ”-cold fluid
Diameter of Vessel with Jacket
πD V π D 2t Area of Jacket= H = 4 4
Outer Shell to Jacket Distance
d− = Jacketed Vessel DiameterOut2 er Shell Diameter of Tank t = SE Pr0. 6P C
Thickness of Jacket
287
NOMENCLATURE A j – Jacket Area, m2 c – Corrosion allowance, in Da – Impeller Diameter, m DT – Inside Diameter of Tank, m E – Distance of impeller from the bottom of the vessel g – Gravitational constant, m/s2 HT – Height of tank, m J – Baffle width, m L – Blade Length of Impeller, m mS – maintenance coefficient, h-1 P – Internal pressure, psi Q – Heat released during reaction, W q p – specific rate of product formation, h-1 Sw – Working Stress, psi tB – Batch time, h tH – Head thickness, mm tR – Reaction time, h tS – Shell thickness, mm Vliquid – Volume of liquid, m3 VT – Volume of tank, m3 W – Impeller width, m XA – Conversion Xo – initial cell density, g/L Y – Impeller distance, m µ - Viscosity of fermented broth, Pa-s µ max – maximum specific growth rate, h-1 ρ – density of fermented broth, kg/m3
288
Design Calculations:
0.017... =0.014... 0.003 0.001 2 t = μ1 ln1 μxq p p
Residence Time of Fermentation
From “Optimization and modeling of Lactic acid production” by Rasfid Roslina
p = . × p = . × p = p = 0 81.3667 g/L
, no product at the beginning of fermentation
Y p/s= 0.8248 kg Lactic acid per kg glucose, ms=0.098/h
q = q = x =
(0.09033 h-1) (0.8248) + 0.098 0.1725 h-1
9.26565 g/L
µ max = 0.09033/h.
289
0. 0 9033 1 ℎ 81. t = 0.09033 l n 1 3 6670 9. 2 6565 0. 1 725 ℎ ℎ = 42.62 hours (1.77days)
Total batch time:
= (Ref: Chemical Process Engineering, Design and Economics by Silla, Table 7.10 p. 397 )
Assuming that it takes the maximum time for all variables, therefore: tf = 2.38 h tc = 2.0 h te = 1.0 h t b = 42.62 h + 2.38 h + 2.0 h + 1.0 h
tb = 48 h (2 days)
290
Number of Units Required
=1 × ×2 days
Number of Units = 2 units Vessel Design In Fermented Broth: Component
Mass (kg)
Density(kg/m3)
Volume(m3)
Calcium Lactate
576.83
1,490
0.3871
Calcium Carbonate
7.44
2,710
0.0027
Calcium Sulfate
7.89
2,320
0.003
97.55
1,540
0.063
Water
5,395.31
1,000
5.395
Sodium Carbonate
6.14
2,540
0.0024
Total
6,094.39
Glucose
5.8535
Total Volume of Feed = 5.8535 m 3 /batch Total Mass = 6,094.39 kg/batch
ρ = ρ = 6,5.0894.53539mkg =
Average Density:
1,041.14 kg/m 3
291
Volume of Feed per unit of Fermenter:
V = 5 . 8 535 m V = 1 unit/bat/batchch = 5.8535 m3 /unit
From Brochure Mobius Bioreactors Specification Sheet, and upscaling the rated capacity of the bioreactor to 6000L:
D = 2.52 m = 99.21 in
(R=49.60 in)
H = 5.05 m
Height of Liquid:
H =
H = .. = P=P ρH gg P=101,325 Pa1,041.14 1.1685 m 9.81 = 1.1685 m
Internal Pressure:
113,259.57 Pa = 16.431 psi
292
Shell Thickness: For Cylindrical shell:
t = SE 0.Pr 6P C For Fully Radiographed Double-butt Welded: EJ = 1.00. For SS304, working stress (SW = 123 MPa = 17,844.56 psi) (Ref: ChE Handbook, 8 th ed., Table 25-11, p. 25-36)
t = ,..−... t =0.0457 in t =0.0457 in 161 in = ≈ , < 0.25 in
0.1081 in
2.748 mm (3mm)
Head Thickness: For Ellipsoidal head:
t = 2SEPD0. 2P C For Fully Radiographed Double-butt Welded: EJ = 1.00. For SS304, working stress (SW = 123 MPa = 17,844.56 psi) (Ref: ChE Handbook, 8 th ed., Table 25-11, p. 25-36)
t = ,..−. .. 293
t =0.0457 in t =0.0457 in in = ≈
, <0.25 in
0.1081
2.747 mm (3mm)
Impeller Design From brochure Mobius Bioreactors Specification Sheet , the impeller used is 4-Pitched Blades. Impeller Diameter:
= 13 = . =. Impeller distance from Vessel floor:
= 13 = . =. Length of Impeller Blade:
= 14 = . =. 294
Width of Impeller Blades:
= 15 = . =. Baffle Width:
= 121 = . =. Distance between Impellers:
= 1.3 = .. =. Power Requirement For NRe>10,000
P= N = Viscosity of Fermentation Broth:
= ∑ 295
Component
Mass (kg)
Mass Fraction
Viscosity
xμ
Calcium Lactate
576.83
0.0946
-
-
Calcium
7.44
0.0012
-
7.89
0.0013
-
-
97.55
0.016
0.00555
2.883
5,395.31
0.8853
0.000864
1,024.653
Carbonate Calcium Sulfate Glucose Water Sodium
1.212 6.14
0.001
6,094.39
1.00
0.000825
Carbonate Total
1,028.748
= ∑ =1,028.748
=
9.72E-04 Pa-s
Computation of the Reynold’s Number:
N = Dμvρ
296
From the brochure Mobius Bioreactors Specification Sheet, the type of impeller used is a 4-pitched blade turbine. The fermenter will be agitated at 150rpm.
,. . × N = .- −
=
2,254,732 > 10,000
Power Requirement
K n D = g ρ For Four-Pitched Blade turbine, K T = 1.27. (Ref: Unit Operations and Processes in Environmental Engineering 2 nd Edition by Reynolds and Richards, Table 8.2 p. 236)
K n D = g ρ . ,. . × P = P = 2,783.33 W ≈ 3.73 hp
297
Approximate Efficiency of an Electric Motor varies between sizes. In this equipment, a less than 5 kW turbine have a motor efficiency ƞ = 80%
(Ref: Chemical Engineering Design by Sinnott R.K., Table 3.1 p. 93 )
= = ..
= 4.66 hp ≈ 5 hp
From, the nearest standard size electric motor is 5 hp.
(Ref: Chemical Process Engineering, Design and Economics by Silla, Table 5.10 p. 240 )
Cooling System (Jacket) Design Surface Area (Heating Area):
A = UΔTQ 298
Q =4,173,629.01 × × × × = 16,101.96 W/unit
Log Mean Temperature Difference:
Fermentation Broth
Cooling Water
Inlet Temperature (°C)
Outlet Temperature (°C)
Inlet Temperature (°C)
Outlet Temperature (°C)
50
37
25
35
′ " ′ " (t t )t t ∆T = ln (t′′ t"" ) t t 5035 3725 ∆T = 5035 ln 3725 ∆ = 13.44 K
The cooling water will flow counter-current to the feed:
Counter-current Flow 60
50
C , e r u t a r 40 e p m e T
30
20 Feed
Cooling Water
299
From Chemical Process Engineering Design and Economics Tab le 7.6; for stirred tank (jacketed) using cooling water with organic solution. U = 50 – 80 Btu/h-ft2-°F. For an average value of U = 65 Btu/h-ft2-°F (369.07 W/m2-K):
(Ref: Chemical Process Engineering, Design and Economics by Harry Silla. 2003, Table 7.6 p. 386)
t A = 369.16,071m01.W9K6 W/uni 13.44 K = ≈ 3.246 m2
3.25 m2
300
Diameter of Vessel with Jacket: Cooling water flowrate is at 99,800 kg/day for Fermenter.
πD V π D 2t Area of Jacket= H = 4 4 × , V = V = m π2.525523×10 −m 99.1.186850 unimt = πD 4 4 ≈ 99.8 m3/unit
= 10.548 m
10.75 m
Outer Shell to Jacket Distance:
d− = Jacketed Vessel DiameterOut2 er Shell Diameter of Tank . − . +× d− = − = ≈ 4.01 m
4.25 m
301
Thickness of Jacket: For SS304, the working stress (SW) = 17,844.56 psi (Ref: ChE Handbook, 8 th ed., Table 25-11, p. 25-36)
t = SE 0.Pr 6P C P=1000 9.81 1.852 m P= 18,168.12 Pa = 2.636 psi
.. t = ,..−. t =0.0073 in t =0.0073 in 161 in = ≈ , < 0.25 in
0.0698 in
1.774 mm (2mm)
302
B. Specification Sheet for Microfilter SPECIFICATION SHEET IDENTIFICATION Name of Equipment Equipment Code Number of Elements Number of tubes per element Function Operation Type Materials Handled
Number Required BASIC DESIGN DATA Pressure Pressure Drop Temperature Filtrate Flow Permeate Flux Permeability Rate of Filtration Filtration Time Membrane Permeability Power Requirement Total Filtering Time Shell Thickness MEMBRANE DESIGN Filter Membrane Used Total element Area No. of tubes Area of membrane/per module Pore Size Membrane Diameter Length Operating Mode HOUSING DESIGN Type Materials of Construction Module Length PUMP DESIGN Pump Type
Microfilter F-3 2 100 To separate the cell mass and other solids from the fermented medium Continuous Tubular Microfiltration Membrane Calcium Lactate, Cell Mass, Calcium Carbonate, Sodium Carbonate, Calcium Sulfate, Residual sugars and Water 1 unit 1.5 bar 1.9738 atm ≈ 2 bar 25 – 30 °C 0.2438 m3/h 18.7402 L/m2-hr 329.3533 L/ m2-hr-atm 13.7 m3/hr 0.4276 hours 329.3533 L/m2-hr-atm 0.2438 hp 0.7276 hours/day 2.0199 x 10-3 m Polyether sulfone (PES) 9.3 m2 100 0.093 m2 0.1 micron 1.55 x 10-3 m 1.022 m Crossflow Filtration 2-port style Stainless steel AISI 316/316L 1.044 m Centrifugal Pump
303
DIAGRAM FOR MICROFILTER (F-3): D0 = 160.6 mm L0= 1022 mm
L0 = 1040 mm I0 = 125 mm
304
ASSUMPTIONS:
1. The Microfiltration is operated at constant pressure filtration. 2. Material of Construction – Stainless steel AISI 316/316L - Pentair X-Flow R-100 Microfiltration Membrane Brochure 3. Type of Microfiltration Membrane: Tubular Membrane - Membrane Filtration Handbook, pg.16 4. Operating Pressure: <2 bar; 1.5 bar - Pentair X-Flow R-100 Microfiltration Membrane Brochure 5. Pressure Drop: 1.9738 atm - Table 14 from Membrane Filtration Handbook 6. Membrane Material: Polyether sulfone (PES) - Pentair X-Flow R-100 Microfiltration Membrane Brochure 7. Theoretical Internal Diameter of permeate tube: 1 in = 0.0254 m - Table 8 Types and Variables of Tubular Membranes, Membrane Filtration Handbook, p.18 8. For Shell Thickness: - Hesse and Rushton Equipment Design - Fm = 1.0, for high tensile strength steel - Fs = 0.25, steel factor - Fa = 1.0, radiographing factor - Fr = 1.0, steel relieving factor - Su = 248 MPa, Table 28-11, p.28-39, Chemical Engineering Handbook 7th Edition - e = 0.7, for V and U single butt joint 9. Length of module: 1040 mm - Pentair X-Flow R-100 Microfiltration Membrane Brochure 10. Viscosity (µ) of the filtrate, since it is composed mostly of water has a value of µ= 0.85 cP or 8.5x10-4 Pa-s - Unit Operation, of Chemical Engineering Appendix 11. The velocity is assumed to be 5 m/s that gives a turbulent flow and good mass transfer, pg.1036, Unit Operations of Chemical Engineering, 7th Edition 12. Size range of calcium lactate: 0.000394 – 0.0015 microns -
Molecular Recipes: Calcium Chloride, Calcium Lactate and Calcium Lactate Gluconate 305
Size range of cell mass: 0.5 – 0.8 microns - JGI Genome Portal 13. Length of tube: 1.022 m - Pentair X-Flow R-100 Microfiltration Membrane Brochure
DESIGN EQUATIONS 1. Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, Equation 29.48, p.1040 υ = k c ln
−−
Where: υ = permeate flux (L/m2-h) K c = Mass Transfer Coefficient Cs = cell mass and CaSO4 concentration in the retentate (kg/m3) C1 = cell mass and CaSO4 concentration in the feed (slurry) (kg/m3) C2 = maltose, dextrin and insoluble solid concentration in (kg/m3) 2. Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, Equation 30.55, p.1041 Dv=
.
Where: Dv = diffusivity (cm2/s) T= operating temperature (K) r o = radius of particles (cm) µ = (cP) 3. Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, Equation 3.10, p.53 NRe =
Where: D = diameter of tube (cm) D= 1 in 2.54 cm V= velocity of fluid (cm/s) ρ = average density of the feed (g/cm3) µ = viscosity of major component in solution fed as assumed (g/cm-s)
≈
4. Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, p.539 NSc =
Where:
306
µ = viscosity of major component in solution fed as assumed (cP)
ρ = average density of feed (g/cm3) = Xi ρ = 1060.256 kg/m3 = 1.060256 g/cm3 Dv = diffusivity (cm2 /s)
5. Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, p.552 NSh = 0.0096 NRe0.913 NSc 0.346 Where: NSh= Sherwood Number NSc= Schmidt Number NRe = Reynolds Number 6. Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, Equation 17.50 p.545 k c =
Where: NSh = Sherwood Number D = diameter of tube (cm) Dv = diffusivity (cm2/s) 7.
∆= −∆ −
8. Hesse and Rushton Process Equipment Design, Equation 4-3, p.87 ts =
Where: ts= minimum shell thickness C = corrosion allowance usually taken as 1/6 inch D = inside diameter P = maximum internal pressure S = working or allowable tensile stress e = efficiency of the welded joints 9. Chemical Engineering Handbook 7th Edition, Equation 10-50, pg.10-23 P=
. ^
Where: H = total dynamic head (Pa) Q = capacity = 13.7 m3/hr
307
DETAILED DESIGN COMPUTATION MEMBRANE PROCESS SELECTION
According to Table 2 from Membrane Filtration Handbook, among the four membrane processes: reverse osmosis, nanofiltration, ultrafiltration and microfiltration; it is best to use microfiltration since its primary purpose in the process is to separate the cell mass and other solids from the fermented medium. Thickness should be in range of 10-150 µm. The pore size will be ranging between 4 - 0.02 µm with membrane module allowed are tubular and hollow fiber. Membrane
materials
allowed
are
ceramic
PP,
PSO
(polysulfone)
and
PVDF
(polyvinylidenedifluoride). The operating pressure should be <2 bar (Wagner, 2001).
308
MEMBRANE MATERIAL SELECTION
✓ ✓
Means high resistance Means low resistance Means either that the information is based on theory of that practical results have proved to be dubious
According to Table 4 in Membrane Filtration Handbook as shown, it is suitable to use Polyether sulfone (PES) because of its high resistance with most of the organic and inorganic compounds. It is suitable even at high operating temperatures and has high resistance in a wide range of pH.
309
From Material Balance:
Table 1: Input/Feed to the Microfilter
Component
Mass (kg/day)
Calcium Lactate Water CaCO3 Na2CO3 Cell Mass CaSO4 Glucose Total
576.83 5,395.31 7.44 6.14 3.2329 7.88 97.55 6,094.38
Mass Fraction (Xi) 0.0946 0.8853 0.0012 0.0011 0.0005 0.0013 0.0160
Density (kg/m3)
Volume (m3 /day)
Xi∙ρ
1,490.00 1,000.00 2,710.00 2,540.00 600.00 2,320.00 1,540.00
0.3871 5.3953 0.0027 0.0024 0.0037 0.0033 0.0633 5.8578
140.954 885.300 3.252 2.794 0.300 3.016 24.640 1060.256
Density (kg/m3)
Volume (m3 /day)
Xi∙ρ
1,490.00 1,000.00 2,540.00 2,710.00 1,540.00
0.3871 5.3945 0.0024 0.0027 0.0633 5.8500
141.252 887.000 2.540 2.981 24.794 1058.567
Table 2: Filtrate/Permeate
Component
Mass (kg/day)
Calcium Lactate Water Na2CO3 CaCO3 Glucose Total
576.74 5,394.48 6.14 6.84 97.54 6,081.74
Mass Fraction (Xi) 0.0948 0.8870 0.0010 0.0011 0.0161
Table 3: Residue/Retentate
Component
Calcium Lactate Water Cell Mass CaSO4 Glucose CaCO3 Total
Mass (kg/day) 0.08 0.82 3.23 7.88 0.01 0.59 12.64
Mass Fraction (Xi) 0.006329 0.064873 0.255538 0.623418 0.000791 0.046677
Density (kg/m3)
Volume (m3 /day)
Xi∙ρ
1,490.00 1,000.00 600.00 2,320.00 1,540.00 2,710.00
0.0000537 0.00080 0.0054 0.0034 0.0000065 0.00022 0.00988
9.43021 64.87300 153.32280 1446.32976 1.21814 126.49467 1801.66858
310
MEMBRANE AREA CALCULATION Diffusivity (D v): From Unit Operations of Chemical Engineering by McCabe and Smith, 7 th Edition, page 538
Dv=
.
Where:
Dv = diffusivity (cm2/s) T= operating temperature (K) r o = radius of particles (cm)
μ
= viscosity (cP)
Size range of calcium lactate: 0.000394 – 0.0015 microns (Molecular Recipes: Calcium Chloride, Calcium Lactate and Calcium Lactate Gluconate) Size range of cell mass: 0.5 – 0.8 microns (JGI Genome Portal)
.+. .+. μ
Dave of calcium lactate =
Dave of cell mass =
Dave = r 0 ave =
. +.
= 9.47 x 10-8 cm
= 6.5 x 10-5 cm
= 3.2547 x 10-5 cm
. − =1.6274 10−
cm
µ = viscosity (cP)
Assume that the bulk concentration comprises major component of the solution which is composed of water with viscosity of 0.85 cP or 8.5x10 -4 Pa-s.
Dv =
.. +. .
= 1.6042 x 10 -8 cm2 /s
Schmidt’s Number (NSc): From Unit Operations of Chemical Engineering by McCabe and Smith, 7 th Edition, p. 539
NSc =
311
Where: µ = viscosity of major component in solution fed as assumed (cP)
ρ = average density of feed (g/cm3) = Xi ρ = 1060.256 kg/m3 = 1.060256 g/cm3 Dv = diffusivity (cm2 /s) NSc =
. . / . /
= 4997399.827
Reynold’s Number (NRe): From Unit Operations of Chemical Engineering by McCabe and Smith, 7 th Edition, p.53
NRe =
Where:
D = diameter of tube (cm) D= 1 in
≈
2.54 cm
V= velocity of fluid (cm/s) ρ = average density of the feed (g/cm3) µ = viscosity of major component in solution fed as assumed (g/cm-s) Table 8 p.18 Types and Variables of Tubular Membranes, Membrane Filtration Handbook
Assume V=5m/s that gives turbulent flow and good mass transfer ( pg. 1036 of Unit Operations of Chemical Engineering, McCabe Smith, 5 th Edition)
NRe =
..
= 14,941.1765
312
Sherwood Number N Sh (for high Schmidt Number): From Unit Operations of Chemical Engineering by McCabe and Smith, 7 th Edition, p.552
NSh = 0.0096 NRe0.913 NSc 0.346 Where: NSh= Sherwood Number NSc= Schmidt Number = 0.0096 (14,941.1765)0.913 (4997399.8270)0.346 = 12,919.6280
Mass Transfer Coefficient (K c): Unit Operations of Chemical Engineering by McCabe and Smith 7th Edition, Equation 17.50, p.545 k c =
Where:
NSh = Sherwood Number D = diameter of tube (cm) Dv = diffusivity (cm2/s) k c =
,... /
= 8.1597 x 10 -5 cm/s
Permeate flux (υ) : From Unit Operations of Chemical Engineering by McCabe and Smith, 7 th Edition, p. 1042
υ = k c ln Where:
−−
υ = permeate flux (L/m2-h) K c = Mass Transfer Coefficient Cs = cell mass and CaSO4 concentration in the retentate (kg/m3) C1 = cell mass and CaSO4 concentration in the feed (slurry) (kg/m3) 313
C2 = maltose, dextrin and insoluble solid concentration in (kg/m3) According to Overall Material balance sheet, since there will be no component of cell mass and CaSO4 in filtrate/permeate, C2 = 0. Permeate flux equation will be: υ = k c ln
For Cs and C1 calculation: Based on Overall Material Balance Data Sheet: Cs =
=
( ) 4
..+./ /
= 1124.4939 kg/m3 C1 =
=
+
..+./ / ../ /
= 1.8971 kg/m3
Since C2 = 0, υ = k c ln
= (8.1597 x 10-5cm/s) ln
= 5.2098 x 10-4 cm/s = 5.2098 x 10-6 m/s
From Table 30.4 Conversion Factors for Permeate Flux in Unit Operations of Chemical Engineering by McCabe Smith
314
− . . =
υ = 5.2098 x 10-6 m/s x υ = 18.7402 L/m2- h
According to the Membrane Filtration Handbook by Wagner, p. 94, there is no general rule for the permeate flux of Microfiltration, and,if in doubt, a low flux value should be used, given that there is also no given permeate flux from the brochures used, thus, this value of permeate flux is acceptable.
Permeability (Qm): From Unit Operations of Chemical Engineering by McCabe and Smith, 7 th Edition, p.885
Qm =
∆−∆
Where:
= permeate flux
Qm = membrane permeability ΔP = pressure drop Δπ = osmotic pressure difference µ = average viscosity of water as assumed major component in feed µ water = viscosity of water (0.85cP)
Osmotic Pressure Difference (Δπ) :
Δπ =
(Cs -C1)
Where:
R= 0.08206 L-atm/mol-K MWave = average molecular weight of cell mass and CaSO4 Cs = cell mass and CaSO4 concentration in the retentate (kg/m3)
315
C1 = cell mass and CaSO4 concentration in the feed (slurry) (kg/m3)
MWave =
+. /
= 14568.07 g/mol
Cs = 1124.4939 kg/m3 = 1124.4939 g/L C1 = 1.8971 kg/m3 = 1.8971 g/L Δπ =
+. .. /
(1124.4939-1.8971) g/L
Δπ = 1.9169 atm
Pressure Drop (ΔP) : For Microfiltration (Process Liquid) from Table 15 of Membrane Filtration Handbook, p.24
Typical Number of Elements = 2 (Table 15 from Membrane Filtration Handbook, p. 23) Maximum allowed pressure drop = 1.0 bar per element (Table 14 from Membrane Filtration Handbook) ΔP= 1 bar (2 elements) = 2 bar ( ΔP = 1.9738 atm = 200 kPa
.
) = 1.9738 atm
Permeability (Q m): Qm=
=
∆−∆
. .
.−. .
Qm = 329.3533 L/m2-hr-atm 316
From Membrane Filtration Handbook, Table 37 Necessary Steps for Designing a System, p.117:
Actual Area of Membrane:
ℎ = 2ℎ Where:
A= area of membrane (m2)
−
v = Permeate flux (
)
Number of tubes per element required: No. of ultrafilter unit =
/ ℎ
=
But since there is a given 9.3 m2 of total membrane area and 100 number of tubes in the Pentair X-Flow R-100 Microfiltration Membrane Brochure, the total membrane area and no. of tubes were not computed.
Ratio of total membrane area / no. of tubes = To solve for total time of filtration:
.
= 0.093 m2 (Filter Area)
From the Pentair X-Flow R-100 Microfiltration Brochure, the flowrate is 13.7 m 3 /hr
Time of Filtration:
. =. .
Backwash Frequency: once every 15 minutes Backwash Frequency for 1 hour:
1 ℎ× 601 ℎ =60 ÷15 =4
Backwash Duration: 5 minutes (average) range is 1 – 10 minutes Total Filtering Time (t): Total time of filtration breakdown: Time of Filtration
=
0.4276 hours 317
Time of Washing
=
0.3 hours
_______________________________________
Total Time
=
0.7276 hours/day
FILTER MEDIA The appropriate material for the filter membrane with respect to the feed and pressure applied is a Polyether sulfone (PES) according to the Pentair X-Flow R-100 Microfiltration Membrane Brochure.
POWER REQUIREMENT From Chemical Engineering Handbook 7th Edition, pg.10-23 Equation 10-50 P=
. ^
Where:
H = total dynamic head (Pa) H = 1.4804 atm = 150000 Pa – 101325 Pa = 48675 Pa Q = capacity = 13.7 m3/hr Assume: 1 day = 24 hour-operation
×. = .× = Pactual =
0.1853 kW = 0.2438 hp
. . =
= 0.2647 kW
TYPE OF PUMP USED: CENTRIFUGAL PUMP From Perry’s Chemical Engineers Handbook 7 th Edition, pg. 10-24 Centrifugal pump is used due to its capacity ran ging from 0.5 m3/h to 2 x 104 m3/h (2 gal/min to 105 gal/min (2 gal/min to 105 gal/min, this type of pump is widely used in the chemical industry for transferring liquids of all types.
SHELL THICKNESS (ts): ts =
− ℎ ,. 4 3, . 87 318
Where: ts= minimum shell thickness C = corrosion allowance usually taken as 1/6 inch D = inside diameter P = maximum internal pressure S = working or allowable tensile stress e = efficiency of the welded joints S = Su * Fs * Fm * Fr * Fa Su = ultimate or yield strength of material (ChE Handbook 8th edition, Table 25-8, p.25-36) Fm = material factor = 1.0 for high tensile strength carbon steel Fs = steel factor = 0.25 Fa = radiographing factor = 1.12 if mandatory and 1,0 if not mandatory Fr = stress relieving factor Su = ultimate yield strength of material (Chemical Engineering Handbook 7th Ed., p.28-39) Where: Fm = 1.0 Fs = 0.25 Fr = 1.0 Fa = 1.0 e = 0.7 for V of U double butt joint Su = 248 x 106 Pa = 2447.5799 atm S = (2447.5799 atm)(1)(1)(0.25)(1)= 611.8950 atm Operating Pressure = 1.4804 atm ts = ts =
− . . ..−. 1.58×10−=2.0199×10−
ts = 2.0199 mm
319
C. Specification Sheet for Carbon Adsorber SPECIFICATION SHEET IDENTIFICATION Name of Equipment Equipment Model
Carbon Adsorption Tank ProtectTM LM-72 Modular Liquid Adsorber (Calgon Carbon Corporation)
Equipment Code
T-4
Equipment Type
Fixed-bed down flow adsorber
Number Required
1 unit
BASIC DESIGN DATA Function
To purify and adsorb the residual sugar
Temperature
25-30 OC
Pressure
107.5 kPa
Hydraulic Loading
0.74 m3 feed/(m2 bed – hr)
Flow Rate
0.665 m3/hr.
Materials Handled
Glucose (C6H12O6), Lactic Acid (C3H6O3) , Water (H2O)
ADSORBER DESIGN Carbon Type
Norit® SX-plus
Carbon Bed Length
23 in.
Contact Time
46.24 mins.
Carbon Replacement
60 days
Carbon Weight
308.4 kg
Pressure Drop
0.24 Pa.
Carbon Support
Succession of two metal screens with sizes 14 and 80 mesh
VESSEL DESIGN Height
48 in.
Diameter
42 in.
Material of Construction
UNS K03005 Carbon Steel 320
Wall Lining
Vinyl ester
Wall Lining Thickness
30 mils
Shell Thickness
1 in.
Head Thickness
1 in.
Welding Type
double-welded butt joints (spot-examined)
321
DT = 42 in.
Influent 30 mils ts = 1 in.
Carbon Charge
. n i 1 1 = L
H . n i 8 4 =
Carbon Bed Surface
. n i 3 2 = b H
T
H
Carbon Discharge Metal Screen
Effluent
Fixed-Bed Carbon Adsorber
322
List of Assumptions
1. Norit® SX-plus will be used as an adsorbent in the process. 2. 1 unit of carbon adsorber will be used. 3. Maximum usable time of adsorbent is 60 days. 4. Carbon Steel (UNS K03005) with vinyl ester lining is used as material of construction in vessel desi adsorption vessel for better abrasion resistance to withstand movement of the hard carbon particles. 5. ASME-UPV vessel design code will be used for the design of vessel. 6. The allowance for vapor space is around 20% of the height of liquid available
Summary of design Equations: Adsorber Design •
Carbon Usage Rate (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, page 3-4)
C C V CUR= W ̇ CUR=Car b on usage rat e CC =Desi =Initiaredl concent r at i o n of adsorbat e i n f e ed concent r at i o n of adsorbat e i n ef f l u ent =Equilibrium or saturation value of adsorbent Where;
•
Volume of Activated Carbon (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, page 3-3)
∗ CUR∙ t V = ρ
Where;
t∗ =Maximum usable time of adsorbent Change Out Period 323
•
Bed Depth
•
Mass of Carbon Needed
•
Linear Flow Velocity / Hydraulic Loading,
= = 4
(Ref: Unit Operations of Chemical Engineering by McCabe et.al, eq. 25.3, p. 847)
∗ = ∗ ̇ =× 4
Where:
=
Maximum usable time of adsorbent, hr
=
Length/Height of adsorber bed, m
=
True density of the bed, kg/m3
=
Equilibrium or saturation value of adsorbent, g adsorbate/g carbon
=
Initial value of adsorbate in the adsorbent, g adsorbate/g carbon
=
Linear flow velocity, m/hr
=
Initial concentration of adsorbate in feed, kg/m3
•
Volumetric Flow Rate of Feed
•
Contact Time (Residence Time) (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, p .3-3)
= ̇
•
Pressure Drop (Ref: Unit Operations of Chemical Engineering by McCabe et.al, eq. 25.4, p. 848)
324
∆ = 150̅ 1 1.75̅ 1 , ∆ ̅ Where:
=
Pressure differential
=
Bed length
=
Linear flow velocity
=
Viscosity
=
Particle diameter
=
Porosity of adsorbent
=
Sphericity of carbon adsorbent
=
Average density of feed
Vessel Design
•
Height of Liquid
= 2 = 10.20 = Since vapor space is around 20%
•
Maximum Allowable Internal Pressure
•
Maximum Allowable Working Stress
•
Shell Thickness
ℎ =
ASME vessel design for cylindrical shell
325
= 0. 6 •
Head Thickness ASME vessel design for ellipsoidal head
= 2 0. 2
Adsorber Design
From Material Balance
Mass, m
Density, ρ
Volume
(kg/day)
(kg/m3)
(m3 /day)
Lactic Acid
470.03
1209.00
0.3889
Water
393.47
995.03
0.395
Glucose
0.46
1540.00
0.0003
Total
863.96
Component
0.7846
Technical Specification of Activated Carbon (Ref: Cabot Norit Activated Carbon Specification)
Carbon Type
:
Norit® SX-plus
Apparent Density
:
608.7 kg/m3
Mean Diameter
:
1.3 mm
Porosity
:
0.95
Carbon Usage Rate (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, page 3-4)
CUR= CWCV ̇
326
Where;
CUR=Car b on usage rat e CC =Desi =Initiaredl concent r at i o n of adsorbat e i n f e ed concent r at i o n of adsorbat e i n ef f l u ent =Equilibrium or saturation value of adsorbent 0. 4 6 1000 1 C = × 0.7846 × 1 × 1000 = 0.59 C = 0.59 × 180.116 × 1000 =3. 2 5 1
Initial glucose concentration in feed
Equilibrium or saturation value of adsorbent: (Ref: Glucose and Cellobiose Adsorption onto Activated Carbon by Yu Sun)
From the graph above; At glucose concentration of 0.59 g/L;
=0.09
Desired concentration of glucose in the effluent
327
=0 m 1000 L 0. 5 9 00. 7 846 × day 1 m CUR= 0. 0 9 =. ≈. /
; Since all glucose component of the feed was adsorb
Therefore:
Volume of Activated Carbon (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, page 3-3)
∗ CUR∙ t V = ρ t∗ =Maximum usable time of adsorbent Change Out Period t∗ Where;
Then:
Maximum usable time of adsorbent per unit is 60 days Change out Period / Carbon Replacement in Unit,
= 60 days
(Ref: Chemical Process Equipment Selection and Design by Walas)
Therefore:
kg 5. 1 4 60 days day V = 608.7 =. =V× kg =0.51 ×608.7 m =.
Mass of Carbon Needed:
Adsorber Diameter and Bed Depth Based on the available diameter of the carbon adsorber with a carbon capacity of around 1000 lbs, then:
328
D =42 ≈1.07 . 36
(Ref: Modular Liquid Adsorber Protect LM Series by Calgon Carbon Corporation)
Then:
= = 4 ×1. 0 7 0.51 = 4 = = . . . ∗ = ; = ∗ ∗ ≈/1
Linear Flow Velocity / Hydraulic Loading,
(Ref: Unit Operations of Chemical Engineering by McCabe et.al, eq. 25.3, p. 847)
Where:
=
=
Maximum usable time of adsorbent, hr Length/Height of adsorber bed, m
=
True density of the bed, kg/m3
=
Equilibrium or saturation value of adsorbent, g adsorbate/g carbon
=
Initial value of adsorbate in the adsorbent, g adsorbate/g carbon
=
Linear flow velocity, m/hr
=
Initial concentration of adsorbate in feed, kg/m3
329
Then: Initial value of adsorbate in the adsorbent
=0
; since fresh carbon is introduced into the unit
Therefore:
= ∗ 608.10.7 9mkg5 0.57 m0.090 = 0.0.784646 60 × 124ℎ =. . /
Volumetric flow rate of feed
, = ̇ ̇ =0.74 ℎ 1.407 ̇ =.
330
Contact Time (Residence Time) (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, p .3-3)
= ̇ Then:
1. 0 7 0. 5 7 4 = 0.665 /ℎ =. ≈.
Pressure Drop (Ref: Unit Operations of Chemical Engineering by McCabe et.al, eq. 25.4, p. 848)
∆ = 150̅ 1 1.75̅ 1 , ∆ 1.86 ̅ 0.74 ≈6.74×10− , ≈0.00277 − ≈ = = 0.863.784696 = 1,101.15 68.74 Where:
=
Pressure differential
=
, Bed length
= =
Linear flow velocity
4.12 cp
, viscosity
(Ref: Viscositv and Densitv of Aqueous L.A. Solutions , p. 1145)
=
1.3 mm 0.00427 ft, Particle diameter
=
0.95, Porosity of adsorbent
=
0.73, Sphericity of carbon adsorbent
(McCabe & Smith, T. 7.1, p.164)
=
average density of feed
331
− 0.00277 1506. 7 4×10 10. 9 5 ∆=1.86 32.2 ∙∙ 0.730.00427 ft 0.95 l b − 1. 7568. 7∙4 ft6.74×10 10.0.9595 32.2 ∙ 0.730.00427 ft l b 1 f t ∆= 0.0049 ft12 in ∆=. ≈. Other Design Data Internal Lining
:
Vinyl ester (30 mils); for better abrasion resistance
(Ref: Adsorption Design Guide by U.S. Army Corps of Engineers, page 44-45)
Carbon Support
:
The bed is supported at the bottom by two metal screens placed in succession wit and 80 mesh supported by steel grid and support bars
(Ref: Chemical Process Equipment Selection and Design by Walas, p. 510)
Inlet Distributor:
Inlet flow distributor will be used for equal distribution of feed in the activated car
332
Vessel Design
Total Height of Adsorber Based on the available height of the carbon adsorber with a carbon capacity of around 1000 lbs, then:
= ≈. . 36
(Ref: Modular Liquid Adsorber / Protect TM LM Series by Calgon Carbon Corporation)
Height of Liquid Since the carbon bed was positioned in the middle of the adsorption tank, the available height for liquid is th
= 2 = 1.22 20.57 =0.325 13 .
Assuming that the allowance for vapor space is around 20% of the height of liquid available, then the height level that must be maintained on the top of the bed is,
= 10. 20 =0.=0.32625≈11 10..20 =
Maximum Allowable Internal Pressure
333
1 14.7 =14.768.74 0.85 12 1 308.1.440×9.78 101325 =. . Material of Construction Carbon Steel UNS K03005 with 30 mils vinyl ester lining (Ref: Adsorption Design Guide by U.S. Army Corps of Engineers) Tensile Strength: 415 Mpa (60,207.25 psi) (Ref: ChE Handbook, 8th ed., Table 25-5, p. 25-30) Factor of Safety: 5
Maximum Allowable Working Stress
ℎ = = 4155MPa =83.00 12,041.45
Shell Thickness ASME vessel design for cylindrical shell
= 0. 6 ⁄2=1.07 ⁄2 =0.535 21.06 21.06 15. 5 9 = 12,041.45 0.85 0.615.59 161 =. . ≈ . Where;
= 0.85, double-welded butt joints (spot-examined) =
= 1/16 in., Corrosion allowance
334
Head/Bottom Thickness ASME vessel design for ellipsoidal head
= 2 0. 2 1.07 × 0.31048 × 121 1 15. 5 9 = 212,041.45 1.00.215.59 16 =. . ≈ . Where;
= 1.0, welding efficiency (seamless) = 1/16 in., Corrosion allowance
To have a uniform thickness adsorber, the head and bottom thickness of the adsorber would be the same as the shell which is 1 in.
335
D. Specification Sheet for Evaporator Specification Sheet IDENTIFICATION Name of Equipment Equipment Code Number Required Feed Capacity Evaporation Capacity Function Operation Type
Evaporator H-2 1 unit 0.4785 m3/hr
0.2888 m3/hr To concentrate Lactic Acid Solution Continuous Tubular Evaporator
Materials Handled Lactic Acid Solution DESIGN DATA Operating Pressure 0.477 MPa Temperature 125 oC Density 1102.77 kg/m3 Steam Economy 0.84 Initial Concentration of Lactic Acid 55 percent by weight Final Concentration of Lactic Acid 85 percent by weight Rate of Water Removal 189.77 kg/hr EVAPORATOR VESSEL DESIGN Design Pressure 30.40 kPa Material of Construction SS-316 L Vessel Volume 1 m3 Diameter 1.5 m Height 2.5 m Shell Thickness 3.0 mm Head Thickness 3.0 mm DISTILLATE TANK DESIGN Design Pressure 30.40 kPa Material of Construction SS-316 L Vessel Volume 1 m3 Diameter 1.0 m Height 2.0 m Shell Thickness 2.5 mm Head Thickness 2.5 mm HEATING SYSTEM DESIGN 1-2 Shell and Tube Heat Exchanger
Fluid Handled
Tube Design Lactic Acid Solution
Shell Design Fluid Handled
Saturated Steam
Mass Flow Rate
527.70 kg/hr
Mass Flow Rate
224.69 kg/hr
Temperature In
95 °C
Temperature In
150 oC
Temperature Out
125 °C
Temperature Out
150 oC
Number of Tubes per pass
9
Shell Diameter
211 mm 336
Number of Passes
2
Baffle Diameter
208 mm
Length
7.0 m
Baffle Spacing
85 mm
Outside Diameter
25.5 mm
Shell Thickness
2 .0 mm
Inside Diameter
20 mm
Pitch
32 mm
Clearance PUMP DESIGN Pump Type
6.5 mm
Power Requirement
Centrifugal 5 hp
337
` 1.5 m
2.5 m
2.0 m
1.0 m
source: PF10 impianti industriali
338
Assumptions and Design Equations: 1. BWG no. 12 with 1 inch Outside Diameter is used in tube design. 2. For the Heat Exchanger the One shell, two – tube passes and Square Pitch tube arrangement is used. 3. For the design of vessel, API-ASME vessel design code is used. 4. For the flash tank, SS316 L will be the material of construction to be u sed. 5. Allowance for safety is 20% of the total volume o f the feed. 6. 30% of the conical vessel volume for the extension of the conical vessel in the form of a cylinder will be used for the vapor space. 7. Pump efficiency is 70%.
RESIDENCE TIME CALCULATION (ref.: Equation 2, page 28; APV Evaporator Handbook)
m=ρLρ3L ρv Where:
m=film thickness
=liquid wetting rate =liquid viscosity =gravitational constant (9.81m/s)
ρρ
=liquid density =vapor density
(ref.: Equation 3, page 28; APV Evaporator Handbook)
R =
339
Where:
R L = liquid volume fraction m=film thickness d=diameter
(ref.: Equation 5, page 28; APV Evaporator Handbook)
t=
Where:
t = residence time A = cross sectional area L = tube length q L = liquid rate
HEAT EXCHANGER DESIGN EQUATION (Ref: Unit Operations of Chemical Engineering by McCabe & Smith, p. 306-307)
Q = UAFt∆TLM (for 1-shell & 2-tube passes)
, , ∆ = (, ,(,) ) , , ,
Tube Side of Heat Exchanger Number of Tubes
N = =
For Square Pitch Tube Arrangement,
Pitch = 1.25 Do
Clearance = 0.25 Do (Ref: Eqn. 12.3b of Coulson and Richardson, p. 648)
Bundle diameter, D b (mm)
=
Shell Side of Heat Exchanger
340
Baffle Diameter = Ds – 4.88 mm
Baffle Spacing= 5 = 2 Shell Thickness
FLASH TANK DESIGN EQUATION Vessel Diameter and Height Using H=1.5D For Conical Vessel,
=0.230669××
Hydraulic Pressure (P) P = Vapor Pressure of Water @ 105°C + ρgH Maximum Stress (S) (Ref: Eq. 4-1 of Process Equipment Design by Hesse and Rushton)
=.
Shell Thickness (ts) (Ref: Eq. 4-7 of Process Equipment Design by Hesse and Rushton)
= 2 161 = 2 where A = 30°
Head Thickness (Ref: Equation 4-10 of Process Equipment Design by Hesse and Rushton, p8.) 297
Using Ellipsoidal Head,
= 2
ACTUAL POWER CALCULATION (Ref: Chemical Engineering Handbook 8 th Ed., p. 10-27)
Power= 3.670×10HQρ 5×n
Where: H = total dynamic head (Pa) Q = capacity (m3/hr) ρ=liquid density (kg/m)3 n= pump efficiency
Pressure Head ( Ref:p. 10-27 Perry’s Chemical Engineering Handbook 8th Ed. By Perry et.al)
H= ∆Pρ
Pressure Drop (Ref: Equation 12.18 p.666 Chemical Engineering Vol. 6, 4 th Edition by Coulson and Richardson)
L ρu ∆P =8j D 2
298
DETAILED DESIGN COMPUTATION
Amount Fed to the Evaporator:
Lactic Acid
Mass Rate (kg/day) 466.33
Water
386.54
TOTAL
854.87
Component
1206
Volumetric Rate (m3 /day) 0.3867
Boiling Pt. (°C at 1 atm) 227.6
1000
0.3865
100
Density (kg/m3)
0.7732
RESIDENCE TIME CALCULATION (ref.: Equation 2, page 28; APV Evaporator Handbook)
m=ρLρ3L ρv Where:
m=film thickness
=liquid wetting rate =liquid viscosity =gravitational constant (9.81m/s)
ρρ
=liquid density =vapor density
(ref.: Equation 3, page 28; APV Evaporator Handbook)
R =
Where:
R L = liquid volume fraction m=film thickness d=diameter
(ref.: Equation 5, page 28; APV Evaporator Handbook)
t=
Where:
t = residence time A = cross sectional area L = tube length 299
q L = liquid rate
Liquid volume fraction, y
From H-2 Vapor
307.42 kg
Liquid (distillate)
547.45 kg
TOTAL
854.87 kg
= 307.854.4827kgkg =0.3596 Vapor density, ρV
From H-2 Components
Mass rate, kg/day
Water
307.42
TOTAL
307.42
ρV
Density, kg/m 3 1000
Vol. flow rate, m3 /day 0.3074
0.3074
= .. =1000 kg/m
Liquid density, ρL
From H-2 Components Lactic Acid Water
TOTAL
Mass rate, kg/day
Density, kg/m 3
Vol. flow rate, m3 /day
466.33
1206
0.3867
81.12
1000
0.0811
547.45
0.4678
= .. =1170.29 kg/m =3.314710^4 0 4210^3 m=9.830.11170.02281. 291170.291000 ρL
From Perry’s ChE Handbook 8th edition, Table 11-12; 300
Using BWG #12 with 1” OD Tube OD = 1 in. = 0.0254 m For heat exchanger, preferred length of tubes is 20 ft = 6.096 m
R = 43.314710^4 0.0254 =0.0522 t= 0.0522.3.95. = 1.62 hr.
Design Operation: Evaporating Time: 1.62 hr./day
1 day = 0.7752 1.62 hr = 0.4785 ℎ 1 day =0.4678 1.62 hr = 0.2888 ℎ =307.42 1.16day2 hr =189.77 ℎ DESIGN CALCULATIONS FOR HEAT EXCHANGER
Heat Transfer Equation:
=∆
Q =767,517.49 kJ/day (from energy balance)
−−℉
U = 250
( from engineeringtoolbox.com)
15095 , , = 150125150125 ∆T = (, ,(,) ) , 15095 , , ∆T =38.05℃ From figure 15.6(a) Unit Operations by McCabe & S mith 6th ed., p438
Ft= NZ
301
where;
Z= ∆∆ u al N = ∆Tact ∆Tmax
Since there is no ∆TH, Ft = 1.0 Heat Transfer Area
kJ 1, 0 00J 1 day 1hr 767, 5 17. 4 9 Q 3600 s day kJ 1 hr A= UFt∆T = BTU W 250 ft hr℉5.6783 ftmhr℉ BTUK 138.05℃ A= 3.95 m2
Tube Side Design Fluid Handled
:
Lactic Acid Solution
Mass Flow Rate kg/s =854.87 daykg × 1.16day2 hr =527.70 kg/hr Volumetric Flow Rate GPM 3 m 264. 1 7 gal = 0.7752 day × 1.16day2 hr × 601 mihrn × 1000L × m3 1000 L 1 =2106.84 gpm . / 0.7752 / =. /
Density (kg/m3) =
Number of Heating Tubes (NT)
N = AA = πdAL
From Perry’s ChE Handbook 8th edition, Table 11-12; Using BWG #12 with 1” OD Tube OD = 1 in. = 0.0254 m
302
Tube ID = 0.782 in. = 0.01986 m For heat exchanger, preferred length of tubes is 20 ft = 6.096 m = 7m
3. 9 5 m N = π0.0254 m6.096 =9 x 2 = For Square Pitch Tube Arrangement Tube Pitch, pt = 1.25 Do = 1.25 (25.4 mm) = 31.75 mm= 32 mm Clearance = 0.25 Do = 0.25 (25.4 mm) = 6.35 mm = 6.5 mm
Shell Side Design Fluid Handled
:
Steam
Mass Flow Rate kghr=364 × 1.162 hr =224.69 /ℎ ( Ref: Steam Tables by engineeringtoolbox.com)
Specific Volume of steam @ 150°C: 0.3934 m 3 /kg
0. 3 934 Volume of Steam /hr =224.69 ℎ × = 88.39 /ℎ Bundle diameter, D b (mm)
=
Eqn. 12.3b, Coulson and Richardson, p. 648
Where,
d o = tube outside diameter, mm Nt = number of tubes From Table 12.4, Coulson and Richardson, p. 649
K 1 = 0.156 n1 = 2.296
303
. 18 =25.40.156 =. =
For fixed tube sheet type:
From Figure 12.10 (Coulson & Richardson, p. 646), Bundle diametrical clearance = 10 mm
Shell diameter, D S = 200.90 + 10 = 210.90 mm = 211 mm ≈ 8.30 in.
Baffle Diameter (Ref: Chemical Engineering Volume 6, 4 th Edition by Coulson and Richardson, Table 12-5 p. 651)
Baffle Diameter = Ds – 4.88 mm Baffle Diameter = 210.90 mm – 3.2 mm = 207.70 mm = 208 mm
Baffle Spacing (Ref: Chemical Engineering Volume 6, 4 th Edition by Coulson and Richardson, Table 12-5 p. 595)
Baffle Spacing= 0.4210.90=.
= 85 mm
Number of Baffles NB + 1 =
mm N 1= 6.09684.x1000 36 mm
NB = 71.26 = 72
Shell thickness Calculation: Internal Pressure
P=P=476.Pressur25 kPa≈69. e of Steam09@150°C 304
Working Stress (Ref Chemical Engineering Handbook, 8 th Ed., Table 25-15, p.25-39)
For SS-316 L Grade of Steel; Tensile Strength: 552 mPa
≈
80,082.90 psi
(Ref: Process Equipment Design by Hesse and Rushton, p.81)
S =S.×F×F×F×F Where;
Fs = 0.25; for temperatures up to 650oC Fm =1; for grade A or high tensile strength carbon steels Fa = 1.0; for non-radiograph vessels Fr = 1.0; for plate thickness of the shell/head at any welded joints do not exceed 5/4 in.
SS =80,=20,082.020.90×0.73 psi25×1.0×1.0×1.0 = 2
(Equation 4-10,p8; Process Equipment Design by Hesse and Rushton)
Where;
C = 1/16 in p= 69.09 in; pressure of steam @ 150°C e= 0.80; for double welded V-butt
20,020.73 psi ≈ 69.09020.735.0. 94 8 161 = 220, =. =. ≈ S=
; working stress
D= Ds= 151.12 mm
5.94 in
305
DESIGN CALCULATIONS FOR EVAPORATION TANK Vessel Capacity
V = 0.7752 m
From Mass & Energy Balance; mVAPOR = 307.42 kg/day
Mass Flow Rate kg/hr =307.42 × 1.162 hr =189.77 /ℎ g 189. 7 7 kg 1000 V = 52.13 dmmol ×1000 dmm ×18kg molg =0.2022 V =V + V 0.2022 m = 0.9774 m V = 0.9774 0.9774
ρwater vapor@ 125°C = 52.13 mol/dm3 (from table 2-305 Ch.E Handbook 8th ed.)
= 0.7752
m3
Using 20% allowance for safety factor, VFLASH TANK = (1.20) (
) = 1.17 m3
Vessel Diameter and Height For Conical Vessel;
=1. 5 2 ×tan60 1 × ×ℎ × = = 3 × 4 4 ℎ=0.230669×× = 0.230669×× = 1.17m 1 . 1 7 √ = ×0.230669 == 1.1.1571.17=≈3.81.47≈. 6 ≈5.76 (from Chemical Engineering Resources.com)
h= height of conical bottom,
306
For the extension of the conical vessel ve ssel in the form of a cylinder for vapor vapo r space; Using 30% of the conical vessel volume:
V = 0.331.1.1717 = 0.351 m D = D = D= 1.1717 m V = πD4 H = π1.17m4 H = 0.351351 m H =0.3265 m Tota ToH tal=l Hei1H.ei76ghtght 0.=3H3=2.H090 9 m 66.86 ftt For Cylindrical Vessel
= 1.5 m
= 2.5 m
Material Specification for Vessel thickness Calculation: Material of Construction
:
SS316 L
Top Head
:
Ellipsoidal Head
Welding Type
:
Double Welded V-Butt
Efficiency
:
0.8
Corrosion Allowance
:
1/16 inch
Hydraulic Pressure
P ⁰ = xP ⁰ xP⁰ ⁰P ⁰ = xP xP⁰ PP ==0.1406 81406.11.1733. 5 5 5 0. 1 9 9 10. 4 4 4 mmHg ≈ 1.85 atm ≈ 27.27.20 psi ⁰ 16 mmHg xA = 0.19
PA = 10.44 mmHg
(Lactic acid)
xB = 0.81
PB = 1733.55 mmHg (H2O)
307
Head Thickness (th) Using Ellipsoidal Head, (Equation 4-10,p8; Process Equipment Design by Hesse and Rushton)
= 2
Where;
C = 1/16 in p= 27.20 psi; internal pressure of vessel e= 0.80; for double welded V-butt S= 20,020.73 psi; working stress
1.10 ≈ = 2227.20,20020.7343.310.8 161 = . = . ≈ . ≈ . D=Dv=
m
43.31 in
Vessel Thickness (Ref: Eq. 4-7 of PED by Hesse and Rushton, API-ASME code)
API-ASME CODE:
≈ = 30 = 2 1/16 = 2cos27.3020psi20,43.020.31730.8 1/16 = . = . ≈ . ≈ .
M = Dv = 1.76 m
69.27 in
A = ½ of included cone angle =
308
DESIGN CALCULATIONS FOR DISTILLATE TANK Vessel Capacity
V =0.4678m
Using 20% allowance for safety factor, VFLASH TANK = (1.20) (0.4678) = 0.5614 m3 Vessel Diameter and Height For Conical Vessel;
=1.5 2 ×tan60 1 × ×ℎ × = = 3 × 4 4 ℎ =0.230669×× = 0.230669×× = 0.5614 m 0. 5 614 √ = ×0.230669 == 0.1.95184180.49184 184≈ = 1.38 ≈ 1.5 (from Chemical Engineering Resources.com)
h= height of conical bottom,
For the extension of the conical vessel v essel in the form of a cylinder for vapor space; Using 30% of the conical vessel volume:
V =0.30.4678 = 0.1403 1403 m D = D = D =0. 9184 m V = πD4 H = π0.91844 m H = 0.1403 1403 m H =0.2118 m Tota ToH tal=l 1.HeiHei38 g38ht 0.=2118 ght H2118==H 1.5918 5918 m 5.5.2222 ft For Cylindrical Vessel
= 1 m
= 2.0 m
309
Material Specification for Vessel thickness Calculation: Material of Construction
:
SS316 L
Top Head
:
Ellipsoidal Head
Welding Type
:
Double Welded V-Butt
Efficiency
:
0.8
Corrosion Allowance
:
1/16 inch
Hydraulic Pressure
P ⁰ =1406.16 mmHg ≈1.85 atm ≈27.20 psi
Head Thickness (th) Using Ellipsoidal Head, (Equation 4-10,p8; Process Equipment Design by Hesse and Rushton)
= 2
Where; C = 1/16 in
p= 27.20 psi; internal pressure of vessel e= 0.80; for double welded V-butt S= 20,020.73 psi; working stress
0.9184 ≈ 27.20020.7336.0. 16 8 161 = 220, =. =. ≈. ≈. D=Dv=
m
36.16in
Vessel Thickness (Ref: Eq. 4-7 of PED by Hesse and Rushton, API-ASME code)
API-ASME CODE: M = Dv =
0.9184 ≈ m
36.16 in
A = ½ of included cone angle =
=30 310
= 2 1/16 = 2cos27.3020psi20,36.020.16730.8 1/16 =. =. ≈. ≈. Steam Economy
307. 4 2 E= massmassof stofevapor = am used 364 =. Pump Design Capacity
m 1 day m Capacity=0.7752 day × 1.62 hr = 0.4785 hr
Pressure Drop (Ref: Equation 12.18 p.666 Chemical Engineering Vol. 6, 4 th Edition by Coulson and Richardson)
L ρu ∆P =8j D 2 Where:
Jf = friction factor L = length of tubes
ρ = density
us = tube side velocity
Do = outer diameter of tubes (Ref: Pubchem.ncbi/compound/lacticacid)
Viscosity of Lactic acid = 1.042 mPa-s
(Ref:Unit Operations by McCabe & Smith, 6 th ed., p478)
Velocity of liquids at film evaporator using centrifugal pump; v=
3 m/s
311
