Flowrate of cracked gas (ethylene) in to the tower = G = 11870 Kg/ hr
Enthalpy per Kg of the cracked gas at 111°C = hs+1 = 558.24Kj/Kg
Quench liquid flowrate irrigated to the tower= Ls = 66760Kg/hr
Specific Heat Capacity of water = Cs = 1 Kcal/kg
Temperature of quench water before section = ts-1 = 53°C
Temperature of water after the section = ts = 73°C
Now using the relation
G (hs+1-hs) = LsCs (ts-ts-1)
Where
G = Hourly ethylene flow rate (Kg/hr)
hs+1 = Cracked gas enthalpy before entering the section (Kcal/Kg of ethylene)
hs = Cracked gas enthalpy after the section ( Kcal/Kg of ethylene)
Ls = Quench liquid flow rate (Kg/hr)
Cs = Heat capacity of quench liquid (Kj/Kg°C)
ts = Temperature of the quench liquid before entering the section (°C)
ts-1 = Temperature of the quench liquid after section (°C)
11870*(558.24 - hs) = 67760 (73 - 53)
hs = 444.22 Kj/kg
Now we know the enthalpy at which the gas is leaving the section, and so we can find the temperature at which the gas is leaving the section by using relation
h = aT2
Where
h = Cracked feed gas enthalpy, (Kcal/Kg of ethylene)
T = Temperature of the cracked gas (°C)
a = A constant, the value of which is defined for different feedstocks.For naphtha feed stocks the value is, a = 0.138.
444.22 = 0.138*T2
T2= 444.22/0.138
T2 =3218.98
Ts = 57°C
Calculations for Number of Ideal Stages
The number of ideal stages for this section ie the lower section can be calculated by using the relation,
ln{(Ts+1-ts)/(Ts-ts-1)}
Ns=_____________________________________
ln{(Ts+1-Ts)/ts-ts-1)} + ln {(Ts+Ts+1)/2(TsTs+1)0.5
Ns=_____________________________________
ln{(Ts+1-Ts)/ts-ts-1)} + ln {(Ts+Ts+1)/2(TsTs+1)0.5
Where
Ts+1= Temperature of the cracked gas before entering the section (°C)
Ts = Temperature of the cracked gas after the section (°C)
ts = Temperature of the quench liquid before entering the section (°C)
ts-1= Temperature of the quench liquid after section (°C)
Now putting the values and solving the equation we get the Number of plates theoretically required,
ln{(111-73/57-53)
Ns= ___________________________________________
ln{(111-57)/73-53)} + ln{(111+57)/2(111*57)}
Ns = 3.029
Now taking the overall thermal coefficient of the plate as 0.45(As reported by Piccioti and in the other literature as well), we find the actual Number of Plates by using relation
(Ns) Eff =Ns/Es
So the actual Number of Plates for the lower section is
(Ns) eff =3.029/0.45
(Ns) Eff = 6.73 = 7
Plate Calculations for Second Section
The same above described procedure is repeated for finding the number of plates in the upper section of the tower, we find the theoretical number of plates for the upper section of the quench tower and these came to be
Ns2 = 3.6
Actual number of plates for the upper section were found to be =8 plates
Total number of plates required = 8+7 = 15 plates
Tower Design Calculations
Estimate vapor and liquid flow rates
Vapor and liquid flowrates are estimated by applying material and energy balances around water quench tower.
Calculate vapor load (VLoad)
The vapor load is given by the relation,
VLoad = Q {ρv/(ρL-ρv)}0.5
Where Q = Volumetric flow of vapors (ft3/sec)
ρv = Density of vapors (lb/ft3)
ρL = Density of liquid (lb/ft3)
Substituting the values Vapour Load= 5.2 ft3/sec
Estimation of the tower Diameter
From the figure the tower diameter comes out to be 4.25ft when a single pass tray is used with a tray spacing of 2 ft.
Calculations of active area(Aa)
The active area is calculated by,
Aa,min = {VLoad + q*L/13000]C*F
Where
q = liquid flowrate (gal/min)
L = 9Dt/N……………….. (1)
Dt = Estimated tower diameter (ft)
N = Number of tray passes
C = 0.44 (as for hydrocarbons S=1 So C*S = C = C*)
F = Flood factor =0.8
From equation (1) L = 38.25 inches.
Putting the values the value comes to be
Aa,min = 14.7 ft2
Calculations of downcomer area (Ad)
The downcomer area Ad, min = q/U*F
Where
U = Ideal downcomer design velocity (gal/min ft2)
U = U*S
The ideal downcomer design velocity U* is found as the smallest value of the following equations
U* = 41[ρL-ρv] 0.5
U* = 7.5[Ts (ρL-ρv)] 0.5
Substituting the values the smallest downcomer velocity is
U* ≈ 250 gal/ min ft2
So the actual downcomer value is
U = U**S
Where S = 1 (for hydrocarbons)
U = 250 gal/ min ft2
The downcomer area Ad, min = 2.55 ft2
Since the down comer area is greater than 11% of the active area hence it is all right.
Calculations of tower area (AT)
The tower area is obtained as equations
AT = Ad, min + Aa, min
The calculated tower area is 17.25 ft2
Calculations of tower diameter
The diameter of the tower is given by the relation
Dt = (4*AT/π) 0.5
= (4*17.25/3.1416)0.5
= 4.7 ft
The tower diameter comes out to be 4.7 ft.
Calculations of valve units
The number of valve units is taken to be 14/ft2 of the active area.
So the number of valve units are = 14*14.7
= 206
Weir Sizing
The ratio Ad/AT = 2.55/17.25
= 0.14
So from the graph weir length/tower dia = 0.78
So weir length is 0.78*4.7 = 3.66ft
Pressure drop calculations
The dry pressure drop is given by
Δ PDry = K2V2h(ρv/ρL)
Where Vh = Velocity of gas through valves =
K2 = A constant = 1.05 (for lighter hydrocarbon) Δ PDry = 3.9 in water/tray
The wet tray Pressure drop is given by
Δ PT = Δ PDry + 0.4[q/Lw]0.67+ 0.4 hw
Where Lw = Weir length, hw = Weir height, q = Liquid flowrate
Putting the values and getting the answer, the total tray pressure drop comes to be 6.6 inches water
Design of the Upper Section
The design of the upper section of water quench tower is parallel to the lower section design
Estimate vapour and liquid flow rates
Mass flow rate of cracked gas (ethylene) = 26114 lb/hr
Volumetric flowrate of cracked gas = 75.6 ft3/sec
Mass flowrate of water in = 106480 lb/hr
Volumetric flowrate of water (q) = 212.4 gal/min
Calculate vapour load
VLoad = 2.96 ft3/sec
Estimation of tower diameter
From the graph the tower diameter comes out to be 3.25 ft and a single pass tray is used with a tray spacing of 2 ft.
Calculation of active area
Aa, min =6.6 ft2
Calculations of downcomer area
The ideal downcomer design velocity comes to be U = 250 gal/min ft2
The downcomer area Ad, min =q/U*F = 1.062 ft2
The down comer area is greater than the 11% of the active area hence it is all right.
Calculations of tower area
AT = 8.724 ft2
Calculation of tower Diameter
The diameter of the tower is given by the relation
Dt = (4*AT/π) 0.5
= 3.3 ft
Calculations of number of valve units
The numbers of valve units are taken to be 14/ft2 of the active surface
So the number of valve units = 16*6.6 = 105
Weir sizing
Weir Length/Tower dia = 0.72
So that weir length = 0.72*3.3 = 2.37 ft
Also down comer width/tower dia =0.15
So the down comer width = 0.15*3.3 = 0.695 ft
Pressure drop calculations
Δ PDry = 5.3 in water/tray
Δ PT = 7.6 in water/plate
THIS IS AWESOME !!!! IS THERE ANY WAY YOU CAN GIVE ME THE REFERENCES FOR ALL OF THE EQUATIONS ?!?!
ReplyDeleteor just the textbook or paper you found them in please !
ReplyDeletedid you get the text book??
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ReplyDeleteI also need the reference books or links please
ReplyDeletecan you add the reference sir? thanks.
ReplyDeletei need references of this design
ReplyDeleteHello, I'm a chemical engineering student currently designing an ethylene plant, it will help me to understand your calculations if you could share the textbook/reference you got these equations from. Hope you reply soon! Thanks
ReplyDeleteCan I get the reference please?
ReplyDeleteHOW TO FIND THE TOWER HEIGHT
ReplyDeleteCan you please provide references?
ReplyDeleteCan you provide references please?
ReplyDeleteEncyclopedia of Chemical Processing and Design: Volume 11 by John J. McKetta Jr
ReplyDeleteCan any one please tell that if I have a gas flow rate, how can I measure the liquid flow rate for designing
ReplyDelete