Vertical Crystalliser Design Calculation for Sugar Massecuite Cooling

Vertical Cooling Crystalliser Design Calculation in Sugar Plant

In the following link covered information regarding the Vertical crystalliser design

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Vertical crystalliser advantages over the series of crystallisers.
Types of Vertical cooling crystallisers like Mono Vertical crystalliser (MVC ), Riser type Vertical Crystalliser , Twin Vertical crystalliser.
Cooling surface requirement for vertical crystalliser ( S/V ratio ).
Heat Transfer coefficient of Vertical cooling crystalliser.
Good vertical crystalliser design aspects as per Peter Rein.
Heat-exchange surface required: (Cooling surface requirement).

Now in this article covered the Vertical Crystalliser Design Calculation like

Requirement of heating surface as per formula with example
Cooling water requirement for crystallizer massecuite cooling
Mechanical Design of vertical crystalliser – shell thickness and Bottom plate thickness.

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Heating Surface Calculation for Vertical Crystalliser

The Basic formula to find heating surface is

M x Cp x ΔT = S x K x ∆Tm. Now it can be written as

Heating Surface =S = [M x Cp x ∆T]/ [ K x ∆Tm]

Consider massecuite & cooled water travels in counter-current direction.

Here ∆Tm called as logarithmic mean temperature difference

∆T = Ti-To ( Massecuite inlet temperature – Massecuite outlet temperature)
$\Delta T_{m} = \frac{\Delta T_{i} - \Delta T_{e}}{\ln \left( \frac{\Delta T_{i}}{\Delta T_{e}} \right)}$
∆Ti = Ti-to ( Massecuite inlet temperature – Water outlet temperature )
∆Te = To-ti ( Massecuite outlet temperature – Water inlet temperature )
M = Weight of the massecuite in kg/hr = L x V x D
L = Factor taking into account if diluting molasses added for lubrication purpose. Otherwise it will be taken as 1.0
V = Volume of massecuite Lts/hr.
D = specific gravity of the massecuite = 1.5
Cp = specific heat of the massecuite = 0.40 to 0.44 Kcal/kg/^oC
K = Heat-transfer coefficient of massecuite.

Example:

” C ” Massecuite Vertical Crystallizer
S. No	Description	Sign	Value	UOM	Remarks
1	Crushing rate	TCH	230	TCH	5000 TCD @ 22 hours basis
2	Massecuite % cane		10	%
3	Weight of the massecuite	M	23000	Kg/hr	230 x 10%
4	Specific heat of massecuite	Cp	0.44	Kcal/kg/^oC
5	Massecuite Inlet temperature	Ti	68	^oC
6	Massecuite outlet temperature	To	40	^oC
7	Water inlet temperature	ti	32	^oC
8	Water outlet temperature	to	40	^oC
9	Heat transfer coefficient	K	25	Kcal/m²/hr/^oC
10	S/V ratio		2.0
11	∆T = Ti – To		28	^oC
12	∆Ti = Ti – to		28	^oC
13	∆Te = To – ti		8	^oC
14	Logarithmic mean temperature difference	∆Tm	16.0	^oC	∆Ti -∆ Te / ( ln(∆Ti/∆Te))
15	Heating Surface	S	709.97	M²	[M x Cp x ∆T]/ [ K x ∆Tm]
16	Volume of the crystallizers	V	355.0	M³

It is better to provide two no.s of vertical crystallisers with 175 M³ capacity each.

Now it can be calculated in another simple way as follow as

Crushing Rate = 230 TCH

” C ” Massecuite % cane = 8 %

Quantity of massecuite = 18.40 T/hr

Massecuite cooling and ripening time required = 30 hours

Cooling crystallizer capacity required = 18.4 x 30 = 552 MT = 552 /1.5 = 368 M3

( Here 1.5 = Density of massecuite )

Cooling surface required = 368 / 2 = 184 m2

( Here considered S/V ratio = 2 )

Cooling water requirement for crystalliser

M x Cp x ΔT =W x Cw x ΔTw

Here

M = Weight of the massecuite in kg/hr
Cp = Specific heat of the massecuite = 0.40 to 0.44 Kcal/kg/^oC
∆T = Ti-To ( Massecuite inlet temperature – Massecuite outlet temperature)
W = Weight of the cooled water in kg/hr.
Cw = Specific heat of the water = 1 Kcal/kg/^oC
ΔTw = to – ti ( Water outlet temperature – Water inlet temperature)

For Example:

S. No	Description	Sign	Value	UOM
1	Weight of the massecuite	M	1	Kg/hr
2	Specific heat of massecuite	Cp	0.44	Kcal/kg/^oC
3	Massecuite Inlet temperature	Ti	68	^oC
4	Massecuite outlet temperature	To	45	^oC
5	Water inlet temperature	ti	30	^oC
6	Water outlet temperature	to	40	^oC
7	Specific heat of the water	Cw	1	Kcal/kg/^oC
8	∆T = Ti-To		23	^oC
9	ΔTw = to – ti		10	^oC
10	Weight of the cooled water	W	1.012	Kg/hr

Mechanical Design of Vertical cooling crystalliser :

These mainly calculated shell thickness and Bottom plate thickness

The thickness of shell :

$\text{Shell Thickness} = \frac{P \times D_{i}}{2 \times F \times J - P} + C$

- P = Maximum allowable pressure in kg/cm²
- Di = ID of the crystalliser in mm
- F = Allowable stress in kg/cm²
- J = Welding Joint efficiency in mm
- C = corrosion allowance in mm

For example, taken

- P = 2. 0 kg/cm²
- Di = 4200 mm ( consider for calculation purposes)
- F = 1400 kg/cm²
- J = 0.75 mm
- C = 3 mm

As per above taken values

The thickness of the shell = 7 mm

But as per standard specifications 12 mm thickness for the crystalliser shell

Some designers follow another formula as follow as

Some designers considered thickness as per the height of the course from the top 16mm/ 12mm/ 10mm

$\text{Shell Thickness} = \frac{50 \times \mu (H - 0.3) \times D}{F \times J} + C$

Here

- µ = Massecuite density
- H = Height of the courses from top in meters
- D = Dia of the vertical crystallizer in meters
- F = Allowable stress in kg/cm²
- J = Welding Joint efficiency in mm
- C= corrosion allowance in mm

For example, taken (Take total height Consider as 15 meters with 10 courses )

- µ = 1.5
- H = Height of the courses from top = 15 meters
- D = 4.2 metres
- F = 1400 kg/cm²
- J = 0.75 mm
- C = 3 mm

According to the above formula, the course height comes as follows

Bottom courses thickness = 7.41 mm

Middle courses thickness = 5.16 mm

Top courses thickness = 3.36 mm

But as per standard specifications considered 16mm / 12 mm / 10mm thickness for the crystallizer shell from bottom to top.

Bottom plate thickness:

Here calculate 250 MT capacity vertical crystalliser bottom plate thickness with 15 meters height and 4 meters Dia

Total momentum of massecuite Mo= M x V / g

M = Total weight of the massecuite = 250 MT = 250 x 10⁶ gm

V = Velocity of inlet massecuite = 0.1 m/sec

g = Gravity factor = 981 cm/sec²

Mo = 250 x 106 x 0.1 / 981 = 25484 gm/cm²

The total load on bottom plate = weight of the massecuite + momentum of massecuite

= 250 x 106 + 25484

= 250025484 gm

Cross-sectional area of the bottom plate = 0.785 x 400 x 400 = 125600 cm² ( 4 metres = 400 cm)

Critical Pressure ( Pc ) = Total load on bottom plate / Cross-sectional area of the bottom plate

Critical Pressure ( Pc ) = 250025484 / 125600

= 1990.64 gm/cm² = 2.0 kg/cm²

Now check the bottom plate thickness by using the following formula

$\frac{D}{900} = \frac{3}{16} \frac{m^{2} - 1}{E_{s} \times m^{2} \times t^{3}} \times P_{c} \times R^{4}$

Here

- D = Dia of the vertical cooling crystalliser bottom plate in mm = 4000mm
- m = Moment of Inertia = 1 / p
- p = Poisson’s ratio = 0.3
- R = Radius of the bottom plate = 4000 /2 = 2000mm
- Es = Modulus factor for MS sheet in kg/cm² =1.9 x 106 kg/cm²
- Pc = Critical Pressure = 2.0 kg/cm²
- t = Bottom plate thickness

By substituting all these values in above equation, then get the value of ” t “

t = 86.47 mm

But as per standard specification, it will be taken 16 mm thickness of bottom plate and it rests on a concrete foundation. So concrete foundation will take the remaining load.

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Vertical Crystalliser Design Calculation for Sugar Massecuite Cooling

Vertical Cooling Crystalliser Design Calculation in Sugar Plant