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INTRODUCTION Crystal growth fundamentals Crystals are formed by the process called ‘nucleation’. Nucleation can start either with the solute molecules or with some solid matter which might be an impurity in the solution. The growth normally occurs by aggregation of molecules that are attracted to each other. The number of crystals formed, crystal sizes and shapes generally depend on properties of the solution like, saturation (solute concentration), operating temperature and mechanical disturbances. In solutions which the solute is near saturation promote fast crystal growth. Supersaturated solutions tend to give crystals which are small in size. If the nucleation is low, such solutions will result in fewer crystals each of larger size. Nucleation is certainly promoted by turbulence and thus mechanical disturbances typically result in smaller crystals. In general, thermal gradient methods tend to produce high quality crystals. Such methods include slow cooling and zonal heating. The latter employs convection by creating a thermal gradient in the crystal growing vessel. The solution becomes more saturated in the warm part of a vessel and crystal growth occurs when the solution is slowly transferred to a cooler region. [1] Rest of this report will discuss about how to design a crystallizer for crystallization of aqueous solution of potash under the following operating conditions:

Absolute pressure - 0.8 atm Temperature - 40oC Mean diameter - 2.5 m Length of cylindrical shell - 5 m

1. Material selection Since an aqueous solution of potash is used as the raw materials for the crystallization process, special attention should paid in order to avoid the corrosion. Therefore it’s better to use Stainless Steel as the fabricating material. Grade 304 (SA-240) is the most widely used stainless steel which is available in a wider range of forms. It has excellent forming and welding characteristics. Post-weld annealing is not required when welding thin sections. Grade 304 is available in roll formed into a variety of components for applications in the industrial, architectural & transportation fields. Grade 304L is the low carbon version of 304, does not require post-weld annealing and so is extensively used in heavy gauge components (over about 6mm). SA-240 also has a excellent corrosion resistance in a wide range of atmospheric environments and many corrosive media. But, it may subject to pitting and crevice corrosion in warm chloride environments, and to stress corrosion cracking above about 60°C. Since the crystallizer is maintained at 40oC this might not be an issue.

Design Pressure & Temperature

i.

Design Pressure (

)

Absolute Pressure The absolute pressure is measured relative to the absolute zero pressure. In other words, relative to the pressure that would occur at absolute vacuum. Under the given operating conditions, operating pressure inside the crystallizer is 0.8atm (absolute). Therefore, this scenario falls under the category of; & Therefore

Therefore;

ii.

is given by,

(

)

Design Temperature (

)

Since the crystallizer should be operated at it is required to be heated. Let’s assume, that the vessel is indirectly heated with using a heating coil. Therefore;

Therefore;

2. Calculation of the wall thickness of the shell economical and safe to

Let’s assume that all the welded joints are butt joints & therefore according to the section II, Part D of ASME, welded joint efficiency ( ) will be 0.7. Theoretical wall thickness for the cylindrical portion of the vessel can be calculated by;

t actual

Pdesign D 2 design

Thickness to resist plastic failure; (

h2

)

(

) (

)

Where, L is the effective length of the vessel. L

h1

Therefore; (

)

(

) (

)

When the actual thickness is calculating, corrosion allowance should be added to the theoretical thickness. Since SA-240 is used & it is a stainless steel corrosion allowance is not needed. Therefore; Critical pressure for elastic failure; (

)

Where K & m are constants depends on Do/L(effective) 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0

For this scenario;

ratio. K 0.185 0.224 0.229 0.246 0.516 0.660 0.879 1.572 2.364 5.144 9.037 10.359

m 2.60 2.54 2.47 2.43 2.49 2.48 2.49 2.52 2.54 2.61 2.62 2.58

Assuming linear interpolation is possible K & m were calculated as follows, Do/L(effective) K m 0.4 0.246 2.43 0.4414 0.3019 2.4424 0.6 0.516 2.49 According to the FIG HA-1 of the page 712 in ASME section II part D, Young’s modulus of SS grade 304 (SA-240) is 193.1GPa. (

)

Assuming t

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Absolute pressure - 0.8 atm Temperature - 40oC Mean diameter - 2.5 m Length of cylindrical shell - 5 m

1. Material selection Since an aqueous solution of potash is used as the raw materials for the crystallization process, special attention should paid in order to avoid the corrosion. Therefore it’s better to use Stainless Steel as the fabricating material. Grade 304 (SA-240) is the most widely used stainless steel which is available in a wider range of forms. It has excellent forming and welding characteristics. Post-weld annealing is not required when welding thin sections. Grade 304 is available in roll formed into a variety of components for applications in the industrial, architectural & transportation fields. Grade 304L is the low carbon version of 304, does not require post-weld annealing and so is extensively used in heavy gauge components (over about 6mm). SA-240 also has a excellent corrosion resistance in a wide range of atmospheric environments and many corrosive media. But, it may subject to pitting and crevice corrosion in warm chloride environments, and to stress corrosion cracking above about 60°C. Since the crystallizer is maintained at 40oC this might not be an issue.

Design Pressure & Temperature

i.

Design Pressure (

)

Absolute Pressure The absolute pressure is measured relative to the absolute zero pressure. In other words, relative to the pressure that would occur at absolute vacuum. Under the given operating conditions, operating pressure inside the crystallizer is 0.8atm (absolute). Therefore, this scenario falls under the category of; & Therefore

Therefore;

ii.

is given by,

(

)

Design Temperature (

)

Since the crystallizer should be operated at it is required to be heated. Let’s assume, that the vessel is indirectly heated with using a heating coil. Therefore;

Therefore;

2. Calculation of the wall thickness of the shell economical and safe to

Let’s assume that all the welded joints are butt joints & therefore according to the section II, Part D of ASME, welded joint efficiency ( ) will be 0.7. Theoretical wall thickness for the cylindrical portion of the vessel can be calculated by;

t actual

Pdesign D 2 design

Thickness to resist plastic failure; (

h2

)

(

) (

)

Where, L is the effective length of the vessel. L

h1

Therefore; (

)

(

) (

)

When the actual thickness is calculating, corrosion allowance should be added to the theoretical thickness. Since SA-240 is used & it is a stainless steel corrosion allowance is not needed. Therefore; Critical pressure for elastic failure; (

)

Where K & m are constants depends on Do/L(effective) 0.1 0.2 0.3 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 5.0

For this scenario;

ratio. K 0.185 0.224 0.229 0.246 0.516 0.660 0.879 1.572 2.364 5.144 9.037 10.359

m 2.60 2.54 2.47 2.43 2.49 2.48 2.49 2.52 2.54 2.61 2.62 2.58

Assuming linear interpolation is possible K & m were calculated as follows, Do/L(effective) K m 0.4 0.246 2.43 0.4414 0.3019 2.4424 0.6 0.516 2.49 According to the FIG HA-1 of the page 712 in ASME section II part D, Young’s modulus of SS grade 304 (SA-240) is 193.1GPa. (

)

Assuming t

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