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In a plant producing styrene (CH:CH-CH2) from ethylbenzene (CH:C_Hz), hydrogen (H) is also generated as the by-product. Accordingly, hydrogen is to be removed from the
In a plant producing styrene (CH:CH-CH2) from ethylbenzene (CH:C_Hz), hydrogen (H) is also generated as the by-product. Accordingly, hydrogen is to be removed from the effluent stream of the dehydrogenation reactor to recover pure styrene. Taking the striking difference in molecular size between styrene and hydrogen as a technical advantage, a membrane pipe system is in operation, as depicted in the Figure below. -Sweep gas Hg CH3CH=CH, H CH,CH=CH, HE membrane m The gas mixture (behaving as ideal gas) flows through the pipe in which hydrogen selectively exits through the membrane and is swiftly swept by sweep gas. The mass flux of the hydrogen jum through the pores of the membrane is expressed as Jum = k (C#m - C5) where k is the mass transfer coefficient (ms) Cum is the hydrogen concentration (mol m) at the inner surface of the membrane and C#, is the hydrogen concentration (mol m) at the outer surface of the membrane. a) In the case of plug-like flow of the gas: (i) Perform the first-principle modelling and show (handwritten) that the partial pressure of hydrogen (Pr, bar) along the axial (z) direction can be expressed as: 2k VOR PH where vo is the axial velocity of the gas and R is the pipe radius. Write down all steps that you take to obtain the above model in detail! (ii) Clearly state the list of assumptions to obtain the above model! (iii) Clearly define the boundary conditions(s) that are applicable to the model! dPM = dz
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