Question

Brown sugar is a mixture of white sugar and molasses. Unrefined brown sugar contains a large portion of molasses. After one round of crystallization of this unrefined sugar, the brown sugar product contains 10.00 wt% molasses and the remainder white sugar. A second round of crystallization reduces the molasses content to 1.40 wt% molasses. A plant wishes to produce a brown sugar ideal for baking that contains 4.00 wt% molasses. In order to acheive this concentration of molasses, a plant feeds once- crystallized brown sugar into a recrystallizer. Some of this feed is diverted into a bypass stream that rejoins the sugar that leaves the crystallizer. Pure molasses leaves the crystallizer as a bypass stream. This process is described by the flow chart below. m3 g/min 0.1000 g molasses/g 0.9000 g white sugar/g mg/min 0.1000 g molasses/g 0.9000 g white sugar/g Crystallizer m2 g/min 0.1000 g molasses/g 0.9000 g white sugar/g m5 g/min ma g/min 0.0140 g molasses/g 0.0400 g molasses/g. 0.9860 g white sugar/g 0.9600 g white sugar/g m4 g molasses/min

Answer 1

ms almin Im Olmin 10-1 g molasses My gimin Mz Slmim 0.1 g molassesla 0.98 white Sugang chys ca Mizes 0:014 g molasses to 0-18 nolassesla 09868 white o sugar / ogg white o mug molasses / min sugas mo grmin 0.04g molassa 0.968 white Sugant 0-99 while sugalla mass balance at whene bypass stheam splits Molasses – mx 0-1 mx01 + MzX0. 1 0 white sugar-m, x0-9=Mx0.9 + MzX0-9-20 equa mass balance around the crystallizes melasses in MX0-1= mx 0. 01 +M ® white sugar- mx0-9 = max 0.986 ☺ Mass balance at bypass mixing and crystallized product Molasses Maxo-/+mX0-014 = mx 0.04 white sugas → m,x0-9 + max 0986 = m*0-96-> mass balance for entine process Molasses – Mx0.1= Mut m 50.04 - © white sugos mx0.9= M +0.96 @

If plant wishes to produce 500 g/mie of brown sugar Brown sugar produce in the process = meg - 500g m=500 From equation ® MX0-9-500x0.96 m=533-338/ min From equation . mx 0.1 = my tm 20:04 533.33 XOL= mets00X0-04 From Mu= 33.33%/min equation © and @ ie Adding © and © Mz tms=mo My Xott MSX ontM M3X0-014+ Max 2014 mx 0014 ma xol Mix0014 mx 0:04 equation @ Mz 20-014-0-) - mr (0.014-0.04) Mz=500 x 0.026 = 151-16 0-086 M3 - 151-160-2834 533.33