Introduction to Modeling of Engineering Systems
A semi-batch mode operates the solids separation process by accumulating and settling solids in a storage tank. The cleaner product accumulates in the storage tank whereas the feed stream with solids flows into the settling tank. The clean liquid flows upward into the tank leaving the solid particles at the bottom. The product stream from the tank has smaller solids than those in the feed stream. The amount of solids keeps increasing in the settling tank as solids increase in the settling time. The exit stream accumulates in the collection vessel. The solids in the settling tank should be removed at some point so that the entire process can restart.
Simulation Model
The simulation model relies on the solid balances of the settling and collection tanks. The total mass and solids determine the rate of the simulation. The total balances in the settling tank will not have any accumulation if the mass in the tank is constant. Numerical integration tracks the concentration of solids in the tanks. The results in the settling tank determine the right time to make runs for the experiment. The model makes recommendations on the amount of process time required before the process is restarted. Plots of concretions in the collection and settling tanks will help the plant engineer in adjusting the operating time of the process.
X/y=0.08
Density=2/ (2-Mass)
Interval time (minutes) =1
Feed Stream
Flow in=10kg/minute
Mass fraction(solid)=0.08
Mass fraction (liquid)=0.92
Flow in =10kg/minute
Solid=0.8kg/minute
Liquid=9.2kg/minute
Mass=80kg
Solid mass fraction=y= (Maximum 0.25)
Liquid Mass Fraction=(1-y)80=B
Product Stream=10kg /minute
Mass fraction (solid)= x
Mass Fraction Liquid= (1-x)
Total
10kg/minute=x kg /minute
X=10kg/minute
Solids
0.08(10).x(80)=dy/dx
(0.08910)-))t=80y+5W
Water
Rate:0.92(10)-(1-10)=dy/dx
(0.92(10)-0)A=(1-Y)(80Kg)
(0.92(10)-0)A=(1-y)(80)=5w
10kg/min
0.08
0.92 X=10kg/minute
X=10+y/x
x/y=0.08
y%=solids
80xx/y=10kg
x/y=0.08
Therefore the rate : x=0.08y
