Introduction to Modeling of Engineering Systems
The model that my group has developed is based upon the separation and accumulation of solids which flow into a settling tank from a feed steam. During this separation procedure, the solid accumulates into the settling tank and the cleaner liquid product accumulates in a storage tank. The feed stream, containing solid particles in liquid, flows continuously to the settling tank, and solids are thus able to settle to the bottom as the liquid moves upward through the tank. A product stream leaves the tank; this stream contains a smaller fraction of solids than the field stream. Eventually the amount of solids which leave the settling tank via the exit stream and into a collection vessel increases over time, as the amount of solids that accumulate in the settling tank increases. At a certain point, the solids which have accumulated in the settling tank must be removed so that the entire process can begin again.
The transient mass balance rates have been determined for both the settling and collection tanks. Based upon experimental data, the ratio of solids in the stream tank and the settling tank i.e., (Y kg solids/kg and x kg solids/kg respectively) have been determined to be constant at 0.080 (i.e 0.08y=x).The process can be discontinued and accumulated solids can be removed at a level of 0.24 of the solid fraction. By utilization of the relationship 2/(2-y), the density of the solutions can be estimated, with x representing the fraction of solids in the solution. Using this reasoning, the collection tank was determined to accept a maximum of 1.05 solid concentrations as accumulated product. The rate of flow of the processed stream is 12.0kg/min and a solid mass of 6.0 is collected. As a result, the mass found within the solution in the settling tank remains constant although the density, concentration and volume parameters constantly change over time. At the initial time point, when t=0, the settling tank contains 80 litres of solution and lacks the presence of any solids, while the collection tank contain neither solution nor solid (Figure 1).
Figure 1. Accumulation of solids in settling and collecting tanks over time. Blue represents accumulation of solid in settling tank and red represents accumulation of solid in collection tank.
Simulation Model
The simulation model is dependent upon on the balance of solids within the settling and collection tanks. As a result, the total mass and the amount of solids determine the simulation rate. As long as the mass in the tank remains constant, the total balances of accumulation will be zero. Quantitative data can be used to follow the concentration of solids which accumulate in each tank. The correct times to begin each run for the experiment can be determined from the results in the settling tank. Recommendations with respect to the amount of time that is required before restarting the process can be made using this model. By graphing the concentration of solids in the collection and settling tanks as in Figure 1, the plant engineer can adjust the processing operating time.
X/y=0.08
Density=2/ (2-Mass)
Interval time (minutes) =1
Feed Stream
Flow in=12kg/minute
Mass fraction(solid)=0.08
Mass fraction (liquid)=0.92
Flow in =10kg/minute
Solid=0.72kg/minute
Liquid=11.4kg/minute
Mass=80kg
Solid mass fraction=y= (Maximum 0.24)
Liquid Mass Fraction=(1-x)80=B
Product Stream=12kg /minute
Mass fraction (solid)= y
Mass Fraction Liquid= (1-y)
