Page 132 - Materials Chemistry, Second Edition

Mass-Balance Concept and Reactor Design 115

Step 5: Perform the necessary analyses/calculations using the proce-
dures described in this chapter.

A few special cases or reasonable assumptions can simplify the general
mass-balance equation, Equation (4.1), and make the analysis easier. Three
common ones are presented here:

No reactions occurring: If the system has no chemical reactions occur-
ring, there will be no increases or decreases of compound mass due
to reactions. The mass-balance equation would become:

 Rate of mass   Rate of mass  Rate of mass
  =   −   (4.2)
 ACCUMULATED  IN   OUT 
     

Batch reactor: For a batch reactor, there is no input into and output out of
the reactor. The mass-balance equation can be simplified into:

 Rate of mass 
 Rate of mass   
  =±  GENERATEDor (4.3)
  ACCUMULATED   
  DESTROYED  

Steady-state conditions: To maintain the stability of treatment pro-
cesses, treatment systems are usually operated under steady-state
conditions after a start-up period. A steady-state condition basi-
cally means that flow and concentrations at any locations within
the treatment process train are not changing with time. Although
the concentration and/or flow rate of the influent waste stream
entering a soil/groundwater system typically fluctuate, engineers
may want to incorporate devices such as equalization tanks to
dampen the fluctuation. This is especially true for treatment pro-
cesses that are sensitive to fluctuations in mass loading (e.g., bio-
logical processes).
For a reactor under a steady-state condition, although reactions are
occurring, the rate of mass accumulation in the reactor would be zero.
Consequently, the left-hand side term of Equation (4.1) becomes zero. The
mass-balance equation can then be reduced to:

 Rate of mass 
 Rate of mass  Rate of mass  
0 =   −   ±  GENERATEDor (4.4)
  IN   OUT   

 
  DESTROYED  