Environmental Engineering Reference
In-Depth Information
m
−3
]
ρ
density
[kg
σ
i
selectivity of a reaction toward species i
[
-
]
τ
residence time
[s]
viscous stress (tensor)
[Pa]
τ
[m
3
kg
−1
]
υ
mass-specific volume
!
f
[
-
]
flux of property
f
s
−1
]
φ
m
mass flow
[kg
s
−1
]
φ
n
mole flow
[mol
[m
3
s
−1
]
φ
V
volume flow
ζ
j
relative degree of conversion
[
-
]
m
−3
s
−1
]
ω
i
formation or destruction rate of species i
[kg
Subscripts
cv
control volume
f
formation
r
radiation
ref
reference
vol
volume
3.1 GENERAL CONSERVATION EQUATION
Biomass conversion processes are subject to elementary physical conservation laws
like any chemical transformation. Setting up the related balance equations forms the
solid point of departure to study and understand such phenomena. These laws concern
conservation of overall mass, mass of all elements involved in the conversion
reactions, momentum, and energy. An extensive fundamental treatise is given in,
e.g., Bird et al. (2007). The concept can even be applied to the economics of a biomass
conversion process plant. The general form of the conservation law for a randomly
chosen system is
Rate of accumulation = rate of supply
−
rate of release + rate of production
ð
Eq
:
3
:
1
Þ
The general conservation equations can be further worked out depending on what
level of detail is required. Balance equations can be set up with the aim to describe
the detailed flow pattern and temperature distribution at every single point (x, y, z
in Cartesian coordinates) in the system considered. Such balances are called
“
micro-
scopic balances,
”
and this way of considering balances is also termed the
“
differen-
tial
approach. When a (larger) finite region is considered with a balance description
of the gross flow and energy exchange effects (e.g., force or torque on a body or the
total energy exchange), this is called the
”
“
control volume
”
or
“
integral
”
method, and in
this case, we deal with
“
macroscopic balances.
”
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