Chemistry Reference
In-Depth Information
1
1 +
L
E
exp(
= 1
.
VQk
0
exp(
−
E
/
R
T
0
)
eE
R
T
0
Lb
Qa
−
L
/
R
T
0
)
L
E
−
L
/
R
T
b
)
exp
α
S
exp(
−
This expression differs from the Semenov critical condition by the term in the square
brackets on the left hand side. According to this expression, the critical conditions
(in the general case) for a volatile explosive can be attained at lower heat removal
(emission) rates due to partial heat removal by volumetric evaporation. On the other
hand, if the liquid vapor pressure is much lower than the ambient pressure or the
thermal effect of the reaction is much higher than the phase transition heat, that is
exp
L
E
Lb
Qa
1 +
L
E
exp(
−
L
/
R
T
0
)
L
/
R
T
b
)
<<
1
,
exp(
−
the critical condition obtained becomes identical to the Semenov one (valid in the
absence of volumetric evaporation).
Since exp(
L
/
E
)(
Lb
/
Qa
)(1 +
L
/
E
)
1 for many practically interesting systems,
the classical theory, which does not take volumetric evaporation into account, can be
used to estimate the critical parameters for thermal explosion provided
P
sv
(
T
0
)
≈
P
∞
.
Now let us consider the critical conditions for thermal explosion (flameless flash)
in a liquid explosive in a more general form.
Introducing the generalized function of heat evolution
F
(
T
)=
α
S
V
(
T
−
T
0
)
,
where
k
0
exp
1
,
−
L
/
R
T
)
E
R
T
LbP
0
exp(
F
(
T
)=
Q
ρ
−
−
Qa
[
P
∞
−
P
0
exp(
−
L
/
R
T
)]
one can rewrite the heat-balance equation for stationary conditions.
Using the Semenov method, one can obtain a set of equations that determine the
critical conditions
F
(
T
∗
)=
α
S
V
(
T
∗
−
T
0
)
,
F
(
T
∗
)=
α
S
V
,
where
T
∗
is the temperature of the liquid under the conditions of the explosion
initiation limit.
These equations implicitly connect the following process parameters in the vicin-
ity of the explosion limit: the ambient temperature,
T
0
, the reduced heat emission,
α
S
/
V
, and the temperature of the liquid,
T
∗
. The analytical expression for the
warm-up and heat transfer in the vicinity of the explosion initiation limit cannot
be obtained in its explicit form due to the significant complexity of
F
(
T
). However,
they can be written in a simple parametric form:
