Thick-wall steel pipes were utilized for test fixtures in the underground fume chamber to
represent the rock confinement, and thin-wall fixtures were taken to reflect weaker
confinement. Work principle results were compared to thick-wall results for which the
quality of detonation remains more reliable though nonideal. Two NOx results were
obtained with two types of instrumentation, which yield two respective results via the
Russian RFT-R rule. The tabulated constants for COz and nontoxic He were retained for
comparisons. The underground tests results readjusted via the reduction-factor technique
in the last column compare rather well with the N-state work principle results in the
middle column, except for Hz. Hydrogen’s tendency to undergo rather cool burning could
be responsible for the notable differences in the table.

When rocks with fissures or other porous strata are blasted, it inhibits the transport of
air into the nonideal combustion zone. The question of whether the slight quantity of air
would have an influence on the transitory combustion results remains unresolved. The
reduction factor technique in Appendix D was used to remove the unwanted booster and
reaction-air influences from the underground test results so they would represent the
nominal field conditions presumed in the work-principle tabulations.

APPENDIX D. THE REDUCTION FACTOR TECHNIQUE

Underground chamber tests restrict the charge size, so that nonstoichiometric boosters
represent a noticeable weight fraction of the total charge. Unlike shots in rock, the fume
reaction zone is rapidly exposed to surrounding air in underground chamber tests. The
residual transitory deflagration that follows the nonideal detonation noticeably influences
the toxic fume spectrum. This wholly reverses the circumstances taken to represent
nominal field conditions in the scaled cloud model: zero ingested air and no (negligible)
booster mass. The resolution of reduction factors requires the retention or removal of
certain ingredients in the work principle tabulations. The reduction factor hypothesis is
that the ratio of tabulated constants cy with and without certain ingredients found
experimentally would be identical to the ratio found theoretically.1° The notation
parameters W, N, X and T stand respectively for: with or not with chosen ingredients, the
experimental or the theoretical result. The reduction factor RF; is defined by the
theoretical ratio and the hypothesis is written:

{WX} = ciAW.T} [6]
c{N,X} 7c, {N,T} .

Though the numerator on the left side of the relationship is feasible, the denominator
that represents shots with zero ingested air and no booster usually remains intractable.
Theoretical modeling is not restricted that way, so the reduction factor is resolved and
the relationship is rearranged to yield the unknown left-side denominator. This technique
was utilized to remove the reactant air and booster influence from the fume spectrum of
reported underground test results. Notice that reduction factors depend only upon ratios
and therefore it remains somewhat insensitive to refinements in the work principle
technique. The work-principle Z-states rather than the N-state are normally utilized in


Table 1. Threshold nonhazardous trapping density prx and scaled
radius rx. [N.R. = Not relevant or not resolved]
Type of | cy, Work | TLV-TWA | Trapping | Scaled | Scaled
Toxic | Principle | or Other Density | Radius | Radius
Fumes | N-state | Criterion(*) pTx TM Tx

Iec/g] [PPM] [g/m] _| [em/g¥} | [m/kg'*]
COz 91.8 5000 54.5 16.4 1.64
co 14.8 25 1.69 52.1 5.21
NO N.R. 25 NR. N.R. N.R.
NO2z N.R. 3 NR. N.R. N.R.
NOx 1.63 25/6.5* 2.36 46.6 4.66
RFT-R 25.4 25* 0.984 62.4 6.24

The cloud’s toxicity remains hazardous for trapping densities over prx or scaled radius
under rx, while it’s nonhazardous for the reverse circumstances. It’s worth noting that the
cloud’s scaled size required for the toxic mixture to reach the nonhazardous threshold
exceeds those of the underlying components, which is logical for multi-component
mixtures.

NUMERICAL EXAMPLES TO ILLUSTRATE THE CLOUD MODEL

Quantitative toxic fume problems are useful to illustrate the resolving capacity of the
scaled cloud model. Though it would be more logical to utilize other types of explosives
under some of the circumstances, ANFO-94/6 is presumed. The Russian formula RFT-R
represents the overall fume toxicity, the NOx composition is regarded as nominal, and the
cloud’s thermodynamic state is taken at the reference condition, k=1. The scaled cloud
model ignores gradients and works with the cloud-average concentration x3, though
logically the real concentration would be higher (lower) closer to the cloud center
(surface).

#1. For remodeling or interior demolition, a total charge of 45 kg was exploded inside a
rectangular-shaped building, 75 m wide, 25 m deep, and 50 m high; the interior walls or
other structures take up negligible space. The walls, windows and doors remained intact
and closed, trapping the fumes, which reached uniform composition. Under these
circumstances, what concentrations of CO, NOx and RFT-R would be registered? Would a
stranded robot that took a gasp of the fumes report a hazardous condition? For yielding a
nonhazardous toxicity, what is the maximum charge that could have been utilized?

The scaled cloud model works regardless of the cloud’s shape, so not all questions
require the cylindrical cloud representation. The charge mass 45 kg dividing by the
room volume 75-25-50 m$ yields the trapping density pr = 0.480 g/m3, whereupon
Equation 1 yields the scaled radius r = 7.92 m/kg”3. The registered quantities of CO
or NOx follow from Equation 3 with the relevant tabulated constants from Table 1
or the relevant graphs noted later. The registered concentrations were xco = {CO} =
7.10 PPM, xnox = {NOx} = 0.782 PPM, so the Russian rule yields {RFT-R} =
{CO}+6.5-{NOx} = 12.2 PPM. The latter result is under the resolved criterion of 25


1x) depends upon the tabulated constants cy and therefore the threshold results depend
upon the charge formulation chosen. The report utilized the traditional Russian rule
RFT-R for the overall relative fume toxicity RFT, since it was compatible with the
imposed model restrictions. It was shown that the RFT-R relation yields CO equivalent
toxicity for nominal NOx. .

For risk/hazard scenarios, the cloud was usually represented with equivalent cylindrical
form in the numerical examples. When different cylinder aspect ratios were considered,
it was recognized that wider (flatter) clouds have higher nonhazardous threshold radii
Rex than their taller (narrower) counterparts. Only the RFT-R results were regarded as
worthwhile for ranking exposure, since the threshold resolution depended upon the whole
fume spectrum of a charge formulation, not isolated components. Threshold trapping
density or scaled radius results for NOx and CO were not useful in that regard, though
they could be utilized for setting up instrumentation to monitor shots. Though the report
tended to disregard the issue of toxic fumes stranded in rocks, it was shown that results
could be reconciled for the fraction trapped. The reduction in the trapping density and
related concentrations were proportional to those without trapping, with the retained
(non-trapped) fraction representing the constant of proportionality.

The range of cloud inflation to the nonhazardous threshold state was roughly ten fold, for
the worst-case of no initial dilution or inflation. Through the model’s relations it is
recognized that the trapping density and the toxic concentrations would undergo a
corresponding thousand-fold reduction to reach nonhazardous threshold condition, in the
worst-case. The tremendous reduction reveals why under-inflated clouds with their
woefully unfinished dilution that drift the wrong way are tremendously dangerous.
Therefore it was thought that risk analysis should consider rare exceptions and not just
the typical statistical possibilities. Questions were raised regarding tradeoffs if non-
workday criteria were utilized, since that would foreshorten the shadow trajectory for the
region threatened and hence the number of circumstances which were regarded as
worrisome. When the ramifications for guideline violations were reviewed in conjunction
with the tremendous uncertainty in cloud mechanics, it was thought that workday
criteria were warranted. This choice also retains the superposition rule for component
mixtures, which is necessary when working with toxic fumes from nonideal mining
explosives.

Understanding worst-case and typical fume concentrations might help reveal blasting
techniques that mitigate toxic hazards. Responsible undertakings with regard to those
hazards can reduce outside concerns and complaints, as well as reduce monitoring costs
by indicating where monitor deployment would be most useful. The utilization of more
water resistant or rugged explosives to reduce risk of unusual fume toxicity is worth
recommending.

APPENDIX A. RUSSIAN FORMULA FOR RFT WITH NOMINAL NOx

The traditional Russian formula utilizes only the weighted superposition of the two major
toxic fume components, within its formula for relative fume toxicity {RFT-R} =


Equation 3 yields the fume concentrations, rounded-off: {CO} = 87 PPM, {NOx} = 9.6
PPM, {NOx}-25% = {NO} = 2.4 PPM, {NOx}:75% = {NO} = 7.2 PPM and {RFT-R} =
150 PPM. The RFT-R is over 25 PPM or r is under rx, so overall toxicity is still
hazardous. Threshold conditions would be reached until r = rx = 6.24 m/kg!,
yielding Rox = 545 m and Hex = 1100 m with Equation 2..When rocks trap the
fumes, the concentration reduction is proportional to the lost fraction. If the rocks
trapped 25% of the fumes, the residual 75% forms the cloud, yielding concentrations
75% of those found.

#4, What constant wind is tolerable so that toxic fumes turn nonhazardous prior to
drifting over the fence surrounding a rectangle property, 4 km x 7 km, if a 25-tonne
charge is detonated to form a water hole at its center? The cylinder cloud remains
compact and the rates of inflation yield threshold conditions in % hr (CHLT), for the
worst possible wind direction.

Working backwards from the fence where the cloud has just reached threshold
conditions, it is recognized that r = 6.24 m/kg’3. The threshold cloud or its terrain
shadow has a radius Rex = 0.16 km from Equation 2, with « = 1 and Mx = 25,000 kg.
The worst-case wind direction would yield the quickest trek over the fence or the
rectangular half-width = 2 km. Subtracting off the threshold cloud radius Rcx then
yields the travel distance for the cloud center = 1.84 km. With 0.5 hour for travel,
the wind speed cannot exceed 3.7 km/hr = 2.3 mph. Under the circumstances
resolved, the toxic fumes would be rendered nonhazardous by natural turbulent
dilution by the time they drift off the property, regardless of whether they remain
noticeable (or observable in some way).

#5. The workday TLV-TWA criteria have traditionally been utilized for toxicity guidelines
in mining regulations, though it is recognized that other guidelines are sometimes
contemplated for ranking fume clouds. For a released puff of NOz, what reduction would
be expected for the nonhazardous threshold rx, if the workday criterion was replaced with
the immediate dangerous to life and health (IDLH) criterion?’ Non-workday guidelines
typically lack superposition rules for fume mixtures, so NO2 was taken from the
restricted choice of molecular species in Table 1. The warning note with NO2’s IDLH of 20
PPM reveals that there is risk of irreversible damage for violating the half-hour criterion
and that quicker extrication is desirable. Presuming the NO: loss (gain) remains
negligible for the transition from the IDLH to TLV-TWA circumstance yields the
proportionality x5 ~ 1-3; for the ratio of two conditions, the constants cy and x disappear in
Equation 3. Therefore they remain irrelevant and could have been readjusted to reflect
an initial transitory loss.

The criteria ratio [IDLH(TLV-TWA)] = 20/3 = 6.67, yields the ratio-of-r = (1/6.67)¥3
= 0.53 from x3 ~ r3. The IDLH scaled radius threshold is 53% of rx for the workday
guideline, which is not a notable reduction considering the ramifications for
criterion violation. The portentous shadowy trajectory in Figure 1 would run roughly
half way if IDLH guidelines replaced the workday ones, presuming the twisted wind
drift and constant rate of inflation. The radius reduction for NOz was minimal when


PPM in Table 1, so the robot took a nonhazardous gasp. The retention of
nonhazardous circumstances would require that the maximum charge mass just
correspond to the threshold scaled radius, rx = 6.24 m/kg, or the related trapping
density, prx = 0.984 g/m’, which is the quicker way. Multiplying the room volume
75-25-50 m$ times prx and dividing by a thousand to transform the units, yields 924%
kg.

#2, Determine the RFT-R threshold radii for nondescript, spherical, and cylindrical,

clouds with cylinder aspect ratio o. = 4,2,1,0.5, or 0.25, for the charge mass Mx = 1Mg

=1000 kg [or metric ton (tonne)].

For nondescript clouds the radius is retained in scaled form or reduced to the
equivalent spherical radius Rsx with units in meters, m, for the charge mass in
kilograms, kg, using Equation 1. For equivalent cylinder clouds Equation 2 is
utilized and the results noted in Table 2. Cylindrical clouds with tall-thin profiles
(high a) have small radius, Rex, while the reverse holds for short-wide profiles. For
risk/hazard scenarios, the portentous shadow on the underlying terrain has related
radius Rox. The tabulated results could be utilized for other charge masses by
multiplying the table numbers by the cube root of the charge mass per tonne. For
the compact cylindrical form the Rcx would be 5.5 m, 55 m, and 550 m for the charge
mass Mx of one kilogram, one tonne (1 Mg or 103 kg ) and one kilo-tonne (1Gg or 108
kg) respectively.

Table 2. Threshold radii for 1 Mg of ANFO-94/6 for
clouds with different forms.

Cylinder Aspect Ratio, a: | 4.0 | 2.0] 1.0 | 0.5 | 0.25

Nondescript Spherical Cylinder Radius, Rex, or
Form, Radius | Radius, Rsx | Circular Shadow Radius

(Im/kg¥4] {m] [m]
6.24 62 34 | 43 | 55 | 69 | 87

#3. There was no wind, when a tremendous quantity of explosive, Mx = 1 kilo- tonne (or 1
Gg), was shot in an open pit mine. The fume cloud quickly took on and retained compact
cylindrical form, remaining close to the relatively flat terrain during inflation. Without
wind drift, the cylindrical rim (surface) of the dispersing cloud ultimately reaches a
rugged monitoring station mounted 300 m from the charge center. When the contact
occurs, what is the detected CO, NO, NOz, NOx, and RFT-R? What would be the
threshold cylindrical radius Rc, when the toxic fume cloud is rendered nonhazardous?
How would the concentrations change from the results found, if 25% of the fumes were
stranded in the rocks?

When the fume cloud just reaches the station, its radius Rc = 300 m, so the cylinder
height Hc = 600 m from Equation 2 with « =1. The cylindrical volume of nRc?Hc =
1.70-108 mS. The trapping density pr = 5.89 g/m’ and scaled radius r = 3.43 m/kg!3
follow from Equation 1. Using the relevant tabulated constants from Table 1,


UNDERESTIMATE OR OVERESTIMATE

Zero-time loss refers to the fumes stranded in the rock or muck pile or other stratum,
decreasing the overall quantity that forms the fume cloud. For rocks with a medium
number of cracks =40% of the gases are released into the working atmosphere, ~20% are
entrapped in shattered rocks, and ~40% in lateral rocks.6 The reduction loss tends to
occur quickly and uniformly, regardless of the fume species. Taking the reduced charge
mass that just forms the fume cloud in the trapping density formula resolves the issue
and yields proportionally smaller concentrations as noted in Appendix B. Though zero-
time loss reduces the fume components uniformly and quickly, dynamic-loss tends to
operate more slowly and selectively on the fume spectrum. ©

Dust/droplet absorption or other transformations reduce the NOx, though not the CO, in
the underground fumes chamber, with a half-time constant (Ts0) of roughly 45 minutes.
The RFT-R has a weighted NOx contribution that roughly approximates its CO
contribution. For reductions of zero in CO and 50% in NOx at Tso, the reduction in RFT-R
would be 25%, so 75% of the original still remains. The rusty-tinted oxidation trends
from the underground fumes chamber reveal that NOs rises quickly, reaching
~40%-{NOx} in two minutes. Thereafter it works its way towards =70%-{NOx} with Tso
=7¥% minutes. While the loss occurs relatively slowly, the cool-temperature oxidation
occurs rather quickly and justifies the utilization of nominal NOx after quarter or half
hour. Remedying the scaled model for the RFT-R loss of roughly 25% would ruin its
underlying simplicity. When the uncertainty of cloud mechanics is considered, worrying
about the RFT-R reduction for lost NOx is not a worthwhile tradeoff, so it was
disregarded throughout the report. .

Unlike the former mechanisms that cause theoretical overestimation, charge
malfunctions can cause underestimation, which is a worse problem for risk/hazard
scenarios. Charge malfunctions can result from the cross-hole impact of shock waves, rift
compression (heave), quasi-static gravitational loading or poor water resistance.
Underestimation with the model occurs from released fumes that are far more toxic than
those rendered by the work principle tabulations. The RFT-R for overall toxicity could
remain unchanged, double, or quadruple due to the unusual quantity of NOx. Therefore
unless rugged explosives with the necessary water-resistant are utilized, there is notable
and unresolved risk related to working with the scaled cloud model.

CONCLUSIONS AND RECOMMENDATIONS

The scaled cloud model for conserved fume components is a restricted though useful work
tool for correlating toxic concentrations with cloud size (scaled radius) and for rendering
simple risk/hazard scenarios. The generalized relationship for Jth fume component,
Equation 3, revealed that the Jth molar concentration x, is proportional to the trapping
density pr for roughly constant thermodynamic cloud condition x and tabulated constants
cy from the refined thermodynamic work principle. The graphical trends display the
universal proportionality x3 ~ r3 for Jth concentrations, which results from replacing the
trapping density pr with the scaled cloud radius r. When the criterion guideline was
taken, it was recognized that the nonhazardous threshold trapping density prx (or radius


Scaled Cloud Model for Released Toxic Fumes

Michael S. Wieland
NIOSH Pittsburgh Research Center
Pittsburgh, Pennsylvania, USA

Recognizing the dynamic nature and possible range of toxic concentrations in the
impending fume cloud prior to undertaking explosive blasting can reduce potential
hazards and mitigate related incidents. The scaled cloud model was formulated to
predict the relevant (major) toxic components in fume clouds released by nonideal mining
explosives used for surface blasting. Natural turbulence unceasingly disperses the toxic
molecules, widening (inflating) the fume cloud while diluting the concentrations,
ultimately rendering nonhazardous conditions. The threshold cloud size depends upon
the type and quantity of total explosives used and the cloud’s thermodynamic condition.
Though the scaled theory works for fume clouds with irregular (odd) shape, an equivalent
upright cylindrical form is useful for rendering simple risk/hazard scenarios. The
cylinder’s projection downward on the underlying terrain yields a circular ‘shadow’
marking the region threatened, thereby permitting a rough estimation of the potential
hazards, were the cloud to settle down there. Wind causes the cloud to drift while it
expands, so the shadow travels while it grows, until the risk/hazard process is truncated
at the nonhazardous threshold.

The overall relative fume toxicity (RFT) is taken from the traditional Russian RFT rule,
which utilizes only the two fume components that tend to dominate the resultant toxicity:
carbon monoxide (CO) and total nitrogen oxides (NOx). Tabulated constants that
characterize the fume spectrum in the cloud model were resolved for ammonium nitrate
(94%) with fuel oil (6%), ANFO-94/6, using a refined thermodynamic work-principle.
Comparable results were found with the reduction factor technique, when test results
from the underground fume chamber were readjusted to reflect nominal field shooting
conditions.

INTRODUCTION

The scaled cloud model looks rather rudimentary, when it is compared to the computer
models for stack plumes or released toxic puffs.!:2 Restrictive assumptions keep the
formulation rigorous though fundamental, minimizing the quantity and type of technical
input required. For risk/hazard purposes, the toxic (average) exposure is relevant, so
concentration gradients and fluctuations within the fume cloud are disregarded. The
reduction in fume toxicity occurs naturally from the mechanical turbulence within the
atmosphere, which perpetually reshuffles the molecules. The toxicity reduction process is
regarded as the ingestion of (outside) air through the cloud’s surface, mixing with and
diluting the (inside) toxic concentrations. To wholly retain or trap the toxic fumes within
the cloud, the cloud’s dimensions undergo inflation. The theoretical foundation upon
which the scaled model rests is the conservation of the number of molecules (or moles) of
suitably chosen (Jth) fume component within the cloud. Reaction transformations that
would render Jth fume component loss over the cloud’s hazardous lifetime (CHLT) must
remain negligible so they can be disregarded. CHLT is the time interval from when the


[4].

Where c, = ; p, = Mx, ce GP
My, V; K, Th

The result is utilized for clouds with non-constant trapping density. For rigid-wall
chamber tests, the relationship yields the tabulated constants cy, where the trapping
density pr remains constant, the thermodynamic condition « and the mole fractions yj of
the trapped fumes are measured. The tabulated constants cy form a reference set with
units that characterize the gaseous fume spectrum of the charge formulation. The
relationship would be rewritten for Ny8/Mx if condensed phases (liquid or solid) were
wanted.

When some of the toxic fumes are stranded in the rocks or muck pile rather than released
in the cloud, the former relationship still works with a simple readjustment. The
rock/muck retention process is regarded to occur so rapidly that the fraction lost is
identical for all fume components. The reduced charge mass Mx* is the fraction fc of the
total charge mass Mx that forms the fume cloud. For fumes stranded in the rocks or other
stratum, the trapped fraction fr is just fr= 1-fc. The reductions are denoted with #,
otherwise the variables retain their original meaning. Multiplying both sides of Equation
4 by the cloud fraction fc and reorganizing the results yields the wanted relationship.

yaXi(e Ny Ms BH _N, Mk
7 Ny M, “N, My

=k fo= [z so. fe = fe “ where [8].
Mt M*
the rati: ‘atios is unity, aX, pha,
ratio of ratios is unity, f; My Pr Ve

Notice the reduction that occurs in the third step when the ratio of ratios is taken as
unity and disappears. For fumes that are quickly trapped, the Jth moles released is
proportional to the released charge mass. The ratio term does not depend upon the degree
of trapping and therefore it remains constant. Furthermore, it must reduce to the original
results without trapping, whence the ratio of ratios remains unity. The reduced
concentration xj* and the reduced trapping density pr* are just the original results,
multiplied by the relevant cloud fraction fc, whence the form of Equation 4 is retained. It
is worth noting that the reduction for trapped fumes does not affect the tabulated
constant cy or the thermodynamic cloud condition x.

The logical interpretation is that the reduced (or released) concentration of the Jth
component xJ* remains proportional to the reduced trapping density pr* regardless of the
fraction trapped in the rocks. The reduced scaled radius r* would replace r in Equation 1


{CO}+6.5-{NOx}.3 The Russian formula circumvents the difficulty of unresolved transitory
species, like the NOx constituents and works only with their resultant sum {NOx} =
{NO}+{NOo}. The NOx composition tends to reverse its compositional percentages rather
quickly under the rusty-tinged oxidation reaction, with the transformed composition
drifting towards nominal NOx within a quarter or half hour in underground tests. The
intention is to show the Russian formula RFT-R yields the RFT for CO equivalent
toxicity, when the NOx is nominal. The resolved equality would not work for nominal NOx
if the TLV-TWA criteria were revised, unless the Russian weighting factor 6.5 was then
readjusted in the necessary way.

The RFT formula for CO equivalent toxicity is found from the resultant sum of weighting
factors times their respective concentrations. The weighting factors are TLV-TWA for CO
divided by TLV-TWA for the Jth component.’ The RFT rule for rendering CO toxicity for
some mixture of CO, NO, and NO:z is {RFT} = {CO}+{NO}+(25/3)-{NOz}, when the unity
factors (25/25) are removed and other components like COz or ammonia (NHs) remain
negligible. The replacements for nominal NOx are {NO} = 25%-{NOx} and {NOs} =
75%{NOx}, which upon insertion yield the Russian formula; that is, {RFT} =
{CO}+6.5-{NOx} = {RFT-R}. The RFT-R criterion is taken as the CO criterion, which is
utilized for ranking the overall fume toxicity throughout the report. Working backwards
with the RFT-R formula yields a rough criterion for an unknown composition of NOx that
technically could not be rendered otherwise. The Russian weighting factor 6.5 is divided
into the TLV-TWA for CO yields 3.8462 PPM.

Restrictions imposed to form the scaled model and the character of the RFT-R rule are
compatible for a couple of reasons: the requisite fume components CO and NOx have
tabulated constants from the work principle, they dominate the resultant toxicity in the
fume spectrum, they are roughly conserved for time intervals thought to resemble CHLT
and they numerically approximate CO equivalent toxicity. Therefore RFT-R is the logical
rule to represent the overall fume toxicity in the scaled cloud model, rather than some
more complex and less tractable algorithm.

APPENDIX B. THE GENERALIZED CONSERVATION RULE

The scaled cloud model rests upon the conservation rule for the Jth fume component.
Without reaction transformations or other loss (gain), the number of moles Ns (or
molecules) remain conserved, retained within the fume cloud. Transforming the observed
thermodynamic cloud state to the reference condition would not readjust the mole
number, hence Ny = Nj, where the ‘R’ denotes the reference state. The tabulated
constant cy represents the total fume reference volume Vy divided by the total explosive
mass Mx. The work-principle utilizes the K-function, which is rendered by the definition,
K= P/R*T, where the pressure P and temperature T represent the thermodynamic state
of the fume zone (or cloud). The reference constant Kr = Pp/R*Tr = 40.874 mol/ce or the
reciprocal of 24,470 cc/mol, for the reference temperature Tr = 25 °C and reference
pressure Pp = 1 ATM. Non-dimensional x is taken as the ratio of the K-function with
respect to its reference Kr. The relationship for the Jth mole fraction yj as a function of
cy, k, and pr follow from reductions using the former notions, the ideal gas law, and the
rearrangement of terms:


compared to the other choices, so it normally represents the worst tradeoff when
risk/hazard and margin-of-safety issues are considered.

Under some circumstances, the IDLH criteria would appear more logical for drifting and
dispersing fume clouds, though now it’s recognized that there would be a respectable size
reduction in the region threatened (shadowy trajectory), and hence a reduction in the
number of circumstances inspected, and thereby some potential dangers overlooked.
Worrisome issues are not always related to statistical averages but rather to rare
circumstances when the clouds remain trapped by inversion, under-inflated, quite toxic,
close to the ground and drifting the wrong way! Worthwhile tradeoffs between the risks of
threshold violations and the tremendous uncertainty in forecasting wandering clouds
must be reckoned with, otherwise the reliability of using the scaled theory to study
risk/hazard scenarios is gravely jeopardized. Taking the nonhazardous threshold from
traditional TLV-TWA guidelines means not only the retention of the mixture
superposition rule, but also a reduction in risk regarding wrongful prediction with the
rudimentary scaled cloud model.

GRAPHICAL RESULTS AND INTERPRETATION

To graph concentrations over the range of inflation regardless of the cloud’s (odd) shape,
the scaled radius ro for the original cloud state is required in conjunction with rx, the
nonhazardous threshold. Equation 3 yields illogical infinite concentration ifr is taken as
zero; mole fractions are restricted to the range: zero-to-unity. The worst-case for ro is
resolved by recognizing what would occur if the cloud formed so quickly, that there was
no time for inflation. Without the related dilution, the trapping density is just the
reciprocal of the total reference volume tabulated for the gaseous reaction products,
which is roughly 1000 ce/g (or 1 m*/kg) for numerous explosives. The reciprocal of that
number yields the trapping density pro at zero-time, pro ~ 1000 g/m (or 1 kg/m’). From
Equation 1, the trapping density yields the scaled radius ro at zero-time,

ro = 0.62 m/kg¥8, which is roughly 10% of rx, the RFT-R threshold.

The Graphs in Figures 2, 3 and 4 display the universal proportionality x3 ~ r3 over the r-
range [ro <r < rx] = [0.62 <r < 6.24] in m/kg” units, with room for crossover into the
nonhazardous regime. They show the concentration trends for CO, NOx and RPT-R with
respect to r, as well as the relevant toxicity guidelines from Table 1. The resolved
nominal NOx criterion, the TLV-TWA criteria for NO and NO: are noted in the NOx
graph. For RFT-R, the overall fume toxicity requires roughly a ten-fold inflation to reach
the nonhazardous threshold from the worst-case initial state. Equation 3 then yields a
thousand-fold reduction in the trapping density and Jth concentration over the same
range. Without dilution and inflation explosive fumes are extremely toxic, roughly a
thousand times more hazardous than their workday criterion. Residual fumes stranded in
the rocks, transformation loss or gain, or unusual fumes from charge malfunctions were
disregarded in the graphical resolutions. Though the graphs are harder to interpret
precisely, they could have been utilized rather the equations for resolving the numerical
examples.


bracketed terms in the formulas usually remain roughly constant or are replaced with a
typical x constant, reflecting the cloud’s thermodynamic condition over its hazardous
lifetime, CHLT.
3c,
Ke P

c T,
% -[}-6, = a where Ke : [3].

R

-

The concentration yj has units in part-per-million [PPM], when the tabulated constant cy
has units [cc/g] and the trapping density pr has units [g/m3]. The non-dimensional x
reduces to the ratio of the cloud’s pressure (P) to the cloud’s temperature (T) taken with
respect to their reference-state conditions: Pr = 1 ATM and’Tr = 25 °C, noted previously.
For cooler conditions like T = 0 °C with reduced pressure like P = 1 bar, k would equal

- 1,077. The tables and graphs in the report utilize, x =1, for the reference state. The
refined work principle technique, reviewed in Appendix C, was utilized to resolve the
tabulated constants cj. When toxic fumes are stranded in the rocks or other strata, the
relation 3 is modified as noted in Appendix B, so the trapping density (or r) refer to the
reduced charge mass forming the fume cloud, yielding proportional reductions in the
concentrations.

TABULATED CONSTANTS Cj AND NONHAZARDOUS THRESHOLDS

Natural turbulent dilution and inflation render the fume cloud nonhazardous for the
threshold cloud size related to a criterion from recommended toxicity guidelines. The
columns of Table 1 respectively contain the fume component type, tabulated constants
from the work principle N-state, the concentration criterion, the threshold trapping
density prx, the scaled radius rx and its transformation to rationalized MKS units. The
threshold cloud conditions with the subscript X (on r or p) for crossing over into the
nonhazardous regime were resolved with Equation 3 and relevant information from the
other columns. The threshold-level value time-weighted average TLV-TWA for workday
exposure in parts-per-million (PPM) was taken as the concentration criterion for the
molecular species.* The traditional Russian rule RFT-R is taken to represent the overall
fume toxicity, regardless of the NOx composition, though for nominal NOx, it reduces to
CO equivalent toxicity. For the weighted mixture RFT-R and un-weighted mixture NOx,
the corresponding criteria in Table 1 with the asterisks, were worked out in Appendix A.

Technically, the resolved information in Table 1 from Equation 3 depends upon the
tabulated constants for the fume spectrum of a charge formulation under investigation,
not isolated fume components. The results in Table 1 presume the cloud’s thermodynamic
condition x was unity and the tabulated constants cy were for ANFO-94/6. For
risk/hazard scenarios, the RFT-R rule for overall toxicity is relevant for ranking the total
exposure to the fume mixture. The nonhazardous cloud condition is therefore uniquely
rendered, via the RFT-R row of results in Table 1. Though individual fume components
are not relevant for ranking net toxic exposure, the other rows of results could be utilized
for the useful placement of monitors or selection of their detection sensitivity.


the reduction factor technique because they are resolved without (user) stipulated
constants and require fewer computations.

Unfortunately chamber tests rarely yield toxic fumes that reflect field blasting without
notable readjustments, which is why the cy are resolved wholly theoretically or the
reduction factor technique is utilized. The older technique of subtracting off weighted
components to remove booster proportion remains faulty. The rate kinetics is nonlinear
and the out-dated technique occasionally yields ill-logical (impossible) negative
concentrations.!0 Using the reduction hypothesis, the relative deviation percentage,
RD%zu, of the underground fume components to the field components is written:

[c, (W,X}-c,{N,X}]-100%

SIN. x) =[RF, -1]:100% [7].

RD%, =

The original reduction factors or the results from the fourth and fifth columns of Table 3
yield the relevant information. Rounded off, RD%-CO = 16%, RD%-COz = 16%, RD%-H2 =
-3%, RD%-NOx = 36%, and RD%-RFT-R = 26%. The resolved differences between
underground chamber shots and nominal field shooting conditions are therefore not
minor.

REFERENCES

' Patrick, D. R. Toxic Air Pollution Handbook. Van Nostrand Reinhold, NY, P.226-240, 1994.

? Stern, A. C. Air Pollution, Third Edition, Volume I, Air Pollutants, Their Transformation and Transport,
Academic Press, NY, P.442- 487, 1976.

* Rossi, B. D. i e
Nauchno-Tekhnicheskoe Gorbnoe Obshchestvo, Scientific and "Technical Mining Society, ‘Varyvnoe Delo,
Collection No.68/28, Translated from the Russian, Izdatel’stvo “Nedra”, Moskva, P.57-89, 1970.

‘ Threshold Limit Values (TLVs) for Chemical Substances and Physical Agents and Biological Exposure
Indices (BEIs). American Conference of Governmental Industrial Hygienists ACGIH, P.15-77, 1999.

5 NIOSH Pocket Guide to Chemical Hazards, National Technical Information Service QNTIS) or the US
Superintendent of Documents, Gevernment Printing Office (GPO), waaburgh PA, 2000.

° Rossi, B. D. Con e ng Work, and New hod ting Industrial Explosive
Nauchno-Tekhnicheskoe Gorbnoe Obshchestvo, Scientific and Technical Mining Society, Vzryvnoe Delo,
Collection No.68/28, Translated from the Russian, Izdatel’stvo Nedra”, Moskva, P.31-42, 1970.

TM Threshold Limit Values (TLVs) for Chemical Substances and Physical Agents and Biological Exposure
Indices (BEIs). American Conference of Governmental Industrial Hygienists ACGIH, Appendix C, P.81-83,
1999.

® Wieland, M. S. Work Principle For Predicting Explosive Toxic Fumes. Proc. 14" Ann, Symposium on
Explosive Blasting Research, Soc. Explosive Eng., Cleveland, OH, P.121-138, Feb. 1998.

° Wieland, M. S. Understanding the Hazard Potentials of Toxic Fumes. Eighth High-Tech Seminar, Blasting
Analysis International, Inc. Allentown, Pennsylvania, P.368-382, July 1998.

» Wieland, M. S. Removing Booster Influence from Toxic Fumes, Proc. 25" Ann. Conf. Explosive. Blasting
Technique, Soc. Explosive. Eng., Cleveland, OH, P.11-28, Feb. 1999.



uniform within the cloud and zero or negligible outside the cloud. The trapping density pr
is defined as ratio of the total explosive mass Mx to the total fume cloud volume Vr. The
cloud’s scaled radius r with units [(cm/g”%) or (m/kg”)] is defined wholly in terms of the

trapping density pr:
r= RCH He where p.
- rae “4M, x 7=
4nr°

Useful reciprocal form: 4.
Pr 3

1.

The relationships for spherical or cylindrical clouds of equivalent fume volume follow the
trapping density definition. Respectively the spherical radius Rs would yield Vr =
4nRs*/3, whereas the cylindrical height Hc and radius Rc would yield Vr = nRc?Hc. The
cylinder’s projection onto the underlying terrain forms a circular ‘shadow’ nRc?
representing the region threatened just now. Under wind drift it tracks out a portentous
swath, as shown in Figure 1.

From a remote perspective, the cloud’s depth is obscured, so the cloud’s profile is
reckoned in terms of its height-to-width ratio, which remains constant, regardless of
range (far) of observation. The cylinder aspect ratio represented by the defining relation a
= Hc/2Rc, characterizes the tall-thin nature of the cylindrical cloud. Gravitational related
influences tend to distort the cloud’s height differently than its width, somewhat
justifying the upright orientation. In conjunction with the former volume equivalence, the
cylinder aspect ratio o is taken equal to the reckoned (or assumed) height-to-width ratio,
yielding a unique prescription for the cloud’s cylindrical form. To resolve the two cylinder
dimensions, Hc and Re, from r and Mx, the cylinder aspect ratio « must be stipulated, as
noted in the rearranged transformations from Equation 1:

2M,
aa

Ro =r} H,=2aR,. [2].

When inflation occurs in a proportional way, « remains constant. Compact cylinders have
maximum volume at constant surface or minimum surface at constant volume, for which
ais unity. The compact cylindrical form is useful for rendering predictions when the
cloud’s height and width remain roughly equal, otherwise a representative numerical
choice or several readjusted choices are utilized.

THE CONCENTRATION OF THE JTH FUME COMPONENT

When reaction transformations representing loss or gain remain negligible for the Jth
toxic fume component, the number of moles Nj remains constant, while the total moles
Nr change during the inflation-dilution process. The resulting uniform non-constant
molar concentration xj within the cloud, x3 = Ns/Nv, depends upon the cloud’s
thermodynamic condition , a tabulated constant cy and the non-constant trapping
density pr. This relationship shown in Equation 3 was derived in Appendix B. The
trapping density pr was replaced with the scaled radius r using Equation 1. The


cloud forms until it is rendered nonhazardous. The constancy restriction holds for reverse
loss (gain), so that the Jth component must have zero or negligible concentration in
outside air taken into the cloud.

Fume components from typical mining explosives which are worth considering in the
scaled cloud model are: carbon dioxide (COz), hydrogen (Hz), carbon monoxide (CO) and
the mixture of nitrogen oxides (NOx), though not the two constituents, nitric oxide (NO)
or nitrogen dioxide (NO2). Toxicologically the role of CO2 is rather minor and Hp is
nontoxic so they receive relatively little attention, though they were retained in some
tables. The total number of NOx moles is conserved under the oxidation reaction that
transforms transparent NO into rusty-tinged NOz at cooler temperatures, though the
dust/droplet interaction or other circumstances that result in NOx loss are disregarded.

The traditional Russian formula {RFT-R} = {CO}+6.5-(NOx} utilizes only the resultant
weighted-sum (superposition) of carbon monoxide {CO} and mixture of nitrogen oxides
{NOx} to yield the relative fume toxicity RFT.3 The terminology nominal NOx is useful
and refers to the composition {NO} = 25%-{NOx} and {NOz} = 75%-{NOx}. When the NOx
composition is nominal, results from the RFT-R rule match those for CO equivalent
toxicity, as noted in Appendix A. The notation with braces is utilized for molar
concentratioris with non-dimensional units, like part-per-million (PPM), or when relevant
transformed concentrations with dimensional units, like (cc/g), taken at thermodynamic
reference conditions of 1 ATM (atmosphere) and 25 °C.

Questionable issues which are recognized in the report are: the notable quantity of toxic
fumes stranded in nearby rocks or the muck pile, the nonideal reaction-zone combustion.
and the role of wind drift. Readjustment for stranded fumes is resolved in Appendix B in
a way that retains the functional form of the original scaling relation. Throughout the
report, the readjustment of results is conveniently ignored, since it reduces to
multiplication by the residual (un-trapped) fraction forming the fume cloud. The work
principle technique in Appendix C and the reduction factor technique in Appendix D to
treat the reaction-zone deflagration that follows nonideal detonation, while total
thermodynamic equilibrium still prevails. Wind drift is a notable and rarely tractable
complication when undertaking risk/hazard analysis, since the region under threat
wanders while it expands, until it disappears at the nonhazardous threshold. Rates of
cloud inflation are not incorporated into the scaled model, which restricts the types of
scenarios that can be resolved. Wind drift was disregarded in the numerical examples,
except for one manageable example, where the CHLT was just stipulated. Rough
quantitative results from the cloud model are useful for recognizing potential hazards, so
that worrisome possibilities can be investigated more thoroughly. For resolving specific
dynamic circumstances with wind drift or fume component losses, the puff or plume
models are worth trying, despite the fact they require more technical information to
render worthwhile predictions.

TRAPPING DENSITY AND SCALED RADIUS RELATION

The scaled cloud model relates toxic concentrations to the trapping density pr, regardless
of wind drift, the cloud’s shape or rate of inflation. Concentrations are regarded as


for the reduced trapping density pr*. The threshold (scaled) results rx or prx in Table 2
relate directly to guideline criterion and would not be readjusted in the reduction
transformation for trapped fumes, though un-scaled radii, Rox, would naturally change
when using reduced charge mass for the un-trapped portion forming the fume cloud.

APPENDIX C. TABULATED CONSTANTS FROM THE WORK-PRINCIPLE

The refined work principle technique in conjunction with a thermodynamic reaction code
can resolve fume products for a wide range of explosive charge formulations with
different types of ingredients.8° The tabulated constants were resolved with an
unpublished refined formulation that incorporates reaction zone loss for work output and
heat transfer to the surroundings. The fuel oil in ANFO-94/6 was written with a
molecular formula of C1sH2 and heat of formation was taken as —247 kJ/mol. Regular
thermodynamics or the underlying work principle are formulations without time and
therefore unable to resolve nonequilibrium circumstances that require rate dynamics.
The work principle is unable to resolve the nonequilibrium cool-temperature oxidation
that renders the rusty-tinged fumes, though worthwhile results are found for NOx, which
remains conserved under the transformation.

Respectively the columns in Table 3 for the tabulated constants cy show the relevant
fume component, the work principle Z-state and N-state results, comparable underground
(average) results, and the modifications from removing unwanted influences using the
reduction factor technique in Appendix D. The Z-state presumes zero loss from the
reaction-fluid zone to the surrounding medium, while the N-state more realistically
presumes nonzero loss. Zero booster weight fraction and zero reactant air were presumed
for the work-principle computations mimicking nominal field conditions, so those
reactants were removed from (not included in) the ingredient tables originally used to
represent underground shots. The reaction transformations were understood to reach
total thermodynamic equilibrium without air, though it could later have a role in
nonequilibrium processes. Cooler temperature nonequilibrium states that transpire to
reach observation (monitoring) conditions remain unresolved in the work principle
technique, unless the fume components remain conserved.

Table 3. Theoretical tabulated constants cy and related observations.
Type of Toxic or Work Work Under- Removing
Non-Toxic Principle | Principle | ground | Booster & Air
Fume Component Z-state N-state | Chamber Influence

[cc/g] [ce/g] [ce/g] [ce/g]
Carbon Dioxide, COz 86.8 91.8 101.5 =87.5
Carbon Monoxide, CO 19.9 14.8 15.4 =13.3
Hydrogen, Hz 22.7 18.1 9.52 =9.80
Nitrogen Oxides, NOx 3.15 1.63 2.58, 2.69 | ~1.90, =1.99
Relative Fume Toxicity 40.4 25.4 32.2, 32.9 | =25.7, =26.2
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