22 Persson P-A., R. Holmberg, and J. Lee. Rock Blasting and Explosives Engineering. CRC Press, Boca Raton,
P. 100-114, 1994.

23 Landau and Lifshitz. Statistical Physics, 34 Edition, Part 1, Course of Theoretical Physics, Volume 5,
Pergamon, P. 57-65, 1980

24 Lavenda, B. H. Statistical Physics, A Probabilistic Approach. John Wiley & Sons, NY, P. 46-49, P. 59, 1991

25 Chang, R. General Chemistry. Random House, NY, P.522, 1986.

26 McBride, B. J. and S. Gordon. m_f ion hemical_Equili

scription. NASA Reference Publication

1311, NASA Lewis Research Center, Cleveland, Ohio, June 1996.

2? Chang, R. General Chemistry. Random House, NY, P.470-474, 1986.

28 Gordon, S. and B. J. McBride. Computer Program for Calculation of Complex Chemical Equilibrium
itions a1 icatio1 is. NASA Reference Publication 1311, NASA Lewis Research Center,

Cleveland, Ohio, October, P.42-43, 1994.

?° Chang, R. General Chemistry. Random House, NY, P.683, 1986.

® Langtord, C. H. and R. A. Beeby. The Development of Chemical Principles. Dover Publications, Inc. NY, 1969.

[Unabridged and corrected replication, p 166, 1995.]

3! Reference 8. The factorials were erroneously dropped from the reported Taylor formulas.

32 Reference 24, P. 150-160, 191-199, 1991.


resolving the fume spectrum was the NASA Lewis Complex Chemical Equilibrium Code. This TDRC
works with idealized forms of condensed phases and gas mixtures; it has a wide range of molecular
species 26 and on occasion reveals unexpected toxic components not recognized by the RFT rules or
detection equipment. Resetting the EOS formula or constants would be rendered ineffectual with the
form reductions taken for the ideal regime, which makes it hard to remedy or to tamper with the work
principle. Furthermore readjustments within the trajectory transition such as restricting certain reactions
are forsaken, and the trajectory key state is rendered as a result, not an optional choice. The reduction
factors, the ratios of Z-state concentrations, were taken from the non-trajectory work principle method
rather than the more traditional trajectory techniques, thereby nullifying uncertainty or dispersion due
to finagling manipulations.

RELEVANCE OF FUME COMPONENT STABILITY

The unfinished work principle model is unable to resolve the unstable fume components, so it is
fortuitous that the hazard potentials taken as RFT rule results are not normally dominated by those
components. The original Z-state concentrations remain relatively unchanged for more stable
components during transition to the Q*-state, representing measurement conditions in the underground
chamber. The reaction products with noteworthy concentrations that were diagnostically useful were
carbon dioxide CO», carbon monoxide CO, hydrogen Hp, and the total nitrogen oxides, NOX. Though
nontoxic, H; represents a notable fraction of the reliable and useful test information and therefore was
retained. Relatively weak concentrations of ammonia, NH3, and methane CH, were observed; they
remain negligible for the theoretical results and of little bearing on the RFT conclusions reached.
Within the measurement hour, nitric oxide NO transforms rather quickly to nitrogen dioxide, NO2, so
they were regarded as unstable. The resultant sum NOX tends to remain more constant, though recent
underground tests with dynamic instrumentation have revealed trends for its rate of disappearance,
making its constancy suspect and warning of some difficulty with our resolution method.

REACTANT AIR AND ‘R’ THE CHEMICAL EQUIVALENCE RATIO

Theoretical TDRC trials to remove the booster influence were resolved without and with the inclusion
of reactant air, wherein the oxidation noticeably reduces r the chemical equivalence ratio. This ratio
depends upon the negative and positive oxidation states of the chemical elements in their commonly
occurring compounds 2” 75, where only one or none of the oxidation states is nonzero. When r is over
unity without air ingestion, r is reduced to unity by raising the quantity of reactant air, which is referred
to as with (or 100%) reactant air or r-stoichiometry. When r is under or equal to unity without air
ingestion, the ingestion is forsaken and r remains unchanged, which is referred to as zero (no or 0%)
reactant air. The ratio of reactant air mass to total reactant mass, with the booster if utilized, is
designated RAX. Typical RAX numbers for r-stoichiometry were 0%, 25% and 50% for roughly 5%,
8% and 10% fuel oil respectively. The original zone dimensions for the reactant air reside within those
for the resulting Z-state fume zone, so that the requisite ingestion occurs without unnatural mass
transfer. The terminology reactant air is retained as a reminder that it now represents a working fluid
component that otherwise was a tiny portion of the underground reservoir that represents the
tremendous non-reactive (inert) component in the work principle model.

SUPERPOSITION RULE FOR INCOMPLETE AIR INGESTION

The zone of fumes is regarded as rapidly formed, so that the reactant air for r-stoichiometry noted
within the TDRC ingredient table might not be wholly consumed upon reaching the Z-state. Originally,


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concentrations and theoretical trend information for a charge formulation with a chosen fuel percent
reveal the non-unique okay or not-okay nature of the different hazard potentials. The reduction factor
technique was workable though there were notorious ill-fitting revelations when the RFT-P formula
was investigated. The requisite unstable fume components NO and NO) within the RFT-P rule were
recognized to cause the worst difficulty.

The unrefined work principle remains useful for resolving the Z-state taken as the last remnant of total
equilibrium, though the nonequilibrium Q*-state remains intractable. Recommendations that the
unfinished model incorporate a non-zero reservoir interaction (N-state), and the transitional rate
kinetics for N—Q* (or rougher Z—Q*) jump to reach the non-equilibrium Q*-state should be pursued.
Thereupon, the optimization Nth order rate rule for the 1-stoichiometry-mixing rule would be
worthwhile, if the refinements reduce the residual differences and resolve the unstable nonequilibrium
states.

APPENDIX: THERMODYNAMIC THEORY UNDERLYING WORK PRINCIPLE

The work principle incorporates a working fluid that interacts irreversibly with a tremendous reservoir
or reversibly upon a mechanical agent. The working fluid can have a reactive composition, transfer
heat to or work upon the reservoir or work upon the mechanical agent in a reversible nonexpansion
way, though the reservoir is unable to interact directly with the mechanical agent. The reservoir must
retain constant thermal mechanical characteristics and therefore have tremendous (mass) proportions
compared to the other two components. None of the components interchange particles so the working
fluid mass remains constant, which is useful for renormalizing other thermodynamic quantities. The
resolution utilizes constraints that work chronologically, though they are not required to formulate the
unrestrained work principle. The work principle incorporates a quasi-potential, Yo, or negative work
function [-Wr], written per unit working fluid mass, since TDRC render their numeric results that way.
The work function and quasi-potential terminology tend to be redundant though useful forms, defined

by the relation:
-W, = Y, =| U-T, -S+ A
F= 9 R ()

The quasi-potential Yq (or Wr) depends upon the working fluid’s energy per unit mass U, entropy per
unit mass S and density p (Rho). Neither the quasi-potential nor the work function qualifies as a state
function of the working fluid since they depend upon reservoir characteristics, temperature Tp and
pressure Pp, despite their requisite constancy 7°. The resulting construction of the quasi-potential,
represented as a superposition of working fluid state functions with constant reservoir multipliers, is
independent of the trajectory pathway, regardless of process irreversibility or nonequilibrium, and
therefore has formidable theoretical capacity. The work principle inequality relation taken from the
noted references can is then

Work < AW, = A[-Y,]

The work done by the working fluid upon the mechanical agent, Work, would equal the work function
tise AWr or A[-Yq] for a reversible path, and the inequality would hold for irreversible process.
Restoration work refers to the work that would be rendered by (not upon) the mechanical agent to
reversibly return the working fluid to its original thermodynamic state. Noting the restoration work is a



the overall reaction process. The H2 data could have strayed as the result of unmixing or disappearance
from the underground chamber. With the reported test information related to the theoretical trends, the
reaction with air was revealed, implying that the mining explosives had undergone nonideal detonation.
Upon reaching the transonic CJ region the reaction mechanics were incomplete, so notable combustion
transpired thereafter, utilizing trapped air in the rapidly widening fume zone. Roughly 75% reactant air
was consumed reaching the last remnant of equilibrium Z-state, whereupon the more stable
components remained roughly unchanged.

RESULTS WITHOUT THE BOOSTER INGREDIENTS

The graphs in Figures 5 through 8 show the test results and theoretical trends for COz, CO, H2, and
NOX concentrations [X(cc/g)] with respect to fuel oil [%], without the booster ingredients. The
reported charge formulation results (dark stars) without the booster were resolved using the reduction
factor technique, discussed shortly. The rationalization noted previously still explains why the trends
start-out identical, branch-out and then undergo wider divergence. The 75% reactant air trends for CO2,
CO, Hz, NOX over, under, under, and over the undrawn trend through the reported results, so
readjusting the superposition constants still would yield no benefit. The residual differences between
the reported test data and their corresponding theoretical traces remained roughly unchanged regardless
of whether the booster ingredients were retained or not.

For the graph in Figure 9, the resultant sum of concentrations of CO2, CO, and CH, were taken,
representing the reaction products that retained the majority of carbon {C*}. Theoretical CHy
concentrations were negligible and rendered no worthwhile influence on the resultant sum, while the
reported CH, results had only a little influence on the resultant test information. The traces without
(with) the booster were remarkable fits to the readjusted (unadjusted) data over the whole range of fuel
percent, regardless of the reactant air taken. The readjusted trend without the booster tended to zero
intercept for zero percent fuel oil, which is logical if that is the only remaining compound containing
carbon. Technically carbon type fumes could have occurred from the reaction of wrapping tape or wire
insulation, but the roughly zero intercept with the transformed readjusted information suggests those
effects were rather minor.

THE REDUCTION FACTORS

Traditionally the booster influence was removed by subtracting the booster fume components from the
corresponding unadjusted test results, which would yield readjustments of a few percent here. Undoing
the superposition of the mixture with subtraction is questionable when there are notable compositional
differences and the Z-state temperature for just the booster reaction is roughly a thousand degrees
hotter than for the charge formulation, implying different reaction kinetics. Quite to the contrary, the
compositional weight percentages and Z-state zone temperatures for the charge formulation with and
without the booster ingredients remain roughly similar, as would most of the reaction kinetics.
Regardless of the reactant air r-stoichiometry condition taken, the following relation defines the
reduction factor for the kth fume component.

X(k
Reduction Factor(k),, = [Fee |
WoBooster _|Reactant

Condition



theoretical trends from the work principle in conjunction with the reported test data raised concerns
about reactant air significantly modifying the fumes. Though the work-principle could not resolve the
incomplete reaction states in an obvious way, numerical superposition of the two resolvable cases with
0% and 100% reactant air could yield the wanted intermediate circumstance. The multiplying constants
in the superposition formula were resolved by regarding the fume zone as spherically symmetric.
Within the fume zone the reactant air consumption was taken as proportional to fractional distance to
the zone surface, ranging from 0% at the zone center to 100% r-stoichiometry on the zone surface.
Averaging the radial fraction over the spherical zone yields the number 75%. The resultant fumes
therefore were taken as though 75% utilized 100% reactant air and the residual 25% utilized 0%
reactant air. The wanted intermediate concentration X(k) of the kth fume component is then determined
by the two tractable work principle concentrations X(k) using the following relation.

XCe)peactant = 0-25: X(k)peacrant + 0-75: X(K)peacrant
‘Air78% Air 0% ‘Kir 100%

Rate consumption proportional to the Nth power of the radial fraction would also be worth
investigating though it would be illogical to expect that graphical trends from the unfinished work
principle could optimize the choice of N, while other recognized and notable shortfalls remain
unaccounted for.

RESULTS WITH THE BOOSTER INGREDIENTS

Without the superposition rule, four types of theoretical results were originally resolved for comparison
with the reported test data: (1) no reactant air and no booster, (2) with reactant air and no booster, (3)
no reactant air with the booster, and (4) with reactant air and with the booster. The quest was to
determine which choice most closely represented the phenomena observed in the underground fume
chamber. For convenience, the graphical plots are subdivided into three regimes: the lean range (under
4%), the mid range (4-7%), and the rich range (over 7%), where numbers within parenthesis refer to
the fuel oil [%] in the ammonium nitrate fuel oi] ANFO. Retention or removal of the booster influence
was ultimately understood from trend comparisons in the lean range, where the r-stoichiometry was
under unity and reactant air was unnecessary and therefore not relevant. The role of reactant air
ingestion was ultimately understood by trend comparisons in the rich range, where retention or removal
of the booster ingredients hardly modified the overwhelming contributions from the rich trial explosive.

The graphs in Figures 1 through 4 show the test results and theoretical trends for CO2, CO, Ho, and
NOX concentrations [X(cc/g)] with respect to fuel oil [%], with the booster ingredients retained. The
75% superposition rule was utilized to forecast the intermediate graphical trend, which was naturally
straddled by those for zero reactant air and r-stoichiometry. The theoretical trends remain identical
without reactant air in the lean range with r under unity, until the r reached unity in the mid-range when
the branching occurred. For higher fuel percent, the r-stoichiometry was restored to unity for the 100%
reactant air trend. Notice that the 75% reactant air trends for CO2, CO, H2, NOX were over, under,
under, and over the undrawn trend through the reported test data (dark circles). Under (over) refers to
the graph’s ordinate direction taken to reach zero (100%) reactant air. With half the residual differences
in opposing directions, there was no readjustment that would tremendously reduce the net deviations or
notably improve the formulated superposition rule.

The reported test results for the four more stable components were closest to the 75% trend, except H2
which was closer to the 100% trend, so it was rather obvious that ingested air played a notable role in



trends near unity, it would be imprudent to suggest that the unfinished work principle method has
sufficient resolution to render with certainty such crucial ranking decisions.

The recent permissibility rule RFT-P results in Figure 16 remains an isolated phenomenon that reveals
the dismal tragedy of utilizing an unfinished theory for determining relative fume toxicity when the
formula rule depends upon relatively unstable components. It is worth recalling that the reduction
factors were resolved for the thermodynamic Z-state, and that would yield wrongful information for the
unstable components that transform noticeably during their transition towards the nonequilibrium
Q*-state. The ill-conceived reduction factors for NO and NO) utilized in conjunction with their
nontrivial measured concentrations rendered the graphic misfit. Recognition need be taken that the
Z-state from the work principle remains rather inflexible and not open to remediation, while a
trajectory type theory could be tampered with to yield closer fits for reported test data in the last graph.

CONCLUSIONS AND RECOMMENDATIONS

The technique for removal of booster influences rests upon the presumption that the reduction factor or
concentration ratio with and without booster ingredients would be identical whether they were resolved
theoretically or experimentally. The reduction factor was tractable theoretically, just by removing
booster ingredients from the TDRC tabulation, though it could not be resolved experimentally for the
chosen charge formulations. The relationship could be confirmed with cap-sensitive charge
formulations that were shot with and without the unnecessary booster. From the graphical inspections it
was recognized that the residual differences of the theoretical trends without or with booster ingredients
respectively were comparable for the readjusted or unadjusted test data. Whence, the reduction factor
technique is tractable, without revealing any strong tendency to worsen or improve the residual
differences between theoretical and reported information. There were no noteworthy revelations
inferred from the removal technique that were not rendered without it, except for the reckoning of the
zero intercept on the readjusted {C*} trend. Working with the unadjusted observations and trends
minimizes the computational hardship and number of presumed conditions. Therefore the retention of
the reduction factor technique is not recommended unless the regulations or guidelines stipulate toxic
fume results with the booster influences removed.

The work principle technique with the zero-net interaction restriction yielded trends with reactant air
that were comparable to the reported fume results in the underground test chamber. Originally this
raised concerns that the fumes results were modified by reactions from air ingestion. Further research
with restricted oxygen shots was started to understand this influence. The rationale for incomplete
reactant air ingestion was that the fume zone undergoes rapid expansion until reaching the last remnant
of equilibrium state, without fully utilizing the quantity of reactant air reckoned from r-stoichiometry. It
is worth noting that the original zone dimensions for the reactant air reside within those for the
tesulting Z-state fume zone, so that the requisite ingestion occurs without unnatural mass transfer.
Numerical coefficients for the superposition rule were resolved utilizing a proportional relationship,
yielding the Z-state mixture rule with r-stoichiometry results weighted at 75% and the residual no
reactant air results weighted at 25%. The trends and reported test results supported the notion that
reactant air was involved in a notable way with the combustion transpiring after the transonic CJ state,
indirectly confirming that the detonation reaction was quite nonideal.

The tentatively unfinished work principle yields results for the RFT-C, RFT-U or RFT-R formula,
which were not unreasonable. The trends for the 75% r-stoichiometry were utilized, regardless of
whether the retention or removal of the booster influence information was taken. Reported fume



Removing Booster Influences from Toxic Fumes

MICHAEL S. WIELAND

ABSTRACT

This report investigates whether it is tractable and thereupon reasonable to remove the booster
influences when ranking the toxic fumes of non-cap-sensitive mining explosives. The hazard potential
is represented by relative fume toxicity RFT, the resultant influence computed from a formulated rule
with a restricted set (tally) of fume components and multiplying constants. The RFT result is compared
to the rule criterion that represents the worst case tolerable toxicity stipulated by regulations or
otherwise. The typical nonstoichiometric booster composition can render notable unwanted influence
on the RFT ranking results. Historically, the remedy was to shoot the booster separately and reduce the
trial concentrations by the relevant subtractions. Unreal negative concentration results were noted on
rare occasions, revealing the faulty nature of the reduction procedure. With thermodynamic reaction
chemistry codes TDRC, on the other hand, the booster ingredients can be retained in or removed from
the reactant tabulation, yielding reduction factors taken as the concentration ratios for the two
circumstances. The underlying presumption regarding reduction factors is that the ratios of component
concentrations with and without the booster ingredients when resolved theoretically ought to equal
those rendered experimentally, when tractable. Upon rearranging the presumed relationship, the
unadjusted fume concentrations divided by theoretical reduction factors yield the wanted readjusted
fume concentrations, thereby removing the booster influence without generating unreal negative
concentrations.

The work principle from thermodynamics restricted by the constraint of zero-net interaction loss is
utilized in conjunction with the TDRC to resolve the wanted (Z-state) fume spectrum. This circumvents
the recognized difficulty with traditional hydrodynamic detonation theory that is related to the nonideal
reaction characteristics of typical mining explosives. The tacit characteristic of the Z-state resolved
from the non-trajectory work principle is that it can not be remedied or tampered with, unlike the
traditional trajectory techniques where the reaction products can be readjusted by changing formula
representations, nullifying specific reactions or otherwise manipulating the thermodynamic trajectory
process. Though the work principle theory is an unfinished formulation, the Z-state results prove
worthy enough for rendering trends and comparisons and reaching otherwise useful conclusions.
Further refinements should yield more reliable fume spectra and indicate explosive composition
teadjustments that would reduce toxic effects within underground mines and the wider world
environment.

THE INTRODUCTION

Toxic fumes cause fatal and nonfatal incidents in underground mining, where the working environment
tends to trap the fumes, restricting natural dilution or forced ventilation, thereby hindering the
restoration of nonharmful work conditions. Though the undiluted fumes are relatively concentrated,
their dangerous concentrations are reduced in time by dilution, cool reactions, or rock and dust
absorption. Warnings related to the hazards of toxic fumes are found in reference books of the industry
'23 Nonhazardous conditions have not always prevailed when work was resumed, resulting in serious
or fatal incidents in underground operations *. Nominal workday threshold toxicity restrictions and
other relevant information were utilized in a rudimentary ventilation model to yield typical waiting



NON TRAJECTORY AND THERMODYNAMIC UNCERTAINTY

Irreversible and reversible fluctuations render the chronological occurrences that force the reduction of
the quasi-potential, though there are other rationale for the retention of pathway uncertainty, including
the quantum mechanics uncertainty principle and the relatively unknown thermodynamic statistical
uncertainty principle >”. Uncertainty principles render trajectory notions obsolete and force worst case
minimum tolerances on canonically conjugate variables. Though our restrained and unrestrained
variable functions do not necessarily form a canonically conjugate pair, there remains an underlying
uncertainty in the working fluid state functions from which they were formed. Trajectory intractability
remains the relevant issue not the obvious fact that TRDC results are fraught with much greater
numerical errors than those imposed by the uncertainty restrictions.

ZERO-NET-INTERACTION ENERGY CONSTRAINT

For zero-net-interaction energy, the terminal trajectory state is resolved by requiring that the working
fluid retain or recover the working fluid energy Uj of the original and unreacted thermodynamic state.
Within the trajectory transition, work done upon or heat transfer with the reservoir is unrestricted and
could render nontrivial influence, while registering no net effect. With reservoir interaction, no
restriction regulates the working fluid’s entropy change, though transformations that would cause a rise
rather than reduction in the quasi-potential are forbidden. The restriction on the terminal trajectory is
written U = x for theoretical resolution, with «x = U; for the numerical resolution using the relevant
TDRC. Utilizing hindsight, the forthcoming results were reduced in form with the K-function defined
as K = P/R*T where R* is the Universal Gas Constant. Upon reaching the reservoir state, the K-
function would equal the constant Kr = Ppr/R*Tr = 40.874 pmol/ce (or mol/m’). The reciprocal of Kg
would equal 24,470 cc/mole for reservoir conditions taken at the standard reference conditions. For the
unrestrained variation the entropy y = S or the logarithmic density y = y respectively yield,

cB)

The working fluid and reservoir are regarded as thermal mechanical stable substances so their state
functions like W=P/p, T, or Tp are restricted to the positive range. Zero temperature is unattainable
according to the third law of thermodynamics. The bracket terms arise regardless of the way the
unrestrained y% was chosen, rendering a nonzero result for nonequilibrium circumstances and reducing
to zero for constrained equilibrium. For explosion (implosion) type processes, the K-function is greater
(less) than the reservoir constant, Kr, and the brackets are positive (negative), so the entropy S must
rise (fall) and the density p must fall (rise), ultimately yielding K = Ke for the trapping minimum. With
the work principle, the restrictions imposed by the bracket terms from the trapping minimum
requirement hold for any working fluid regardless of its equation of state EOS. The tenability of the
restrictions remains unaffected when studied numerically, though results are worthwhile only if the
chosen TDRC and related EOS characterize the working fluid in the thermodynamic domain under
investigation. The working principle is resolved numerically by trial and error with TDRC retaining
results, which reduce and ultimately minimize the quasi-potential.

a[-w, ], = 8¥,]

When the zero net interaction Z-state constraint is removed, unresolved nonequilibrium circumstances
prevail, though the restorative influences must ultimately recover the requisite K = Kr circumstances at
the reservoir conditions. Real gas formulations evaluated at the Z-state condition reduce to the unique



way to recognize the working fluid’s propensity for undergoing transformation via chemical reaction *°,
The resulting work done upon the mechanical agent over a whole cycle would be zero or negative,
Work <0, regardless of the process undertaken. Therefore, the mechanical agent would render the
restoration work forever, without taking recourse in the reverse possibility, forbidding any prospect of a
perpetual motion machine.

Natural processes are regarded as macroscopic (non-infinitesimal) transitions that are somewhat
irreversible, however slight, with or without reversible fluctuations. For resolving toxic fumes,
restriction is taken to natural processes with no Work, as though the mechanical agent was
dysfunctional. Technically the mechanical agent is not removed from the work principle model, just
rendered moot, so it is unnecessary to identify some contraption in the reaction process or underground
fumes chamber with it. Under this restriction, the work principle relation reduces to

AW, 20 or AY,<0

For a natural process without the mechanical agent to render restoration work, it is impossible to return
to the starting state. Restoration work remains an illusion that requires the reverse process, with the
opposite and wrong chronology. With normal chronology, the reduction in the quasi-potential A[-YQ]
or the rise in the work function AWs registers the restoration work that would be necessary to undo the
deterioration.

RENDERING OF IMPOSED CONSTRAINTS

The rendering of imposed constraints refers to the utilization of relative minimum trapping conditions
to stall the trajectory motion. The Yq partial derivatives taken with respect to the unrestrained x, while
holding « constant, form the constraint representation with thermodynamic state variables. The
unrestrained infinitesimal change 5y taken while holding « constant would remain unrestricted were it
not for the requisite reduction of the quasi-potential. The change of the quasi-potential Yq or negative
work function Wr is resolved according to a Taylor’s expansion in unrestrained y, while x remains
constant with normal (not reverse) chronology understood *!.

(8x)! BY,
a[- pI =or, «2. SI <0

Technically, the subscripts should bear witness to the restriction of chemical equilibrium, though that
requirement is universal for our terminal ‘key’ state resolution, so the reduced notation just displays the
« constraint. Retention of only the lower order J terms is required for resolving and interpreting the
transformations, as noted by the grave accent on the summation symbol. For resolving the minimum
trapping state, OY q/@x|K would reduce to zero, while @Yq/6y’|x would be positive. The multiplication
of nonzero unrestrained 5y-5y with positive @Yq/0,7|K yields the wrong sign for the inequality
relation. The only workable solution requires that the unrestrained 5y reduce to zero, which represents
stalled trajectory motion, until the constraint is replaced with a different restriction or unrestrained
travel occurs towards the reservoir state.



The theoretical concentrations X(k) were normalized by the formulation charge mass under test,
without the booster mass, regardless of whether it was in the TDRC ingredient tabulation. The
underlying presumption regarding reduction factors is that the ratios of component concentrations with
and without the booster ingredients when resolved theoretically ought to equal those rendered
experimentally, when tractable. Transformations of results to the standard reference conditions are
implied. Therefore by rearrangement, the unadjusted fume concentrations divided by resolved
theoretical reduction factors would yield the wanted readjusted fume concentrations. The reduction
factors formed theoretically could never be negative and therefore unlike the traditional subtraction
method could never reverse the numerical sign when transforming the reported test concentrations
(normally positive). The unadjusted test concentrations could be negative if they were rendered by
subtraction of imperfect instrumentation results, like [NO] = [NOX] — [NO}].

The reduction factors required the theoretical concentrations from the graphs referred to previously, so
their discussion was postponed until now. Reduction factors can have unexpected nature because of the
nonlinearity of the relations characterizing the complex chemical reactions, so different circumstances
of air ingestion were investigated as noted in Figures 10, 11 and 12. Though the reduction factors
stayed under 14, the ordinate scale was restricted to 7 so overlap regions would have more graphical
resolution. Reduction factors for the kth component remained identical within the lean range, where
reactant air was not required. For the rich range, the reduction factors tended to unity, though NO, NO2
and their sum NOX were notable exceptions, revealing untypical divergence. The graphical trend
dispersion for 75% reactant air resembled the r-stoichiometry case rather than the zero reactant air case.
Reduction factors were normally over unity so the readjusted results were normally diminished, though
the reverse case of augmented results is not ruled out for the nonlinear relationships that characterize
reaction processes.

FORECASTING THE RELATIVE FUME TOXICITY

With the work principle, the thermodynamic mixture state can be rendered for a chosen circumstance.
The reduction factors with 75% reactant air were taken to resolve the hazard potentials, since the
related concentrations resembled the reported test data more closely overall. The RFT results shown in
Figures 13 through 16 were computed from their formulas in Table 1 for the relevant tally of
unadjusted or readjusted concentrations. They were then normalized with respect to the rule criterion.
The readjusted test data (dark stars) ought to be compared to the theoretical trends without the booster
(dashed traces), while the unadjusted test data (dark circles) ought to be compared to the theoretical
trends with the booster (solid traces). Often the reduction factor corrections were minor, so the dark
circles hid the dark stars. The reported test data or trend points on the normalized graphs that were
under (over) unity represent tolerable (unacceptable) circumstances, so that the charge formulations
had okay or not-okay hazard potentials, depending upon the RFT rule invoked.

The RFT-C graph in Figure 13 and Figure 5 resemble each other because the Fume Class rule without
H)S would just yield renormalized CO information. The RFT-C results under unity in the lean regime
would pass the fume class requirement, while those over unity in the rich regime would not. For the
RFT-U trend, Figure 14, the reported and theoretical information universally remain under unity and
therefore pass the older US toxicity test. The restricted form of the unweighted RFT rules are unable to
reflect the differential toxicity within their tally of components, and they tend underestimate CO
equivalent toxicity when compared to rules with nonunity multiplying constants *. The theoretical trend
results for the Russian rule in Figure 15 show relatively close fits with the reported test data. With the



TROUBLES WITH TRADITIONAL THEORY AND NONEQUILIBRIUM

The nonideal detonation of mining explosives 7"? is not reconcilable with the traditional requirements
of the Zeldovich von Neumann Doering (ZND) theory. For the unmodified ZND theory, the reaction
thermicity reduces to zero upon reaching the Chapman Jouguet CJ sonic condition. Nonideal
explosives react through the transonic region, so the zero-thermicity requirement is a recognized
conflict, resulting in a numerical infinity. Incorporating some representative loss term in the ZND
formulation can render the difficulty moot, so the relevant theoretical relationships remain numerically
bounded ’. The resolution raises questions regarding the true reaction process undertaken and renders
some philosophical room for invoking the work principle from thermodynamics *,*. For rock mining
or chamber testing, the restoring influences that try to uphold mechanical and thermal equilibrium
rapidly widen the zone of fumes within the surrounding medium, via Le Chatelier’s principle *°. Under
the transitory circumstances with declining zone temperatures the relaxation times for chemical
reactions rise drastically and the restorative forces trying to sustain chemical equilibrium falter. Wall or
dust interactions, or other types of residual nonequilibrium reactions persist noticeably at the cooler
temperatures in the underground chamber within the hour of measurement, ruining the presumption of
terminated reactions. Trying to reckon the last respectable remnant or state of total thermodynamic
equilibrium for TDRC resolution now turns into a worthwhile undertaking.

Thermodynamic reaction chemistry codes TDRC yield results only for total equilibrium circumstances
and they would therefore not be appropriate for resolving the nonequilibrium circumstances. Reaction
restrictions like frozen-flow are usually imposed for chosen temperatures on the late stage (post-CJ)
trajectory to inflict a reaction type of constrained equilibrium. Reckoning the fumes by tracking the
thermodynamic trajectory downward from the high-density region could be wrong or unreliable, if the
equation-of-state EOS formula is ill founded, yielding undesirable results for ranking their toxicity. The
work principle can not be tampered with or remedied in this fashion.

Work PRINCIPLE FOR PREDICTING TOXIC FUMES

The work principle, which is described more thoroughly in the Appendix, was developed for
theoretically resolving toxic fumes from the nonideal detonation of charge formulations. The whole
description of wanted process refers to macroscopic changes resulting from removing and imposing
thermodynamic constraints that work chronologically to render trajectory key states. The work
principle utilizes a quasi-potential or negative work function, with numeric resolution requiring a
TDRC for the terminal thermodynamic regime under consideration. The work principle method is
unable to restrict reactions, tailor the work output or otherwise resolve states within the jump
transitions, so that the trajectory terminology is utilized only in a figurative way. The work principle
incorporates a workin, g fluid that interacts irreversibly with a tremendous reservoir or reversibly upon a
mechanical agent 7‘, For modeling underground fume tests rather than rock blasting or other
circumstances, the working fluid represents the reaction ingredients undergoing transformation to
resulting products within the fume zone. The reservoir represents the underground chamber walls and
the contained air. The mechanical agent remains an uncorrelated item in our restricted interpretation °.

Rather than coping with the hard issues of nonequilibrium, the toxic fumes were resolved numerically
for the Z-point, rendered by a zero-net-interaction constraint. Though ZND techniques require complex
equation-of-state EOS for the whole trajectory from the original dense reactant state, the work principle
formulation requires an EOS that works just for resolving the terminal key state. The resulting rarefied,
thermally hot Z-state is reconcilable with the ideal gas domain, therefore the TDRC that was used for


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implement, though it would not yield a rigorous CO equivalent toxicity, unless the constant were
replaced with a function of the NOX components. The unweighted resultant sum rules RFT-C without
NOX and the RFT-U are retained, while the Fume Class II and III rules and the RFT-C> with NOX
were not pursued further. Recently the TLV-TWA for CO was reduced from 50 to 25 ppm 18 which
without renormalization would double the CO multiplier. Renormalization would return the CO
multiplier to unity, halve the remaining multipliers, and justify the same reduction in the rule criterion.
These readjustments are not incorporated into the current regulations or guidelines and therefore were
not utilized in our investigation.

“Table 1. “Txaditional and Recent Underground | RET Rules & Criteria”

ROLE OF MINING CONDITIONS AND UNDERGROUND TEST FACILITY

Numerous circumstances control the nature of toxic fumes: the type or grade of charge formulation,
hole contaminates, mixture uniformity, water resistance, eae initiation, stratum confinement, rock
hardness, dust interactions, and other usage conditions The surrounding stratum regulates the
work output, reduces the rate of fume expansion, and temporarily traps the reaction products so that
otherwise tardy reactions transpire. Hole-to-hole waves can marginally desensitize the charge
formulation, resulting in unusual reaction kinetics and weak detonations ‘518 Under rift compression
(or heave), some reaction gases are forcefully driven into the cracks and pores of the roof, walls and
floor. Fumes trapped within the rock and dust can be released back into the working environment '
Recognition was taken that the carbon oxides tend to increase with hard rock confinements, while the
nitrogen oxides tend to increase in cracked or friable rock conditions '*,

Traditional techniques for measuring toxic fumes from cap-sensitive explosives would not work for
blasting agents, which normally require larger charge diameters and total masses to shoot properly and
yield typical fumes. Recently an underground test chamber was developed for Measuring toxic fumes
from those blasting agents ° The underground NIOSH fumes facility has a 274-m” chamber, which
contains 324-kg air within the walls. The mining explosive under test has a typical mass of 4.54 kg
confined by a 10.2-cm diameter cylindrical steel pipe for proper detonation. Though the typical 172-g
pentolite booster is roughly 4% of the trial explosive weight, it can have a notable influence on the
fume spectrum. Traditionally the booster influences were removed by shooting it separately and
subtracting off the corresponding fume components 20 The resulting nonphysical negative
concentrations noted on rare occasions warn of the faulty nature of this remedial technique.


times, roughly a few hours, required to restore nonharmful working conditions *°. Though fume
dissipation is relatively unrestricted for surface shots, the tremendous quantity and harmful nature of
the reaction products can still have an unacceptable impact on the work force, nearby community, or
the overall environment.

The relevance of the traditional hydrodynamic theory of detonation remains questionable for nonideal
detonation of mining explosives, without some type of theoretical readjustment ’. The work principle of
thermodynamics was reformulated with a constraint theory for resolving the remnant (close to last)
equilibrium state of the reacting medium *, The fume spectrum for mining explosives undergoing
nonideal detonation and subsequent rapid combustion i is then resolved with the TDRC. Theoretical
results from the nontrajectory work principle and TDRC show respectable fit with a number of reported
mine shots *, so that outright refutation of the restrained work principle technique would be rather
difficult. Theoretical trends for recent underground chamber shots noted later also yield rather
comparable results. Notable differences that were observed were not wholly illogical and they could
diminish with further refinements in the unfinished work principle theory.

The relative fume toxicity RFT rules utilized to yield hazard potentials and understand risks do not
remove or replace the requirements or conditions set forth by relevant guidelines or regulations.
Though the recent and older permissibility RFT rules are utilized in this report, forewarning is given
that this has no bearing on regulation fume tests that are undertaken for cap-sensitive explosives which
require no booster. It is worth noting that the RFT tally choices and formula multipliers are not unique
and none of the rules incorporate the whole range of possible toxic components, yielding a wide range
of hazard potential results that tends to cloud the risk issues. Regulation ranking tests tend to restrict the
types of toxic problems, which ought not to be interpreted as rendering complete or useful measure of
the hazards involved. Workers, therefore, need to remain cautious of hazardous circumstances, not just
rule implications, for there are numerous and unexpected influences that govern the formation of
dangerous toxic fumes *"°. The possibility of utilizing remote or portable instrumentation to monitor or
detect multi-component toxic fumes should not be overlooked.

TRADITIONAL AND RECENT UNDERGROUND RFT RULES

The hazard potentials taken as results from formulated RFT rules utilize uniform notation and units,
rather than their original guideline or regulation formats. The respective columns of Table 1 show the
RFT reference or role name, the tag, formula and criterion. The RFT rules work with a restricted set
(tally) of concentrations, the bracket terms within the formulas that represent fume component volumes
per unit explosive mass. Reported test results are transformed to standard reference conditions of 25 °C
and one atmosphere. For regulation testing, candidate explosives fail when RFT results exceed their
criterion, which represents worst case toxicity tolerable, thereby denying their usage under the relevant
mining conditions. The last column represents criterion with unit conversions from the original format
to those for the Russian criterion (metric). The fume class requirements were transformed by
stipulating the cartridge mass as 200 grams ''. The graphical trends worked out later yield results that
were normalized with respect to their criterion for convenience, so that reported test data or theoretical
trend states under (over) unity would be regarded as tolerable (unacceptable).

The RFT-P rule multiplying constants are those required to render the carbon monoxide, CO,
concentration for equivalent toxicity '". The Russian formula RFT-R is the widely recognized
forerunner of the weighted rule formulations, with a nonunity multiplier taken in recognition that
harmful influences depend upon the fume composition 3. The Russian rule is more tractable to


ideal form, which is wholly compatible with the rarified and thermally hot state. Under such
circumstances, the work principle renders the Z-state molar density of the reaction fumes equal to Kr,
regardless of the charge formulation, and forecasts that it would ultimately reach that result for the
reservoir conditions. When the nonequilibrium working fluid transitions to the reservoir conditions,
notable quantities of condensed phases (i.e. water) are normally incurred, thereby ruining the ideal gas
presumption and the recovery of the molar density Kg at the reservoir Q*-state.

1 Rossi, B. D. Control of Noxious Gases in Blasting Work, and New Methods of Testing Industrial Explosives.
Nauchno-Tekhnicheskoe Gorbnoe Obshchestvo, Scientific and Technical Mining Society, Varyvnoe Delo,
Collection No.68/25, Translated from the Russian, Izdatel’stvo “Nedra”, Moskva 1970. [Israel Program for
Scientific Translations, Jerusalem, 1971).

2 Blasters’ Handbook, 16“ Edition, Du Pont Company, P.52-54, 472, 1977.

3 CIL Blasters’ Handbook, Canadian Explosives Limited, Montreal — Quebec, P.9-11, 442-445, Reprint 1959.

‘ D'Andrea, D. V., J. W. Kopp and L. R. Fletcher. Mine Blasting Update. Proc. 17th Ann. Conf. Expl. Blast.
Tchngq., Soc. Expl. Eng., Cleveland, OH, P.251-262, Feb. 1991.

5 Wieland, M. S. Understanding Toxic Fumes from Mining Explosives. Seventh High-Tech Seminar, Blasting
Analysis International, Inc. Allentown, Pennsylvania, P.93-108, July 1997.

° Wieland, M. S. ing the Hazard Px i ic Fumes. Eighth High-Tech Seminar, Blasting
Analysis International, Inc. Allentown, Pennsylvania, P 305-282. July 1998.

7 Dussel E. The Nonideal Detonation, Seventh High-Tech Seminar, Blasting Analysis International, Inc.
Allentown, Pennsylvania, P.403-418, Revised copy, July 1997.

* Wieland, M. S. Work Principle For Predicting Explosive Toxic Fumes. Proc. 14th Ann. Symp. Expl. Blast.
Rsrch., Soc. Expl. Eng., Cleveland, OH, P.121-135, Feb. 1998.

® Rossi, B. D. f the Study of Noxious Gases in Blasti i Control of
Gases, P.5-7, Within Reference 1.

1° Wieland, M. S. Dese i e 3s
High-Tech Serainar, Blasting Analysis International, Inc. Allentown, Pennsylvania, P.223-242, July 1994.

4 Cook. M. A., The Science of Industrial Explosives. Irreco Chemicals, P.411-428, 1974.

12 US Code of Federal Regulations, Mineral Resources, Part 30, Requirements for Approval of Explosives and
Sheathed Explosive Units, Subpart B, Requirements for Approval of Explosives, §15.20, Technical
Requirements, P.54-56, Revised July 1, 1995.

'S Rossi, R. B. and V. A. Usachev. Quantitative Determination of Noxious Gases Formed During the Explosion
Conversion of Explosives Under Laboratory Conditions. Within Reference 1.

\ Threshold Limit Values for Chemical Substances and Physical Agents and Biological Exposure Indices. 2"
Printing, American Conference of Governmental Industrial Hygienists ACGIH, P.VI-38, 1996.

'S Wieland, M. S. Detecting Cross-Hole Wave Interactions and Charge Malfunctions in Underground Shots.
Proc. 11th Ann. Symp. Expl. Blast. Rsrch., Soc. Expl. Eng., Cleveland, OH, P.62-75, Feb. 1995.

18 Liu, Q., P. Tidman, D. Tunaley, and J, Mullay. The Observation of the Shock Resistance in Emulsion
Explosives in Rock Blasting. Proc. 11th Ann. Symp. Expl. Blast. Rsrch., Soc. Expl. Eng., Cleveland, OH, P.26-
31, Feb. 1995.

T Dudyrev A. N., V. V. Oborin, I. M. Il’ina, and V. A. Reshetova. Desorption of Noxious Gases From Mining
Dust. Within Reference 1.

'® Gagauz F. G. and A. V. Drebnitsa. Composition and Quality of Noxious Gases During Blasting Operations
in Underground Mines. P.14-18, Within Reference 1.

18 Mainero, R. J. A Technique for Measuring Toxic Gases Produced by Blasting Agents. Proc. 23rd Ann. Conf.
Expl. Blast. Tchnq., Soc. Expl. Eng., Cleveland, OH, P.595-604, Feb. 1997.

Chaiken, R. F., E. B. Cook, and T. C. Ruhe. Toxic Fumes From Explosives: Ammonium Nitrate-Fuel Oil
Mixtures, Report of Investigation 7867, PRC, US Dept. of Interior, Table 3, p17, 1974.

2\ Cook, M. A. The Science of High Explosives, Reinhold Publishing Corporation, P. 48-59, 123-133, 166-170,
238-244, 1958.



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